Download or read book Analysing the Solution of Word Problems in Mathematics an Exploratory Study written by Jeremy Kilpatrick and published by . This book was released on 1967 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analyzing the Solution of Word Problems in Mathematics written by and published by . This book was released on 1967 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Making Sense of Word Problems written by Eric de Corte and published by CRC Press. This book was released on 2000-01-01 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Word problems have been a staple of mathematics instruction for centuries, yet the rationale for their use has remained largely unexamined. A range of findings have shown how students consistently answer them in ways that fail to take account of the reality of the situations described. This monograph reports on studies carried out to investigate this "suspension of sense-making" in answering word problems. In Part One, a wide range of examples documenting the strength of the phenomenon is reviewed. Initial surprise at the findings was replaced by a conviction that the explanation lies in the culture of the mathematics classroom, specifically the rules implicitly governing the nature and interpretation of the word problem genre. This theoretical shift is reflected in Part Two. A detailed analysis of the way in which word problems are currently taught in typical mathematical classrooms is followed by reviews of design experiments illustrating how, by immersing students in a fundamentally changed learning environment, they can acquire what the authors consider to be more appropriate conceptions about, and strategies for doing, word problems. Part Three turns to a wider discussion of theoretical issues, a further analysis of the features of the educational system considered responsible for outcomes detrimental to many students' understanding and conception of mathematics, and suggestions for rethinking the role of word problems within the curriculum.
Download or read book Teaching and Learning Mathematical Problem Solving written by Edward A. Silver and published by Routledge. This book was released on 2013-04-03 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: A provocative collection of papers containing comprehensive reviews of previous research, teaching techniques, and pointers for direction of future study. Provides both a comprehensive assessment of the latest research on mathematical problem solving, with special emphasis on its teaching, and an attempt to increase communication across the active disciplines in this area.
Download or read book Problem Solving in Mathematics Education written by Torsten Fritzlar and published by WTM-Verlag Münster. This book was released on 2016-06-30 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: From 3rd to 5th of September 2015 the 17th international ProMath conference (Problem Solving in Mathematics Education) took place at the Faculty of Education of the Martin Luther University Halle-Wittenberg (Germany). For the first time, it was combined with the annual meeting of the working group “Problem Solving” of the Society of Didactics of Mathematics. This book contains 20 peer reviewed articles of researchers from five European countries. The topics of the papers evolved around different areas of learning and problem solving. There are some theoretical papers on problem oriented mathematics instruction and specific aspects of problem solving and creativity as well as reports on detailed studies of problem solving processes of pupils and preservice teachers. Authors also present experiences with “real” problem solving instruction in different countries, considerations and teaching experiments on didactic concepts to foster pupils’ problem solving abilities, and they describe mathematically rich problem fields and their potentials for mathematical investigations in class. ProMath is a group of experienced and early career researchers in the field of mathematics education who are interested in investigating and fostering mathematical problem solving and problem oriented mathematics teaching.
Download or read book Mathematical Problem Solving written by ALAN H. SCHOENFELD and published by Elsevier. This book was released on 2014-06-28 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is addressed to people with research interests in the nature of mathematical thinking at any level, topeople with an interest in "higher-order thinking skills" in any domain, and to all mathematics teachers. The focal point of the book is a framework for the analysis of complex problem-solving behavior. That framework is presented in Part One, which consists of Chapters 1 through 5. It describes four qualitatively different aspects of complex intellectual activity: cognitive resources, the body of facts and procedures at one's disposal; heuristics, "rules of thumb" for making progress in difficult situations; control, having to do with the efficiency with which individuals utilize the knowledge at their disposal; and belief systems, one's perspectives regarding the nature of a discipline and how one goes about working in it. Part Two of the book, consisting of Chapters 6 through 10, presents a series of empirical studies that flesh out the analytical framework. These studies document the ways that competent problem solvers make the most of the knowledge at their disposal. They include observations of students, indicating some typical roadblocks to success. Data taken from students before and after a series of intensive problem-solving courses document the kinds of learning that can result from carefully designed instruction. Finally, observations made in typical high school classrooms serve to indicate some of the sources of students' (often counterproductive) mathematical behavior.
Download or read book Problem Solving and Intelligence written by Helga A. H. Rowe and published by Taylor & Francis. This book was released on 2024-03-08 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1985, Problem Solving and Intelligence was the result of the author’s efforts to understand the nature of human intelligence and the differences in the cognitive functioning of individuals which we observe again and again. The book contains two types of material. First it presents an overview of major contributions to the conceptualization and investigation of problem solving and intelligence, which was derived from the extensive, largely non-cumulative literature at the time. Second it reports a comprehensive, empirical study of the manifestation of intelligence in problem solving. The subject matter was at the interface of three traditional areas of psychological inquiry: namely, the study of cognitive processes, individual differences, and the characteristics of the stimulus. What was innovative is that intellectual performance is investigated in relation to the simultaneous operation of variables from these dimensions. The book was intended, primarily, as a contribution to the understanding and investigation of the nature of intelligent behavior, as well as an introduction to intelligence and problem solving. Today it can be read and enjoyed in its historical context.
Download or read book Research in Education written by and published by . This book was released on 1971 with total page 1188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Resources in Education written by and published by . This book was released on 1998 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Implementation Research on Problem Solving in School Settings written by Inga Gebel and published by WTM-Verlag Münster. This book was released on 2019 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Content of the Book The University of Potsdam hosted the 25th ProMath and the 5th WG Problem Solving conference. Both groups met for the second time in this constellation which contributed to profound discussions on problem solving in each country taking cultural particularities into account. The joint conference took place from 29th to 31st August 2018, with participants from Finland, Germany, Greece, Hungary, Israel, Sweden, and Turkey. The conference revolved around the theme “Implementation research on problem solving in school settings”. These proceedings contain 14 peer-reviewed research and practical articles including a plenary paper from our distinguished colleague Anu Laine. In addition, the proceedings include three workshop reports which likewise focused on the conference theme. As such, these proceedings provide an overview of different research approaches and methods in implementation research on problem solving in school settings which may help close the gap between research and practice, and consequently make a step forward toward making problem solving an integral part of school mathematics on a large-scale. Content PLENARY REPORT Anu Laine: How to promote learning in problem-solving? pp 3 – 18 This article is based on my plenary talk at the joint conference of ProMath and the GDM working group on problem-solving in 2018. The aim of this article is to consider teaching and learning problem-solving from different perspectives taking into account the connection between 1) teacher’s actions and pupils’ solutions and 2) teacher’s actions and pupils’ affective reactions. Safe and supportive emotional atmosphere is base for students’ learning and attitudes towards mathematics. Teacher has a central role both in constructing emotional atmosphere and in offering cognitive support that pupils need in order to reach higher-level solutions. Teachers need to use activating guidance, i.e., ask good questions based on pupils’ solutions. Balancing between too much and too little guidance is not easy. https://doi.org/10.37626/GA9783959871167.0.01 RESEARCH REPORTS AND ORAL COMMUNICATIONS Lukas Baumanns and Benjamin Rott: Is problem posing about posing “problems”? A terminological framework for researching problem posing and problem solving pp 21 – 31 In this literature review, we critically compare different problem-posing situations used in research studies. This review reveals that the term “problem posing” is used for many different situations that differ substantially from each other. For some situations, it is debatable whether they provoke a posing activity at all. For other situations, we propose a terminological differentiation between posing routine tasks and posing non-routine problems. To reinforce our terminological specification and to empirically verify our theoretical considerations, we conducted some task-based interviews with students. https://doi.org/10.37626/GA9783959871167.0.02 Kerstin Bräuning: Long-term study on the development of approaches for a combinatorial task pp 33 – 50 In a longitudinal research project over two years, we interviewed children up to 6 times individually to trace their developmental trajectories when they solve several times the same tasks from different mathematical areas. As a case study, I will present the combinatorial task and analyze how two children, a girl and a boy, over two years approached it. As a result of the case studies we can see that the analysis of the data product-oriented or process-oriented provides different results. It is also observable that the developmental trajectory of the girl is a more continuous learning process, which we cannot identify for the boy. https://doi.org/10.37626/GA9783959871167.0.03 Lars Burman: Developing students’ problem-solving skills using problem sequences: Student perspectives on collaborative work pp 51 – 59 Using problem solving in mathematics classrooms has been the object of research for several decades. However, it is still necessary to focus on the development of problem-solving skills, and in line with the recent PISA assessment, more attention is given to collaborative problem solving. This article addresses students’ collaborative work with problem sequences as a means to systematically develop students’ problem-solving skills. The article offers student perspectives on challenges concerning the social atmosphere, differentiation on teaching, and learning in cooperation. In spite of the challenges, the students’ experiences indicate that the use of problem sequences and group problem solving can be fruitful in mathematics education. https://doi.org/10.37626/GA9783959871167.0.04 Alex Friedlander: Learning algebraic procedures through problem solving pp 61 – 69 In this paper, I attempt to present several examples of tasks and some relevant findings that investigate the possibility of basing a part of the practice-oriented tasks on higher-level thinking skills, that are usually associated with processes of problem solving. The tasks presented and analysed here integrate problem solving-components – namely, reversed thinking, expressing and analysing patterns, and employing multiple solution methods, into the learning and practicing of algebraic procedures – such as creating equivalent expressions and solving equations. https://doi.org/10.37626/GA9783959871167.0.05 Thomas Gawlick and Gerrit Welzel: Backwards or forwards? Direction of working and success in problem solving pp 71 – 89 We pose ourselves the question: What can one infer from the direction of working when solvers work on the same task for a second time? This is discussed on the basis of 44 problem solving processes of the TIMSS task K10. A natural hypothesis is that working forwards can be taken as evidence that the task is recognized and a solution path is recalled. This can be confirmed by our analysis. A surprising observation is that when working backwards, pivotal for success is (in case of K10) to change to working forwards soon after reaching the barrier. https://doi.org/10.37626/GA9783959871167.0.06 Inga Gebel: Challenges in teaching problem solving: Presentation of a project in progress by using an extended tetrahedron model pp 91 – 109 In order to implement mathematical problem solving in class, it is necessary to consider many different dimensions: the students, the teacher, the theoretical demands and adequate methods and materials. In this paper, an implementation process is presented that considers the above dimensions as well as the research perspective by using an extended tetrahedron model as a structural framework. In concrete terms, the development and initial evaluation of a task format and a new teaching concept are presented that focus on differentiated problem-solving learning in primary school. The pilot results show initial tendencies towards possible core aspects that enable differentiated problem solving in mathematics teaching. https://doi.org/10.37626/GA9783959871167.0.07 Heike Hagelgans: Why does problem-oriented mathematics education not succeed in an eighth grade? An insight in an empirical study pp 111 – 119 Based on current research findings on the possibilities of integration of problem solving into mathematics teaching, the difficulties of pupils with problem solving tasks and of teachers to get started in problem solving, this article would like to show which concrete difficulties delayed the start of the implementation of a generally problem-oriented mathematics lesson in an eighth grade of a grammar school. The article briefly describes the research method of this qualitative study and identifies and discusses the difficulties of problem solving in the examined school class. In a next step, the results of this study are used to conceive a precise teaching concept for this specific class for the introduction into problem-oriented mathematics teaching. https://doi.org/10.37626/GA9783959871167.0.08 Zoltán Kovács and Eszter Kónya: Implementing problem solving in mathematics classes pp 121 – 128 There is little evidence of teachers are using challenging problems in their mathematics classes in Hungary. At the University of Debrecen and University of Nyíregyháza, we elaborated a professional development program for inservice teachers in order to help them implementing problem solving in their classes. The basis of our program is the teacher and researcher collaboration in the lessonplanning and evaluation. In this paper we report some preliminary findings concerning this program. https://doi.org/10.37626/GA9783959871167.0.09 Ana Kuzle: Campus school project as an example of cooperation between the University of Potsdam and schools pp 129 – 141 The “Campus School Project” is a part of the “Qualitätsoffensive Lehrerbildung” project, whose aim is to improve and implement new structures in the university teacher training by bringing all the essential protagonists, namely university stuff, preservice teachers, and in-service teachers – together, and having them work jointly on a common goal. The department of primary mathematics education at the University of Potsdam has been a part of the Campus School Project since 2017. Thus far several cooperations emerged focusing on different aspects of problem solving in primary education. Here, I give an overview of selected cooperations, and the first results with respect to problem-solving research in different school settings. https://doi.org/10.37626/GA9783959871167.0.10 Ioannis Papadopoulos and Aikaterini Diakidou: Does collaborative problem-solving matter in primary school? The issue of control actions pp 143 – 157 In this paper we follow three Grade 6 students trying to solve (at first individually, and then in a group) arithmetical and geometrical problems. The focus of the study is to identify and compare the various types of control actions taken during individual and collaborative problem-solving to show how the collective work enhances the range of the available control actions. At the same time the analysis of the findings give evidence about the impact of the collaborative problemsolving on the way the students can benefit in terms of aspects of social metacognition. https://doi.org/10.37626/GA9783959871167.0.11 Sarina Scharnberg: Adaptive teaching interventions in collaborative problem-solving processes pp 159 – 171 Even though there exists limited knowledge on how exactly students acquire problem-solving competences, researchers agree that adaptive teaching interventions have the potential to support students‘ autonomous problem-solving processes. However, most recent research aims at analyzing the characteristics of teaching interventions rather than the interventions’ effects on the students’ problem-solving process. The study in this paper addresses this research gap by focusing not only on the teaching interventions themselves, but also on the students’ collaborative problem-solving processes just before and just after the interventions. The aim of the study is to analyze the interventions‘ effect on the learners’ integrated problem-solving processes. https://doi.org/10.37626/GA9783959871167.0.12 Nina Sturm: Self-generated representations as heuristic tools for solving word problems pp 173 – 192 Solving non-routine word problems is a challenge for many primary school students. A training program was therefore developed to help third-grade students to find solutions to word problems by constructing external representations (e.g., sketches, tables) and to specifically use them. The objective was to find out whether the program positively influences students’ problemsolving success and problem-solving skills. The findings revealed significant differences between trained and untrained classes. Therefore, it can be assumed that self-generated representations are heuristic tools that help students solve word problems. This paper presents the results on the impact of the training program on the learning outcome of students. https://doi.org/10.37626/GA9783959871167.0.13 Kinga Szűcs: Problem solving teaching with hearing and hearing-impaired students pp 193 – 203 In the last decade the concept of inclusion has become more and more prevalent in mathematics education, especially in Germany. Accordingly, teachers in mathematics classrooms have to face a wide range of heterogeneity, which includes physical, sensory and mental disabilities. At the Friedrich-Schiller-University of Jena, within the framework of the project “Media in mathematics education” it is examined how new technologies can support teaching in inclusive mathematics classrooms. In the academic year 2017/18, the heterogeneity regarding hearing impairment was mainly focussed on. Based on a small case study with hearing and hearing-impaired students a problem-solving unit about tangent lines was worked out according to Pólya, which is presented in the paper. https://doi.org/10.37626/GA9783959871167.0.14 WORKSHOP REPORTS Ana Kuzle and Inga Gebel: Implementation research on problem solving in school settings: A workshop report 207 On the last day of the conference, we organized a 90-minute workshop. The workshop focused on the conference theme “Implementation research on problem solving in school settings”. Throughout the conference, the participants were invited to write down their questions and/or comments as a response to held presentations. https://doi.org/10.37626/GA9783959871167.0.15 Ana Kuzle, Inga Gebel and Anu Laine: Methodology in implementation research on problem solving in school settings pp 209 – 211 In this report, a summary is given on the contents of the workshop. In particular, the methodology and some ethical questions in implementation research on problem solving in school settings are discussed. The discussion showed how complex this theme is so that many additional questions emerged. https://doi.org/10.37626/GA9783959871167.0.16 Lukas Baumanns and Sarina Scharnberg: The role of protagonists in implementing research on problem solving in school practice pp 213 – 214 Based on seminal works of Pólya (1945) and Schoenfeld (1985), problem solving has become a major focus of mathematics education research. Even though there exists a variety of recent research on problem solving in schools, the research results do not have a direct impact on problem solving in school practice. Instead, a dissemination of research results by integrating different protagonists is necessary. Within our working group, the roles of three different protagonists involved in implementing research on problem solving in school practice were discussed, namely researchers, pre-service, and in-service teachers, by examining the following discussion question: To what extent do the different protagonists enable implementation of research findings on problem solving in school practice? https://doi.org/10.37626/GA9783959871167.0.17 Benjamin Rott and Ioannis Papadopoulos: The role of problem solving in school mathematics pp 215 – 217 In this report of a workshop held at the 2018 ProMath conference, a summary is given of the contents of the workshop. In particular, the role of problem solving in regular mathematics teaching was discussed (problem solving as a goal vs. as a method of teaching), with implications regarding the selection of problems, its implementation into (written) exams as well as teacher proficiency that is needed for implementing problem solving into mathematics teaching. https://doi.org/10.37626/GA9783959871167.0.18
Download or read book Investigations in Mathematics Education written by and published by . This book was released on 1969 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Beyond Constructivism written by Richard A. Lesh and published by Routledge. This book was released on 2003-05-01 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has two primary goals. On the level of theory development, the book clarifies the nature of an emerging "models and modeling perspective" about teaching, learning, and problem solving in mathematics and science education. On the level of emphasizing practical problems, it clarifies the nature of some of the most important elementary-but-powerful mathematical or scientific understandings and abilities that Americans are likely to need as foundations for success in the present and future technology-based information age. Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching features an innovative Web site housing online appendices for each chapter, designed to supplement the print chapters with digital resources that include example problems, relevant research tools and video clips, as well as transcripts and other samples of students' work: http://tcct.soe.purdue.edu/booksULandULjournals/modelsULandUL modeling/ This is an essential volume for graduate-level courses in mathematics and science education, cognition and learning, and critical and creative thinking, as well as a valuable resource for researchers and practitioners in these areas.
Download or read book Enhancing Mathematics Understanding through Visualization The Role of Dynamical Software written by Habre, Samer and published by IGI Global. This book was released on 2013-05-31 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is, by its very nature, an abstract discipline. However, many students learn best by thinking in terms of tangible constructs. Enhancing Mathematics Understanding through Visualization: The Role of Dynamical Software brings these conflicting viewpoints together by offering visual representations as a method of mathematics instruction. The book explores the role of technology in providing access to multiple representations of concepts, using software applications to create a rich environment in which a students understanding of mathematical concepts can flourish. Both students and instructors of mathematics at the university level will use this book to implement various novel techniques for the delivery of mathematical concepts in their classrooms. This book is part of the Research Essential collection.
Download or read book Annotated Compilation of Research on Secondary School Mathematics 1930 1970 Compilation of dissertations Summary and conclusions written by Marilyn N. Suydam and published by . This book was released on 1972 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Exploratory Study of the Effects of Instruction in Heuristics Upon the Mathematical Problem solving Ability and Attitudes of Preservice Elementary Teachers written by Gary Paul Knippenberg and published by . This book was released on 1978 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Exploratory Study of the Use of Problem Solving Heuristics in the Playing of Games Involving Mathematics written by William Harvey Kraus and published by . This book was released on 1980 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Exploratory Study of the Diagnostic Teaching of Heuristic Problem Solving Strategies in Calculus written by John F. Lucas and published by . This book was released on 1972 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt:
