Download or read book The Mathematics Education for the Future Project Proceedings of the 14th International Conference written by Alan Rogerson and published by WTM-Verlag Münster. This book was released on 2017-07-01 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the papers presented at the International Conference on Challenges in Mathematics Education for the Next Decade held from September 10-15, 2017 in Balatonfüred, Hungary. The Conference was organized by The Mathematics Education for the Future Project – an international educational project founded in 1986.
Download or read book The Mathematics Education for the Future Project written by Alan Rogerson and published by . This book was released on 2017 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Mathematics Education for the Future Project Proceedings of the 13th International Conference Mathematics Education in a Connected World written by Alan Rogerson and published by WTM-Verlag Münster. This book was released on 2015-07-01 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the papers presented at the International Conference on Mathematics Ed-ucation in a Connected World held from September 16-21, 2015 in Catania, Italy. The Con-ference was organized by The Mathematics Education for the Future Project – an international educational project founded in 1986.
Download or read book Theory and Practice An Interface or A Great Divide The Mathematics Education for the Future Project Proceedings of the 15th International Conference written by Alan Rogerson and published by WTM-Verlag Münster. This book was released on with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the papers presented at the International Conference on Theory and Practice: An Interface or A Great Divide? and held from August 4-9, 2019 at Maynooth University, Kildare, Ireland. The Conference was organized by The Mathematics Education for the Future Project – an international educational project founded in 1986 and dedicated to innovation in mathematics, statistics, science and computer education world-wide. Oouder, Fouze Abu; Amit, Miriam: Incorporating Ethnomathematical Research in Classroom Practice – The Case of Geometrical Shapes in Bedouin Traditional Embroidery. pp 1 – 4 Ethnomathematics asserts that in addition to the formal mathematics taught in schools, there are other forms of mathematics, which have been taught in different societies and cultures around the world. Research and educational experience has shown that combining ethnomathematics with the formal mathematics curriculum in the classroom can improve students’ academic achievement, since it strengthens their self-image and reinforces their motivation for studying mathematics. We adopted this approach with Bedouin students who are defined as ‘underachievers’ in national mathematics tests. In this paper, we offer an ethnomathematical analysis of Bedouin embroidery samples taken from traditional dresses made by Bedouin women. We then describe how ethnomathematical elements were incorporated in the teaching of mathematics for Bedouin students, and how doing so contributed to their learning. https://doi.org/10.37626/GA9783959871129.0.01 Adams, Nadine; Hayes, Clinton: Providing Synchronous Mathematics Instruction to Distance Students- Workshop. pp 5 – 8 In theory technology breaks down boundaries and allows us to more easily connect to our students. But in practice despite all of the technology available mathematics instruction is still best given in a “talk and chalk” format. The use of instructional videos, where the student is able to watch handwritten instruction, has become standard. These are great in that they provide asynchronous instruction and allow the student to learn at a time that suits them. What these videos lack is the interactive component that makes face-toface teaching preferable. To overcome this online lectures are conducted using a combination of Zoom, PDF Annotator and a Tablet PC. Students are provided with an experience much closer to that of face-to-face. https://doi.org/10.37626/GA9783959871129.0.02 Adenegan, Kehinde Emmanuel: Managing Pupils with Dysgraphia in Early Child Numeracy. pp 9 – 13 Dysgraphia is a specific learning difficulty which is a brain-based disorder that impacts on writing skills whereby affected individuals have difficulty with forming letters, writing figures, spacing words and even organizing text into complete sentences. Early child numeracy is a competence built in the young child at an early childhood stage in the mathematical skills needed to cope with everyday life and an understanding of information presented mathematically. To this end, this paper presents dysgraphia, its symptoms in pupils, offers measures on how to manage dysgraphia pupils by teachers and parents and highlights strong recommendations to assist such pupils in performing and competing favourably in Mathematics and other subjects with other pupils in the classroom. Keywords: Dysgraphia, Early Child Numeracy (ECN), Mathematics, Pupils, Numerophobia. https://doi.org/10.37626/GA9783959871129.0.03 Anhalt, Cynthia O.; Cortez, Ricardo: Mathematical Modeling Thinking: Laying the Foundation for Mathematical Modeling Competency. pp 14 – 19 Mathematical modeling competency requires frequent practice and sufficient time to derive experience solving open-ended contextual problems. Specific ways of thinking necessary in modeling are identified by contrasting Pólya’s general problem-solving framework, which may be familiar worldwide. These ways of thinking are developed through mathematical activities that promote dispositions for eventual success in modeling. We posit that mathematical modeling thinking (MMT) is necessary for building modeling competency. This paper describes MMT and illustrates how it can be developed through a well-known problem of universal human cultural greeting exchange. While connecting to world cultures, we examine ways to promote MMT practices such as making useful simplifications, looking for patterns, utilizing multiple representations, mathematizing the situation, and reflecting on the solution. We conclude with practical ways to effect MMT as the foundation for developing mathematical modeling competency. https://doi.org/10.37626/GA9783959871129.0.04 Ashleigh, Glenda Jean: Individual Differences in Cognition and Affect in Multiplicative Knowledge in Basic Mathematics Problems. pp 20 – 25 This paper discusses the roles that individual differences in cognitive and affective variables play in the formation of increasingly complex multiplicative knowledge structures in basic mathematics problems. The effectiveness of learner strategies and teaching strategies to optimise the development of authentic multiplicative knowledge will vary according to these individual differences. https://doi.org/10.37626/GA9783959871129.0.05 Banach, Katarzyna: Ok Notebook as an Untypical Form of Student´s Notebook – Own Experience. pp 26 – 28 In recent years, the methods of work at the Polish school have been evaluated. From the Prussian school model, we are slowly moving to the model of a modern school meeting contemporary challenges. At the present time, much attention is devoted to the search for new working methods and teaching tools. We draw on the experience of other countries. We test our own solutions. This paper deals with the use of formative assessment in association with the untypical formula of a student’s notebook. https://doi.org/10.37626/GA9783959871129.0.06 Bateiha, Summer; Mir, Sadia: Engaging with Mathematics through Three Types of Storytelling. pp 29 – 33 Throughout history, storytelling has been used as a way to appeal to people’s imagination and emotions. When stories are told in the mathematics classroom, the subject comes to life. Students begin to understand the purpose of learning the content, and mathematics becomes something greater than a plethora of irrelevant facts and formulas that are meant to be memorized, applied, and repeated. This workshop focuses on the use of storytelling as a way to engage students in a nontraditional and pertinent form of learning mathematics. In this session, participants will listen to stories used with predominantly Arab students in an American university in Qatar and partake in doing mathematical tasks related to the stories presented. Although the stories in this workshop were applied in an Arab context, the ideas can be edited for use in any cultural context. https://doi.org/10.37626/GA9783959871129.0.07 Bedwell, Mike: Freedom of Speech. pp 34 – 35 This paper rues the fact that submissions to some academic journals are treated increasingly badly by the publishers, with little succour offered by the editor. The writer gives an example where changes in terminology, spelling and punctuation were introduced after the paper had been accepted by the peer appraisers. This paper also argues for rigid ruling on the graphical presentation of quantitative data, such as the dimensionless labelling of the axes in Cartesian graphs, and the default rule for ordering the nominal variables on a bar-chart. https://doi.org/10.37626/GA9783959871129.0.08 Bentley, Brianna: College Studens´ Views of Fraction Arithmetic. pp 36 – 41 College students view mathematics, specifically fraction arithmetic, as a series of tricks that can lead them to the correct answer. This view of mathematics is a direct reflection of their lack of conceptual understanding of fraction arithmetic and their reliance on procedural understanding. College students have an imprecise remembrance of fraction arithmetic and instead rely on tricks they vaguely remember and cannot explain. This reliance on procedural processes that they do not fully understand causes them to make mistakes in their arithmetic. If we do not require students to think critically about the mathematical processes they are completing when first taught a subject and require this critical thought as students progress through mathematics courses, mathematics loses meaning and our students will not have the ability to think critically or conceptually about mathematics. https://doi.org/10.37626/GA9783959871129.0.09 Betts, Paul; et al: Foundational Experiences as a Design Principle for Mathematics Curriculum for Children. pp 42 – 47 Students must make sense of the mathematics they are learning, if they are to understand it. When students are encountering a mathematics topic primarily through that topic’s mathematical forms—its symbols, terminology, definitions, operations, and algorithms—the richness, potency, and completeness of their understanding will depend on their prior, pre-formal experiences with that topic. Foundational experiences activities enable students to construct images, patterns, and ideas—in a word, memories—that will enable them to see the sensibility of the topic’s mathematical forms when they learn them. We invite participants to explore some examples of instructional activities designed to provide foundational experiences for multiplication. What are the qualities that we should invest in foundational experience activities? How can such activities be positioned within curriculum design, with the goal of increasing the quality of students’ understandings of mathematics topics, in pursuit of success for all participants in school math? https://doi.org/10.37626/GA9783959871129.0.10 Billings, Esther; Kasmer, Lisa: Learning via Teaching: Examples of Mediated Field Experiences in Early Coursework of Pre-Service Teachers. pp 48 – 53 Twenty years ago, Ball and Cohen (1999) described a vision for practicebased professional education in which teachers’ learning is situated within practice. We have purposefully designed practice-based educational experiences early in teacher preparation coursework around McDonald et al.’s (2013) learning cycle to include mediated field experiences. Such experiences are structured to explicitly connect coursework and fieldwork and are organized around core practices; preservice teachers (PSTs) deepen their learning of mathematics and ways to teach mathematics by doing the work of teachers within authentic K-12 classroom settings. In this paper we describe examples of mediated field experiences structured on McDonald et al.’s (2013) learning cycle that occur early in PSTs‘ coursework, prior to student teaching. https://doi.org/10.37626/GA9783959871129.0.11 Brahier, Daniel J.: Research into Practice: 29 Years of Classroom Teaching. pp 54 – 59 The preparation and professional development of mathematics teachers requires instructors who are not only proficient in their content and pedagogy but can bring successful teaching experiences to the classroom. In this paper, the author shares his experience of 29 years of simultaneously teaching in a K-12 secondary school, while also serving as a university professor who teaches mathematics methods courses. Examples of classroom experiences that enhanced university methods courses are described, as are some of the benefits of teaching in both settings to connect research and practice in mathematics teaching. https://doi.org/10.37626/GA9783959871129.0.12 Browning, Sandra: Elementary Preservice Teachers and Questioning Strategies in Mathematics. pp 60 – 65 Research has demonstrated an interest in the relationship between teachers’ questioning strategies and children’s ability to reason and learn (Baroody & Ginsburg, 1990; Buschman, 2001; Fennema, Franke, Carpenter & Carey, 1993). Helping preservice teachers develop effective questioning strategies is an important component of a teacher education program. This session describes an exploration designed to determine if EC-6 preservice teachers can (a) recognize effective questioning strategies when observing inservice teachers and (b) use Hess’s Cognitive Rigor Matrix to analyze the level and effectiveness of their own questioning strategies during field experiences. https://doi.org/10.37626/GA9783959871129.0.13 Burrill, Gail: Statistical Literacy and Quantitative Reasoning. pp 66 – 71 Given a world awash with data, students of today will be consumers of statistical information whatever their future. What can we do to make them critical consumers as articulated by researchers such as Gal and Steen and as suggested in the National Council of Teachers of Mathematics Catalyzing Change, able to process information, ask the right questions and make informed decisions? This paper explores what it means to be statistically literate able to reason with quantitative information in today’s world and why it is important from both a personal and professional perspective. Examples from several fields illustrate features of essential core concepts that should be components of the curriculum for all students if we are to have statistically literate citizens capable of thinking and reasoning in quantitative situations. The discussion will also address some of the challenges we face in making this recommendation a reality. https://doi.org/10.37626/GA9783959871129.0.14 Cametti, Cristina; et al: Advantages, Challenges and Opportunities in Teaching Statistics in Doctoral Training to a Heterogeneous Group: the Case of FLAMES Summer School. pp 72 – 77 FLAMES is an inter-university doctoral training network in which all Flemish universities of Belgium collaborate. It aims to support young researchers, in need of methodological and statistical insights and skills, by offering them high quality training at basic, intermediate and advanced levels. One of our most successful activities is a yearly two-week summer school which features a range of modules on research design, statistical methodology and data analysis. Each module connects theory with hands-on exercises, focusing on various disciplines and using different software packages. In this paper, we discuss the FLAMES approach in teaching statistics to a heterogeneous group of young researchers from various disciplines with a different background in statistics and methodology. FLAMES’ ‘measuring is knowing’ principle is used to evaluate the content, applicability and educational aspects of the current modules and to receive suggestions for future topics. https://doi.org/10.37626/GA9783959871129.0.15 Castro Miguez, Luis Alexander; et al: Diagrammatic Reasoning from Reflections on Peircean Semiotics. pp 78 – 83 The document illustrates some elements of reflection on Peirce’s semiotics focused on reasoning through diagrams. The solution of a Euclidean geometry problem is taken as a reference in which mathematical diagrams are recognized as epistemological tools in the learning and teaching of geometry. This is how an interpreter, who systematically observes and experiments with a geometric diagram, generates different interpretants by means of abductive, inductive and deductive reasoning. https://doi.org/10.37626/GA9783959871129.0.16 Chapman, Olive; Babb, Paulino Preciado: Prospective Secondary Mathematics Teachers´ Development of Knowledge of Modelling for Teaching. pp 84 – 89 Given the growing attention on modelling in school mathematics curriculum, prospective teachers are likely to need special help to develop a rich sense of mathematical modelling [MM] and effective classroom practices to support students’ development of MM competencies. This paper is based on a study involving the use of inquiry-based activities to engage prospective secondary mathematics teachers [PTs] in developing such knowledge of MM for teaching. Participants were students in a mathematics education course. Data sources included course work and field notes. We report findings related to the inquirybased activities and the learning they afforded in the participants’ understanding of specific components of problem-solving [PS] and MM knowledge for teaching and the relationship between them. https://doi.org/10.37626/GA9783959871129.0.17 Chin, Kin Eng; Jiew, Fui Fong: Misconceptions or Preconceptions in Making Sense of Decimals. pp 90 – 95 This paper aims to explore the root causes of students’ misconceptions in decimals. A set of decimal tasks and follow-up interviews were used to gather the relevant data. Eight Year Six primary school students participated in this study on a voluntary basis. In this paper, data collected from two students were reported because they showed qualitatively distinct responses and could cover the spectrum of responses of this group of participants. Findings revealed that students’ misconceptions maybe regarded as preconceptions that were developed from work experiences in other contexts such as integers. This shows that the learning experiences from other contexts may impede future learning of students in new contexts. https://doi.org/10.37626/GA9783959871129.0.18 Civil, Marta; Hunter, Roberta: Supporting Mathematics Teachers to Build Deep Understandings of the Home Contexts of their Students. pp 96 – 99 Teachers face many challenges in meeting the cultural diversity they encounter in current mathematics classrooms. To avoid marginalisation of specific groups of students we advocate for a strength-based approach in which teachers are supported to build deep understandings of the lived home context of their students. We discuss findings from our research projects with immigrant students (Pāsifika) in New Zealand and with Mexican American students in the United States. While our contexts are quite different, our approaches have much in common, in particular through their focus on teachers learning from and about their students’ communities to then build on this learning in their mathematics teaching. Bridging theory and practice, we share specific strategies that we have used to support teachers as learners of their students’ home contexts (e.g., home visits; parents’ classroom visits; school meetings led by parents). https://doi.org/10.37626/GA9783959871129.0.19 Clemmer, Katharine; et al: Collaborative Solution Discovery: A Problem Solving Process. pp 100 – 103 Loyola Marymount University (LMU) has developed a new approach to problem solving, Collaborative Solution Discovery (CSD), to help practitioners in a school system leverage their individual passions in a way that grows students’ positive math identity through mathematical thinking, problem solving, and self-regulation. By focusing on how students and teachers interact with each other in real-time in an ideal classroom, practitioners take ownership of a process to guide their students in growing their positive math identity and thus taking ownership of their own math learning. Practitioners measure progress along the way through metrics that are created, defined, used, and continually refined by themselves to attain their ideal math learning environment. The entire CSD process results in a system that owns ist improvement efforts—improvement efforts that are flexible, adaptable, and sustainable. https://doi.org/10.37626/GA9783959871129.0.20 Coggins, Porter; et al: The Mathematical Culture of Ojibwe Students – An Ethnographic Study. pp 104 – 109 Human beings have an innate capacity to communicate, count, detect patterns, locate, and create. With these capacities we invent, design, play, and explain. Regardless of academic background, we also have the innate capacity to use mathematics in meaningful ways. However, in spite of this innate capacity, there is a large disconnect between innate function and success in academic mathematics. Our research is based on interviews of 14 Ojibwe-identifying tribal college students. The instrument was constructed based on Bishop’s (1988) set of six universals or activities people have always done. We present the development of the instrument, interview process, and initial findings. Findings include common ethnomathematical threads found among the interviewed students. Our goal is to use this research to improve ourpreK-12 professional education teacher program and positively impact Ojibwe student learning. https://doi.org/10.37626/GA9783959871129.0.21 Collins, Ken: Using CAS to Improve Student Understanding of Calculus Concepts. pp 110 – 114 This session will explore two areas of application of CAS: one focusing on how teachers can improve student learning using CAS, the other focusing on how students can use CAS directly to help them improve their understanding of calculus concepts. We will illustrate the first area by sharing some examples of calculus teaching lessons that use CAS to help students understand or apply a particular concept. We will illustrate the second area by sharing some examples of student explorations that utilize CAS. These allow students to explore some relationships and applications we use in calculus that would be difficult to do otherwise. For example, the Mean Value Theorem (MVT) is one of the most important theorems in calculus. Many first year calculus students have difficulties really understanding or applying the MVT. Using CAS, a student can explore how to apply the MVT to a differentiable function and develop a better understanding of the MVT and its graphical interpretation. This session will focus on first year calculus topics. https://doi.org/10.37626/GA9783959871129.0.22 Curry, Marjorie: Culturally Responsive Math. pp 115 – 117 Using the Ready for Rigor framework, Zaretta Hammond’s book Culturally Responsive Teaching and the Brain: Promoting Authentic Engagement and Rigor Among Culturally and Linguistically Diverse Students gives educators a neuroscience-based approach to closing the achievement gap. The Ready for Rigor framework consists of four strands: awareness, learning partnerships, information processing, and community building. Acknowledging that all four strands are paramount to culturally responsive teaching but restricting focus to information processing, this session will give participants examples of and strategies for making their mathematics lessons more culturally responsive. More specifically, participants will learn to game-ify it, story-ify it, and make it social. https://doi.org/10.37626/GA9783959871129.0.23 Czarnocha, Bronislaw: Constructivist Teaching Experiment: Constructivist Research and Constructivist Teaching. pp 118 – 123 The aim of the discussion is twofold: first, we formulate and present examples of the creative bisociativity inherent in teaching-research TR/NYCity model (Section 1). Second, we bring the creative model of teaching-research as the precise solution to the difficulties experienced by Common Curriculum Standards in Mathematics (CCSM). Section 2 analyzes the reason for extraordinary difficulties in successful introduction of the curriculum into practice, which manifest themselves among others, by the necessity of scripted lessons telling teachers exactly what to do in all different moments of the lesson time. The root reason for the contemporary difficulties is the absence of teachers involvement in the design process It is in contradiction with the irreducible presence of teaching within the central constructivist instrument of research- constructivist teaching experiment of Cobb and Steffe (1983). https://doi.org/10.37626/GA9783959871129.0.24 Das, Mili: Curriculum for Mathematics Education – An Approach to Discuss Relation Between Theory and Practice. pp 124 – 129 A new curriculum has been introduced in Teachers’ Training course as the course is shifted from one year to two-year course in West Bengal, a state of India. In this curriculum in each course-paper theory and practicum are given equal importance so is in mathematics education also. In this new approach most of the educational experiences in mathematics education, gathered by the trainees are set and organized by combining theory and practicum. So, instead of only theory in this paper relationship is discussed on intertwined function of theory and practicum with practice. https://doi.org/10.37626/GA9783959871129.0.25 De Lange, Jan: Curious Minds: Serious Play. pp 130 – 135 We describe the background, theory, implementation and results so far of the Curious Minds Project, carried out by seven Dutch and Belgian Universities. The present article focuses on the Utrecht University’s involvement and results. Issues addressed are: hypothesis, role of manipulatives (toys), designing student activities from pre-primary to primary, creativity and curiosity, the role of adults and the challenges for professional development. Keywords: Early Childhood, Curiosity, Scientific Reasoning, Practice. https://doi.org/10.37626/GA9783959871129.0.26 Demirbec, Maifer Remzie: Puerto Rico Gas Prices Fall – „The Math of Cheap Oil“. pp 136 – 138 This project is an application of “Rate of change” and “Equation of the line” in business and finance field, as part of College Algebra and Trigonometry syllabus. The goal of this project is to develop students’ skills to understand and interpret graphs, tables, Math concepts as absolute value and percent change by showing them how Math is connected with real life issues. Also, is to engage students with the topic and through that how to use their Math knowledge of reading tables, complete tables, calculate the absolute and percent change, construct and interpret graphs. https://doi.org/10.37626/GA9783959871129.0.27 Dick, Thomas P.; Pilgrim, Mary E.: Learning (and Learning Teaching) by Doing Problems. pp 139 – 144 Active learning is often a challenge to find in mathematics classrooms at the post-secondary level. Still, teachers are expected to be experts in studentcentered approaches despite not having experiences with such approaches as students. The aim of this workshop is to introduce participants to a totally problem-based instructional experience, with the opportunity to actively engage in mathematics as students. During the workshop, participants will engage in discourse and reflection – reflection on both mathematics as well as the impact such a problem-based instructional experience could have on their practice. https://doi.org/10.37626/GA9783959871129.0.28 Dorrington, Pam: Family Maths: Experiential Learning. pp 145 – 149 The international Family Maths programme adopts an inquiry teaching and learning approach and it encourages learners, often from diverse backgrounds, to participate fully in the learning process. The programme also aims to develop the vocabulary necessary for meaningful communication in mathematics, develop problem solving skills and increase confidence and enjoyment of mathematics. The programme has proven to be a powerful catalyst in this regard and holds important lessons for both curriculum development and developing positive attitudes towards mathematics teaching and learning. This experiential learning, interactive work-session focuses on primary school mathematics curricula (for pupils approximately 9 – 13 years of age) and aims at giving participating conference delegates an opportunity to engage with and experience some of the hands-on problem solving activities used in the Family Maths programme. Discussion will be encouraged around the relevance of these activities for the teaching and learning of mathematics. Our conference organisers encourage presenters to consider the relationship between research and classroom teaching, and how, and if, these relate to each other in practice. Can the Family Maths philosophy and practice be a catalyst in narrowing the divide between the theory and practice of effective mathematics teaching and learning? https://doi.org/10.37626/GA9783959871129.0.29 Ferrarello, Daniela; et al: Serious Games in Teaching/learning Mathematics: the Experience of FunGo. pp 150 – 155 In this paper we present a general overview of serious games and their educational potential. We focus in particular on serious games for the teaching/learning of mathematics, highlighting how the method of horizontal teaching is effective in enabling students to achieve the learning objectives set by the teacher. FunGo, a serious game designed by the authors (researchers in mathematics education) in synergy with a group of graphic designers and computer scientists, is part of this line of ideas. We will show how FunGo has a multiple usability: it has, in fact, a double didactic use and has been used in public events of dissemination of mathematics, reporting in both cases positive results. https://doi.org/10.37626/GA9783959871129.0.30 Fine, Benjamin; et al: The Impact of Mathematics and Mathematicians. pp 156 – 160 The 1600’s ushered in our modern world, but not in the way most people learn in school. There was a revolution; started by Kepler, continued by Galileo, Descartes and Fermat and culminating in Newton and Leibniz. This revolution allowed for the development of modern mathematics which in turn led to modern science and engineering to advance. Hence, the technological revolution occurred which has shaped our present-day existence much more than anything else. In this article we examine these developments during the amazing seventeenth century. We keep an eye on the fact that for whatever reason human beings for the most part seem not to do hard engineering until the hard science is developed and not to do the hard science until the correct mathematics has been discovered. https://doi.org/10.37626/GA9783959871129.0.31 Fox, Courtney: Clean Water for Women and Children. pp 161 – 163 This workshop gives participants an outline of a full unit in Trigonometry that covers right triangle trigonometry, the law of sines, and the law of cosines. Attendees will participate in abbreviated student tasks. In the unit students are introduced to the world water crisis and how it affects women and children the most and why this is. Using their knowledge of trigonometry and the Desmos (or other graphing) calculator to “solve” a water crisis in a town and bring clean sanitation to a remote island. This unit helps students develop critical thinking and problem-solving skills, numerical literacy, and global awareness. Students make connections to the “real world” using mathematics and become world citizens. https://doi.org/10.37626/GA9783959871129.0.32 Galluzzo, Ben; Kavanagh, Katie: Getting Started Getting Students Modeling: Designing and Facilitating Open-ended Math Modeling Experiences. pp 164 – 167 “Modeling” is a term that has several meanings in general, but particularly in mathematics. Here math modeling refers to the process of creating a mathematical representation of a real-world scenario to make a prediction or provide insight. There is a distinction between using a formula that arises from an application (for example, distance equals rate times time) and the actual creation of a mathematical relationship itself that can be useful in an applied setting. In this two part workshop, we demonstrate how to develop authentic math modeling challenge problems that are accessible and relevant to students. In the second part of the workshop we talk about how to facilitate math modeling so that students have an opportunity to be creative and innovative in their modeling process while having ownership over their solution. https://doi.org/10.37626/GA9783959871129.0.33 Gazit, Avikam: Mathe Teachers´ Attitudes toward integrating Humor in Math Lessons. pp 168 – 172 The purpose of this study was to examine the attitudes mathematics teachers toward integrating humor in math lessons. Mathematics and humor are not seen as consistent with each other. Mathematics is seen as a subject is difficult to understand and its subject matter is isolated without any humanistic elements. Integrating humor in math lessons may create a pleasant atmosphere and reduce math anxiety. Humor can increase motivation as well as promoting creative thinking. A sample of 25 math teachers, most of them from elementary schools, answered a questionnaire. An important conclusion to be drawn from the findings is the positive attitudes of the teachers regarding the integration of humor in math lessons. It recommended strengthen math teacher to integrate humor in their lessons. https://doi.org/10.37626/GA9783959871129.0.34 Gill, Eoin: Maths Week Ireland: Promoting a Positive Attitude to Mathematics in Ireland. pp 173 – 176 Maths Week Ireland is an annual festival established in 2006 by people in the STEM community as an all-island event including the Republic of Ireland and Northern Ireland. Particular effort is made to highlight maths for life, for careers and as part of our culture. While the core principle is “Maths for All” the main engagement is with schools. In 2018 teachers reported 354,000 primary and second level pupils participating through in-school activities, online activities and events at partner centres. Maths Week creates an opportunity to disseminate new ideas in maths education. It also creates a space whereby teachers can try out new ideas and invent and create new activities with their pupils. This paper describes the organisation and activities of Maths Week and discusses the impact of the initiative with particular reference to evaluation with teachers. https://doi.org/10.37626/GA9783959871129.0.35 Goodell, Joanne E.: Learning to Teach Mathematics Through Project-Based Instruction. pp 177 – 182 Project-based instruction (PBI) is gaining prominence in the USA as an instructional innovation that promotes deep and connected understanding in mathematics. In this paper, I describe a program developed at the University of Texas at Austin known as UTeach that is being replicated in 45 universities across the USA. Concepts of inquiry teaching, problem-based and projectbased instruction are developed across the program. In this paper I argue that the structure, timing and location of student teaching impacts whether or not pre-service teachers are able to implement PBI during student teaching, which in turn impacts satisfaction with the student teaching experience and ultimately the intention to enter and continue in the teaching profession. https://doi.org/10.37626/GA9783959871129.0.36 Gordon, John; et al: A Problem-Solving Approach to the Introduction to Ordinary Differential Equations for Undergraduate Students at an American Two-year College. pp 183 – 188 Undergraduate students in STEM (Science, Technology, Engineering, and Mathematics) at City University of New York (CUNY)-Queensborough Community College (QCC) working toward a baccalaureate degree at one of CUNY’s senior colleges are required to take an introductory course in ordinary differential equations (ODE). Faculty in the Mathematics Department at QCC are experimenting with a problem-solving approach to this course in which students engage in learning course material through the development of mathematical models of real-world problems. The results seem promising and we outline them in this paper. Key-Words: First-order, linear system, integrating factor, homogeneous equation, research-based. https://doi.org/10.37626/GA9783959871129.0.37 Grzegorczyk, Ivona: Magic Tricks and Activities Supporting Abstract Thinking in Mathematics. pp 189 – 192 This workshop will involve you in mathematics based magic tricks activities promoting pattern recognition and algebraic modeling in various contexts. The interactive, hands-on activities are designed for introductory algebra courses, but they can be modified to generate more complexity and advanced mathematical thinking. https://doi.org/10.37626/GA9783959871129.0.38 Gurevich, Irina: Do Future Mathematics Teachers Need the Course „Integration of Digital Technologies in Teaching Mathematics“, and if so, what exactly can it help them with? pp 193 – 198 In the current research we analysed our teaching experience in the course “Integration of digital technologies in teaching mathematics”. The students were mathematics student teachers. The main goal of the course was to demonstrate the potential of digital technologies in teaching mathematics and to provide the students with basic skills in the intellectual use of these technologies. During the course the students, after getting acquainted with various mathematical software packages, build and present their own teaching units. We were interested to analyse the students’ attitudes towards the course. A multiple-choice questioner was formulated, and the collected data were analysed. We observed that most of the students found the course being helpful for their future teaching. The obtained results indicated that the described course provided them a didactic model to emulate. https://doi.org/10.37626/GA9783959871129.0.39 Hansen, Heidi B.; Magiera, Marta T.: Working Together: A Cross-cultural Study Addressing Mathematics Anxiety in K-8 Pre-service Teachers. pp 199 – 204 This study will present data from research on K-8 pre-service teachers’ math anxiety across three universities: one public, one private and one non-U.S. The article discusses background rationale, literature, tools used and results of this study. The results of the study indicated that similar math anxiety levels exist in students in all three types of academic institutions. The paper also incorporates discussion of the importance of including the topic in pre-service teacher training, and possible interventions for alleviating math anxiety. https://doi.org/10.37626/GA9783959871129.0.40 Hansen-Smith, Bradford: Why the Circle cannot be Squared. pp 205 – 210 Squaring the circle using compass and straight edge in such a way that both have the same area is not possible. The question is, why not? Math logic assumes there must be an area equal to both. Presumably there is a need to make these very different 2-D shapes equal, possibly to find a geometric proof to an inverse mathematical concept about differences. To “square the circle” gives preference to the square, four straight lines and four 90° angles, over a single line of the circle without angles. Maybe the emphasis more correctly is about the relationship of difference. Logically the truncation process suggests the circle is origin to the square, meaning there can be no polygon equal to the circle. Folding the circle gives a unique perspective about the relationship of circle to square, revealing 90° to be an angle of change, of directional movement between two points before any construction of a fixed angle or measuring of lines and areas. https://doi.org/10.37626/GA9783959871129.0.41 Herrelko, Janet M.: Change the Paradigm of Solitary Lesson Planning to Collaborative Planning that Unites Research and Practice. pp 211 – 216 Teachers are planning mathematics lessons using a basic protocol created in the 17th century. The results of the Programme for International Student Assessment provide evidence that this is not a successful approach to teaching students mathematical concepts today. Research in cognitive sciences has established how people attend to, sort, and store new content. Educational research provides case studies of successful pedagogical methods that help students learn. It is time for mathematics educators to unite these resources to create integrated lessons that focus on problem solving with experiential learning. This is a proposal to have teachers integrate educational and cognitive research creating lessons that improve access and equity to help students learn mathematics. https://doi.org/10.37626/GA9783959871129.0.42 Horwitz, Kenneth: Utilizing Analytics to show Representations used in Comparing and Ordering Unit Fractions. pp 217 – 222 Video Analytics bring together the world of educational research and classroom teaching with technology and the internet. Through use of more than 4500 hours of video data, an open source analytic creation tool, this study creates a video analytic that supports a research paper. In addition to supporting research, analytics can be a reflective tool for teachers, as well as support professional development as all levels. This report illustrates the video analytic, Using Meredith’s models to reason about comparing and ordering unit fractions, (Horwitz, 2015, available at http://dx.doi.org/doi:10.7282/T33J3FQG), as well as the methods used in the creation of the analytic used to support research in student use of representations to make sense of fractions. https://doi.org/10.37626/GA9783959871129.0.43 Huang, Hsin-Mei E.; et al: Investigating Junior High School Students´ Length Estimation Ability and Strategies. pp 223 – 228 This study investigated junior high school students’ length estimation ability with respect to everyday objects with lengths between 1 millimetre and 1 meter. Students’ strategies used for estimating the length of the longer side of a basketball court in school were analysed. A total of 240 Grade 7-9 students from cities in northern Taiwan completed a paper-and-pencil test assessing length estimation abilities. Results showed a significant gender effect on length estimation, but neither effects of grade level nor any interaction between grade level and gender on length estimation. About 40% of the students used effective strategies for estimating length measures, including visualizing, utilizing body parts, applying previous experiences, using a mental ruler, and making use of objects nearby. Still, about 60% of the students used ineffective strategies such as guessing. Implications for research and education practices are discussed. https://doi.org/10.37626/GA9783959871129.0.44 Humarán Martínez, Yuitza T.: Using Manipulatives to Develop the Understanding of the Concept of the Fraction of Preservice Elementary Teachers: The Meaning of Measure. pp 229 – 234 Manipulatives are a tool when that well-implemented can contribute to the development of mathematical concepts and processes, and is a popular strategy in elementary school. However, educators usually don’t use this technique efficiently for several reasons. For example, they had never used manipulatives before starting to work at school. In this quasi-experimental research, the understanding of preservice elementary school teachers of the concept of the fraction, specifically, the meaning of measure, was studied. Statistically significant evidence was gathered to conclude that the understanding of the meaning of measure improves after the implementation of the lesson with tangible manipulatives. https://doi.org/10.37626/GA9783959871129.0.45 Hydorn, Debra L.: Tools for Modern Mathematics: A Course to Introduce Experimental Mathematics. pp 235 – 239 The accessibility of computational methods and resources has made it easier to include undergraduates in mathematical research projects. However, based on the traditional form of mathematics education, many students aren’t confident in developing their own research questions or conjectures. Originally created to introduce students to programming tools (R, Mathematica and MATLAB), this course has evolved into an introduction to experimental mathematics. Students first learn the fundamentals of programming along with algorithmic structures and methods of simulation. Then, following the approach used by the Summer Undergraduate Research Institute in Experimental Mathematics at Michigan State University, students participate in (1) an experimental phase, where they use algorithms and simulations to produce output, (2) a conjecture phase, where they review their output to identify potential relationships and patterns, and (3) a 2nd experimental phase where additional output is produce to determine if any of their conjectures are still viable. The focus of the course is on developing students’ ability to pose research questions and their ability to use computational tools to address those questions. https://doi.org/10.37626/GA9783959871129.0.46 Iji, Clement O.; Andortan, Joseph A.: Brandishing Ethno-Mathematics Approach as an Interface for Improving Upper Basic Education (UBE) Students´ Interest and Achievement in Number and Numeration. pp 240 – 244 The study considered how ethno-Mathematics approach could be brandished to serve as an interface to improving UBE students’ interest and achievement in number and numeration (NN). The study was carried out in Obudu, a rural community in Cross River State of Nigeria. It adopted a quasi-experimental of pre-test post-test control groups design with intact classes used. Population of study comprised all the 6,226 upper basic education students from the 23 government controlled basic education schools in the study area. Two instruments were used for data collection. The study found among other things that when ethnomathematics was properly brandished, the UBE students improved in their interest and achievement in the NN concepts taught during the period of this study. It was also found that the initial noted gap between the male and female UBE students’ interest and achievement in NN was drastically reduced. Key words: Brandishing, Ethnomathematics, Interface, Number and Numeration, Upper Basic Education, Interest and Achievement https://doi.org/10.37626/GA9783959871129.0.47 Innabi, Hanan; et al: Patterns of Variation in the Work of „Mathematics in the City Project“: A Suggested Research Question. pp 245 – 250 The framework of this paper is based on the variation theory (VT), which explains the necessary conditions for learning. According to this theory, students have to experience patterns of variation for learning to take place. This paper highlights the patterns of variation that can be found in the work of the “Mathematics in the City” (MitC) project. Some examples are presented, and a research question is proposed related to using VT as a tool to analyze students’ learning in the MitC classrooms. https://doi.org/10.37626/GA9783959871129.0.48 Jackson, Colin: Going Against the Grain: Critical Thinking in and Beyond Mathematics. pp 251 – 256 In the UK, it is almost universal that secondary mathematics is taught in classes organised on the basis of differential ‘ability’: all-attainment teaching is rare. This paper is based on data collected from in-depth interviews with a small number of teachers whose beliefs and practices defy this norm. A number of themes emerged in their teaching, but in this paper I explore, very briefly, how the teachers enacted their belief in the importance of developing their students’ critical thinking skills as well as their mathematics. https://doi.org/10.37626/GA9783959871129.0.49 Jiew, Fui Fong; Chin, Kin Eng: The Embodiment of Mathematical Meanings with Special Reference to Multiplication: Issues and Challenges. pp 257 – 262 This paper aims to illustrate how two primary school teachers (Doreen and Edwin – pseudonyms) make sense of mathematics in particular the multiplication of fractions and decimals. The meaning of a particular mathematical expression and symbol could be conveyed through language however a mathematical procedure that is performed for a purpose may be difficult to make sense sometimes. Data were collected through semistructured interviews. Findings revealed that Doreen recognised the meaning of multiplication as the notion “of” in the contexts of fractions. Both of them rote learned the mathematical procedures in the multiplication of fractions and decimals and they could not make sense of them. One of the main reasons for this was because they were not aware of the changes of mathematical meanings across different contexts. https://doi.org/10.37626/GA9783959871129.0.50 Johnston, Peter; et al: Supporting Transition for Mathematics and Science Students under an Assumed Knowledge Approach. pp 263 – 268 In Australia there is concern over the poor mathematical skills of students entering University STEM degrees (King & Cattlin, 2015). Challenged by the introduction of an assumed knowledge approach for mathematics dependent university degrees, we noted diagnostic testing approaches (Ní Fhloinn et al., 2014) and sought to adapt the successful GetSet2 quiz that previously had been applied only to pre-requisite mathematics university entry (Burton et al., 2013). We introduced the on-line self-assessment Get Ready Maths/Science quizzes for commencing science and mathematics students. This allowed students to receive timely personalised feedback on their level of knowledge and skills compared with the expected assumed/pre-requisite knowledge for university entry. This paper reviews the design, development and initial implementation of transition quizzes under the challenges of an assumed knowledge framework, instead of a pre-requisite framework. https://doi.org/10.37626/GA9783959871129.0.51 Johnston-Wilder, Sue; Lee, Clare: How can we Address Mathematics Anxiety more Efficiently as a Community? pp 269 – 274 Mathematics anxiety has been discussed for over 60 years. The majority of those suffering belong to an identifiable subgroup, often identified as ‘female’, or learners with a ‘feeling’ rather than a ‘thinking’ preference, or empathisers. These learners prefer to understand the value, meaning, purpose and narrative of the mathematical tools they are required to learn. Ten years ago, we planted a seed for a change in practices that engender anxiety to those that build a positive stance. This seed has grown into a group of teacher and research practitioners working to overcome mathematics anxiety and build mathematical resilience. The paper discusses what is known, by these researchers and teachers, and how to develop innovative communication in order to work internationally toward elimination of the acquired, disabling condition of mathematics anxiety. https://doi.org/10.37626/GA9783959871129.0.52 Kaino, Luckson Muganyizi: Enhancing Mathematical Modeling Activities in Classroom Instruction. pp 275 – 280 The ability of students in mathematical modeling was enhanced through activities that involved systems of linear equations with two variables. Students involved were in form four, at the final year of the ordinary secondary school level where they were expected to have mastered the knowledge on systems of linear equations with two variables. Students’ knowledge on ill-conditioned linear systems was explored as well as their knowledge on practical problems in linear equations. Then after, mathematics subject teachers guided students to identify practical problems in linear equations of two variables. Students were put into groups to think of problems in real life and come up with solutions. The solutions were related to the real situations in the environment and each group had to make a presentation in the class. Problems in transportation, manufacturing, production and diet were identified by students and the results presented for discussion. It came out clearly that students acquired knowledge on solving real life problems at the end of the activities. Before these activities, students had theoretical knowledge on solving problems with two unknowns without relating these to real life problems. While knowledge on independent and inconsistent systems was known to students, enthusiasm was noted among students at the end of the activities when they got involved in real aspects of solutions obtained. It was concluded that with more time availed in the school curricula, students can acquire useful knowledge on mathematical modeling to achieve problem-thinking skills that involve real life situations. https://doi.org/10.37626/GA9783959871129.0.53 Kania, Sylwia: Solving Mathematical Problems in the Context of Some Obstacles between Teachers and Students. pp 281 – 286 Great mathematical discoveries are mostly based on huge knowledge of their explorers and long, solid work leading slowly to the finding. There are also well known cases of the “accidental” discoveries that happened quickly, intense and their founders did not even realize the range of the discovery, because they were working on something else at the time. Nevertheless, each finding requires energy, devotion and concentration of its discoverer. Solving mathematical problems demands quite the same things, thus teachers may find some opportunities to create curious, open-minded young discoverers. It is not an easy job to do though, because there is a great risk of killing pupils’ enthusiasm by teacher’s skepticism, there is a large chance to nip pupils’ energy in the bud by routine operations and there is a huge possibility to discourage pupils’ endeavors by giving them wrong-chosen problems to solve. https://doi.org/10.37626/GA9783959871129.0.54 Kennedy, Tierney: Exploring the Nature of Teacher Questioning withing Challenging Tasks for Inducing Conceptual Change. pp 287 – 292 Recent research has considered how to support teachers using challenging tasks in mathematicswith students who struggle. Teacher questioning in response to correct or incorrect answers has been identified as an important element for maintaining the cognitive load. This paper examines the nature of teacher questioning within challenging tasksin which struggling students were noted to change their own conceptionsand proposes a minor change to includea questioning phasewithin the Launch-Explore-Summarise structure by Lappan et al. (2006). It presents evidence from a two-year study in which the combination of conceptual change questioning with challenging tasks led to substantial gains for low-performing students across six primary schools on standardised tests compared with Education Department expectations (d = 0.7). https://doi.org/10.37626/GA9783959871129.0.55 Klymchuk, Sergiy; Wilson, David: Integrating Pen-enabled Tablet PCs in Teaching Engineering Mathematics. pp 293 – 298 The paper analyses the attitudes and experiences of two university lecturers involved in integrating pen-enabled Tablet PCs (penTPCs) in teaching engineering mathematics. The first lecturer has an engineering background and teaches an advanced engineering mathematics course (year four). The second lecturer has a mathematics background and teaches a second year engineering mathematics course. Two rounds of interviews with the lecturers on using penTPCs were conducted in 2015 and 2019. Analysis of these interviews suggests that, for the lecturer in mathematical disciplines, a key factor in their initial adoption of penTPC technology may be their perception of the usefulness of the technology in enhancing delivery within the context of existing pedagogical approaches in a classroom/lecture setting. https://doi.org/10.37626/GA9783959871129.0.56 Krevisky, Steve: Using Sports Data in Statistics and Math Classes: An Overview and Update. pp 299 – 300 Sports data can be a very good way to motivate students, in both statistics and math classes. Background to this usage will be discussed, along with some new ideas on how to employ this in the classroom. https://doi.org/10.37626/GA9783959871129.0.57 Kusaka, Satoshi: Analysis of the Characteristics of Mozambican Primary Mathematics Textbooks compared with Japanese Textbooks focusing on Tasks and Problems related to the Real World. pp 301 – 305 This study aims to clarify the pertinent characteristics of Mozambican primary mathematics textbooks from a sociocultural perspective (in comparison to Japanese ones) by focusing on how they treat ‘real-world’ mathematics. The following four perspectives are discussed: (1) Proportion of the tasks related to the real world via the introduction of new learning content (2) Proportion of problem solving exercises related to the real world (3) Categorization of the situation of the tasks and problems related to the real world (4) Appearance of socially open-ended problems and their content. As a result, we found that there are few problems which are related directly to the real world in the Mozambican primary mathematics textbooks. The content of the problems related to the real world are about the tax system and salaries, which means students are given opportunities to view and think mathematically about their social system right from the primary school age. https://doi.org/10.37626/GA9783959871129.0.58 Laskasky, Katie; et al: Innovative Problem Solving: What happens when Math Education, Business, and Engineering Perspectives Interact. pp 306 – 311 For years, practitioners and researchers have attempted to solve the same math education problem. Though the approach varies, they use outdated processes and see few results. Thus, there is an overall need to use new strategies. This paper explores how one K-12 school district uses an innovative, collaborative, problem solving process to understand its math learning problem. Stakeholders engage diverse viewpoints, use researchbased recommendations to define success in how students learn mathematics, develop context-sensitive solution options, and evaluate those options’ adaptability. This innovative problem solving process’ foundation emerges from research and best practice recommendations found at the intersection of multiple disciplines: math education, business, systems engineering, and implementation science. The current observation and interview data indicate that stakeholders feel a sense of ownership, embrace variability in problem solving, and understand how to collect data about students’ math learning. https://doi.org/10.37626/GA9783959871129.0.59 Lemieux, Collette; Roettger, Eric: Students´ Reasoning During a Calculus Two-Stage Exam. pp 312 – 317 For a two-stage exam, students first write their exam individually and then repeat it in a small group. This study analyzed the discussions that students had during the group stage of a two-stage exam in a first-year calculus course in order to investigate students’ reasoning and how they arrived at their answers. Data, consisting of 14 transcripts of audio-recordings of the students’ discussions, were analyzed qualitatively, guided by Lithner’s (2007) conceptual framework on mathematical reasoning. The results suggest that, though students primarily used imitative reasoning or rote learning to answer many questions, they also demonstrated creative reasoning by using a novel & plausible approach and grounding their reasoning in mathematics. Further, though the imitative reasoning relied primarily on remembering a theorem or term in calculus, creative reasoning was demonstrated in multiple ways. https://doi.org/10.37626/GA9783959871129.0.60 Corredor, Olga León; et al: Integrating Technology and Didactic Resources for Enhancing Learning Processes. An Exploratory Study. pp 318 – 323 Some limitations that affect the learning of mathematics are related to two dysfunctional issues: lack of acknowledgment of students‘ differences in the didactic designs and of the students’ awareness about their learning skills. Accessible and affective didactic designs aim to overcome such dysfunctional issues. In this direction, the document presents three contributions: first, the exploration of technological relationships that foster cognitive convergence between the student and tools; second, a revision of hypotheses that give support to accessible and affective didactic designs; and third, the documentation of the learning trajectories that some diverse Colombian populations made while they were playing the game called The Jumper. The methodologies used in the research were Design Science Research and Teaching Experiments. https://doi.org/10.37626/GA9783959871129.0.61 Liang, Su: Enquiry-Based Learning in College Mathematics Education: Theory and Practice. pp 324 – 329 The practice of Inquiry-Based Learning (IBL) has a very long history. In the western world, the ancient Greek philosopher, Socrates (469 – 399 B.C.) had utilized IBL to engage his interlocutors in dialogue for discovering basic truth and principles. In the Eastern world, the ancient Chinese philosopher and educator Confucius (551 -479 B.C.) had also raised the idea of IBL approach for teaching and learning. Confucius had said: “I hear, I forget; I see, I remember; I do, I understand”. Active learning is the essence of IBL way of teaching. The IBL discussed in the paper is guided IBL. In the research literature, many research showed evidence that guided IBL produced better learning outcomes comparing to pure lecture approach. In recent years, promoting IBL in the field of education becomes a trend, because researchers believe that the features of IBL can fulfill the 21st century education through cultivating students’ critical and creative thinking, nurturing inquiry mind of problem-solving, and preparing life-long learners, for our society. However, in reality, the traditional way of teaching – lecture is still dominated at school teaching. Why has IBL been promoted in the educational research but most teachers still never employ it in their teaching practice yet? In this paper, I will discuss the challenging we are facing and propose some ideas for IBL implementation. https://doi.org/10.37626/GA9783959871129.0.62 Lipovec, Alenka; Ferme, Jasmina: Some Factors Influencing Effectiveness of Mathematics Homework. pp 330 – 335 Empirical research, which examines the relationship between mathematical achievement of elementary school students and mathematics homework assignments, gives inconsistent results. We present the results of the crosscultural study (N = 1061) with 12-15 years old students from Slovenia, Croatia and Slovakia. The results show that homework frequency, teacher responses, and the support of parents are not related to students’ mathematics achievements; but parental control and the time spent doing homework are negatively related to those achievements. https://doi.org/10.37626/GA9783959871129.0.63 Lousis, Michael: Recommendations for Instructional Designers and Textbook Writers Concerning the Correction of Significant and Pesistent Errors in Arithmetic and Algebra. pp 336 – 342 An error analysis of the 200 English and 150 Greek learners’ tests in arithmetic and algebra was accomplished. Those tests stemmed from the Kassel Project. Following this error analysis, specific recommendations are presented in each domain of arithmetic and algebra that should be taken into account by instructional designers and textbook writers. These recommendations were founded on terms of psychology and cognitive science as applied to information-processing. The study has shown the educational media (textbooks etc.), as being responsible for the emergence and persistence of these errors in the learners’ minds too, since instruction is mostly based on the use of those media. Key words: error analysis, Kassel Project, textbooks, educational media, recommendations. https://doi.org/10.37626/GA9783959871129.0.64 Marchand, Patricia: Interface between Theoretical Guidelines and Classroom Practices to Create Activities that Enhance the Development of Spatial Reasoning in Elementary School. pp 343 – 346 The spatial reasoning has been identified by many researchers as being linked to positive mathematical performance and, therefore, is a determining factor in mathematics and scientific success at elementary, secondary and upper levels (Davis & The spatial reasoning study group, 2015). Also, spatial reasoning has been proven to be a type of reasoning that is malleable and can be develop, implying that teachers are empowered in this development (Moss, Bruce, Caswell, Flynn & Hawes, 2016; Wai, Lubinski & Benbow, 2009; Marchand, 2009a; Berthelot & Salin, 1992). The goal of this workshop is to expose theoretical guidelines to analyse and to create classroom activities focusing on developing spatial reasoning in elementary school. The interface between these theoretical guidelines and classrooms activities allows us to unfold new ideas to deal with spatial reasoning at the elementary level. https://doi.org/10.37626/GA9783959871129.0.65 Markun, Urska; Kos, Jasna: Research Work in a Secondary School Classroom: How Well are Teachers Equipped for it? pp 347 – 352 A university degree is not enough in itself to equip a mathematics teacher for successful secondary school-teaching in the longer term. Without continuous training and career-long learning, a teacher will not be able to provide adequate support for students in activities such as extended essays or explorations, both of which are compulsory components of the IB programme. In this paper, we present some examples of such work by IB students at our school. In addition, some Slovenian secondary school students regularly participate in a national research competition for which they must submit project-based work in various fields. The present article describes how university departments co-operated with our secondary school in the course of such research. Examples of research carried out by a number of 16-year-old students at our school are also presented here. https://doi.org/10.37626/GA9783959871129.0.66 Mart, Malgorzata: The Impact of Teacher Self-Efficacy on the Level of Implementation of Graphing Technology in Teaching Factoring Quadratic Functions in Introductory Algebra. pp 353 – 357 The purpose of the study was to determine whether there is a relationship between self-efficacy of global and local algebra teachers and their level of incorporating technology in teaching factoring quadratic functions to introductory algebra students. The participants (54 mathematics educators form 15 countries and five continents) replied to the UVGIA survey instrument. Quantitative analysis of data brought the conclusion that there is a strong positive relationship between the level of self-efficacy of teachers and their level of implementations of technology regardless of country of origin. https://doi.org/10.37626/GA9783959871129.0.67 Mason, Ralph; et al: Foundational Experiences as a Curriculum Design Principle for Secondary Mathematics. pp 358 – 363 Students must make sense of the mathematics they are learning, if they are to understand it. When students are encountering a mathematics topic primarily through that topic’s mathematical forms—its symbols, terminology, definitions, operations, and algorithms—the richness, potency, and completeness of their understanding will depend on their prior, pre-formal experiences with that topic. Foundational experiences activities enable students to construct images, patterns, and ideas—in a word, memories—that will enable them to see the sensibility of the topic’s mathematical forms when they learn them. We invite participants to explore some examples of instructional activities designed to provide foundational experiences for the mathematics of powers, from power laws through geometric sequences to exponential functions. With these examples, participants will consider these questions: How can foundational experiences contribute to students’ understandings of the math behind the topic’s formal content? What are the qualities that we should invest when designing foundational experience activities? https://doi.org/10.37626/GA9783959871129.0.68 May, Bernie (Dov): Engage Students More Hopscotch Mathe has Students Jumping for Joy. pp 364 – 367 The goal was to create a system to teach children deep thinking skills, as well as problem solving skills which they could later use in tomorrow’s innovation economy. The by-product is they learn the Times Table. We cover more in less time…under 5 hours, we go up to 20×20, and introduce the children to complex algebraic equations, too. Guess what? They love it – and ask for more! The times table represents the problem to be solved. Each intersection represents a smaller aspect of the problem. They learn various techniques. No dumb sing-song melodies. They build on what they know. We do not go linearly through the table. We jump around…and cover whatever we can. When we are through I show them that if they only knew 7×4 = 28, they have the problem solving skills where they can solve the whole table. The idea behind Kinestetic Math is to get into their world, and reach them at their level. Children like to run, jump, colour and move around – so do we. We use our fingers, our knuckles, and our legs to learn the Times Table. This paper covers a small section of the program, Magic Squares and Hopscotch Math, as an introduction to a different kind of thinking and how innovative thinking can be applied to teaching. I introduce the program with a 10×10 grid representing the times table. Every time we solve one of the blocks on the table, they get to color the block however they want. https://doi.org/10.37626/GA9783959871129.0.69 Menz, Petra; Mulberry, Nicola: Open Source Differential and Integral Calculus Material Development to Support Student Accessibility and Learning. pp 368 – 373 Educational resources in mathematics are an important aspect of the teaching and learning landscape. Moreover, resources have come a long way from the spoken word with such inventions as paper and the computer to the point where there is now an infrastructure around open educational resources (OER) that has matured into viable alternatives to traditional resources. The newfound prevalence of these materials provides opportunities to customize OER to the specific needs of students and institutions. We designed open source material for the social science strand of differential and integral calculus by adopting an open source textbook and adapting it for our needs. Along with the course notes, we developed lecture notes, student notes based on the Cornell note-taking system, and assignments with solutions. Students are appreciative of free material, but moreover, the cohesiveness and interconnectivity among the various course materials provides for a smoother learning journey through our courses. This paper presents our philosophy, an overview of our open source material, and the operation of both courses. https://doi.org/10.37626/GA9783959871129.0.70 Michelsen, Claus: The MACAS Symposiums 2005 – 2019. Mathematics Education in an Interdisciplinary Context. pp 374 – 379 The symposium series Mathematics and its Connections to the Arts and Sciences (MACAS) has been held since 2005. The vision which the MACASinitiative is based upon is to develop a humanistic approach to education that combines various disciplines in a single curriculum. According to this vision the aim is to educate students by enabling them to pursue diverse fields of research, while at the same time exploring the aesthetic and scientific connections between the arts and science. In view of the challenges of the 21st century, a modern approach to education with a focus on multi- and interdisciplinarity is more important than ever. Five MACAS symposiums have been held since 2005, and the proceedings of the symposiums provide an insight into ideas, experiences, conceptual frameworks, and theories to connect mathematics education to the arts and sciences. Based on the symposiums proceedings we provide an overview of five main themes addressed at the MACAS symposiums (i) mathematics and science (ii) mathematics and art (iii) mathematics and technology, (iv) mathematics and literature, and (v) educational perspectives on interdisciplinarity. The overview highlights the need for joint empirical investigations that operationalize, model and study the rich ideas presented in at the symposiums. https://doi.org/10.37626/GA9783959871129.0.71 Miheso-O´Connor, Marguerite K.: Teaching Mathematics through Historic Environment. A Time-Travel Grounded Pedagogy. pp 380 – 385 Mathematics has been used by generations to make important decisions for a long period of time. History is littered with problem solving events which are results of mathematization of tasks based on available tools in any given generation. While History of mathematics focuses on what each culture contributed to present day conventional mathematics as taught in schools as a subject, Mathematics in a Historic environment focuses on identifying mathematical thinking that exists in all historical events. Historical events when enacted through the Time Travel approach learners get the opportunity to relive past events in the present context. Teaching mathematics in historic environment uses the time travel events that are practised by bridging ages international, to provide a reflective meaningful conceptualization of mathematics is a living subject. The strategy illuminates the centrality of mathematical thinking in all historical events. This paper shares findings from a study carried out on the effectiveness of this approach for teaching mathematics and provides an opportunity to discuss the approach as a viable pedagogic strategy that can be replicated across the curriculum https://doi.org/10.37626/GA9783959871129.0.72 Missen, Jenny: Researching and Implementing in the Mathematics Classroom Australian Curriculum General Capabilities. pp 386 – 391 The Australian Curriculum (AC) provides teachers with a great amount of detail in each curriculum area. In addition to teaching these curricula, the AC requires incorporation of Cross-Curriculum Priorities and General Capabilities. This paper documents the work done on an action research project considering ways in which the General Capabilities (GCs) of the Australian Curriculum could be incorporated into teaching Mathematics and the difficulties I faced as a teacher researching during the teaching term. https://doi.org/10.37626/GA9783959871129.0.73 Morge, Shelby: Addressing Teachers´ Culturally Responsive Teaching Beliefs through Course Activities. pp 392 – 397 Making data-based decisions about course content is a difficult process for teacher educators. This difficulty is amplified when considering complex issues focused on diversity. In order to understand and address pre- and in-service teachers’ culturally responsive teaching beliefs, the Culturally Responsive Teaching Outcome Expectancy Scale (Siwatu, 2007) was administered during graduate and undergraduate courses in mathematics education at two southeastern US universities. From the survey results instructors identified items with high and low means (on a 100 point scale). The lowest items provided a basis for constructing future course activities. In this paper we share the expectancy scale results and course activities that were implemented. We also discuss opportunities for improving the culturally relevant practices and activities in our courses in order to ensure the transferto classroom practice. https://doi.org/10.37626/GA9783959871129.0.74 Morska, Janina: From the Purpose oft he Lesson to Success. pp 398 – 400 This paper deals with efficiency in teaching. The purpose of the lesson and the criterion of success are complex elements in the didactic process. Between these elements are theory and practice, various forms of work, feedback and student self – evaluation. I would like to share my professional experience as an apprenticeship teacher, as well as a deputy head teacher (vice-director) observing the work of other teachers in formative assessment. https://doi.org/10.37626/GA9783959871129.0.75 Moscardini, Lio; et al: Collaborating Across the Pond: Cognitively Guided Instruction Project. pp 401 – 405 This paper describes a primary-school (ages 5-11) project implemented in Scotland, based on the United States research from Cognitively Guided Instruction (CGI), and as envisioned by Dr. Lio Moscardini. Three schools, two public and one private, participated in this two-year long initial study that focused on helping teachers to understand the developmental stages pupils naturally progress through in order to understand the mathematics for their class level as defined by the Scottish government. This project provides evidence that a rise in attainment can occur by focusing on teachers’ knowledge, pedagogy, and pedagogical content knowledge in relation to mathematics rather than by focusing on attainment itself. Additionally, this project addresses the teaching and learning of a diverse group of students, i.e. inclusion, low socio-economics. https://doi.org/10.37626/GA9783959871129.0.76 Movshovitz-Hadar, Nitsa; et al: Bridging between School Mathematics and Contemporary Mathematics: Turning a Dream into Reality. pp 406 – 411 In many countries, school mathematics curriculum does not go beyond the 18th century mathematics. Any solution for bridging this gap must consider students’ limited background, as well as teachers’ time constrains. Our ‘bridge’ consists of periodically interweaving Mathematics-News Snapshots (MNSs), i.e., short descriptive presentations of recent mathematical results, throughout the teaching of the ordinary math curriculum during the three years of senior high school. More than 20 MNSs are already available (see https://MNS.co.il). Our two-part workshop is aimed at sharing our solution. This will include a discussion of its underlying principles, a reverse engineering analysis of sample MNSs vis-à-vie the MNS authoring guidelines, an overview of three teacher preparation models, and results of our implementation follow-up studies. Finally, in the spirit of the conference, we’ll invite attendees to adopt our solution, and possibly also to participate in developing more MNSs, thus turning our dream of bridging the gap into reality. https://doi.org/10.37626/GA9783959871129.0.77 Narayanan, Ajayagosh: Peer Tutoring: Developing and Sustaining Effective Teaching Practices with Mathematics Teachers in Lesotho. pp 412 – 417 This paper shows how a group of educators initiated in-service workshops for primary and secondary mathematics teachers since 2012 in collaboration with the Ministry of Education and Training (MoET) in Lesotho. The prime focus of these workshops was to develop teachers’ capacity building in mathematics through peer-support. The paper also narrates how a chain of these workshops evolved to a capacity building program with innovative approaches in classrooms. These workshops explored ideas on numbers, shapes (through the use of origami) and problem solving for effective teaching/learning of mathematics. The concept of peer tutoring/learning had emerged from these workshops as an idea that suits Lesotho education system. A capacity building program was thus recommended for the sustainability of these activities. https://doi.org/10.37626/GA9783959871129.0.78 Navarro Robles, María Estela: Variation Theory used to make a Personalized Diagnostic in the Level of Knowledge of Fundamental Concepts about Rational Numbers and their Operations in Undergraduate Students. pp 418 – 421 This lecture explains how through Marton Variation Theory was designed and evaluated a test about rational numbers to identify for each student the specific knowledge and skills about the theme to solve problems and to make operations and thus which concepts theyneed to learn or what skills they need to develop. The variation theory was used in the sense of one problem, multiple changes. The test was answered by 115 students of 7 groups of a private university, who are enrolled in a leveling course. From the answers of the students it was characterized the lived object of learning and this was the start point to classify the conceptual or operational needs of each student. With the detailed results it was possible to design a personalized route of learning. Key words: Rational numbers, variation theory, undergraduate student, personalized course https://doi.org/10.37626/GA9783959871129.0.79 Niess, Margaret L.: Online Strategies Enhancing Mathematics Teacher Knowledge for the Digital Age: Discourse and Critical Reflection. pp 422 – 427 This study designed online graduate courses to enrich inservice mathematics teachers’ Technological Pedagogical Content Knowledge (TPACK). The effort identified key experiences to engage teachers in discourse and critical reflections for relearning, rethinking, and redefining teaching and learning as they know and learned it, transforming their TPACK with respect to teaching with digital technologies. The experiences modeled inquiry tasks merging content, technology and pedagogy as described in TPACK, connecting teachers with experiences as students learning about and with technologies. Critical reflections on the experiences as learners and as teachers combined with the online community of learners’ discourse, transforming their teacher knowledge. The collection of strategies involving discourse and critical reflection did enhance the participants’ TPACK, providing recommendations for designing online inservice teacher education courses. https://doi.org/10.37626/GA9783959871129.0.80 O´Dell, Jenna R.; Frauenholtz, Todd R.: An Unsolved Graph Theory Problem: Comparing Solutions of Grades 4, 6, & 8. pp 428 – 433 This study investigated how students in Grades 4, 6, and 8 reasoned through a non-routine, unsolved problem. The study took place at a K-8 school in the Midwestern United States. Each grade participated in two or three task-based sessions lasting between 45 and 60 minutes with the researchers. During the sessions, students engaged in the Graceful Tree Conjecture where they examined graceful labelling for Star, Path, and Caterpillar Graphs. We examined differences in students’ generalized solutions across the grades and how they were able to provide justifications and state generalizations of a graceful labelling for the graphs in the Path Class. Descriptions of students’ generalized solutions are included for each grade level. https://doi.org/10.37626/GA9783959871129.0.81 O´Meara, Niamh; Faulkner, Fiona: Professional Development for Out-of-field Post-primary Teachers of Mathematics: A pre and post Analysis of the Impact of Mathematics Specific Pedagogical Training. pp 434 – 439 The Professional Diploma in Mathematics for Teaching is a 2-year part-time programme dedicated to out of field teachers of mathematics in second level education in Ireland. The programme was introduced in Ireland after a report highlighted that 48% of second level teachers of mathematics in Ireland were not qualified to teach mathematics (Ní Ríordáin & Hannigan 2011). The programme has been running since 2012 and is currently upskilling its 6th cohort of out-of-field teachers. As part of the programme, teachers are required to undertake mathematics content modules as well as mathematics specific pedagogy modules. One such mathematics specific pedagogy module requires students to undertake five 3-hour workshops which examine mathematics content contained on the second level curriculum and offers suggestions on how to teach it for conceptual understanding. Teachers in Cohort 5 of the programme completed a questionnaire prior to completing the 5 workshops to outline how confident they felt teaching particular aspects of the second level mathematics curriculum. They were also asked to best describe the teaching approaches that they favoured at that point in time. Upon completion of the 5 workshops, this same cohort of teachers completed a similar questionnaire investigating their level of confidence in teaching the curriculum and any changes in their teaching practices that occurred as a result of participation in this module. https://doi.org/10.37626/GA9783959871129.0.82 Pagge, Jenny: Effective Use of ICT and Storytelling to Teach Statistics in the Preschool Classroom. pp 440 – 444 New school curricula and modern teachers are trying to get the child engaged and interested in statistics through accessibility and enjoyment. This has been backed up by much research into the correlation of a child’s engagement and their academic achievement (Gunuc, & Kuzu, 2014). Using storytelling as a teaching method, teachers can provide a meaningful context for statistics which can change this prejudice from a young age (Casey et al., 2004, Walters et al 2018) and is shown to have many educational benefits for children (Sherwood, 2018). In the last years ICT tools, games and storytelling have been used to achieve this engagement (Lekka et al, 2017, Walters 2018). ICT provides children with the opportunity to enhance their communication skills, creativity, high-order thinking and practical technological skills which are needed in a modern society (Corel, 2019). This paper includes a brief overview of research that looks at the use of ICT applications, and use of storytelling to teach descriptive statistics in the preschool classroom. https://doi.org/10.37626/GA9783959871129.0.83 Paolucci, Catherine: Supporting Pre-service Mathematics Teacher Development through Transformative Community Engagement. pp 445 – 449 Opportunities for field-based transformative learning are a critical part of mathematics teacher education, yet several factors limit the extent to which teacher preparation programs can offer them. This paper discusses the value of transformative learning for pre-service mathematics teachers and presents an example of an international community engagement program that was specifically designed to support transformative learning for pre-service teachers in both the United States and South Africa. It highlights evidence of key aspects of transformative learning in the reflections of both the pre-service teachers and the students in the program and discusses the implications of this for future research and program development. https://doi.org/10.37626/GA9783959871129.0.84 Pearn, Catherine; et al: Developing and Assessing Algebraic Reasoning in the Middle Years. pp 450 – 455 New school curricula and modern teachers are trying to get the child engaged and interested in statistics through accessibility and enjoyment. This has been backed up by much research into the correlation of a child’s engagement and their academic achievement (Gunuc, & Kuzu, 2014). Using storytelling as a teaching method, teachers can provide a meaningful context for statistics which can change this prejudice from a young age (Casey et al., 2004, Walters et al 2018) and is shown to have many educational benefits for children (Sherwood, 2018). In the last years ICT tools, games and storytelling have been used to achieve this engagement (Lekka et al, 2017, Walters 2018). ICT provides children with the opportunity to enhance their communication skills, creativity, high-order thinking and practical technological skills which are needed in a modern society (Corel, 2019). This paper includes a brief overview of research that looks at the use of ICT applications, and use of storytelling to teach descriptive statistics in the preschool classroom. https://doi.org/10.37626/GA9783959871129.0.85 Pearson, Esther: „STEPS“ to a Brighter Future. pp 456 – 461 The „Science, Technology, Engineering, Precollege Studies“ (STEPS) program was developed in 1988 by Dr. Esther Pearson. The STEPS program has served thousands of youth over the past two decades to provide academic support and mentoring to minorities and women students. The STEPS program focuses on demonstrating a connected learning approach to STEM academics. Students participate in mentoring through the STEM pipeline of course choices, extra-curricular activities, and exposure to STEM practitioners. Students learn to overcome the challenges that prevent successful matriculation into STEM fields. Minority and women students in elementary through college in the Boston and greater Boston areas learn how to navigate from a desire for a STEM career to achieving one. https://doi.org/10.37626/GA9783959871129.0.86 Pilgrim, Mary E.; Dick, Thomas P.: Actively Engaging in Calculus to Support all Students. pp 462 – 466 Research findings support the use of active engagement in the mathematics classroom. Active learning not only has the potential to positively impact student learning, it also helps to address equity issues in the mathematics classroom. However, with limited experiences in student-centered instruction and little to no pedagogical training, mathematics faculty are often underprepared to meet the needs to today’s STEM majors. In addition, content-specific professional development is typically not readily available to faculty on their campuses. With a focus on calculus, this workshop aims to fill this professional development gap by providing participants with the opportunity to engage in student-centered activities as well as reflect and discuss the implications for their own mathematics classrooms. https://doi.org/10.37626/GA9783959871129.0.87 Pomuczné Nagy, Ildikó-Anna: How and wherer can a Mathematics Teacher Utilize his 33 Years of Teaching Experience? A Math Teacher about Teaching Mathematics-Excerpt from 33 Years of Teaching Experience. pp 467 – 472 This paper shows how a mathematics teacher can utilize his teaching experience. I have been working as a mathematics and physics teacher in Hungary for 33 years. I have taught at various levels of the education system: at elementary school, high school, teacher training college, and in teacher training too, but at most time of my job I taught at high school. I am currently working on the series of a new mathematics textbook for 10 to 14-year-old students. It is based on the traditions of the Hungarian mathematics education, but using the opportunities offered by the 21st century, it also includes modern sample tasks that fit into the curriculum, for example Geogebra files, written by me. I would like to share how I use my teaching experience in textbook writing and how I focus primarily on the didactic aspects of teaching mathematics. I pursue my PhD research in the topic of problem-solving thinking, so I study the mathematical thinking of my students studying in different school types. In my lecture, I analyse different tasks by focusing on mathematical methodological aspects. For example I will tell that I believe it is advantageous to introduce mathematical definitions with examples which are astonishing for students in order to draw attention to maths as much as possible. I will give examples of how I build my experience into the textbook in order to make the system of mathematical concepts optimal for pupils. I would like it if give you an insight into a segment the current Hungarian mathematics education, the current teaching of problem-solving thinking and the different ways of students’ thinking. https://doi.org/10.37626/GA9783959871129.0.88 Povey, Hilary: Moral and Political Dilemmas in Working with the Concept of Citizenship within Mathematics Teaching in Schools: a Personal Perspective. pp 473 – 478 This paper springs out of my engagement with a curriculum development project framed in response to a European Union call for action on global citizenship. But citizenship is a complex and elusive concept – slippery, dangerous and contested. Inevitably, tensions arise as we seek to find a way of acting in the world and trying to find, however limited and partial, an answer to the question: „what is to be done?“. In this paper, I identify and offer a personal response to some of moral and political dilemmas we have identified during the design and implementation of the project. https://doi.org/10.37626/GA9783959871129.0.89 Prendergast, Mark; et al: Incentivising the Study of Higher Level Mathematics. pp 479 – 484 In Ireland, mathematics has been assigned a special status within the postprimary school curriculum with the introduction of a Bonus Points initiative (BPI) in 2012. Students are now awarded an extra 25 points in their upper post-primary school state examination results if they achieve a passing grade at Higher Level (HL) mathematics. The culmination of points that student achieve in six different subjects acts as a gatekeeper to tertiary level education. Mathematics is the only subject in which there are extra points awarded. The initiative was introduced to encourage more students to study the subject at an advanced level. Anecdotally there have been many mixed reviews about the success of the BPI. While the numbers taking HL mathematics have steadily increased, there have been concerns expressed that many students who are not mathematically capable of performing up to the standard required are now opting for the HL paper and that the difficulty of this examination and the marking schemes have been adjusted accordingly. This paper investigates the advantages and disadvantages associated with the BPI from the perspective of mathematics teachers (n=266). https://doi.org/10.37626/GA9783959871129.0.90 Raja, Shagufta; et al: Using GIS to Develop Spatial Reasoning and Analysis of Data. pp 485 – 490 The Geographic Information System (GIS) is a spatial analysis tool that allows users to capture, store, analyze, and visualize data related to real-world problems. GIS is used daily in multiple STEM fields to solve complex problems. Educators find GIS useful for students to be able to interpret data in a spatial context. Students develop quantitative and spatial analysis reasoning using GIS to understand and develop solutions for many current scientific concerns. This paper presents two cases highlighting middle grade students’ use of GIS. The cases illustrate how GIS promotes students’ development of spatial reasoning as they think about patterns and relationships made evident through data visualization. The cases demonstrate how students engage in finding relative and absolute mapped features, geographic patterns, and changes over time as they make decisions using geographic inquiry, spatial thinking and problem solving. https://doi.org/10.37626/GA9783959871129.0.91 Ramsay, John R.: Mentored Teams of Undergraduates in Real World Consulting. pp 491 – 496 One of the difficulties in mathematics education is providing a good answer to the “What can I do with mathematics?” question. Applied examples and projects within existing mathematics courses can help answer this but often aren’t close enough to real world applications and they can consume considerable course time. We have addressed this difficulty with a summer program that employs students to solve actual applied problems. The College of Wooster Applied Methods & Research Experience is a summer program that puts teams of students to work as consultants in the local community. Student teams are usually composed of three students with a mathematics or computer science faculty member acting as mentor. Clients of the program come from business, industry, government agencies, and service organizations. The program also includes a significant professional development component in order to increase the educational benefit to the participants. https://doi.org/10.37626/GA9783959871129.0.92 Rugelj, Marina: Counting with 10 Fingers as a Man, with 8 fingers as a Hen or with 2 Switches as a Computer. pp 497 – 502 In the high school curriculum of mathematics in Slovenia one of the goals is “Students can convert from decimal to binary number”. In most high schools, an algorithm for conversion is presented, which the students learn by heart like a cooking recipe, without proper understanding. A different method will be presented, where pupils play, explore and find certain conclusions on their own. This helps students to understand and learn the new concept much more efficiently, comparing to when they only listen to the instruction. Hence, the knowledge gained this way is hopefully more solid and lasting. https://doi.org/10.37626/GA9783959871129.0.93 Sack, Jacqueline; Quander, Judith: Secondary Math Teacher Candidates´ Perspectives on a Co-Taught Blended Content & Methods Geometry Course. pp 503 – 508 Two faculty, from the mathematics and education departments in an urban university, co-teach a blended methods and content geometry course for preservice secondary teachers who are also math majors. The course is entirely inquiry-based, a departure from traditional instructor-centered maths courses, and utilizes design-based trajectories developed by one of the authors over 12 years. We conducted two individual clinical interviews and one focus-group interview with 6 volunteer students, to ascertain their perspectives on how they best learn mathematics; to gauge how they perceived the inquiry-based experiences from this course; and, their reflections on inquiry-based instruction in mathematics as they move forward in their goals to become teachers. We used narrative inquiry as a research method to study the experiences of these students individually and collectively. https://doi.org/10.37626/GA9783959871129.0.94 Sáenz-Ludlow, Adalira; Jiménez, Alexandra Jiménez: Linkages between a Teacher´s Preparation and the Potential for Students´ Learning. pp 509 – 514 From the Peircean perspective of diagrammatic reasoning, the paper presents a teacher’s analysis of a task with a square array of dots. She conceptualizes different partitions of the array and transforms it into different tasks of sequences of squares to facilitate her inductive thinking and the emergence of different generalizations pertaining square numbers. https://doi.org/10.37626/GA9783959871129.0.95 Santhanam, S. R.: Welcome 2019 – A Workshop on Framing Non-Routine Problems in Mathematics for all Levels. pp 515 – 516 The main aspect of mathematics is problem solving. A non-routine problem is any complex problem that requires some degree of creativity to solve. There are no standardised methods to solve a non-routine problem, if there is one then it becomes a routine problem. What about framing a non-routine problem? It is all the more difficult. In this workshop the author attempts to make the audience to understand non-routine problems and their solutions and further to frame problems of this nature. https://doi.org/10.37626/GA9783959871129.0.96 Shamash, Josephine: From Equations to Structures: Linking Abstract Algebra and High-School Algebra for Secondary School Teachers. pp 517 – 522 The high-school curriculum in algebra deals mainly with the solution of different types of equations. Modern algebra has a completely different viewpoint and is concerned with algebraic structures and operations. The course Algebra: From Equations to Structures is part of an M.Sc. programme for Israeli secondary school mathematics teachers. It provides an introduction to algebraic structures and modern abstract algebra, and links abstract algebra to the high-school curriculum in algebra. It follows the historical attempts of mathematicians to solve polynomial equations of higher degrees, attempts which resulted in the development of group theory and field theory by Galois and Abel. This approach leads naturally to examining topics and fundamental theorems in both group theory and field theory. Along the historical “journey”, many other major results in algebra in the past 150 years are introduced, and current research in algebra is highlighted. We examine the relevance of the course to the teachers‘ work. https://doi.org/10.37626/GA9783959871129.0.97 Showers, Dennis: Real-world Maths: Preparing Teachers to use Real-life Contexts for Teaching Maths. pp 523 – 525 Common Core Mathematics in the US promotes eight Standards for Mathematical Practice to guide instructional reform. Standard 2 includes the practice of “decontextualizing” or abstracting a given situation and representing it symbolically to solve real-world problems. Preparing teachers to employ this practice in classrooms requires knowledge and skill to apply technology to bring the real world into the classroom and the ability to discuss personal experiences in a mathematical way. Professional development with New York teacher candidates and in-service teachers in Nicaragua, China, and the US indicates the need for further dissemination with a research program to evaluate its efficacy. https://doi.org/10.37626/GA9783959871129.0.98 Shriki, Atara; Lavy, Ilana: Shedding New Light on Common Algorithms: What can we Learn from Vedic Mathematics? pp 526 – 528 In Sanskrit, the ancient Hinduism language, ‘Vedas’ means ‘knowledge’. The Vedas are a corpus of more than 1,000,000 ancient philosophical writings divided into Sutras, some of which deal with mathematics. These mathematics Sutras, termed ‘Vedic Mathematics’, concern various fields of mathematics. The Vedic methods are coherent, logical and simple, and students enjoy practicing them. Besides ’spicing up‘ the regular mathematics lessons by integrating some of the Vedic algorithms, engaging students in proving them supports the development of their insights regarding the rationale underlying the formal rules and algorithms included in the curriculum. In this workshop, we present some of the basic Vedic arithmetic and algebraic algorithms, involve the participants in proving the them and discuss the advantages and disadvantages of integrating Vedic mathematics into classes at different age groups and study levels. https://doi.org/10.37626/GA9783959871129.0.99 Sibbald, Timothy: The Confluence of Numeracy with Interdisciplinary Mathematics. pp 529 – 534 Interdisciplinary mathematics, such as STEM, but not limited to it, has received considerable attention in recent years. Its role in mathematics is the provision of practical circumstances that support learning mathematical concepts. The validation of concepts through the adoption to interdisciplinary purposes has a broad base of examples. Furthermore, among the concepts bridging mathematics and another discipline is a group of concepts that transcend a variety of other disciplines and, within that scope, numeracy emerges. Since this is not a traditional definition of numeracy it is reconciled with other definitions of numeracy and the implications of that reconciliation with interdisciplinary instructional approaches is examined. https://doi.org/10.37626/GA9783959871129.0.100 Siemon, Dianne: Connecting Research and Practice – The Case of Multiplicative Thinking. pp 535 – 540 There is very little of any substance that can be achieved in school mathematics, and beyond without the capacity to recognise, represent and reason about relationships between quantities, that is, to think multiplicatively. However, research has consistently found that while most students in the middle years of schooling (i.e., Years 5 to 9) are able to solve simple multiplication and division problems involving small whole numbers, they rely on additive strategies to solve more complex problems involving larger numbers, fractions, decimals, and/or proportion. This paper describes how this situation can be addressed through the use of evidence-based formative assessment tools and teaching advice specifically designed to support the development of multiplicative thinking. https://doi.org/10.37626/GA9783959871129.0.101 Smith, Raymond; et al: Insights Gained from Implementing Teaching Toolkits: A Case of Activating Prior Knowledge. pp 541 – 546 In designing teaching toolkits for teachers the effectiveness of such a resource depends on mutual enactment and engagement by the designer, the teacher and the learners. It is a recursive process and illuminates the tensions between the intended outcomes envisaged by the designer and the realised outcomes in the classroom. In the qualitative research tradition, the exploratory investigation captured in this paper employed a descriptive phenomenological approach. With this orientation, and along the theoretical trajectory led by Todres (2005:107), this study sought to collect detailed descriptive accounts of personal experience. Data were gathered by collecting samples of learners’ work, teacher interviews and classroom observations. This paper draws attention to the practical disjuncture between assessing and activating prior knowledge. Insights acquired may contribute both to the design approach and to teaching practice. https://doi.org/10.37626/GA9783959871129.0.102 Spooner, Kerri: Authentic Mathematical Modelling Behaviours for Secondary School Students. pp 547 – 551 Mathematical modelling is part of many curricula around the world. Some of these curriculum statements are vague and general. There is a need for statements to be more specific with supporting examples for implementation of curriculums. There is also a need for further development of activities focused on authentic mathematical modelling behaviour. To address this problem, an ethnographic study in New Zealand was carried out to identify the behaviours of a real world mathematical modelling team. These behaviours were then explored to determine what they could look like for a sixteen-year-old student. This paper will present the modelling behaviours of the real world modelling team and the potential authentic mathematical modelling behaviours of a secondary school student. https://doi.org/10.37626/GA9783959871129.0.103 Stephens, Max: Developing Algorithmic Thinking in Mathematics in the Primary and Junior Secondary Years. pp 552 – 557 The fourth industrial revolution is already changing what we mean by mathematical reasoning in its different forms, such as algebraic, spatial and geometric, and statistical. Algorithmic thinking is one particular form of mathematical reasoning, emphasizing decomposition (breaking a complex problem down into component sub-problems and sub-tasks), pattern recognition, generalization and abstraction. With a growing global emphasis on using algorithmic thinking in coding and computing programs in schools, it is necessary to examine how algorithmic thinking should be included more explicitly in the teaching and learning of mathematics. https://doi.org/10.37626/GA9783959871129.0.104 Takahashi, Tadashi: Proving in Mathematics Education – On the Proof using ATP. pp 558 – 563 The aim of the mathematics education is the acquisition of “knowledge/skill of the mathematics” and “the mathematical thinking”. Proving is a chain of the logic in mathematics and is “mathematical thinking” itself. So, proving is the domain that is important from a point of view that can evaluate the acquisition of enough “mathematical thinking”. There is a variety of sense of values in the present situation of the proof using the ATP (Automated theorem proving). We should establish a clear vision as mathematics education in this situation. That is, in mathematics education, we should build sense of values for proof using the ATP newly. To that end, we fix contents of the mathematics, and it is necessary to prove them by using ATP. We would like to assume the aim the theorems of Euclid’s Elements. Because the contents are the basics of the mathematical thinking. The proving is an important aim in the mathematics education, it is necessary to clarify new value by using the ATP as mathematics education. https://doi.org/10.37626/GA9783959871129.0.105 Tannor, David: Effective Mathematics Instruction: Two-Year College Mathematics Instructors´ Knowledge and Self-Efficacy. pp 564 – 569 In this article are findings from a 2017 mixed methods study on two-year college mathematics instructors’ knowledge and self-efficacy on effective pedagogy. https://doi.org/10.37626/GA9783959871129.0.106 Temple, Barbara Ann; et al: Designing a Transdisciplinary Approach to Elementary Math Literacy Learning through Science & the Arts. pp 570 – 574 Engaging with subject matter in isolation stymies creativity, promotes rote learning, and limits development of divergent thinking skills. Conversely, a transdisciplinary approach to math develops critical and creative thinking skills, strengthens problem solving capacity, and promotes metacognition. In this pilot study, the design-based research process began with sharing initial intervention ideas for elementary Math lessons with participants at an international elementary Math conference. Utilizing participant feedback as part of the iterative process, three specific interventions for second-grade Math concepts were designed with intentional infusion of Science and the Arts. The ultimate goal for this research is the design of an effective elementary Math curriculum offering authentic, real-world learning through a transdisciplinary approach. https://doi.org/10.37626/GA9783959871129.0.107 Thomas, Jeffrey: Learning through Self-Assessment towards Understanding the New B.Ed. Curriculum in South Africa: Experiences from the new B.Ed. Programme at Sol Plaatje University. pp 575 – 580 The mismatch between instruction and learning could pose a serious barrier to effective teaching and learning. Effective teaching should be a dynamic alignment and realignment of teaching and learning styles to optimise achievement. When teaching and learning styles do not complement each other students may become anxious, frustrated and disengaged which may have negative effects on their performance. The focus of the study is to gather evidence on how students perceive their own learning in order to adapt the teaching approach which will accommodate the students’ preferred way of learning. The main findings in this study showed that students prefer to work independently and that elements of metacognition are present during their efforts to learn. This study therefore suggests that self-assessment activities should become an integral part of the teaching and learning process. Thus, students are afforded the opportunity to advance personal learning through the development of metacognition as self-monitoring and corrective actions. Key words: Self-assessment, metacognition, self-regulated learning https://doi.org/10.37626/GA9783959871129.0.108 Toro-Clarke, José A.: A Participative and Individualized Laboratory: A Strategy for Increasing Student Success in College-Level Mathe Courses. pp 581 – 586 This research was carried out within a qualitative research paradigm. The objective was to observe, analyze and enrich pedagogical practice through the use of pedagogical learning strategies. The learning strategy was a participative and individualized laboratory carried out during a research project in a non-Traditional Laboratory (LnT, abbreviated in Spanish form). The primary aim of this research was to observe if the LnT assists the students and in this way maximizes success and knowledge in the Introductory Math course (MATE3001) on the University of Puerto Rico campus. The LnT contributed to: (1) students improved their study habits; (2) the students had greater participation in the solution of math problems, their practice and discussion; (3) they accepted that the research professor supervise their work as it was carried out and understood that the presence was for their benefit. https://doi.org/10.37626/GA9783959871129.0.109 Vacaretu, Ariana-Stanca: Developing High-School Students´ Competences through Math Research Workshops – the M&L Project. pp 587 – 592 Mathematics is or it should be about problem solving and math thinking. However, what mathematics students learn in schools is more about procedures for solving different types of math exercises and problems. In many cases, students learn by heart algorithms and words (math concepts) and use them for solving different math tasks. School math is very far from what mathematicians do and, in many cases, doesn’t motivate students for learning math. This paper presents the way we organized the assessment of the students’ skills developed through math research workshops and some of the assessment results. Even though we didn’t assess all the competences the students develop through the math research workshop, the findings show that the students certainly develop their problem-solving skills. https://doi.org/10.37626/GA9783959871129.0.110 Walsh Jr., Thomas: Exploring Computer Science with MicroworldsEX to Learn Geometry and Logo Programming Code. pp 593 – 598 Future employment of computer-programming jobs will be best for applicants with experience in different languages and coding tools (Bureau of Labor Statistics, 2018). Empirical and meta-analysis research studies support of teaching Logo programming in developing student cognitive problem-solving skills has been documented. Using guided instruction with teacher-mediated scaffolding Exploring Computer Science with MicroworldsEX (Walsh, 2013-2017) has been found as an effective method in preparing students using the Logo code programming language to create geometric graphic, animation, and gaming projects. More research is needed to study teacher scaffolding and mediation skills to support learning Logo coding and transfer to other domains including other programming environments. https://doi.org/10.37626/GA9783959871129.0.111 Walsh Jr., Thomas: The Survey Toolkit Curriculum Methodology for Researching Information, Survey Questioning, and Analyzing Data with TinkerPlots. pp 599 – 604 In an era where social media traffics fake news websites that publishes misinformation it is imperative to provide students’ experiences in The Survey Toolkit and TinkerPlots curriculum teaching sound research principles and information gathering techniques. The field-tested program was found effective in guiding students choosing research questions, writing a research report using a paragraph cluster information strategy, developing unbiased survey questions using reliable sampling, analyzing survey data with TinkerPlots, and sharing results. The paper will present support for teaching the curriculum, development based on research direction, implementation considerations, and use of the curriculum with elementary to middle school students. https://doi.org/10.37626/GA9783959871129.0.112 Warren, Lynae; Wohlhuter, Kay: Merging Theory and Practice in Statistics in Communities of Mathematical Inquiry. pp 605 – 606 This workshop will engage participants in statistical problem solving with reallife data, using technology. Participants will work in a Community of Inquiry, (CoI, Garrison, 2016) with other participants to formulate questions that will be answered in their community. The participants will engage in problem solving using 2018 data about world populations, to determine how best to answer their questions and how their answers may become part of a larger exploration. The facilitators will share examples from their work with developmental mathematics students and mathematics teacher candidates regarding how they use the CoI model to merge theory and practice in the areas of: teaching & learning, educational technology, curriculum development, teachers’ preparation and development, and issues of equity. Participants will need access to a computer or tablet with web access and spreadsheet software. https://doi.org/10.37626/GA9783959871129.0.113 Watson, Steven: Bridging Theory and Practice: a Posthuman Perspective on Mathematics Teacher Education. pp 607 – 612 This paper considers posthumanism in the context of mathematics teacher professional learning. Posthumanism presents a challenge to Enlightenment rationality and the privileged position and potential capability of the human mind. Posthuman perspectives present knowledge and knowing as an embodied and experiential process. Learning, then, is not simply about the acquisition of knowledge and skills, it is an embodied experience in which the learner acts within an environment and comes to make sense of this experience through a reflective process. As well as presenting a theoretical account of mathematics professional learning and the implications of the posthuman to this field, I illustrate this with my own research in mathematics teachers’ preservice education and the professional development of practising teachers. https://doi.org/10.37626/GA9783959871129.0.114 Webb, Lyn; et al: Enabling Grade 3 Teachers to Transform an Intended Curriculum into an Enacted Curriculum in Mathematics Classrooms. pp 613 – 617 The introduction of a new mathematics curriculum is usually heralded by the production of a plethora of learner workbooks and teacher aids. In South Africa this study researches the effect of curriculum change on Grade 3 mathematics teachers in an endeavour to understand what elements enable the transition from an intended curriculum to an enacted curriculum. The theoretical framing for this paper is Fullan’s (2006) change theory that focuses on new materials, new practices and new beliefs. The research identifies that current South African curriculum documents and workbooks focus on mathematical content almost exclusively, and give minimal guidance concerning pedagogical content knowledge and teacher agency. A tri-level system is suggested to narrow the gap between policy and praxis. https://doi.org/10.37626/GA9783959871129.0.115 Webb, Paul: Towards Unifying Logic for the Pedagoy of Mathematics in South Africa. pp 618 – 622 South Africa’s performance in mathematics at school level is not impressive, even when measured against countries with fewer resources. As a country, it is one of the lowest performers in the world with a wide range of achievement between schools, with historically white schools achieving results much closer to the international average compared to historically-black African schools. The South African National Planning Commission has identified mathematics education as a key area of concern, particularly amongst poor children. In response, the Mapungubwe Institute for Strategic Reflection (MISTRA) initiated a research project to explore the possibility of a ‘unifying pedagogy’ that could help improve mathematics teaching across the range of schools in the country. This paper presents a summary of the ‘cumulative resonances’ of ‘sagacious’ members of the mathematics education community in South Africa and abroad. The data generated by these ‘sagacious’ sources’ in academia and governmental and non-governmental organisations were analysed thematically in order to explore the possibility of framing a unifying pedagogy of mathematics for South African conditions. https://doi.org/10.37626/GA9783959871129.0.116 Wickliff, Gregory A.; et al: Communicating Mathematics and Science: Teaching and Tutoring Writing in a Summer Program for High School Students. pp 623 – 628 Supplemental instruction and tutoring in writing, genre, and document design and illustration, can improve the quality of formal mathematics and science papers and presentations composed by rising high school junior and senior students in a four-week summer program. This paper discusses the program history and goals, its structure, the methods of instruction and tutoring, and the professional and student writing samples delivered through the University of North Carolina at Charlotte’s Summer Ventures in Science and Mathematics program. The program is a no-cost, state-funded program for academically talented students who aspire to careers in science, technology, engineering, and mathematics. Participants reside on the university campus for four weeks and conduct research around topics of their own interest individually or in collaboration with like-minded peers. Participants engage in research under the supervision of university faculty. https://doi.org/10.37626/GA9783959871129.0.117 Willson, Ian: Formative Assessment and Middle-School Classroom Tasks with the Wolfram Language. pp 629 – 630 Middle-school classroom tasks with the Wolfram Language can play a very significant role in the growth and development of mathematical competence. This can occur at the intersection of challenging Mathematical tasks, coding skills, exploration, discovery, collaboration and formative assessment. This workshop will reference all of these elements as they informed and underpinned classroom activities conducted at several different secondary schools in Melbourne Australia. https://doi.org/10.37626/GA9783959871129.0.118 Woodcock, Stephen: Not all Equals are Equal: Decoupling Thinking Processes and Results in Mathematical Assessments. pp 631 – 636 One of the greatest challenges in mathematics education is in fostering an understanding of what mathematicians would recognise as “mathematical thought.” We seek to encourage students to develop the transferable skills of abstraction, problem generalization and scalability as opposed to simply answering the specific question posed. This difference is perhaps best illustrated by the famous – but likely apocryphal – tale of Gauss’s school days and his approach to summing all positive integers up to and including 100, rather than just summing each sequentially. Especially with the rise of technology-enabled marking and results-focussed tutoring services, the onus is on the educator to develop new types of question which encourage and reward the development of mathematical processes and deprioritise results alone. Some initial work in this area is presented here. https://doi.org/10.37626/GA9783959871129.0.119 Zell, Simon: Weekly 10-minute-tasks to Promote Students Solving Equations in a Content-oriented Manner. pp 637 – 642 When solving equations in school, students often rely on routines and do not consider alternative ways of solving. Even basic equations which could be solved quite fast using common sense are regularly solved in a complicated way. To overcome this reliance on routine, a study with 17 classes of grade 10 students was carried out. Weekly 10-minute-tasks, which contained appropriate subtasks to enhance content-oriented solving, were solved by students over the course of one school year. These tasks were designed with the purpose of reducing the dominance of routines and the aim of using insight in the solving of equations. https://doi.org/10.37626/GA9783959871129.0.120 Zollman, Alan: Collective Participation: A Story of Business, Community, Schools, and University Partnering in STEM Education. pp 643 – 648 The quality of the public school teacher has the greatest in-school impact on nurturing cognitive abilities, developing content knowledge, and increasing motivation of students (Ferguson & Ladd 1996; Haycock 1998; Rivkin, Hanushek, & Kain 2005; Rice 2003; Sanders & Rivers, 1996; Zollman, Tahernezhadi, & Billman, 2012). We also know from educational research (Johnson & Sondergeld, 2015) that traditional professional development formats do not result in improvement of teacher practices nor substantial gain in student achievement. This paper reports on a shift in the traditional professional development project – one to enhance the quality of the public school teacher in STEM education projects through a synergy of business, community, and school districts partners with education and science university faculty. https://doi.org/10.37626/GA9783959871129.0.121 Zonnefeld, Ryan G.; Zonnefeld, Valorie L.: Innovative Pathways in STEM Teacher Preparation: Bridging the Gap between University Expectations & Secondary School Needs. pp 649 – 651 Innovative teacher preparation programs for STEM education are essential for meeting the goal of ensuring that secondary school students receive instruction from a certified teacher. This exploratory workshop examines the role that interdisciplinary STEM and mathematics programs can have to increase the number of certified teachers prepared to teach STEM classes from an interdisciplinary approach. https://doi.org/10.37626/GA9783959871129.0.122
Download or read book The Mathematics Education for the Future Project Proceedings of the 13th International Conference Mathematics Education in a Connected World written by Alan Rogerson and published by . This book was released on 2015 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Mathematics Education for the Future Project written by Alan Rogerson and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Building on the Past to Prepare for the Future written by Janina Morska and published by . This book was released on 2022 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proceedings Of The 14th International Congress On Mathematical Education In 2 Volumes written by Jianpan Wang and published by World Scientific. This book was released on 2024-06-07 with total page 1609 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Congress on Mathematical Education (ICME) is the largest international conference on mathematics education in the world. This quadrennial event is organized under the auspices of the International Commission on Mathematical Instruction (ICMI). This book, the Proceedings of ICME-14, presents the latest trends in mathematics education research and mathematics teaching practices at all levels. Each chapter covers an extensive range of topics in mathematics education.Volume I consists of 4 Plenary Lectures, 3 Plenary Panels, 5 Lectures of Awardees, 4 Survey Teams, 62 Topic Study Groups, 13 Discussion Groups, 20 Workshops, a Thematic Afternoon, and an Early Career Researcher Day. Plenary Lectures recognize substantial and continuing contributions to the growth of the field of Mathematics Education. Plenary Panels address three major challenges currently facing mathematics educators across the globe. The Survey Teams have a particular emphasis on identifying and characterizing important new knowledge, recent developments, new perspectives, and emergent issues. The Topic Study Groups provides a coverage of important topics in mathematics education.Volume II consists of 50 invited lectures which present the work and reflections of both established and emerging researchers from around the world. These lectures cover a wide spectrum of topics, themes and issues that reflect the latest challenges and development in the field of mathematics education.
Download or read book All Attainment Teaching in Secondary Mathematics written by Colin Jackson and published by Springer Nature. This book was released on 2022-02-09 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the promotion of all-attainment teaching in the mathematics classroom. The book contains the individual stories of six teachers working in three different schools: an inner London comprehensive with a largely working class intake, a comprehensive on the south coast and a rural comprehensive in Cambridgeshire. Each story describes and explains in brief the background of the teacher and how each came to teach all-attainment groups in mathematics. The research reported in this book is the only close examination and analysis of the practices and methodologies of successful all-attainment educators in the modern age. Three major themes are identified and examined: what sustains the teachers; how they introduce, develop and maintain all-attainment teaching; and how they make all-attainment work in the classroom. From an analysis of these findings, the book presents two interrelated models of the knowledge and understandings the research has generated. The first one is an overarching model of situation and horizon. Used as a means of visualizing and understanding the current situation for teachers, it can aid in encouraging change for the better. The second model offers teachers a way to think of all-attainment teaching as an enabler for all students, most especially for disadvantaged students. Both models have original and explanatory power and offer new ways of conceptualizing how mathematics teaching for social justice might be understood and implemented, offering fresh perspectives and unique insights. As such it will be of help to students at undergraduate, Masters and doctoral level and to education researchers more widely.
Download or read book Women in Mathematics written by Janet L. Beery and published by Springer. This book was released on 2017-12-02 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of refereed papers celebrates the contributions, achievements, and progress of female mathematicians, mostly in the 20th and 21st centuries. Emerging from the themed paper session “The Contributions of Women to Mathematics: 100 Years and Counting” at MAA's 2015 MathFest, this volume contains a diverse mix of current scholarship and exposition on women and mathematics, including biographies, histories, and cultural discussions. The multiplicity of authors also ensures a wide variety of perspectives. In inspiring and informative chapters, the authors featured in this volume reflect on the accomplishments of women in mathematics, showcasing the changes in mathematical culture that resulted as more women obtained tenure-track and tenured academic positions, received prestigious awards and honors, served in leadership roles in professional societies, and became more visibly active in the mathematical community. Readers will find discussions of mathematical excellence at Girton College, Cambridge, in the late 19th and early 20th centuries; of perseverance by Polish women in mathematics during and after World War II and by Black women in mathematics in the United States from the 1880s onward; and of the impact of outreach programs ranging from EDGE's promotion of graduate education to the Daughters of Hypatia dance performances. The volume also provides informative biographies of a variety of women from mathematics and statistics, many of them well-known and others less well-known, including Charlotte Angas Scott, Emmy Noether, Mina Rees, Gertrude Cox, Euphemia Lofton Haynes, Norma Hernandez, Deborah Tepper Haimo, and Teri Perl. These essays provide compelling reading for a wide audience, including mathematicians, historians of science, teachers of mathematics, and students at the high school, college, and graduate levels. Anyone interested in attracting more girls and women as students, faculty, and/or employees will also find this volume engaging and enlightening.
Download or read book The Origin and Significance of Zero written by and published by BRILL. This book was released on 2024-03-11 with total page 787 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zero has been axial in human development, but the origin and discovery of zero has never been satisfactorily addressed by a comprehensive, systematic and above all interdisciplinary research program. In this volume, over 40 international scholars explore zero under four broad themes: history; religion, philosophy & linguistics; arts; and mathematics & the sciences. Some propose that the invention/discovery of zero may have been facilitated by the prior evolution of a sophisticated concept of Nothingness or Emptiness (as it is understood in non-European traditions); and conversely, inhibited by the absence of, or aversion to, such a concept of Nothingness in the West. But not all scholars agree. Join the debate.
Download or read book Symposium Proceedings Innovative Teaching Practices written by Janina Morska and published by WTM-Verlag Münster. This book was released on 2023-06-14 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the papers presented at the International Symposium: Innovative Teaching Practices held on August 14-18 2023 in The Queen’s College, Oxford University. The Symposium was organized by The Mathematics Education for the Future Project - an international philanthropic project founded in 1986 and dedicated to innovation in mathematics, science, computer and statistics education.
Download or read book Handbook of Research on the Psychology of Mathematics Education written by and published by BRILL. This book was released on 2006-01-01 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a compilation of the research produced by the International Group for the Psychology of Mathematics Education (PME) since its creation, 30 years ago. It has been written to become an essential reference for Mathematics Education research in the coming years.
Download or read book Building on the Past to Prepare for the Future written by Janina Morska and published by WTM-Verlag Münster. This book was released on 2022-09-01 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract of Book This volume contains the papers presented at the International Conference Building on the Past to Prepare for the Future held from August 8-13, 2022, in King’s College, Cambridge, UK. It was the 16th conference organised by The Mathematics Education for the Future Project - an international educational and philanthropic project founded in 1986 and dedicated to innovation in mathematics, statistics, science and computer education world wide. Contents List of Papers and Workshop Summaries Fouze Abu Qouder & Miriam Amit The Ethnomathematics of the Bedouin - An Innovative Approach of Integrating Socio Cultural Elements into Mathematics Education https://doi.org/10.37626/GA9783959872188.0.001 First page: 1 Last page: 6 Abstract Our study attempted to address young Bedouin (desert tribes) students’ persistent difficulties with mathematics by integrating ethnomathmematics into a standard curriculum. First, we conducted extensive interviews w 35 Bedouin elders and women to identify: 1. The mathematical elements of their daily lives- particularly traditional units of length and weight, 2. The geometrical shapes in Bedouin women’s traditional dress embroidery. Then we combined these with the standard curriculum to make an integrated 90 hours 7-8th grade teaching units that were implemented in Bedouin schools and in the Kidumatica Math Club for Excellent Students. Comparisons between the experimental groups (186) and the control group (62) showed that studying by the integrated curriculum improved:1.The cognitive aspects of the students 2.The affective aspects. Keywords: Bedouin Cultures, ethnomathematics. ======================================================= Nadine Adams & Clinton Hayes Why Everyone should know Statistics! https://doi.org/10.37626/GA9783959872188.0.002 First page: 7 Last page: 11 Abstract “Decision is the central intellectual activity in our everyday lives” and statistics is central to these activities (Longford, 2021, p. xi). The ability to manipulate and interpret data is an important component in decision making. A misunderstanding or poor grasp of data distributions and statistical methods can lead to assumptions that are not accurate. When these inaccurate assumptions are presented as factual to decision makers also possessing little or no statistical knowledge, poor decisions can be made. This paper investigates how an interpretation of statistics played a role the decision to remove multiple-choice questions from invigilated examinations at a regional Australian university. The case is further argued that it is important for everyone to have a basic understanding of statistics. ======================================================= Anita N. Alexander The Perspectives of Effective Teaching and Learning of Current Undergraduate and Graduate Mathematics Students https://doi.org/10.37626/GA9783959872188.0.003 First page: 12 Last page: 17 Abstract Some mathematics professors engage their students in discourse and explorations to promote a deep understanding of critical concepts. Still, lecture remains the norm in mathematics courses according to current mathematics students’ survey responses (Mostly Lecture 52%; Lecture & Discussions 35%; N = 89). Students were asked the best way for them to learn mathematics, whether their career plans are teaching related (Teaching Related: Yes 22%; Not Sure 36%; No 42%), as well as what they enjoy and want to change about their mathematics courses. Students requested “more discussions, and more questions to solve in class,” and described lecture as “an unacceptable way to teach,” and that “it is the worst way to learn.” Students’ perspectives on effective teaching and learning are critical for their continued passion to pursue STEM related fields, rather than stating that “I do not love mathematics anymore.” ======================================================= Clement Ayarebilla Ali & Ernest Kofi Davis Applications of Basketry to Geometric Tessellations https://doi.org/10.37626/GA9783959872188.0.004 First page: 18 Last page: 23 Abstract We present applications of basketry to geometric tessellation in the primary school mathematics. Even though there are various forms of tessellations, we present three regular and Archimedean tessellations for conceptual analysis of the geometric concepts. With a case study design of 15 pupils through interviews and observations, the findings show that pupils can apply baskets to learn geometric tessellations. It was there recommended that baskets be used to extend learning as they play, game and fun. ======================================================= Nurten Alpaslan & Emre Alpaslan Mathematics for Everybody https://doi.org/10.37626/GA9783959872188.0.005 First page: 24 Last page: 25 ======================================================= Cynthia Oropesa Anhalt, Ricardo Cortez, Brynja Kohler & Will Tidwell Interrogation of Social Justice Contexts in Mathematical Modeling: The Use of Simulations of Practice in the Mathematical Preparation of Teachers https://doi.org/10.37626/GA9783959872188.0.006 First page: 26 Last page: 31 Abstract Research in prospective teachers’ development of mathematical modeling knowledge for teaching is gaining momentum. The Mathematics of Doing, Understanding, Learning, and Educating for Secondary Students [MODULE(S2)]* project developed a curriculum in modeling for teacher education that includes simulations of practice, in which prospective teachers reflect on and plan a discussion around student thinking, their models, and the contextualization of their results. We present an analysis of prospective teachers’ modeling work on the decreasing area of Indigenous reservation land in the U.S., and a simulation of practice which explores different methods for finding the area of land in connection to the injustice deeply rooted in the treatment of Indigenous people. This problem explores a critical social issue and calls for explicit attention to pedagogical knowledge in structuring discussions around the contextualization of the mathematical results. ======================================================= Takako Aoki & Shin Watanabe Find out Mathematics on a Football: Making a football with paper https://doi.org/10.37626/GA9783959872188.0.007 First page: 32 Last page: 34 Abstract We are aiming for a workshop method as a way to teach mathematics in future school education. It is important to cooperate with each other and understand mathematics. In this workshop, we aim to discover the mathematics hidden in the footballs we handle every day. As an aid to thinking, I would like to make football by paper first and learn mathematics while looking at concrete things. You need 20 equilateral triangles. A regular hexagon is made from this equilateral triangle, and a regular pentagon uses the method of making a hole. In particular, pay attention to the four-color problem in mathematics, make sure that the colours of adjacent regular hexagons are different, and use three colours (red, green, yellow). For example, in a football, how many equilateral triangles of each colour are used is one of the issues. I am looking forward to holding a workshop to see what kind of problems there are. Key words: football Introduction with paper, the truncated icosahedron, the color coding of the three colors, Euler's polyhedral formula ======================================================= Sarah Bansilal Analysing the Demands of an Assessment in a Geometry Pedagogic Content Knowledge Module https://doi.org/10.37626/GA9783959872188.0.008 First page: 35 Last page: 40 Abstract With the onset of the pandemic, universities were forced to move to online platforms for teaching and for assessments. In this paper, I reflect on the use of multiple-choice questions in a geometry PCK module for pre-service mathematics teachers. The study involves a secondary analysis of the data generated by the responses of 92 students to an assessment consisting of 25 items. The aim of the study was to distinguish between, and if possible, characterise possible levels of demands of the test items. The results suggested that there are four distinct groups of items relating to common content knowledge of early and late high school respectively, PCK related to deductive reasoning skills and critical thinking in an open book setting. ======================================================= Mike Bedwell Three or Four numbers: A Teacher’s Tale https://doi.org/10.37626/GA9783959872188.0.009 First page: 41 Last page: 43 ======================================================= Esther Billings & Lisa Kasmer Learning Experiences that Support Primary Teacher Candidates’ Understanding and Enactment of Core Mathematics Teaching Practices https://doi.org/10.37626/GA9783959872188.0.010 First page: 44 Last page: 49 Abstract In many teacher preparation programs, instruction focuses on learning about strategies and practices for teaching rather than directly enacting and honing these skills (Grossman, Hammerness, & McDonald, 2009): a corepractice approach in teacher education necessitates organizing coursework and fieldwork around practices of the teaching profession while simultaneously providing teacher candidates (TCs) ample opportunities to “practise” by enacting these teaching practices. In this paper, we share our corepractice instructional strategies, along with TC work used in our teacher preparation mathematics education courses (prior to student teaching) to engage TCs’ understanding and development of their ability to enact core practices, specifically the mathematics teaching practices outlined in National Council of Teachers of Mathematics (NCTM) (2014). ======================================================= Victoria Bonaccorso, Joseph DiNapoli & Eileen Murray Promoting Meaningful Conversations among Prospective Mathematics Teachers https://doi.org/10.37626/GA9783959872188.0.011 First page: 50 Last page: 55 Abstract Recent circumstances due to the COVID-19 pandemic and restrictions on entering public schools have created barriers for prospective teachers (PT) to gain valuable exposure to real classrooms. As a result, we have transitioned some teacher preparation from in person experiences to video case study analysis. Our research seeks to determine how this transition can foster development of critical teaching skills by infusing a model of powerful teaching with video of real classrooms. Our findings suggest that with online video case analysis PTs were able to advance their discursive conversations to strategic conversations by building on and transforming each other’s articulation of proposed teacher moves. This model for PT preparation has the potential to foster more meaningful discourse among participants by providing a space to build on and refine their understanding of mathematics teaching. ======================================================= Primo Brandi, Rita Ceppitelli & Anna Salvadori Elementary Dynamic Models: A Strategic Bridge Connecting School and University https://doi.org/10.37626/GA9783959872188.0.012 First page: 56 Last page: 62 Abstract We present an innovative educational path thought as a link between High School and University studies. The topic is the introduction to dynamic models (both discrete and continuous) which represent a key tool in a wide range of disciplines: sciences, techniques, economics, life sciences and more. ======================================================= Simone Brasili & Riccardo Piergallini Introducing Symmetry and Invariance with Magic Squares https://doi.org/10.37626/GA9783959872188.0.013 First page: 63 Last page: 68 Abstract Magic squares are key tools in mathematics teaching. They favor reasoning and creativity in problem-solving. As well, they bring students closer to the history of mathematics. Our work presents the magic squares in a learning progression introducing the symmetry linked with the idea of invariance “sameness in change” early at primary school in Montegranaro (Italy). Using the 3x3 magic square and manipulation games, a sample of 101 pupils (8 years) internalizes symmetries, reflections, and rotations associated with the square. The proposed activities provide tools and experience for geometric cognitive processes transferable from magic squares to main geometric shapes. The findings confirm that symmetry linked to the search for invariance is appropriate and accessible for primary school pupils through manipulation games. ======================================================= Angela Broaddus & Matthew Broaddus Assessing Mathematical Reasoning: Test Less – Explain More https://doi.org/10.37626/GA9783959872188.0.014 First page: 69 Last page: 74 Abstract Mathematics educational researchers have long offered recommendations for effective mathematics teaching, learning, and assessment, yet educators still struggle to implement fair and practical assessments that promote engagement and inspire students. This study describes assessments that (1) reduced anxiety, frustration, and rote imitation of procedures; (2) increased accessibility, motivation, and psychological resilience; and (3) improved engagement, strategic competence, self-assessment, and depth of understanding. Writing assignments prompted students to explain their reasoning about problems or their understanding of main ideas. Students revisited assignments in response to feedback and resubmitted them later in the course, which motivated students to deepen their understanding over time. Sample assignments, responses, and lessons learned will be shared. ======================================================= Irena Budínová & Jitka Panáčová Children with Reduced Cognitive Effectivity, their Problems and Optimal Way of Education https://doi.org/10.37626/GA9783959872188.0.015 First page: 75 Last page: 80 Abstract The contribution deals with children with reduced cognitive efficiency, their specific, and frequent difficulties in learning mathematics in the first years of education. Two examples of children with reduced cognitive efficiency will illustrate the specific ways in which reduced cognitive efficiency can manifest itself in mathematics, how children can be helped to overcome the mathematics curriculum. Problems in learning two basic arithmetic operations will be presented. The differentiation of teaching will be briefly introduced as an effective opportunity to work with these children. ======================================================= Gail Burrill Data Science and Mathematical Modeling: Connecting Mathematics to the World in which Students Live https://doi.org/10.37626/GA9783959872188.0.016 First page: 81 Last page: 89 Abstract The increasing need for statistical and quantitative thinking and reasoning makes it more important than ever that using mathematics and statistics to make sense of the world should be a central component of schooling. Data have transformed the way we look at the world. Shouldn’t this emphasis on data also impact what we teach both in mathematics and statistics? Research suggests that engaging with real data can motivate students, encourage them to take an interest in STEM fields, and allows the interests of diverse communities to be used as opportunities for learning. This paper summarizes the research looking at why connecting mathematics to the world is important for student learning, describes the role of data science and modeling in doing so, and provides examples of opportunities for students to interact with the world in which they live and work. “The development of mathematics is intimately interwoven with the progress of civilization,..” (Ebrahim, 2010) ======================================================= Gail Burrill & Thomas Dick Connecting Mathematics to the World: Engaging Students with Data Science https://doi.org/10.37626/GA9783959872188.0.017 First page: 90 Last page: 94 Abstract Mathematics and statistics can be used to describe, explore, and understand this complicated world in which we live. The workshop focus is on several potentially messy, real-world problems from predicting herd immunity, to exploring the quality of life across countries to modeling the change in CO2 levels. Each situation begins with a question and a set of data. The activities are open ended with multiple ways students might develop mathematical and statistical models, use technology to analyze the data, and make sense of terms such as herd immunity or vaccine efficacy or to investigate situations such as optimizing resources during a flood. ======================================================= Elizabeth A. Burroughs & Mary Alice Carlson Fostering Empathy in Mathematics through Mathematical Modeling https://doi.org/10.37626/GA9783959872188.0.018 First page: 95 Last page: 100 Abstract Modeling, a cyclic process by which mathematicians develop and use mathematical tools to represent, understand, and solve problems, provides learning opportunities for school students. Mathematical modeling situates mathematical problem solving squarely in the middle of everyday experiences. Modeling engenders the habits and dispositions of problem solving and empowers students to identify critical issues important to them, use their mathematical tools to address these problems, and view mathematics as a force for societal good. ======================================================= Bernardo Camou The Adventure of Learning Mathematics and Lakatos’s Legacy https://doi.org/10.37626/GA9783959872188.0.019 First page: 101 Last page: 104 Abstract Mathematics is normally described as abstract, exact, general and perfect. However, mathematics is a human creation and thus we can ask: How can humans with flaws and defects are able to create something perfect and infallible? Mathematics have its foundations in concrete problems, trials and errors approximations and representations. Learning mathematics is a fascinating trip, back and forth between concrete and abstract, between approximations and accuracy, between particular and general. Our poor representations are the road to conceptualize mathematical objects that then, seem to become perfect. In this workshop we will handle polyhedral and work with Euler’s Formula, with angular defects and its relation with surface´s curvature. In Lakato’s book Proofs and Refutations the author might have committed a mistake, though his book gives us a brilliant insight about the logic of mathematical discovery. ======================================================= Carrie Chiappetta, Christopher Walsh, Annie Smith & Javier Perez K-12 Schools after the Global Pandemic: How a Regional School District in the United States Accelerated Learning for Students, Teachers & Administrators https://doi.org/10.37626/GA9783959872188.0.020 First page: 105 Last page: 110 Abstract After the global pandemic, Regional School District 15 will start the 2021-2022 school year by accelerating learning for students, teachers, and administrators. For teachers, the focus will be on “purposeful planning,” “differentiation,” and “formative assessment” to ensure that all students learn grade level content. For administrators, the focus would be on supporting teachers in these three areas of focus. The Assistant Superintendent, the Mathematics/Science Department Chair, and the elementary and middle school mathematics instructional coaches will share the plan that they have implemented to work with K-12 teachers and administrators to ensure that students were able to learn grade level content even after the interrupted education that occurred during the global pandemic. ======================================================= Kathleen Cotter Clayton Fractions of the Future https://doi.org/10.37626/GA9783959872188.0.021 First page: 111 Last page: 116 Abstract Explore the simplicity and beauty of fractions of the future with a linear model, not with circle sets. When fractions are approached with this linear perspective, fractions can be easily taught, explored, and applied in daily life. Learn how to ask the right questions to guide your pupils to a solid understanding. Children as young as five can see that 1/3 is less than 1/2 and more than 1/4. They can also see why 9/8 is more than 1, why 1/4 plus 1/8 is 3/8, and why 1/2 × 1/2 is 1/4. Fractions are a delight when they are taught the right way. Allow the children to explore the whole picture and relationships within the whole using the linear fraction model. Learn about activities and games to build confidence and develop a deep understanding of fractions. Uncover the joy of fractions! ======================================================= Joan A. Cotter Teaching Primary Mathematics without Counting and Place Value with Transparent Number Naming https://doi.org/10.37626/GA9783959872188.0.022 First page: 117 Last page: 122 Abstract Counting - memorizing the sequence and coordinating pointing with recitation - is problematic for many children. Children with poor counting skills often struggle to learn their beginning math with various approaches. Yet, counting is unnecessary. Babies are born with the ability to subitize; that is, to detect quantities at a glance, up to three. By age 3, they can subitize up to five; by age 4 they can subitize up to 10 by grouping in fives, similar to their fingers. After children know the names for quantities 1 to 10, their next step should be place-value starting with temporary transparent number naming. For example, 11 is “ten-1”, 12 is “ten-2”, and 24 is “2-ten-4.” The counting words in Far Asian languages reflect this transparency, enhancing their pupils’ mathematics achievement. Place-value knowledge combined with subitizing gives pupils a way to master number combinations. ======================================================= Celisa Counterman M.A.T.H. = Making Algebraic Thinking Holistic https://doi.org/10.37626/GA9783959872188.0.023 First page: 123 Last page: 127 Abstract Students in mathematics often need more than just definitions and examples. The first step is leaving their anxiety at the door. Hands-on work engages students by utilizing group learning, discovery, and active learning both with and without technology lessening the fears of math. Faculty members will be given sample activities, rubrics, and sample student work. Special focus on creating Spirolaterals and quilting teach geometric movement and pattern recognition. Puzzles are created with mathematical problems in linear equations, linear inequalities, and compound inequalities bringing the focus on skills and historical facts. Faculty members will work in teams to recreate the materials themselves to see where issues in understanding come from. There will be time for both questions and answers. ======================================================= Scott A. Courtney The Impact of Remote Instruction on Mathematics Teachers’ Practices https://doi.org/10.37626/GA9783959872188.0.024 First page: 128 Last page: 133 Abstract The coronavirus pandemic has impacted all aspects of society. As the virus spread across the globe, countries and local communities closed workplaces, moved schools to remote instruction, limited in-person contact, cancelled public gatherings, and restricted travel. At one stage, over 91.3% of students worldwide, from pre-primary through tertiary education, were impacted by school closures. In the United States, many institutions continue to provide remote and hybrid learning options throughout the 2021-2022 academic year. Attempts to mitigate Covid-19 through mass remote instruction has provided unique opportunities for researchers to examine the resources teachers utilize to drive and supplement their practices. In this report, I describe remote instruction’s ongoing impact on grades 6-12 mathematics teachers and their students in rural area and small-town schools in the Midwestern United States. ======================================================= Mili Das Building on the Past to Prepare for the Future - Impact of Teaching Skills and Professionalism to Reduce Mathematics Phobia https://doi.org/10.37626/GA9783959872188.0.025 First page: 134 Last page: 138 Abstract In India mathematics is a compulsory subject for the primary, upper primary and secondary classes. In secondary school curriculum among the compulsory subjects MATHEMATICS is the most vital subject and at the same time it is the most difficult one as per the learners’ opinion as well as the parents. So, the subject is neglected by many students and as a consequence Mathematics Phobia is often developed in the students’ mind. There are many more factors which are connected to this growing distaste in learning mathematics like in appropriate curriculum organization, methodology of teaching, teachers’ knowledge, assessment techniques [Das,M.2010] and management of classroom environment. The said problem is not a new one but in present teachers’ training course special attention is given on it. In this paper author will discuss that how the teaching skills and teachers’ professionalism can create a positive environment to motivate students. Keywords: Mathematics Teacher, Learners, Curriculum, Professionalism ======================================================= Thomas P. Dick Combining Dynamic Computer Algebra and Geometry to Illustrate “the most marvelous theorem in mathematics” https://doi.org/10.37626/GA9783959872188.0.026 First page: 139 Last page: 144 Abstract Dynamic geometry software (DGS) allows for constructions and measurements that instantly update when a virtual geometric figure is manipulated. Likewise, dynamic computer algebra systems (CAS) enable symbolic calculations that instantly update when an expression or equation is altered. Linking geometric objects to symbolic parameters combines these two powerful tools together. We will illustrate a unique feature of “locked” measurement in a special DGS to create a Steiner ellipse. We then illustrate the use of a dynamic CAS to create dynamic first and second derivative zeroes of a cubic function whose zeroes can be graphically manipulated. Finally, we will link a dynamic geometric construction based on these zeroes to illustrate the Siebeck-Marden Theorem, an astounding result that has been justifiably called “the most marvelous theorem in mathematics.” ======================================================= Hamide Dogan, Angel Garcia Contreras & Edith Shear Geometry, Imagery, and Cognition in Linear Algebra https://doi.org/10.37626/GA9783959872188.0.027 First page: 145 Last page: 150 Abstract This paper discusses features of five college-level linear algebra students’ geometric reasoning, revealed on their interview responses to a set of predetermined questions from topics relevant to linear independence ideas. Our qualitative analysis identified three main themes (Topics). Each theme, furthermore, revealed similarities and differences, providing insight into technology’s potential effect. ======================================================= Ann Dowker, Olivia Cheriton & Rachel Horton Age Differences in Pupils’ Attitudes to Mathematics https://doi.org/10.37626/GA9783959872188.0.028 First page: 151 Last page: 156 This study investigated children’s and adolescents’ attitudes to mathematics, with a particular focus on whether and how these are affected by age and gender. 216 pupils from Years 2, 6, 9 and 12 participated in the study. They were given (1) the Mathematics Attitude and Anxiety’ questionnaire (Thomas & Dowker, 2000), which assesses levels of maths anxiety; unhappiness at failure in maths; liking for maths, and self-rating in maths; and (2) the British Abilities ScalesNumber Skills Test to establish actual mathematics performance. Age had a significant effect on both liking for maths and selfrating in maths: older children were lower than younger children in both. Gender had a significant effect on self-rating: boys rated themselves higher than girls, though there was no significant gender difference in mathematical performance. Self-rating, but not anxiety, predicted mathematics performance. ======================================================= Alden J. Edson & Elizabeth Difanis Phillips The Potential of Digital Collaborative Environments for Problem-Based Mathematics Curriculum https://doi.org/10.37626/GA9783959872188.0.029 First page: 157 Last page: 162 Abstract In this paper, we present an overview of the design research used to develop a digital collaborative environment with an embedded problembased curriculum. We then discuss the student and teacher features of the environment that promote inquiry-based learning and teaching. ======================================================= Belinda P. Edwards Learning to Teach Mathematics using Virtual Reality Simulations https://doi.org/10.37626/GA9783959872188.0.030 First page: 163 Last page: 168 Abstract Researchers (Lampert, et al., 2013; Zeichner, 2010; Grossman, et al., 2009a) recommend the use of rehearsals in teacher education classrooms to help preservice teachers (PST) bridge theory to practice. Rehearsals enable PSTs to practice teacher moves, such as asking purposeful questioning and engaging students in mathematical discourse during an episode of teaching a lesson (NCTM, 2014). During a rehearsal, the PST’s teacher education instructor provides coaching that helps the PST make flexible adjustments to their instruction. Using a phenomenological approach, this research investigates the use of Virtual Reality (VR) simulations to support PSTs learning to teach mathematics through rehearsals. The presentation will include samples of PSTs’ mathematics teaching episodes with attention to successes, challenges, and lessons learned from the use of VR simulations in teacher education classrooms. ======================================================= Allison Elowson, Kristen Fye, Gregory Wickliff, Christopher Gordon, Alisa Wickliff, Paul Hunter & David Pugalee Student Research in a Mathematics Enrichment Program https://doi.org/10.37626/GA9783959872188.0.031 First page: 169 Last page: 174 Abstract Increasing emphasis is placed on the development of research skills for students in STEM content areas. As part of a four-week summer enrichment program, 24 high school students participated in a mathematics course highlighting the historical development of mathematics through the lens of history and culture. Each student designed and conducted their own research study under the mentorship of instructors with expertise in mathematics, writing and technical communication, and student research. This paper presents a case study of one project selected on the basis of strong performance in meeting course goals. Data demonstrates the mathematical understanding of the student researcher, their scientific literacy and research skills, and their mathematical communication. The student prepared both a paper and a poster to report their research study. ======================================================= Antonella Fatai Improving Relational and Disciplinary Competences by Rondine Method https://doi.org/10.37626/GA9783959872188.0.032 First page: 175 Last page: 180 Abstract The present work describes an educational experience, being implemented since 2015, based on the Rondine Method application in mathematics teaching. This experience has involved 135 students from State Schools throughout Italy. The general method was developed by an Italian research team aiming at resolving conflicts in situations of contrast. The goal of the work is highlighting how the care of relationships may be a means for overcoming difficulties in mathematics. Below we describe activities referring to the general principles of active education and of socio-constructivism, which are oriented to train students both in learning by action and participation, and in bringing their own contribution to the whole class work. ======================================================= Courtney Fox Integrating Mathematics and Science: A Plan for a High School Integrated Pre-Calculus and Physics Course https://doi.org/10.37626/GA9783959872188.0.033 First page: 181 Last page: 185 Abstract This paper explores the integration of mathematics and science as a means to improve learning for high school students. Scholars have acknowledged the benefits of integration for over 50 years, but in the United States we have failed in large measure to adopt an integrative curriculum. This work provides a corrective to this problem by creating a practical curriculum for an integrated Pre-Calculus and Physics course with suggestions for implementation in any school. ======================================================= Kathy R. Fox Building an Understanding of Family Literacy: Changing Perspectives Regarding Authentic Learning Opportunities in the Home https://doi.org/10.37626/GA9783959872188.0.034 First page: 186 Last page: 191 Abstract Home to school engagement has often been a one-way path, with teachers seen as facilitators only. When schools were forced to rapidly switch to virtual instruction, teachers were suddenly entering kitchens, living rooms and other spaces to deliver virtual instruction. Findings from this qualitative study of eleven practicing teachers showed new teaching opportunities through virtual home visits. Doors were literally and figuratively opened as teachers became beneficiaries of cultural and academic practices in the home. Math instruction took on a real-world quality, as teachers were privy to home environments for authentic teaching materials. As schools open and teacher, parent, and caregiver relationships return to a more distant space, these participants described small but significant changes in the way they continued to engage parents and caregivers after the experiences of the virtual home visits. ======================================================= Grant A. Fraser Mathematics for Living: A Course that Focuses on Solving Problems in Today’s World https://doi.org/10.37626/GA9783959872188.0.035 First page: 192 Last page: 195 Abstract The author has developed and taught a course for University students who are not specializing in mathematics, science, or engineering. In contrast to traditional courses of this type, this course focuses on topics from the real world that students will encounter in later life. The aim of the course is to provide students with mathematical tools that they can use to create meaningful, practical solutions to problems that arise in these topics. Students work individually on projects and present their solutions in class. Other students then critique these solutions. With practice, students develop the skills necessary to analyze more complicated kinds of problems. A final project enables students to use their newly acquired techniques to deal with more realistic problems. The author discusses the content of the course and the impact it has had on students. ======================================================= Toshiakira Fujii Roles of Quasi-variables in the Process of Discovering Mathematical Propositions https://doi.org/10.37626/GA9783959872188.0.036 First page: 196 Last page: 201 Abstract The purpose of this paper is to clarify roles of quasi-variables by focusing on the process of discovering mathematical propositions. For this purpose, the author analyzed the assignment reports of third-year undergraduate students. As a result, the author found that "looking back" is important in the generalization-oriented inquiry process, but it is not enough. It is important to "re-examine" the found matter and its form of expression from the perspective of a new concept. In the process of "looking back" and "re-examine", it was confirmed from the description of the metacognitive part of the students that the use of quasi-variables clarified the object of consideration and made it easier to clarify which numbers contributed to the generalization and expansion in what sense. ======================================================= Ben Galluzzo, Katie Kavanagh, Karen Bliss, Michelle Montgomery & Christopher Musco Math Modelling: Common Pitfalls and Paths for Student Success https://doi.org/10.37626/GA9783959872188.0.037 First page: 202 Last page: 207 Abstract Mathematical modelling refers to the process of creating a mathematical representation of a real-world scenario to make a prediction or provide insight. There is a distinction between applying a formula and the actual creation of a mathematical relationship. Approaching open-ended problems can be challenging for students. In this two part workshop, we first share examples of how students can get off-track while creating models, in particular making choices or assumptions that undermine the solution quality. In the second part, we demonstrate how to facilitate authentic math modelling so that students can be creative and innovative in the modelling process while having ownership over their solution. Participants will assess real student modelling solutions from Mathworks Math Modeling Challenge (M3 Challenge), a program of Society for Industrial and Applied Mathematics (SIAM), and discuss ways that they would advise teams towards improvement. ======================================================= Parker Glynn-Adey &Ami Mamolo Modelling Beauty: Hands-on Experiences in Group Theory https://doi.org/10.37626/GA9783959872188.0.038 First page: 208 Last page: 213 Abstract In the 19th century, geometric models were valued as tools for exploring complex mathematics. Quartic surfaces and hyperboloids elaborately modelled with plaster gave access to powerful ideas and brought alive wonderful new mathematics. In this workshop, we explore a diverse set of geometric models that capture mathematical beauty and we showcase how they can be used to bring alive wonderful new-for-students mathematics. We discuss the value of these experiences for fostering mathematical ways of being that can help disrupt preconceived notions about a homely, rote and rigid nature of mathematics, and capture some of the visual richness of older mathematical models. ======================================================= Gerald A. Goldin, Lisa B. Warner, Roberta Y. Schorr & Daniel Colaneri Exploring Prospective Mathematics Teachers’ Motivating Desires during Group Problem Solving Activity https://doi.org/10.37626/GA9783959872188.0.039 First page: 214 Last page: 219 Abstract Earlier research has characterized recurrent patterns of cognition, affect, and behavior during in-the-moment mathematical activity. Each pattern, termed an “engagement structure,” is named by a specific motivating desire that evokes it: e.g., Get The Job Done, I’m Really Into This, Value My Culture, etc. This study explores prospective teachers’ motivating desires as they engage in small-group problem solving sessions. Participants were enrolled in courses required for teaching certification at two eastern U.S. state universities. Based on survey, individual interview, and focus group data, we identify the most frequently occurring desires, their perceived importance and accompanying emotional feelings. We present and discuss some findings briefly, including the motivating desire to Carry My Weight with a team of peers. ======================================================= John Gordon & Kehinde Emmanuel Adenegan Are Abstract Mathematical Thinkers Born or Can They Be Trained? https://doi.org/10.37626/GA9783959872188.0.040 First page: 220 Last page: 224 Abstract Abstract mathematical thinkers in the fields of pure Mathematics and theoretical computer science have contributed significantly to the body of knowledge that has fundamentally altered the course of human civilization and technological advances. This paper explores whether these thinkers are naturally gifted or if there are pedagogical strategies that can be implemented that will bring about the same outcomes. Keywords: Abstract, critical, thinkers, Mathematics ======================================================= John Gordon Reuniting Exponents and Logarithms: Teaching Exponents, Inverse functions, and Logarithms, as one Cohesive Pedagogical Unit https://doi.org/10.37626/GA9783959872188.0.041 First page: 225 Last page: 230 Abstract Exponents, inverse functions, and logarithms are fundamentally important concepts in almost every branch of technical science. However, they are not taught together as a cohesive, comprehensive, pedagogical unit in many instances. As a result, students lose deep insight into their meaning and applicability. Additionally, particularly in the concept of the inverse function, the richness, and beauty inherent in the concept are reduced to a purely mechanical process. This paper seeks to remedy this situation by outlining a pedagogical strategy that links exponents, inverses, and logarithms together in such a manner as to preserve their natural dependence, coherency, and logic. Keywords: Exponents, inverse, functions, logarithms. ======================================================= Debra Hydorn Infographics to Develop Graphical Literacy https://doi.org/10.37626/GA9783959872188.0.042 First page: 231 Last page: 236 Abstract Tools for easily creating infographics are widely available, both online and through statistics, mathematics, and other programs. Determining the appropriate graphs to produce for different kinds of data is an important skill for students at all levels to learn, as is determining the best graph for a specific audience. With the increased availability of data comes the increased expectation that researchers in all disciplines can effectively communicate their findings to a wide range of audiences. Experts in graphical design have defined aspects of “graphical excellence,” but the effectiveness of graphically portrayed information depends a great deal on the needs and abilities of the intended audience. To create effective graphs, students not only need to be familiar with tools for creating graphs, they also need to be familiar with the communication, cognitive, and aesthetic principles associated with infographic design. ======================================================= Andrew Izsák Foregrounding Multiplicative Structure in Essential Calculus Topics https://doi.org/10.37626/GA9783959872188.0.043 First page: 237 Last page: 242 Abstract Approaches to calculus have emphasized limits, derivatives, and integrals, among other topics. Yet, across different approaches, the subject continues to pose significant challenges. The present study reports a new approach to calculus that takes multiplicative structure as an equally essential topic that is often overlooked or taken for granted. In an experimental course, 18 college students learned to reason about multiplication understood as coordinated measurement with two different units and proportional relationships understood from the variable-parts perspective. They then worked with piecewise linear functions and step functions to derive key calculus results. A first strand involved division, proportional relationships, slopes of lines, function composition, and the chain rule. A second strand involved multiplication, areas, inversely proportional relationships, and integration by substitution. ======================================================= Brian L. Johnson & Ioannis Gkigkitzis Interesting Facts about Terminating Decimals https://doi.org/10.37626/GA9783959872188.0.044 First page: 243 Last page: 248 Abstract The set of rationals is dense in R. In fact, this is even true for the smaller family of terminating decimals. Unlike density ratios in the physical world, this is an absolute property implying that infinitely many such decimals exist in even the "smallest" intervals we can imagine. However, it is possible to construct this infinite density in an increasing sequence of finite "densities"--starting with the discrete set of integers. While the terminating decimals do not seem to receive as much formal discussion as Z, Q and R, they are an essential part of the mathematics curriculum, from elementary school through college. Keywords: integers, rational numbers, algebra, density. ======================================================= Iris DeLoach Johnson Exploring a Collection of Approachable, Stimulating and Thought-Provoking Problems: Face-to-Face or Virtual? Related or not? https://doi.org/10.37626/GA9783959872188.0.045 First page: 249 Last page: 253 Abstract Students thrive when engaged in solving problems that they find to be approachable, stimulating, and thought-provoking. This workshop includes many such problems with various real-world and contrived contexts. Participants will work in groups to find the solutions as well as identify similarities and contrasts among the problems. We will explore whether there are related mathematical concepts (e.g., algebra, discrete mathematics, geometry) or mathematical processes (reasoning, connecting, communicating, representing, problem-solving, selecting tools and strategies). Many of these problems are taken from resources published broadly for students from ages 11-19+. We will compare our findings and experiences with those of school students and discuss use of technology in both face-to-face and online settings: from the past to the future! Keywords: problem-solving, reasoning, communication, collaboration, algebra, representations, Chalk Talk, Thinker-Doer problems ======================================================= Gibbs Y. Kanyongo, Nandini Bhowmick & Erika Williams Structural Equation Modeling: Focus on Confirmatory Factor Analysis https://doi.org/10.37626/GA9783959872188.0.046 First page: 254 Last page: 255 Abstract This workshop will expose participants to the statistical technique of Structural Equation Modeling (SEM), with a focus on confirmatory factor analysis (CFA), using the statistical software AMOS. Structural equation modeling is a multivariate statistical analysis technique that is used to analyze structural relationships. Confirmatory Factor Analysis examines whether collected data fit a hypothesized model of what the data are meant to measure. It is the measurement part of SEM, which shows relationships between latent variables and the observed variables. ======================================================= Anna Khalemsky & Yelena Stukalin Combining Various Data Mining Techniques in Binary Classification Teaching https://doi.org/10.37626/GA9783959872188.0.047 First page: 256 Last page: 260 Abstract Binary classification is one of the most common data analytics tasks. It appears in a wide range of applications including finance, sociology, psychology, education, medicine, and public health. In statistical and analytics courses, binary classification is usually handled by logistic regression. Other alternatives, such as decision trees, neural networks, and Naïve Bayes are not commonly taught in traditional undergraduate programs. We suggest making these methodologies accessible as alternatives or complementary approaches to binary classification. We treat the teaching of the subject as a dynamic process that involves the understanding of the analytical task, understanding terms and concepts, visualizing, analyzing, interpreting the results, and decision making. ======================================================= Richard Kitchen Leveraging Pólya’s Heuristic to Support Mathematical Reasoning and Language Development https://doi.org/10.37626/GA9783959872188.0.048 First page: 261 Last page: 266 Abstract An iteration of an instructional framework designed to provide emergent bilinguals (EBs) with opportunities to simultaneously engage in mathematical reasoning and learn the language of mathematics is illustrated in this paper. The “Discursive Mathematics Framework” (DMF) builds on Pólya’s iconic problem-solving heuristic by integrating research-based “language practices” and essential teaching practices. Videotapes and student work from problem solving lessons were examined using grounded theory methodology to illustrate the development of the DMF. Theoretically, this study contributes to the literature by providing explicit examples of how practices that promote mathematical reasoning and the learning of the language of mathematics can be taught concurrently during problem solving lessons. ======================================================= Sergiy Klymchuk An Innovative Way of Teaching and Assessing Critical Thinking in Mathematics https://doi.org/10.37626/GA9783959872188.0.049 First page: 267 Last page: 272 Abstract This paper deals with the use of deliberately misleading mathematics questions in teaching and assessment as an innovative pedagogical strategy. The intention of using such questions is to enhance students’ critical thinking. Critical thinking is understood here as “examining, questioning, evaluating, and challenging taken-for-granted assumptions about issues and practices” as defined by the New Zealand Ministry of Education. The study is based on a survey of 82 secondary school mathematics teachers who attended introductory workshops on the suggested pedagogical strategy at their regional conferences. Although the vast majority of the participants (96%) agreed to use such strategy in teaching, only 63% percent of the participants were willing to use it in assessement. Teachers’ attitudes are analysed in the paper. Key words: critical thinking, assessement, school mathematics teachers. ======================================================= Allison M. Kroesch & Albert Otto Magic Throughout the Years https://doi.org/10.37626/GA9783959872188.0.050 First page: 273 Last page: 276 Abstract Too often teachers use the word “trick” in their mathematics lessons. There are no tricks in mathematics, but there are explanations for what appears to be a trick. Throughout this paper, we will address this history of magic, including the history of playing cards. ======================================================= Aradhana Kumari Do not Teach the Symbols in Mathematics, Teach the Meaning of the Symbols https://doi.org/10.37626/GA9783959872188.0.051 First page: 277 Last page: 282 Abstract Unnecessary use of symbols in introducing ideas in mathematics makes it difficult to learn. From a student's perspective, these symbols are the hurdle for them to understand the concepts/ideas in mathematics. One example is when we ask students the following: What is the meaning of the square root of a number, often their reply is the symbol √. This shows that they did not understand the actual meaning of the square root of a number, which is the number raised to power one-half. I will present many examples and show how we can avoid using unnecessary symbols and teach the ideas and concepts in mathematics. ======================================================= Sebastian Kuntze, Marita Friesen, Jens Krummenauer, Karen Skilling, Ceneida Fernandez, Pere Ivars, Salvador Llinares, Libuše Samkova & Lulu Healy Support for Mathematics Teachers through Representations of Practice - Vignette-based Approaches in the Project coReflect@maths https://doi.org/10.37626/GA9783959872188.0.052 First page: 283 Last page: 288 Abstract Teachers' analysis of vignettes can be a key for connecting specific classroom situations with mathematics education theories. As vignettes are representations of practice with relevance for professional requirements of the mathematics classroom, vignettes also represent or portray meaningful theoretical elements. The use of vignettes in pre-service and in-service teacher professional development needs, however, conceptual and evidencebased exploration. Building on prior work with video, text, and cartoon vignettes, the project coReflect@maths aims at exploring the potentials of vignette-based work both for supporting professional learning and for research into aspects of mathematics teachers' expertise. Key aspects of the project work will be presented. ======================================================= Barbara H. Leitherer, Pankaj R. Dwarka, Entela K. Xhane & Jignasa R. Rami Undergraduate Research in a 2-Year College: Climate Change, Global Learning, Process and Observations https://doi.org/10.37626/GA9783959872188.0.053 First page: 289 Last page: 294 Abstract In order to thrive and be successful in an increasingly interconnected world, 21st century students require multiple opportunities to engage with global learning (Landorf et al., 2019). Mathematics faculty guided 2-year college honors students in the US through an independent study analyzing real-world global climate change data supplied by the World Wildlife Fund (WWF). This proposal will elaborate in depth about the undergraduate research process, lessons learned, and observations made. Presenters will reflect on strategies used to support both collaborative and independent learning; how students increased their awareness of climate change as a global problem; how this contributed to students’ ownership, success and enhancement in undergraduate research leading to preparedness for further education and a successful career in science, technology, engineering, and mathematics. ======================================================= Hadas Levi Gamlieli, Alon Pinto & Boris Koichu Secondary-Tertiary Transition and Effective Ways of Coping with it: A Perspective of Lecturers https://doi.org/10.37626/GA9783959872188.0.054 First page: 295 Last page: 300 Abstract The secondary-tertiary transition (STT) in mathematics education is a longstanding concern. This study explores university mathematics lecturers’ perspectives on the challenges underlying STT and on the effectiveness of university-level coping measures currently employed. The analysis of 311 responses to an international survey suggests that there is considerable variability regarding the prevalent perspectives on STT among university lecturers. While most respondents recognized school-related factors, the coping measures they recommended were mainly university-related. The findings stress the need to improve communication, both between university mathematics lecturers and the school mathematics education community, and across universities, for promoting comprehensive initiatives to address STT. ======================================================= Sigal Levy & Yelena Stukalin Introducing Main Statistical Concepts to Non-statisticians https://doi.org/10.37626/GA9783959872188.0.055 First page: 301 Last page: 303 Abstract In this paper we present and discuss the results of an academic open-end mid-term statistics exam given to high-school teachers qualifying to teach Mathematics at a matriculation-exam level. The exam focused mainly on defining and understanding key terms and concepts in statistical inference. The purpose of this study is to identify what questions would be good predictors of the overall score, thus indicating a good understanding of statistics. Item analysis showed that the ability to properly define a parameter, state research hypotheses and interpret the findings were more inclined to do well in the exam. Keywords: Statistical concepts, teaching statistics, non-statisticians ======================================================= Nicole Lewis, Ryan Andrew Nivens, Jamie Price, Jennifer Price & Anant Godbole Pandemic-Driven Mathematical Initiatives within the East Tennessee State University Center of STEM Education https://doi.org/10.37626/GA9783959872188.0.056 First page: 304 Last page: 309 Abstract We describe three Mathematics Education initiatives launched as a result of the global pandemic. (i) The Eastman-funded MathElites professional development (PD) program for K-8 teachers was offered online. Teachers were vastly more involved due to their greater autonomy. Old outcomes and those from 2020 will be compared. (ii) ETSU’s Governor’s School, which offers high school students Statistics and Biology college courses, went online too, and we used Columbia University Virology lessons and Covid19 data sets to make the courses more engaging to students. Student projects were assessed to be of a higher quality than in years past. (iii)With Niswonger Foundation support,we have launched a PD thrust for teachers in 2021, in the new areas of Epidemiology, Artificial Intelligence, and Statistics-with-R. ======================================================= Po-Hung Liu Students’ Perceptions of Paradoxes of the Infinity https://doi.org/10.37626/GA9783959872188.0.057 First page: 310 Last page: 315 Abstract Infinity is a significant element for understanding calculus, yet studies consistently suggest that its counter-intuitive nature confused college students. The purpose of this study was to investigate Taiwanese college students’ perceptions of paradoxes of the infinity and observe how their perspectives shifted back and forth while facing contradictory facts. It was found the 1-1 correspondence was the most used criterion for comparing the cardinality of infinite sets, which is somewhat different from previous studies, and students’ reasoning on Zeno’s paradoxes was feeble. The study suggests future research of this line should pay attention to the dialectical process of students’ discourse to detect their core beliefs about the infinity. ======================================================= Hong Lu & Xin Chen The Relationship between Teacher-student Relationship, Interest, Self-efficacy and Mathematics Achievement – Does Gender Play a Role in it? https://doi.org/10.37626/GA9783959872188.0.058 First page: 316 Last page: 321 Abstract This study compared the mechanism by which the teacher-student relationship (TSR) affects mathematics achievement in different gender groups through interest and self-efficacy in mathematics. The results suggest that (1) in both samples, TSR positively predicted interest and self-efficacy, interest positively predicted self-efficacy, and self-efficacy in turn positively predicted mathematics achievement; (2) Gender differences were also detected; The positive relationships of TSR to self-efficacy, and interest to self-efficacy, were stronger among the male than the female students. Overall, the findings confirm that TSR have an important influence on Chinese students’ mathematics academic motivation and achievement and that gender differences affect the patterns of these relationships. Possible explanations for the results and practical implications are discussed. Key words: teacherstudent relationship, interest, self-efficacy, mathematics achievement, crossgender comparison. ======================================================= Cheryl Ann Lubinski & Allison Kroesch Developing, Not Teaching, Problem-Solving Strategies https://doi.org/10.37626/GA9783959872188.0.059 First page: 322 Last page: 324 Abstract Many teachers use explicit instruction to teach students how to solve a problem and then have their students practice a specific strategy. Research indicates this type of teaching does not necessarily improve problem solving skills. Students need to solve problems using their intuitive strategies which might include pictures and concrete materials. For a specific problem, we will share the strategies used by students in the United States, 17-year-old brothers and their family in Poland, and teachers of students ages 5-17 in Zimbabwe. Findings indicate that most people do not choose a picture strategy but a trial-and-error strategy using symbols. Most are unsuccessful at solving the problem. We will share teaching strategies that encourage developing, not teaching, problem-solving strategies. ======================================================= Jürgen Maaß Professional Mathematical Modelling: What we can Learn about Teaching Real World Mathematics from the Real Application of Mathematics in our World? https://doi.org/10.37626/GA9783959872188.0.060 First page: 325 Last page: 330 Abstract lessons, more motivation and a more sustainable learning success. Professional mathematical modelling is an important foundation for modern, technology-based societies. We are all significantly influenced by the results of mathematical modelling. The decisions for lock down, masks and travel restrictions in connection with Corona are a current example. This article drafts what we as teachers & researchers can learn about successful mathematical modelling from professional working mathematicians who are using & applying mathematics in the natural sciences, technology development, medicine, economics, social and humanities research & practice, consultancy for politics, the financial world & other economic sectors). The background for this article is my research on mathematics as a technology, its acceptance as a concept and ways of technology transfer, as well as decades of experience with colleagues from industrial mathematics (https://www.indmath.uni-linz.ac.at/) and the RISC (https://www.jku.at/institutfuer-symbolisches-rechnen-risc/anwendungen/risc-software-gmbh/) who started their work here in Linz a long time ago. As a co-founder and co-organizer, I organized and enjoyed many lectures on mathematics and society, industrial mathematics, etc. at the Johannes Kepler Symposium (https://www.numa.unilinz.ac.at/JKS/2020/ ======================================================= Jodelle S. W. Magner & Susan McMillen Making Word Problems Accessible to All: Innovating through Meaningful Models https://doi.org/10.37626/GA9783959872188.0.061 First page: 331 Last page: 332 Abstract Working with a large urban district over 14 years of Mathematics Science Partnership [MSP] grants, over 500 teachers of mathematics, special education teachers, mathematics coaches and administrators have come together to create engaging mathematics within grade 3 through 12 classrooms.Workshop participants will engage with an innovative use of a mathematical model and learn how it makes mathematics more accessible to students at all levels, especially to English Language Learners. Workshop participants will experience the use of the model in a variety of problem-solving contexts. Obstacles to teachers adopting these materials to use within their instruction and strategies used to overcome these challenges will be discussed. ======================================================= Rafael Alberto Méndez-Romero & María Angélica Suavita-Ramírez The mINNga Labs: an Initiative of the Universidad del Rosario to Strengthen STEM Skills, Social Sensitivity and Youth Empowerment in Colombia https://doi.org/10.37626/GA9783959872188.0.062 First page: 333 Last page: 337 Abstract The challenge of educating the generation of the digital age leads us to resort to pedagogical innovations that are sensitive, empathetic, analytical and multidisciplinary in nature. Additionally, these new student communities are characterized by appropriating causes, mobilize, manifest and are genuinely curious, which confronts us as educators with a greater and fascinating challenge. On the other hand, the historical moment of Colombia forces us to seek the unity of the country and generate a sum of forces from the specific talents of the people in the regions, to solve, as a body, the emerging needs of the moment. In this article we show a technological pedagogical innovation designed at the Universidad del Rosario, which is based on strengthening STEM skills and youth empowerment through the use of our mINNga labs, a version of a living laboratory as a social an open innovation. ======================================================= Jennifer Missen A Process for Updating Mathematics Teaching for 21st Century Students https://doi.org/10.37626/GA9783959872188.0.063 First page: 338 Last page: 343 Abstract It is inevitable and necessary that the curriculum, pedagogy, and school and classroom structures for the teaching of Mathematics will continue to change over the next 30 years. However, teachers are time poor, there are more and more who are teaching Mathematics when it is not their primary content area, and who may have knowledge of Mathematics but not the current pedagogical knowledge. Early career teachers need support in building a portfolio of tools and resources that work for them and their students. Experienced, traditional teachers are more comfortable with direct teaching and mastery practice and, understandably, are resistant to change. Inquiry based teaching and collaborative strategies, differentiated and tailored for the class and its individuals, combined with direct teaching and mastery practice, allow for greater equity and increased preparation of students for the ever-changing workforce. This two part workshop has participants work through the process of transitioning existing, traditional or textbook units of work to flexible, differentiated units with enough detail and resources to support any teacher to walk into the classroom knowing that they will serve all the students well. ======================================================= Shelby Morge & Christopher Gordon Using Squeak Etoys to Model Mathematical Ideas https://doi.org/10.37626/GA9783959872188.0.064 First page: 344 Last page: 349 Abstract Effective mathematics instruction involves students in making sense of mathematical ideas and reasoning mathematically (NCTM, 2014). Unfortunately for many US students in grades 6-8 (ages 10-14), mathematics is a repeat of topics learned in elementary school with an emphasis on computation. For this reason, students start to see mathematics as something that is hard to understand and not enjoyable. In this workshop, we share how a technology tool, Squeak Etoys, was used in a lesson to engage grade 6-8 students in discovering the relationship between the number of sides and the angle measure in regular polygons. We describe a lesson implementation and engage participants in the development of a Squeak Etoys computer model. In addition, conclusions related to mathematics instructional practices are shared. Key words: Squeak Etoys, modeling, problem solving, lesson,geometry, polygons ======================================================= Janina Morska New Methods and Forms of Work during Online Maths Lessons https://doi.org/10.37626/GA9783959872188.0.065 First page: 350 Last page: 353 Abstract In more than 38 years as a mathematics teacher, I have always tried to look for interesting methods and new forms of work. I wondered how to explain the new material to students so that they would understand and be able to use the information in the future. The previous school year has been a huge challenge in the field of distance learning. From October 2020 to May 2021, all teachers in Poland conducted Online lessons. As a result, we had to switch from traditional classroom teaching to online teaching. So I decided to look for appropriate tools and solutions of how to conduct such lessons. Keywords: online learning, distance learning, applications, computer programs, teaching materials, virtual notes, IT tools, online mathematics. ======================================================= Patricia S. Moyer-Packenham Relationships among Semiotic Representational Transformations and Math Outcomes in Digital Games https://doi.org/10.37626/GA9783959872188.0.066 First page: 354 Last page: 354 ======================================================= Svenja Müller & Anna Fath-Streb Risk Literacy in the Context of Stochastics and Mathematical Education https://doi.org/10.37626/GA9783959872188.0.067 First page: 355 Last page: 360 Abstract The purpose of this risk literacy study was to explore the ways of integrating examples of global challenges into mathematics education. The examples follow an approach to introduce risk literacy in teacher education along with a curriculum analysis for secondary education in Germany to include risk literacy within the given requirements and constraints. Two main examples, microplastic pollution and extreme events due to climate change, are analysed in the interdisciplinary context of global challenges and their understanding of mathematical knowledge for teaching and learning stochastics. ======================================================= M. Estela Navarro Robles Elementary Teachers Reaching a Quasi-complete Knowledge of Rational Numbers through an Online Course https://doi.org/10.37626/GA9783959872188.0.068 First page: 361 Last page: 366 Abstract There is evidence that most of the Elementary Teachers in Mexico have various conceptual deficiencies in their knowledge about rational numbers; however, the deficiencies were not the same in all the cases. So, we decided to design a non-traditional-personalized online course, constructed as an adaptative system, in which it was identified if the participant covered each one of the different conceptual approaches in various contexts. When it was identified that a conceptual approach was not covered, interactive materials and videos were presented to them that allowed them to understand what they had not covered. The aim of the course is to enable teachers to reach a quasicomplete conceptualization, whose meaning for us it is to understand the topic from different conceptual approaches in a deep way. This paper presents the structure of one module of the course, one detailed example, and results of the pilot test of this module. ======================================================= Benita P. Nel Noticing through Self-reflection by Mathematics Teachers using Video Stimulated Recall https://doi.org/10.37626/GA9783959872188.0.069 First page: 367 Last page: 372 Abstract Continuous professional development should be navigated in a teacher’s own context, addressing their particular needs where timeous feedback can be of great benefit. However, the major teachers’ union in South Africa hindered government officials to enter the classroom, limiting support. Most professional development (PD) initiatives are thus off-site and not always customised to the needs of the individual teacher. In this study, the use of Video-stimulated recall (VSR) was used as a PD tool where self-reflection is foregrounded, reporting on one teacher. The research question was: What did the teachers notice and act upon when VSR was incorporated as a PD amongst mathematics teachers? Through Mason’s discipline of noticing the teacher’s noticing was investigated. Key Words: Video-stimulated recall, Mathematics education; continuous professional development; teacher noticing; in-house setting ======================================================= Zanele Ngcobo Evoking School Mathematical Knowledge among Preservice Secondary Mathematics Teachers through Error Analysis https://doi.org/10.37626/GA9783959872188.0.070 First page: 373 Last page: 373 Abstract This article explores how attention to Specialised Content Knowledge (SCK) could evoke the development of school mathematics concepts among pre-service mathematics teachers (PSMTs). At the heart of the repeated debate about the delivery of professional mathematics teacher education curricula has been the reported lack of development of PSMTs knowledge for teaching. However, discussion of what mathematical knowledge for teaching is needed by PSMTs and how it should be developed had been uneven. In South Africa, attention to improving the status quo of learners’ poor performances in mathematics has been directed toward improving in-service teachers’ mathematical knowledge for teaching. However, research has shown that the problem does not only emerge when teachers become practitioners. The problem of low levels performance and of understanding of school mathematics by pre-service teachers has been identified by many studies but is often not addressed during teacher training. This article explores an under-examined strategy for addressing the repeated concerns about the quality of pre-service mathematics teachers’ education. It examines how attention to specialised content knowledge (SCK) within a preservice teacher education curriculum could potentially influence deeper quality mathematical knowledge to pre-service mathematics teachers’ professionality. This is a qualitative study conducted in 2018 and 2019. Data was generated from (n=61) PSMTs that were enrolled for Bachelor of Education majoring in mathematics. Data was conducted using written task, open ended questionnaires and focus group interviews. The findings from this small-scale study showed that error analysis has the potential to influence the development of SMK. Furthermore, findings suggest that attention to SCK has the potential to evoke school mathematics concepts and the evolution of subject matter knowledge. Based on the findings it is recommended that future research should be conducted to determine the veracity of these conclusions and their generalization to other mathematical topics. Considering the suggestions made by in literature that the description of knowledge is only valid at the time of the investigation, there is a need of large scale to ascertain the effect of error analysis toward the development of PSMTs' SMK of other school mathematics topics. Keywords: Error analysis, Pre-service mathematics teachers, Specialised Content Knowledge. ======================================================= Jenna O’Dell & Todd Frauenholtz Recruiting Mathematics and Mathematics Education Majors to a University https://doi.org/10.37626/GA9783959872188.0.071 First page: 374 Last page: 377 Abstract This paper will present strategies used to recruit students to a four-year university to complete a double major in mathematics and mathematics education, then enter the teaching field. The recruiters are two professors who work in both the Mathematics and Education departments at a university in the United States. The mathematics department has been especially supportive of the initiative as it will double the number of mathematics majors in their programs for two years from four to nine students. The recruiting included contacting community colleges, professional organizations, word of mouth, the university marketing department, and visits to collegiate mathematics classrooms at the level of calculus and above. This project was supported by The National Science Foundation (NSF) as a Noyce project and will support students financially with full cost of attendance for the final two years of the four-year program. ======================================================= Elizabeth Oldham & Aibhín Bray Undergraduate Mathematics Students’ Reflections on School Mathematics Curricula after a Major Curriculum Change in Ireland https://doi.org/10.37626/GA9783959872188.0.072 First page: 378 Last page: 383 Abstract After decades in which the Irish post-primary (grades 7-12) mathematics curriculum changed incrementally, a major innovation project was approved in 2008, and a “reform”-type curriculum was phased in over several years. The project was controversial, and some students developed negative attitudes to the change. This paper examines recent students’ opinions: in particular, the opinions of mathematics undergraduates who had experienced the transition and who took a Mathematics Education module at one Irish university in 2019- 20. They studied old and new curriculum documents and examination papers, and watched videos of reform-type lessons; their reflective comments were posted to a discussion board. Thematic analysis of posts from the 18 (out of 25) students who gave permission for use of their work in research indicates that, by then, these students supported many aspects of the reformed curriculum. ======================================================= Nick Vincent Otuma Mismatch between Spoken Language and Visual Representation of Mathematical Concepts https://doi.org/10.37626/GA9783959872188.0.073 First page: 384 Last page: 388 Abstract This paper examines secondary students’ mismatch in meaning between spoken language and visual representation of mathematical concept of a rightangled triangle. Forty-eight students, age 16-17years participated in the case study. Students were asked to select plane figures that matched the descriptions given on each questionnaire item. In group interview, participants were asked to give properties of selected plane figures and draw a diagram representing the same plane figures. The results of this research suggested that many students had similar imperfect conception of a right-angled triangle. Keywords: Mathematical language, conceptual understanding. ======================================================= Jenny Pange & Alina Degteva Project-based Learning in Statistics https://doi.org/10.37626/GA9783959872188.0.074 First page: 389 Last page: 394 Abstract Online teaching process is triggered by the Covid-19, and project-based learning (PBL) goes through a new stage of development as it includes ICT tools and up-to-date teaching methods. We applied this approach in an online undergraduate course in statistics. This paper describes the process and evaluates the outcome of PBL in teaching statistics course to a group of undergraduate students at the University of Ioannina, Greece. Students had to attend the class and react to practical exercises according to the demands of the PBL. They were asked to use questionnaires and go through interviews to evaluate the teacher-to-student, student-to-student, and student-to-content interactions in PBL method. Data obtained from online questionnaire and were analysed. The results implied high level of interactions during PBL in statistics.Key words: project-based learning, statistics, ICT tools, interaction ======================================================= Andrea Peter-Koop School-Readiness in Mathematics: Development of a Screening Test for Children Starting School https://doi.org/10.37626/GA9783959872188.0.075 First page: 395 Last page: 400 Abstract The study reported in this paper involved the development of a screening test to be applied by teachers with the whole class at school entry. The goal of this screening instrument is the identification of children who are at risk with respect to their school mathematics learning and therefore need immediate support and intervention. The paper reports the results of a study with 1757 children from 97 Grade 1 classes in 39 primary schools in Germany that have been tested with the new screening, one month after starting school. ======================================================= Maria Piccione & Francesca Ricci The Importance of Early Developing Symbol-sense https://doi.org/10.37626/GA9783959872188.0.076 First page: 401 Last page: 406 Abstract In this paper we deal with the mathematical-objects symbolic representation, as a relevant educational problem. In particular, we refer to the semiotic approach, a teaching model caring the distinction among sign-meaning-sense, proposing its adoption since the very beginning of the school experience. Focusing on the development of symbol-sense means sharing relational learning principles, reconsidering usual instrumental learning ways. We aim at promoting students’ awareness in managing mathematical language, taking into account its widespread weakness, also shown by our investigation. Awareness is a powerful mental attitude which enables facing difficulties and generating a proper conception of what mathematics and doing mathematics really are, then enhancing affect. ======================================================= Maria Piccione & Francesca Ricci Activities and tools for Early Developing Symbol-sense https://doi.org/10.37626/GA9783959872188.0.077 First page: 407 Last page: 412 Abstract This work deals with practical aspects of semiotic and relational approaches in teaching/learning. It is based on the Early Algebra principle by which mental models of algebraic thought can be constructed starting with Primary School, by teaching Arithmetic "algebraically". Here, the problem of the symbolic representation of mathematical objects is tackled. The aim is to allow students to clearly distinguish between the two worlds - the one of signs and the one of meanings - and to use signs of mathematical language with full awareness rather than just manipulating them. We present activities and tools which take into consideration different semiotic fields (gestural, iconic, natural, …) to achieve the mathematical field. ======================================================= Shelley B. Poole The “Yes, and…” Approach to Teaching Mathematical Modelling https://doi.org/10.37626/GA9783959872188.0.078 First page: 413 Last page: 417 Abstract Mathematical modelling can be a particularly creative tool when students are asked to solve open-ended problems. As instructors, when implementing mathematical modelling in the classroom, we can build on the ideas of our students. Utilizing the concept of "yes, and..." from improvisational theatre, we can foster students' creativity and empower them to take ownership of the mathematics when solving open-ended problems. Using this approach allows us an opportunity to let go of the structure of old and embrace new approaches and ideas in the classroom. ======================================================= Jordan T. Register & Christian H. Andersson Analysing PSTs Ethical Reasoning in a Data Driven World https://doi.org/10.37626/GA9783959872188.0.079 First page: 418 Last page: 423 Abstract The prevalence of Big Data Analytics as a proxy for human decision-making processes in globalized society, has catalyzed a call for the modernization of the mathematics curriculum to promote data literacy and ethical reasoning. To support this initiative, ten preservice mathematics teachers (PSTs) in Sweden (SWE) and the United States (US) were interviewed to identify what ethical considerations preservice teachers (PSTs) make in their mathematical analyses of data science contexts. Preliminary results indicate that teachers make a myriad of ethical considerations in their mathematical work that are tied to their critical mathematics consciousness (CMC), conceptions of data literacy, and experiences. As a result, it is imperative that educators simultaneously design educational curricula to foster students’ CMC and work to transform teacher held definitions of data literacy to reflect changes brought on by globalization. ======================================================= Sarah A. Roberts, Cameron Dexter Torti & Julie A. Bianchini A Mathematics Specialist Supporting District Shifts in Instruction for Multilingual Learners through Studio Days https://doi.org/10.37626/GA9783959872188.0.080 First page: 424 Last page: 428 Abstract Mathematics specialists fill a gap in providing individualized professional learning for classroom teachers, including furnishing much needed professional learning related to multilingual learners. This qualitative study examines the role a secondary district mathematics specialist in the United States played in supporting shifts in instruction for multilingual learners through the enactment of studio days professional learning. Interviews across two years with a mathematics specialist were examined. Using a framework of multilingual learner principles and adaptive reasoning, we share instructional shifts around the adaptive reasoning categories of flexibility, understanding, and deliberate practice, as related to multilingual learners. We conclude with implications for both research and practice related to secondary mathematics specialists, multilingual mathematics instruction, and studio day professional learning. ======================================================= Keith Robins Applying Mathematical Thinking Principles to Real Life Situations to Create an Objective Thinking Strategy https://doi.org/10.37626/GA9783959872188.0.081 First page: 429 Last page: 433 Abstract Teaching set thinking can make a great difference in teaching and learning mathematics as it demonstrates its relevance to real life. The following examples include how socialising is a mathematical process and how one can create a mathematical model for any experience or system rather than creating perceptions. ======================================================= Christine Robinson & Karen Singer-Freeman Digital Enhancements for Common, Online Mathematics Courses https://doi.org/10.37626/GA9783959872188.0.082 First page: 434 Last page: 438 Abstract The University of North Carolina System Office (UNC System) established the Digital Enhancement Project to rapidly develop high-quality, online course materials to support faculty and student success in online courses. Content was created for Calculus I, a course that is critical to student progress, is in high demand, and has large enrollments. To evaluate the usefulness and impact of the materials, project evaluators developed assessment instruments that included a survey for students enrolled in classes being taught by early adopters. Overall, students rated the quality of classes using project materials to be high. However, underrepresented ethnic minority students were somewhat less positive than other students and all students were less positive about the alignment of course content with course assessments than they were about other aspects of the course design. ======================================================= Ann-Sofi Röj-Lindberg Trends in Mathematics Education in Finland https://doi.org/10.37626/GA9783959872188.0.083 First page: 439 Last page: 444 Abstract Since PISA 2000 there has been a huge international interest towards education in Finland. Are there particular explanations to the PISA-success, a philosophers' stone, to be found? Is it possible to export innovative components found in Finnish schools to other countries and what exactly are these components? Is it about accessibility? Can the successful components be noticed and described? And why has the Finnish PISA-results in mathematics dropped lately? Questions like these have been asked over the years. In the paper I discuss trends in the Finnish public schooling that I find to be of particular importance and highlight changes in the curriculum and trends in mathematics education generally. I connect my arguments to research findings as well as to anecdotal stories. ======================================================= Sheena Rughubar-Reddy & Emma Engers Video Tutorials and Quick Response Codes to Assist Mathematical Literacy Students in a Non-classroom Environment https://doi.org/10.37626/GA9783959872188.0.084 First page: 445 Last page: 450 Abstract This paper discusses effectiveness of video tutorials, accessed via Quick Response codes, on Grade 10 mathematical literacy students’ ability to complete their homework. To assist them outside of the classroom, an intervention involving video tutorials explaining specific sections of work and how to go about solving problems, was devised. Students could access the relevant tutorials on a mobile device via the scanning of barcodes provided on the worksheets. The effectiveness of the intervention was assessed both quantitatively and qualitatively, through analysis of the participating students’ homework submissions and interviews with the students after the intervention had ended. Feedback from students via focus group interviews and questionnaires revealed that they found the tutorials helpful. This would indicate that the intervention was potentially beneficial. Keywords: Quick Response codes, video tutorials, homework. ======================================================= Sheryl J. Rushton, Melina Alexander & Shirley Dawson Mathematics to Teacher Education Persistence https://doi.org/10.37626/GA9783959872188.0.085 First page: 451 Last page: 456 Abstract In 2017, a university in Northern Utah’s Teacher Education and Mathematics Departments moved from a two-course mathematics requirement to incorporate a three-course mathematics requirement for Elementary and Special Education Teacher Education majors to satisfy university and Utah State Board of Education Quantitative Literacy graduation requirements. The proposed research seeks to determine how persistence rates differ from the original two-course math series to the new three-course destination series. ======================================================= Robyn Ruttenberg-Rozen In-the-Moment Narratives: Interventions with Learners Experiencing Mathematics Difficulties https://doi.org/10.37626/GA9783959872188.0.086 First page: 457 Last page: 462 Abstract Despite a significant amount of planning, so much of what occurs in mathematics teaching and learning intervention interactions, for both teacher and learner, are based on fleeting in-the-moment decisions and responses. At the root of these in-the-moment interactions are narratives that position the learner, teacher, and mathematics. In this paper I explore the interplay between in-the-moment decisions and responses, narratives, and positioning within a mathematical intervention for a learner experiencing mathematics difficulties. I use data from a mathematics intervention study of learners experiencing mathematics difficulties to show that interventions in mathematics can be a reciprocal and partnered activity. Importantly, since these narratives emerge in the reciprocal space of an intervention, narratives also evolve through the interaction. ======================================================= Tanishq Kumar Sah Extension of Theories https://doi.org/10.37626/GA9783959872188.0.087 First page: 463 Last page: 465 Abstract From an atom to this universe, from a bowl of water to the cosmic ocean this constant is present everywhere. This constant is π ( periodicity of the tangent function). For tangent function we know that tan(tan-1(x))=x, but the expression tan(ntan-1(x)) looks very complicated but is actually an expression of the type polynomial divided by another polynomial. The sine function is very important not only for graphs but for geometry too. There are some inputs whose behavior is very strange from the usual ones. Geometrical shapes and their relations are very important for many thing such as for vectors and many more but the triangle is very special because it is the least sided polygon. Riemann zeta function is very crucial for prime numbers. Infinite series related to them may be a game changer for it. Wallis’s integral formula is a boon but its domain is very constrained and needs another solution to it. ======================================================= Ishola A. Salami & Temitope O. Ajani Mathematics Songs to Hip-hop Music: Power to Engage Pupils and Improve Learning Outcomes in Primary Mathematics https://doi.org/10.37626/GA9783959872188.0.088 First page: 466 Last page: 471 Abstract Song-based strategy has been one of the most effective approaches of making learners remembering rule-governed educational contents like that of Mathematics. But the extent to which learners enjoy Mathematics songs and get engaged in it within and outside the school system is limited. Besides, many of the available Mathematics songs are for preschool while research studies have shown that learners’ scores in Mathematics started to decline from Primary IV class. One of the music types children love most is hip-hop and they easily memorize the lyrics. This led to the production of Mathematics hip-hop music with its lyrics being Mathematics principles, ideas, formulae and procedures for upper primary classes. This study determines the effectiveness of Mathematics Hip-hop music on improved Mathematics learning outcomes. Keywords: Hip-hop music, MATMUSIC, Upper primary Mathematics. ======================================================= S R Santhanam Teaching Mathematics using Storytelling and Technology https://doi.org/10.37626/GA9783959872188.0.089 First page: 472 Last page: 475 Abstract Storytelling coupled with technology is an attractive method to teach geometry. The following story was told to a set of students of the age group 14 – 16 years, who are familiar with the GeoGebra software. A pirate hid his treasures in an island and left a note for the treasure hunt to his son. The instructions are as follows. “Find two palm trees in the island with markings of a heart (🤍) on them. There will be a very small pond near them. From the pond go to one palm tree and turn 90 degrees and proceed equal distance to mark a point P on the ground. Do the same for the second palm tree to get another point Q. The treasure is hidden at the midpoint of PQ”. When his son went there, he could find the two palm trees but there was no pond nearby. But with his geometric knowledge, he could find the treasure. How? The students tried and some found the solution. In this short paper, this is discussed. ======================================================= Ipek Saralar-Aras & Betul Esen Designing Lessons for the 5th Graders through a Design Study on Teaching Polygons https://doi.org/10.37626/GA9783959872188.0.090 First page: 476 Last page: 481 Abstract It has been argued by researchers that learning about polygons is important. Student performance on polygons, particularly at the middle school level, was found to be lower than expected. Thus, this paper presents brief summaries of RETA-based lesson plans on polygons. The RETA is a maths model, which supports realistic, exploratory, technology-enhanced and active lessons. The participants of the study were 60 middle school students. Data was collected through lesson recordings of 5 lessons, pre-tests and post-tests to measure students’ performance on polygons, lesson evaluation forms and interviews. The findings show that students found the RETA-based lessons engaging but some of the parts were difficult for them. The lesson plans presented in this paper were the 2nd version of the plans, amended after the 1st cycle of designbased research. It is hoped that the lesson plans set an example for teachers and teacher candidates. ======================================================= Stephanie Sheehan-Braine & Irina Lyublinskaya A Framework for Online Problem-Based Learning for Mathematics Educators https://doi.org/10.37626/GA9783959872188.0.091 First page: 482 Last page: 487 Abstract Research shows that problem-based learning (PBL) has the capacity to make mathematics culturally relevant, so there is a need to adapt this successful learning model to virtual environments. This study proposes the Framework for Online Problem-Based Learning for Educators (OnPBL-E) to add this challenge. The content components of the OnPBL-E framework were developed by unpacking PBL instructional principles and identifying interactions between the essential elements of PBL: the context, the educator, and the learner. Then, the Multimodal Model for Online Education was used to identify online modules for these interactions. This study also describes an example of implementing PBL in an online mathematics modeling course. ======================================================= M. Vali Siadat Keystone Model of Teaching and Learning in Mathematics https://doi.org/10.37626/GA9783959872188.0.092 First page: 488 Last page: 493 Introduction Keystone model presents a holistic approach to math education at the college. It is a dynamic system of frequently assessing student learning and adjusting teaching practices. Its philosophy is based on the belief that all students can learn mathematics provided they are engaged in the learning process. Keystone views classroom as a learning community where through peer-to peer interaction and cooperation, all students achieve. Contrary to other programs that put the students in competition with one another, essentially pitting them against each other for grades, our program challenges students to cooperate so that all attain the standards of excellence. Keystone is an alternative model to traditional educational practices and its basic principles should be applicable to all disciplines. ======================================================= Parmjit Singh, Nurul Akma Md Nasir & Teoh Sian Hoon The Dearth of Development in Mathematical Thinking Among High School Leavers https://doi.org/10.37626/GA9783959872188.0.093 First page: 494 Last page: 499 Abstract The prime rationale of the high school math curriculum is to develop the intellectual mind of learners who can think and apply learnt content into solving problems of different areas of learning. Thus, to assess this context, a mixedmethod approach was undertaken to assess the levels of the 640 High school leavers’ mathematical thinking acumen in the context of their preparation in facing the challenges of tertiary level. The findings depict low-level mathematical thinking attainment regarding their dearth in critical thinking and creative thinking to solve higher-order thinking tasks. They lack a heuristics repertoire to use their contextual knowledge in solving fundamental nonroutine problems. This then begs the question: how are these students to face the upcoming hurdles and challenges bound to be thrown their way at the tertiary level? Keywords: Mathematical thinking, problem solving, non-routine, heuristics ======================================================= Praneetha Singh Mathovation- Creativity and Innovation in the Mathematics Classroom https://doi.org/10.37626/GA9783959872188.0.094 First page: 500 Last page: 505 Abstract The 21st century is predicted as the century of rapid development in all aspects of life. People are creative, but the degree of creativity is different (Solso, 1995). The perspective of mathematical creative thinking expressed by experts such as Gotoh (2004) and Krulik and Rudnick (1999) refer to a combination of logical and divergent thinking, which is based on intuition but has a conscious aim and process. This thinking is based on flexibility, fluency and the uniqueness of mathematical problem solving. This paper will aim to assist the readers to find out the competencies that are required to assess the creative thinking ability and characteristic of mathematical problems that can be used in creative thinking. ======================================================= Charles Raymond Smith & Cyril Julie Towards Understanding Integrating Digital Technologies in the Mathematics Classroom https://doi.org/10.37626/GA9783959872188.0.095 First page: 506 Last page: 511 Abstract In the context of ICT integration, a presentation by a teacher during a continuing professional development session is analyzed from the instrumental orchestration as well as the Technological Pedagogical (And) Content Knowledge (TPACK) perspective. The results indicate that some of the components of instrumental orchestration were used by the teacher during the presentation. In realising these orchestrations, the teacher had to delve into the different knowledge components that constitute TPACK. It is concluded that CPD providers need to take such complexities into account when delivering training programs. Keywords: GeoGebra, ICT integration, instrumental orchestration, TPACK, mathematics teacher practices ======================================================= Panagiotis Stefanides “Generator Polyhedron”, Icosahedron Non-Regular, Discovered Invention https://doi.org/10.37626/GA9783959872188.0.096 First page: 512 Last page: 517 Abstract The Invented [2017] Polyhedron, is a Non-Regular Icosahedron, it has 12 Isosceli triangles and 8 Equilateral ones. Its Skeleton Structure consists of 3 Parallelogramme Planes Orthogonal to each other, with sides’ ratios based on the Square Root of the Golden Number [ratios of 4/π specially for π = 4/T= 3.14460551.., where T is the Square Root of the Golden Number (√Φ) equal to 1.27201965..] and related directly to the Icosahedron, whose structure is based on the Golden Number and to the Dodecahedron, whose structure is based on the Square of the Golden Number. Its geometry relates to Plato’s Timaeus “Most Beautiful Triangle”, a proposed theorization by the author [“contra” the standard usual International interpretations], presented to various national and international conferences [the Magirus/ Kepler one is a constituent part of this triangle, similar to it, but not the same with it]. ======================================================= Michelle Stephan & David Pugalee The Future of Mathematics Education in the Digital Age https://doi.org/10.37626/GA9783959872188.0.097 First page: 518 Last page: 521 Abstract How do the mathematics content and processes taught in school today need to change in order to prepare students for participation in the digital and information age? We propose to stimulate a discussion about what mathematics education should aim for in preparing students for employment and local/global citizenship in this ever-changing technological world. Our group will develop a forward-minded agenda on implementation of mathematics content and practices. This will include detailing 1) what content/practices should be kept, changed or deleted from the curriculum, 2) potential impediments to teachers implementing them and possible strategies to address these, and 3) necessary research projects to study implementations in order to make ongoing recommendations. We will aim to start with middle school (ages 12-15) with a vision to continue this working group through multiple conferences. ======================================================= Yelena Stukalin & Sigal Levy Introducing Probability Theory to Ultra-Orthodox Jewish Students by Examples from the Bible and Ancient Scripts https://doi.org/10.37626/GA9783959872188.0.098 First page: 522 Last page: 525 Abstract Cultural diversity in the classroom may motivate teachers to seek examples that reflect their students’ cultural backgrounds, thus making the course material more appealing and understandable. In this context, the Holy Bible is a source of many stories and anecdotes that may be included in teaching probability theory to even ultra-Orthodox Jews. This paper aims to demonstrate the use of stories from the Bible to introduce some concepts in probability. We believe that this approach will make learning probability and statistics more understandable to the Ultra-Orthodox students and increase their motivation to engage in their studies. Keywords: cultural diversity, biblical examples, non-statisticians ======================================================= Emily K. Suh, Lisa Hoffman & Alan Zollman STEM SMART: Five Essential Life Skills Students Need for their Future https://doi.org/10.37626/GA9783959872188.0.099 First page: 526 Last page: 530 Abstract To be successful in a future STEM-focused world, students need to know more than content: students need to be STEM SMART. A STEM SMART student has the mindset of an intellectual risk taker, the tenacity to tackle tough problems while learning from mistakes, and the critical thinking skills to separate scientific information from opinions and beliefs. We use the SMART acronym (Struggle, Mistakes, All, Risk, Think) to introduce five essential life skills not obviously related to STEM (Science, Technology, Engineering, and Mathematics) disciplines but necessary for success in STEM. For each of our five essential skills, we provide an explanation of its importance, connections to relevant educational research, and real-world applications. ======================================================= Janet (Hagemeyer) Tassell, Jessica Hussung, Kylie Bray, Darby Tassell & Haley (Clayton) Carbone Elementary Pre-Service Teachers’ Beliefs about Mathematics Fluency: Transforming Through Readings & Discussions https://doi.org/10.37626/GA9783959872188.0.100 First page: 531 Last page: 536 Abstract Teacher candidates continue to enter Elementary Math Methods with the belief that mathematics fluency is synonymous to speed and rote memorization –assessed best by timed tests. In the Elementary Math Methods 2018-2021 school years, fall and spring semesters, qualitative data were gathered from pre-service elementary mathematics teachers’ pre/post-assessments of reading mathematics fluency journal articles, viewing video samples, and participating in full-class discussions. The pre- to post-assessment themes show that reading research articles may be a possible intervention to add to their clinical school observations in the K-6 setting. ======================================================= Eleni Tsami, Dimitra Kouloumpou & Andreas Rokopanos The Gender Gap in Statistics Courses: A Contemporary View on a Statistics Department https://doi.org/10.37626/GA9783959872188.0.101 First page: 537 Last page: 541 Abstract Gender equality remains a strategic objective of the EU educational system. The present paper provides a contemporary view of the gender balance in the Department of Statistics and Insurance Science at the University of Piraeus. Our results indicate that a gender gap is prevalent in this specific department, although this gap is only marginal in terms of the statistics on students. On the other hand, statistics for the academic staff reveal that the department is clearly male dominated, thus stirring the discussion of gender preferences and systemic gender bias. Our findings support the notion that the institutional change currently taking place across departments and academic communities worldwide is yet to come to fruition and considerable effort is needed in order to bridge the gender gap in science, technology, engineering and mathematics (STEM) courses. ======================================================= Ching-Yu Tseng, Paul Foster, Jake Klinkert, Elizabeth Adams, Corey Clark, Eric C. Larson & Leanne Ketterlin-Geller Using Cognitive Walkthroughs to Evaluate the Students’ Computational Thinking during Gameplay https://doi.org/10.37626/GA9783959872188.0.102 First page: 542 Last page: 547 Abstract In this paper, we describe how a team of multidisciplinary researchers, including game designers, computer scientists, and learning scientists, created a learning environment focused on computational thinking using a commercial video game Minecraft. The learning environment includes a Minecraft mod, a custom companion application, and a learning management system integration. The team designed the learning environment for students in Grades 6-8. Working with a group of educators, the researchers identified eleven high-priority Computer Science Teacher Association (CSTA) standards to guide game development. The team decomposed the standards into essential knowledge, skills, and abilities. In this study, we describe how we used a cognitive walkthrough with a middle school student to investigate: (a) the ways in which the game supports student learning (b) the barriers to learning, and (c) the necessary changes to facilitate learning. ======================================================= Ariana-Stanca Vacaretu GROWE in Math https://doi.org/10.37626/GA9783959872188.0.103 First page: 548 Last page: 553 Abstract Getting Readers on the Wavelength of Emotions (GROWE) is an Erasmus+ project initiated with the aim to develop all (including math) teachers’ competences to address students’ literacy and emotional learning needs. The GROWE classroom approach includes meaningful reading and writing learning activities and develops mastery of such strategies using diverse authentic texts (i.e. not `clean` textbook texts), while learning the discipline. Simultaneously, the students enhance their social-emotional skills by learning to recognise and manage their emotions, establish positive relationships, and make responsible decisions. This paper presents my experience in implementing the GROWE approach in my maths lessons with high-school students: the authentic texts I used and related tasks, and some implementation results. ======================================================= Shin Watanabe & Takako Aoki In School and Out School https://doi.org/10.37626/GA9783959872188.0.104 First page: 554 Last page: 559 Abstract Currently, learning in developed countries is centred on school education. It is not only Japanese teachers who regret that few students enjoy learning mathematics under the current school system. And in the age of 100 years of life, everyone should continue to study academics even after graduating from school. Unfortunately, learning mathematics is difficult after graduating from school. It is clear that lifelong learning has now become an important learning venue for all. I decided to call this school education “In School”, and to be released from the school system and call learning “Out School”. I will describe the richness of the future of “Out School”, which is a place for learning in the future. Out School is an important mathematical education that is an extension of In School. Key words: In School, Out School, Creativity, Mathematical Learning ======================================================= Laura Watkins, Patrick Kimani, April Ström, Bismark Akoto, Dexter Lim Representational Competence with Linear Functions: A Glimpse into the Community College Algebra Classroom https://doi.org/10.37626/GA9783959872188.0.105 First page: 560 Last page: 565 Abstract Teaching and learning strategies that encourage students to develop the ability to use mathematical representations in meaningful ways are powerful tools for building algebraic understandings of mathematics and solving problems (American Mathematical Association of Two-Year Colleges [AMATYC], 2018). The study of functions in algebra courses taught at community colleges in the United States provides students the opportunity and space to make connections between important characteristics of various families of functions. Using examples of teaching and learning linear functions from intermediate and college algebra courses in community colleges, we explore the ways instructors and students use a variety of representations (visual, symbolic, numeric, contextual, verbal, and/or physical) in teaching and learning linear functions, while connecting between and within these representations. ======================================================= Ian Willson Formative Assessment Activities for Introductory Calculus https://doi.org/10.37626/GA9783959872188.0.106 First page: 566 Last page: 568 Abstract A hands-on workshop in which participants engage as beginning learners in an extensive range of stand-alone tasks, and in which some of the tenets and guiding principles of formative assessment are used to highlight what many consider to be the best kind of teaching practice—and that which is critically important if we are to improve the quality of instruction for all. The idea is that clear articulation of just what is meant by formative assessment is provided in the actual context of ready-to-use classroom tasks. ======================================================= Kay A. Wohlhuter & Mary B. Swarthout Number Talks: Working to Deepen and Grow Number Sense Knowledge https://doi.org/10.37626/GA9783959872188.0.107 First page: 569 Last page: 573 Abstract Deep, flexible number understandings are foundational for mathematics learning. This workshop is based on two mathematics teacher educators’ journey to better understand how to facilitate future teachers’ development and use of number sense. Engaging preservice teachers in Number Talks enabled the educators to identify and to examine the strategies preservice teachers used during number talks while also providing a context for improving and expanding their own professional knowledge about number sense. Participant engagement includes experiencing Number Talks, examining preservice teachers’ work samples, and responding to the educators’ observations about number sense language (decomposition of numbers, fluency and flexibility with numbers, and mathematical properties). ======================================================= Ryan G. Zonnefeld & Valorie L. Zonnefeld Rural STEM Teachers: An Oasis in the Desert https://doi.org/10.37626/GA9783959872188.0.108 First page: 574 Last page: 579 Abstract Teacher preparation programs for STEM education should prepare teachers for all settings, including rural schools. Students across geographic locales show equal interest in STEM fields, but rural students often lack access to highly qualified STEM teachers. UNESCO (2014) notes that the disparity in education between rural and urban schools is a concern of many countries. In the United States, the National Center for Educational Statistics confirms that twenty percent of students are educated in rural schools and the STEM teachers in these schools are often the only STEM expert. These teachers become backbone teachers that set the foundation and direction of STEM education in the entire school. This paper reviews the landscape of STEM education in rural schools, explores strategies for ensuring high-quality STEM education in rural schools, and outlines early successes of a university teacher preparation program in meeting these needs. ======================================================= Valorie L. Zonnefeld Pedagogies that Foster a Growth Mindset Towards Mathematics https://doi.org/10.37626/GA9783959872188.0.109 First page: 580 Last page: 584 Abstract Research demonstrates that a student’s mindset plays an important role in achievement and that mindsets are domain specific. Carol Dweck claimed that mathematics needs a mindset makeover and has shown that teachers can foster a growth mindset through their pedagogical choices. This paper shares how one university trains preservice teachers in mathematics pedagogies that are key to fostering a growth mindset. These practices include educating students on brain function, equitable access, metacognition strategies, feedback practices, the importance of productive struggle, and learning from mistakes.
Download or read book Proceedings of the 14th International Congress on Mathematical Education written by Jianpan Wang and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Proceedings of the 14th International Congress on Mathematical Education. Presents the latest trends in mathematics education research and mathematics teaching practices at all levels"--
Download or read book Proceedings of the International Conference the Future of Mathematics Education written by International Conference The Future of Mathematics Education. 2004, Ciechocinek and published by . This book was released on 2004 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proceedings of the Fourth International Congress on Mathematical Education written by M. Zweng and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt: Henry O. Pollak Chairman of the International Program Committee Bell Laboratories Murray Hill, New Jersey, USA The Fourth International Congress on Mathematics Education was held in Berkeley, California, USA, August 10-16, 1980. Previous Congresses were held in Lyons in 1969, Exeter in 1972, and Karlsruhe in 1976. Attendance at Berkeley was about 1800 full and 500 associate members from about 90 countries; at least half of these come from outside of North America. About 450 persons participated in the program either as speakers or as presiders; approximately 40 percent of these came from the U.S. or Canada. There were four plenary addresses; they were delivered by Hans Freudenthal on major problems of mathematics education, Hermina Sinclair on the relationship between the learning of language and of mathematics, Seymour Papert on the computer as carrier of mathematical culture, and Hua Loo-Keng on popularising and applying mathematical methods. Gearge Polya was the honorary president of the Congress; illness prevented his planned attendence but he sent a brief presentation entitled, "Mathematics Improves the Mind". There was a full program of speakers, panelists, debates, miniconferences, and meetings of working and study groups. In addition, 18 major projects from around the world were invited to make presentations, and various groups representing special areas of concern had the opportunity to meet and to plan their future activities.