Mathematics Teaching and Learning


Book Description

The purpose of this research is to identify the categories of South Korean elementary teachers’ knowledge for teaching mathematics. Emerging from the data collected and the subsequent analysis are five categories of South Korean elementary teachers’ knowledge for teaching mathematics: Mathematics Curriculum Knowledge, Mathematics Learner Knowledge, Fundamental Mathematics Conceptual Knowledge, Mathematics Pedagogical Content Knowledge, and Mathematics Pedagogical Procedural Knowledge. The first three categories of knowledge play a significant role in mathematics instruction as an integrated form within Mathematics Pedagogical Content Knowledge. This study also demonstrated that Mathematics Pedagogical Procedural Knowledge might play a pivotal role in constructing Mathematics Pedagogical Content Knowledge. These findings are connected to results from relevant studies in terms of the significant role of teachers’ knowledge in mathematics instruction.




Mathematics Teachers at Work


Book Description

This book compiles and synthesizes existing research on teachers’ use of mathematics curriculum materials and the impact of curriculum materials on teaching and teachers, with a particular emphasis on – but not restricted to – those materials developed in the 1990s in response to the NCTM’s Principles and Standards for School Mathematics. Despite the substantial amount of curriculum development activity over the last 15 years and growing scholarly interest in their use, the book represents the first compilation of research on teachers and mathematics curriculum materials and the first volume with this focus in any content area in several decades.




Diversifying Mathematics Teaching: Advanced Educational Content And Methods For Prospective Elementary Teachers


Book Description

'What one takes away from this book is the notion that there’s a lot of potential to do more with these students, and the book stands as a resource for anyone who shares that opinion … Books like Abramovich’s are a welcome addition to our options as we try to do our best by these students, and by extension, their future students.'MAA ReviewsThe book is written to enhance the preparation of elementary teacher candidates by offering teaching ideas conducive to the development of deep understanding of concepts fundamental to the mathematics curriculum they are to teach. It intends to show how the diversity of teaching methods stems from the knowledge of mathematics content and how the appreciation of this diversity opens a window to the teaching of extended content.The book includes material that the author would have shared with teacher candidates should there have been more instructional time than a 3 credit hour master's level course, 'Elementary Mathematics: Content and Methods', provides. Thus the book can supplement a basic textbook for such a course by extending content and diversifying methods.Also, the book can support graduate level mathematics education programs which have problem-solving seminars/courses in their curriculum. The book is well-informed with (available in English) the mathematical standards and recommendations for teachers from Australia, Canada, Chile, England, Japan, Korea, Singapore, and the United States.




Elementary Mathematics Curriculum Materials


Book Description

The book presents comparative analyses of five elementary mathematics curriculum programs used in the U.S. from three different perspectives: the mathematical emphasis, the pedagogical approaches, and how authors communicate with teachers. These perspectives comprise a framework for examining what curriculum materials are comprised of, what is involved in reading and interpreting them, and how curriculum authors can and do support teachers in this process. Although the focus of the analysis is 5 programs used at a particular point in time, this framework extends beyond these specific programs and illuminates the complexity of curriculum materials and their role in teaching in general. Our analysis of the mathematical emphasis considers how the mathematics content is presented in each program, in terms of sequencing, the nature of mathematical tasks (cognitive demand and ongoing practice), and the way representations are used. Our analysis of the pedagogical approach examines explicit and implicit messages about how students should interact with mathematics, one another, the teacher, and the textbook around these mathematical ideas, as well as the role of the teacher. In order to examine how curriculum authors support teachers, we analyze how they communicate with teachers and what they communicate about, including the underlying mathematics, noticing student thinking, and rationale for design elements. The volume includes a chapter on curriculum design decisions based on interviews with curriculum authors.




Learning Policy


Book Description

Education reformers and policymakers argue that improved students’ learning requires stronger academic standards, stiffer state tests, and accountability for students’ scores. Yet these efforts seem not to be succeeding in many states. The authors of this important book argue that effective state reform depends on conditions which most reforms ignore: coherence in practice as well as policy and opportunities for professional learning. The book draws on a decade’s detailed study of California’s ambitious and controversial program to improve mathematics teaching and learning. Researchers David Cohen and Heather Hill report that state policy influenced teaching and learning when there was consistency among the tests and other policy instruments; when there was consistency among the curricula and other instruments of classroom practice; and when teachers had substantial opportunities to learn the practices proposed by the policy. These conditions were met for a minority of elementary school teachers in California. When the conditions were met for teachers, students had higher scores on state math tests. The book also shows that, for most teachers, the reform ended with consistency in state policy. They did not have access to consistent instruments of classroom practice, nor did they have opportunities to learn the new practices which state policymakers proposed. In these cases, neither teachers nor their students benefited from the state reform. This book offers insights into the ways policy and practice can be linked in successful educational reform and shows why such linkage has been difficult to achieve. It offers useful advice for practitioners and policymakers seeking to improve education, and to analysts seeking to understand it.




Knowing and Teaching Elementary Mathematics


Book Description

The 20th anniversary edition of this groundbreaking and bestselling volume offers powerful examples of the mathematics that can develop the thinking of elementary school children. Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. Along with the original studies of U.S. and Chinese teachers’ mathematical understanding, this 20th anniversary edition includes a new preface and a 2013 journal article by Ma, "A Critique of the Structure of U.S. Elementary School Mathematics" that describe differences in U.S. and Chinese elementary mathematics. These are augmented by a new series editor’s introduction and two key journal articles that frame and contextualize this seminal work.




Active Mathematics Teaching


Book Description




Embracing Mathematics


Book Description

This alternative textbook for courses on teaching mathematics asks teachers and prospective teachers to reflect on their relationships with mathematics and how these relationships influence their teaching and the experiences of their students. Applicable to all levels of schooling, the book covers basic topics such as planning and assessment, classroom management, and organization of classroom experiences; it also introduces some novel approaches to teaching mathematics, such as psychoanalytic perspectives and post-modern conceptions of curriculum. Traditional methods-of-teaching issues are recast in a new discourse, provoking new ideas for making mathematics education meaningful to teachers as well as their students. Co-authored by a professor and coordinator of mathematics education programs, with illustrative contributions from practicing elementary, middle, and high school mathematics teachers, this book is a unique collaboration across all pre-college grades, making it ideal for teacher discussion groups at any level. Embracing Mathematics: integrates pedagogy and content exploration in ways that are unique in mathematics education features textboxes with reflection questions and suggested explorations that can be easily utilized as homework for a course or as discussion opportunities for teacher reading groups offers examples of teachers’ action research projects that grew out of their interactions with the main chapters in the book is not narrowly limited to mathematics education but incorporates curriculum studies – an invaluable asset that allows instructors to find more ways to engage students in self-reflexive acts of teaching Embracing Mathematics is intended as a method text for undergraduate and master’s-level mathematics education courses and more specialized graduate courses on mathematics education, and as a resource for teacher discussion groups.




Enacted Mathematics Curriculum


Book Description

This volume is an outgrowth of the Conference on Research on the Enacted Mathematics Curriculum, funded by the National Science Foundation and held in Tampa, Florida in November 2010. The volume has the potential to be useful to a range of researchers, from established veterans in curriculum research to new researchers in this area of mathematics education. The chapters can be used to generate conversation about researching the enacted mathematics curriculum, including similarities and differences in the variables that can and should be studied across various curricula. As such, it might be used by a curriculum project team as it outlines a research agenda for curriculum or program evaluation. It might also be used as a text in a university graduate course on curriculum research and design. The chapters in this volume are a natural complement to those in Approaches to Studying the Enacted Mathematics Curriculum (Heck, Chval, Weiss, & Ziebarth, 2012), also published by Information Age Publishing. While the present volume focuses on a range of issues related to researching the enacted mathematics curriculum, including theoretical and conceptual issues, the volume by Heck et al. provides insights into different instrumentations used by groups of researchers to study curriculum enactment.