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.




The Mathematics Education of Elementary Teachers


Book Description

This book is an edited volume addressing specific issues of significance for individuals involved with the undergraduate mathematics content preparation of prospective elementary teachers (PSTs). Teaching mathematics content courses to this group of students presents unique challenges. While some PSTs enter their teacher preparation with weak mathematical skills and knowledge, many also hold negative attitudes, anxiety, and misguided beliefs about mathematics. This book is designed to support instructors who teach these students in mathematics content for elementary teachers courses. Elementary teachers need a richly developed understanding of the mathematics they are teaching in order to teach it effectively. Providing them with the needed preparation is difficult, but can be eased with a solid understanding of the mathematical concerns and limitations PSTs bring to the learning of mathematics and a familiarity with the standards and curricula topics PSTs will be expected to teach. Chapter One makes the argument that elementary mathematics is not trivial. This is followed by an analysis of four central issues related to the mathematical preparation of elementary teachers, specifically: (1) selecting/creating/modifying and implementing mathematical tasks (2) noticing/understanding children’s ways of thinking as a foundation for learning mathematics, (3) developing mathematical habits of mind in PSTs, and (4) understanding the role affect plays in the mathematical learning of PSTs. The final chapter presents three international examples of programs that currently consider these factors in the implementation of their courses.




Relearning Mathematics


Book Description

This book is grounded in the author’s experiences of teaching mathematics for prospective elementary school teachers and conducting research on their understanding of mathematical concepts. It is a reflection on practice and an attempt to cope with a double challenge: that of a teacher, in helping prospective teachers make sense of mathematics, and that of a researcher, in an attempt to understand and describe the challenges faced by students. This work fits within the current community interest on teacher education and provides a novel focus, with both theoretical and practical considerations. The central claim in this book is that encounters with mathematical content by prospective elementary school teachers constitute relearning, rather than learning, of mathematics. The specific focus is on topics related to elementary number theory (e.g. divisibility, prime factorization), which is referred to as a “forgotten queen” (following Gauss’ reference to number theory as a queen of mathematics). This is the content area that has not received significant attention in mathematics education research. The book can be summarized as an attempt to address the following questions: What is relearning of mathematical content and how is it similar to or different from learning? What are the examples of specific mathematical topics or concepts that require relearning? What pedagogical approaches can support relearning? The detailed analysis of research data and pedagogical approaches presented in the book are intertwined with stories of personal experiences of the author, which makes the reading not only intellectually stimulating but also enjoyable.




Mathematics Content for Elementary Teachers


Book Description

THE book for elementary education mathematics content courses! Designed to help prospective teachers of elementary school mathematics learn content beyond the rote level, this text stimulates readers to think beyond just getting the problem right and fosters their development into thoughtful, reflective, self-motivated, life-long learners. It stresses the what and why of elementary school mathematics content. Hints are provided about how to teach the content but this is mostly left to courses and texts that are dedicated to that purpose. The text is organized around the National Council for Teachers of Mathematics' Principles and Standards for School Mathematics. The Standards dictate the basic sections of the text. Within each section, appropriate specific topics are developed, intertwined with technology, problem solving, assessment, equity issues, planning, teaching skills, use of manipulatives, sequencing, and much more. In addition, major focal points of the Standards are emphasized throughout: effective teachers of mathematics should be able to motivate all students to learn, should understand the developmental levels of how children learn, should concentrate on what children need to become active participants in the learning environment, and should be engaged in ongoing investigations of new mathematical concepts and teaching strategies. Mathematics Content for Elementary Teachers is based on several fundamental premises: *The focus of mathematics education should be on the process, not the answer. *Elementary teachers should know the mathematics content they are teaching, know more than the content they are teaching, and teach from the overflow of knowledge. *It is important for teachers to be flexible in allowing students to use different procedures--teaching from the "overflow of knowledge" implies knowing how to do a given operation more than one way and being willing to examine many different ways. *Teachers need to learn to carefully cover the topics to be taught, to reflect upon them, and to be able to organize them. To help prospective elementary teachers concentrate on the mathematics content they will be expected to teach and begin to build the foundation for the methods they will use, this text includes only elementary mathematics content and does not address middle school concepts. Pedagogical features: *The text is organized according to NCTM Standards. *An informal writing style speaks directly to readers and is geared to pre-service teachers. *Focus is given to multiple methods of problem solving at four developmental levels. *Questions, exercises, and activities are interspersed throughout each section rather than gathered at the end of each chapter. *Complete solutions for exercises are provided.




Mathematics Teacher Education in the Public Interest


Book Description

Mathematics teacher education has a critical role to play in preparing teachers to put at center stage goals to support equity in mathematics education and to diversify student interest and participation in mathematics. These goals must also resonate with broader public interest goals to improve educational and social conditions both in the U.S. and abroad. The Mathematics Teacher Education in the Public Interest book aims to support mathematics teacher educators to prepare teachers with new knowledge and skills to support all students to learn mathematics and to become informed, engaged, and critical citizens within their community, nation, and world. While internationally there is considerable interest among mathematics educators in issues of equity and social justice, the literature on mathematics teacher education for equity and social justice thus far has been very limited.The book provides theoretical discussions on the need for equity and social justice emphases in mathematics teacher education, as well as practical examples from mathematics teacher educators, documenting their own professional efforts to center practices on equity and social justice. Section emphases include critical perspectives on mathematics teacher education, the use of equity and social justice-themed activities in mathematics teacher preparation courses, and issues of identity and community and cultural contexts in mathematics teacher education. In addition syntheses of major ideas of the book are offered by experienced researchers.




Specialized Understanding of Mathematics


Book Description

This dissertation study informs the field on how, when and where a specialized understanding of math (SUM) might be developed within a teacher education program by focusing on the three following research questions and related methodology. 1) What are the strengths and weaknesses in prospective elementary teacher's specialized understanding of mathematics as they enter their mathematics methods course? The Number and Operation and Geometry items from the Content Knowledge for Teaching Mathematics instruments, which have been developed at The University of Michigan's Learning Mathematics for Teaching Project, were administered to 244 prospective elementary teachers at four universities during the first two weeks of the mathematics methods course. An item analysis sheds light on areas of strengths and weaknesses, and a statistical analysis was conducted to see any relationships between content understanding and quantity and type of content courses. A relationship was found between participants who took specialized content courses and the pretest scores. Another interesting finding was that simply taking more mathematics content courses is not related to higher scores. 2) Does the specialized understanding of mathematics change as they take the mathematics methods course? The CKTM items were administered as a post test during the last two weeks of the methods course and compared with the pre test to look at changes, both as a paired samples t test and an item analysis. Growth in SUM was found between the pretest and posttest. 3) What learning opportunities during the methods course may improve the specialized understanding of mathematics of prospective elementary teachers? Interviews were conducted with mathematics methods instructors who saw significant growth on specific items. The general philosophy of the course, as well as specific learning opportunities that may have helped understanding in the specific items that saw growth were explored, and a framework was created of learning opportunities that may impact understanding of mathematics. The learning opportunities that seem to add to improved SUM include readings, communication, experiencing children's mathematical thinking, mathematics activities, manipulatives, and field experiences.




Research Advances in the Mathematical Education of Pre-service Elementary Teachers


Book Description

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.




International Handbook of Mathematics Teacher Education: Volume 2


Book Description

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.




Knowing and Learning Mathematics for Teaching


Book Description

There are many questions about the mathematical preparation teachers need. Recent recommendations from a variety of sources state that reforming teacher preparation in postsecondary institutions is central in providing quality mathematics education to all students. The Mathematics Teacher Preparation Content Workshop examined this problem by considering two central questions: What is the mathematical knowledge teachers need to know in order to teach well? How can teachers develop the mathematical knowledge they need to teach well? The Workshop activities focused on using actual acts of teaching such as examining student work, designing tasks, or posing questions, as a medium for teacher learning. The Workshop proceedings, Knowing and Learning Mathematics for Teaching, is a collection of the papers presented, the activities, and plenary sessions that took place.