Download or read book Eliciting Elementary Preservice Teachers Mathematical Knowledge for Teaching Using Instructional Tasks that Include Children s Mathematical Thinking written by Lauren Lee Goggins and published by ProQuest. This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A challenge that teacher educators face is how to determine if teacher preparation programs provide preservice teachers with opportunities to develop the mathematical knowledge that teachers use in their practice. This qualitative, interpretive study examines the mathematical knowledge for teaching that four preservice teachers exhibited when they engaged in a set of three instructional tasks that included children's mathematical thinking and were designed to replicate the work of teaching mathematics. Each task largely elicits a different kind of mathematical knowledge for teaching from preservice teachers. In addition, the formats of the children's mathematical thinking examples influence the mathematical knowledge for teaching that is elicited from preservice teachers by the complete set of instructional tasks. This study informs teacher educators how instruction in teacher preparation programs and professional development programs can be developed to measure mathematical knowledge for teaching. And, it advances the current understanding of the mathematical knowledge that is needed in the work of teaching mathematics.
Download or read book Research Advances in the Mathematical Education of Pre service Elementary Teachers written by Gabriel J. Stylianides and published by Springer. This book was released on 2017-11-16 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines new trends and developments in research related to the mathematical education of pre-service elementary teachers, and explores the implications of these research advances for theory and practice in teacher education. The book is organized around the following four overarching themes: pre-service teachers’ mathematics content and mathematics-specific pedagogical preparation; professional growth through activities and assessment tools used in mathematics teacher preparation programs; pre-service mathematics teachers’ knowledge and beliefs; and perspectives on noticing in the preparation of elementary mathematics teachers. Including contributions from researchers working in 11 different countries, the book offers a forum for discussing and debating the state of the art regarding the mathematical preparation of pre-service elementary teachers. By presenting and discussing the findings of research conducted in different countries, the book offers also opportunities to readers to learn about varying teacher education practices around the world, such as: innovative practices in advancing or assessing teachers’ knowledge and beliefs, similarities and differences in the formal mathematics education of teachers, types of and routes in teacher education, and factors that can influence similarities or differences.
Download or read book Learning and Teaching Early Math written by Douglas H. Clements and published by Routledge. This book was released on 2014-05-23 with total page 741 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this important book for pre- and in-service teachers, early math experts Douglas Clements and Julie Sarama show how "learning trajectories" help diagnose a child’s level of mathematical understanding and provide guidance for teaching. By focusing on the inherent delight and curiosity behind young children’s mathematical reasoning, learning trajectories ultimately make teaching more joyous. They help teachers understand the varying levels of knowledge exhibited by individual students, which in turn allows them to better meet the learning needs of all children. Using straightforward, no-nonsense language, this book summarizes the current research about how children learn mathematics, and how to build on what children already know to realize more effective teaching. This second edition of Learning and Teaching Early Math remains the definitive, research-based resource to help teachers understand the learning trajectories of early mathematics and become quintessential professionals. Updates to the new edition include: • Explicit connections between Learning Trajectories and the new Common Core State Standards. • New coverage of patterns and patterning. • Incorporation of hundreds of recent research studies.
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2009-07 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Rethinking Field Experiences in Preservice Teacher Preparation written by Etta R. Hollins and published by Routledge. This book was released on 2015-03-12 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this book is the centrality of clinical experiences in preparing teachers to work with students from diverse cultural, economic, and experiential backgrounds. Organized around three themes—learning teaching through the approximation and representation of practice, learning teaching situated in context, and assessing and improving teacher preparation—Rethinking Field Experiences in Preservice Teacher Preparation provides detailed descriptions of theoretically grounded, research-based practices in programs that prepare preservice teachers to contextualize teaching practices in ways that result in a positive impact on learning for traditionally underserved students. These practices serve current demands for teacher accountability for student learning outcomes and model good practice for engaging teacher educators in meaningful, productive dialogue and analysis geared to developing local programs characterized by coherence, continuity, and consistency.
Download or read book International Handbook of Mathematics Teacher Education Volume 2 written by and published by BRILL. This book was released on 2019-12-16 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tools and Processes in Mathematics Teacher Education describes and analyze various promising tools and processes, from different perspectives, aimed at facilitating mathematics teacher learning/development. It provides insights of how mathematics teacher educators think about and approach their work with teachers.
Download or read book An Exploration of Pre service Elementary Teachers Mathematical Knowledge for Teaching written by Michael Jarry-Shore and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "AbstractMathematical knowledge for teaching, or MKT, is a critically important knowledge of mathematics unique to teachers and teaching. One aspect of MKT, specialized content knowledge (SCK), involves the ability to interpret nonstandard student solutions, represent relevant mathematical content non-symbolically, and explain standard math algorithms (Ball, Thames, & Phelps, 2008). A number of measures are currently available to those seeking to assess teachers' SCK, and still, this knowledge domain has "yet to be fully mapped" (Hill, 2010, p. 537). Nowhere is this lack of mapping more apparent than among pre-service teachers, who, due to a lack of teaching experience, are likely to exhibit SCK that is markedly different from that displayed by their in-service counterparts (Hill, 2010). Teacher practices and dispositions, while not a part of existing frameworks for SCK, are likely to play a key role in shaping the nature of this unique mathematical knowledge. This study sought to examine the nature of 11 pre-service teachers' specialized content knowledge, practices, and dispositions through the use of hour-long structured interviews (Ginsburg, Jacobs, & Lopez, 1998). In each interview, study participants were asked to interpret non-standard student solutions to two math problems, one involving a comparison of fractions and another involving multi-digit multiplication. Data gathered in this study indicate that pre-service teachers, unlike experienced teaching professionals, require greater support in two key aspects of SCK: generating non-symbolic representations and interpreting non-standard student solutions (Hill, 2007; Hill, 2010). Additionally, it would appear as though pre-service teachers would benefit from efforts to foster a flexible disposition, as such flexibility appears to augment one's specialized content knowledge (Hill. Dean & Goffney, 2007). The results of this study will inform teacher educators, who must make difficult choices when deciding how to design courses so as to make efficient use of what little time they are given to prepare pre-service teachers (Ball, Sleep, Boerst, & Bass, 2009; Hill, 2010; Kajander, 2010).Keywords: mathematical knowledge for teaching, specialized content knowledge, disposition, pre-service teacher" --
Download or read book The Best Laid Plans written by Lesley R. Wagner and published by . This book was released on 2003 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Reasoning and Sense Making in the Elementary Grades Prekindergarten Grade 2 written by Michael T. Battista and published by National Council of Teachers of English. This book was released on 2016 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on extensive research conducted by the authors, Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2, is designed to help classroom teachers understand, monitor, and guide the development of students' reasoning and sense making about core ideas in elementary school mathematics. It describes and illustrates the nature of these skills using classroom vignettes and actual student work in conjunction with instructional tasks and learning progressions to show how reasoning and sense making develop and how instruction can support students in that development. Students who can make sense of mathematical ideas can apply those ideas in problem solving, even in unfamiliar situations, and can use them as a foundation for future learning. Without them, students are reduced to rote learning, often experiencing frustration and failure. But what do reasoning and sense making during learning and teaching look like? Each chapter of Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2 explores a different topic that young children encounter in mathematics, demonstrating with actual student work and classroom dialogue how their mathematical knowledge and reasoning ability move through "levels of sophistication" or learning progressions: After opening with a discussion of the nature of reasoning and sense making and their critical importance in developing mathematical thinking, chapter 1 examines how young students attempt to make sense of the concepts of place value and length measurement. Chapter 2 focuses on how early childhood instruction can engage students in mathematical reasoning while helping them construct a rich sense of number and operations. Chapter 3 identifies core algebraic ideas and shows how students can engage with these ideas in ways that not only deepen their understanding of arithmetic but also lays the foundation for the future study of algebra. Children's reasoning and sense making as they decompose and compose geometric shapes--including reasoning about area--is examined in chapter 4. The use of learning progressions to understand students' reasoning and to guide their sense making with appropriate teaching is also discussed. Not just a theoretical discussion, the book also provides specific suggestions for related instructional activities for each topic. Supplementary online resources can be accessed at NCTM's More4U website. Reasoning and Sense Making in the Mathematics Classroom, Pre-K-Grade 2 will be a valuable and practical addition to your professional library.
Download or read book Eliciting Student Thinking in Elementary School Mathematics Classrooms CRESST Report 725 written by Megan L. Franke and published by . This book was released on 2007 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: The importance of student talk in mathematics classrooms figures prominently in curriculum and teaching standards. Student talk is a vehicle for increasing student learning and for helping teachers monitor student understanding and inform student instructional practices. Although researchers have begun to study the moves teachers may make to support students in making their mathematical thinking explicit, sharing out with others and using it as the basis of conversation, much remains to be known about the teacher practices that help students clarify and communicate their mathematical thinking. To learn more about these teacher practices, authors look at what teachers say and do as they engage with their students in mathematical conversation and how students participate in relation to what teachers say and do. This report examines the questions teachers ask and how those questions support students to detail their mathematical thinking. Although all teachers in this study asked students to explain how they solved problems, an important teacher practice for encouraging further student elaboration and giving complete and correct explanations was asking further questions about specific aspects of student answers or explanations. The authors describe the variety of teacher questioning practices and the differences in patterns of student participation that emerged. (Contains 2 footnotes and 7 tables.) [This work was also supported by the Academic Senate on Research, Los Angeles Division, University of California; and the Diversity in Mathematics Education Center for Learning and Teaching (DIME).].
Download or read book Engaging with Mathematics and Learning to Teach An Integrated Approach to Mathematics Preservice Education written by Hilary Povey and published by WTM-Verlag Münster. This book was released on 2017-07-31 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics education research indicates the value of a meaning-making and problem-solving approach to the teaching mathematics in primary and lower secondary classrooms. Yet teachers, most of whom have not experienced such pedagogies in their own mathematics learning, often find it difficult to implement such approaches. Based on over twenty-five years in mathematics preservice education, this book is intended to support preservice tutors and their students in bridging this gap. The book takes six topics from the primary and lower secondary curriculum: place value number systems; the four rules of number; polygons, their properties and their symmetries; natural numbers including factors, multiples, powers and simple number theory; fractions, decimals and irrational numbers; and polyhedra. Each topic is located very briefly in the research literature and its place in or linked to the primary and lower secondary curriculum is discussed. Relevant mathematical activities follow, many of which can transfer directly from the university to the school classroom with very little adaptation. The final topic chapter is rather different. It deals with group theory, an aspect of mathematics which is related to primary and lower secondary mathematics structurally but not in terms of recognisable content. There is an emphasis throughout on the need to reflect on mathematical experience, to develop sensitivity and self-awareness and to promote an approach to the subject that is creative and inclusive.
Download or read book Children s Mathematics written by Thomas P. Carpenter and published by Heinemann Educational Books. This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a focus on children's mathematical thinking, this second edition adds new material on the mathematical principles underlying children's strategies, a new online video that illustrates student teacher interaction, and examines the relationship between CGI and the Common Core State Standards for Mathematics.
Download or read book Learning to Teach Mathematics written by Jian Wang and published by . This book was released on 1998 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Preservice Teachers Questioning in Elementary Students Mathematical Problem Solving written by Yi-Jung Lee and published by . This book was released on 2019 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quality of teacher questioning affects the extent of its utilization, particularly in a dynamic teacher-student interaction. I first analyze 13 preservice teachers' questioning moves while elementary school students were engaged in mathematical problem solving. I then examined six preservice teachers' questioning practices on whole-number arithmetic tasks in their single-student mathematical field experiences (SSMFE) and focused on the construction and functioning of teacher-student interactional turns to describe the functions of interactional turns and patterns. Data were collected in the form of observations, video recordings, and course assignments and analyzed using theme-based coding from an integrated framework including categories of questioning moves and interactional patterns. The findings regarding questioning moves revealed four influential features in preservice teachers' questioning: (a) flexibility in the setup, (b) limited extent of inquiry, (c) non-specific probing questions, and (d) neglect of the child's unexamined but valuable strategies. The analyses show that 1) Task Clarification (TC) moves were successes when teachers provided flexible support in questioning, and 2) Procedural Understanding (PU), Making Connections (MC), Rationale Behind a Strategy (RA), and Alternative Strategy (AS) moves resulted in deviated from the contextual features and mathematical relationship in problem solving and indicate that the preservice teachers' functional moves have potential to elicit multidimensional facets of students' mathematical thinking and yet may not be enacted competently in mathematical problem solving. These findings not only detail the conditions for enacting functional moves but also contribute to better document the successes and struggles a functional move prompted. Based on the findings, suggestions for developing a practice-based training curriculum to enhance the cultivation of teacher questioning are presented. In addition, how to effectively utilize student-produced discourse to inform teacher questioning strategies in early field experiences has important implications for curriculum designers, teacher education programs, and for teacher educators and researchers.
Download or read book Preservice Teachers Developing Mathematical Knowledge for Teaching written by Jennifer L. Edelman and published by . This book was released on 2014 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This descriptive study examines the elements of mathematical knowledge for teaching that preservice teacher candidates exhibited as they planned, taught, and reflected on a mathematics lesson that integrated children's literature. A collective case study design was used in which three groups were selected from the total population of 10 groups; the groups were selected based on demographics and in an effort to illustrate the widest varieties of experiences during the study. Data for each group consisted of written lesson plans, observations of enacted literature-based lessons, lesson artifacts, and written reflections on the lessons. Data were analyzed for elements of knowledge of content and students, knowledge of content and teaching, and knowledge of content and curriculum. Additionally, the procedures each group used to select their book were analyzed. A second cycle of coding was applied to connect the findings of this study with the existing literature on developing mathematical knowledge for teaching and the effects of using children's literature in mathematics teaching and learning. This study illustrates the need for further development of candidates' ability to locate mathematical concepts in children's literature, as well as the need for supporting candidates' critical analysis of curricular materials and mathematical representations to find the best possible method for teaching various mathematical concepts. Recommendations for future research are included.
Download or read book The Effects of a Model Developmental Mathematics Program on Elementary and Middle School Preservice Teachers written by Lindsey N. Gerber and published by . This book was released on 2012 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teacher quality is instrumental in improving student performance. Unfortunately, discrepancies between teacher preparation programs and national and state K-12 student standards have contributed to the difficult task of producing quality teachers. The contemporary mathematics education paradigm used at most colleges and universities relies on instructors transmitting mathematical content knowledge to students through didactic discourse; whereas, research suggests that preservice teachers need to be taught using the types of instruction emphasized in grades K-12 state and national standards-standards-based best practices. The developmental mathematics program at Texas State University implements these standards-based best practices via the Algorithmic Instructional Technique (AIT) and the Concrete to Representational to Abstract (CRA) models, thereby exposing preservice teachers to pedagogy in conjunction with mathematics content. To determine if the Model Developmental Mathematics Program (MDMP) course(s) contribute to preservice teachers' mathematical knowledge for teaching and positive disposition, this study compared elementary and middle school preservice teachers on the MDMP track to those on the College Algebra track. These groups' mathematical knowledge and disposition were compared based on their scores on the Early Indicators of Effective Teachers instrument, a modified Mathematical Knowledge for Teaching (MKT) assessment and a lesson plan writing activity. In addition, the researcher conducted interviews with the participants to evaluate their pedagogical, content, and pedagogical content knowledge and disposition. For further investigation, case study analyses were performed on four selected MDMP track participants.
Download or read book Building Support for Scholarly Practices in Mathematics Methods written by Signe E. Kastberg and published by IAP. This book was released on 2017-09-01 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building Support for Scholarly Practices in Mathematics Methods is the product of collaborations among over 40 mathematics teacher educators (MTEs) who teach mathematics methods courses for prospective PreK?12 teachers in many different institutional contexts and structures. Each chapter unpacks ways in which MTEs use theoretical perspectives to inform their construction of goals, activities designed to address those goals, facilitation of activities, and ways in which MTEs make sense of experiences prospective teachers have as a result. The book is organized in seven sections that highlight how the theoretical perspective of the instructor impacts scholarly inquiry and practice. The final section provides insight as we look backward to reflect, and forward with excitement, moving with the strength of the variation we found in our stories and the feeling of solidarity that results in our understandings of purposes for and insight into teaching mathematics methods. This book can serve as a resource for MTEs as they discuss and construct scholarly practices and as they undertake scholarly inquiry as a means to systematically examine their practice.
