Synopsis
There is today a greater awareness that elementary mathematics is rich in important ideas and that its instruction requires far more than simply knowing the “math facts” and a handful of algorithms. Mathematics courses for teachers must reflect the intellectual depth and challenge of the elementary school curriculum. The Conference Board of Mathematical Sciences (CBMS) recommends that the preparation of mathematics teachers include courses that develop a “deep understanding of the mathematics they teach,” that are designed to “develop careful reasoning and ‘common sense’ in analyzing conceptual relationships, . . . that develop the habits of mind of a mathematical thinker and that demonstrate flexible, interactive styles of teaching” (CBMS, 2000, pp. 7-8).
Judy Sowder, Larry Sowder, and Susan Nickerson recognize and accept the challenge of presenting mathematics to teachers in a manner that addresses these recommendations. In doing so they provide instruction that will lead teachers of mathematics to reconceptualize the mathematics they often think they already know, thus allowing them to develop a deeper understanding of the mathematics they will teach. The authors believe that teachers must know mathematics differently than most people do. Teachers need to know the mathematics they teach in a way that allows them to hold conversations about mathematical ideas and mathematical thinking with their students. A persistent pursuit of explanation is a hallmark of a classroom in which learning is taking place.
A common axiom is that teachers teach the way they were taught. Prospective teachers are unlikely to demonstrate flexible, interactive styles of teaching unless they have experienced mathematics taught this way. Instructors of the Reconceptualizing Mathematics courses, however, may not have experienced such instruction themselves. Thus the authors provide many forms of instructional assistance to help instructors better understand the mathematics their prospective teachers need to know, to begin to model teaching strategies that these prospective teachers will be expected to use in their own classrooms, and to assist them in many ways throughout the course.
Judy Sowder, Larry Sowder, and Susan Nickerson recognize and accept the challenge of presenting mathematics to teachers in a manner that addresses these recommendations. In doing so they provide instruction that will lead teachers of mathematics to reconceptualize the mathematics they often think they already know, thus allowing them to develop a deeper understanding of the mathematics they will teach. The authors believe that teachers must know mathematics differently than most people do. Teachers need to know the mathematics they teach in a way that allows them to hold conversations about mathematical ideas and mathematical thinking with their students. A persistent pursuit of explanation is a hallmark of a classroom in which learning is taking place.
A common axiom is that teachers teach the way they were taught. Prospective teachers are unlikely to demonstrate flexible, interactive styles of teaching unless they have experienced mathematics taught this way. Instructors of the Reconceptualizing Mathematics courses, however, may not have experienced such instruction themselves. Thus the authors provide many forms of instructional assistance to help instructors better understand the mathematics their prospective teachers need to know, to begin to model teaching strategies that these prospective teachers will be expected to use in their own classrooms, and to assist them in many ways throughout the course.
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About the Author
Judith Sowder is a Professor Emerita of Mathematics and Statistics at San Diego State University. Her research has focused on the development of number sense and on the instructional effects of teachers' mathematical knowledge at the elementary and middle school level. She served from 1996 to 2000 as editor of the Journal for Research in Mathematics Education and served a three-year term on the National Council of Teachers of Mathematics Board of Directors. She has directed numerous projects funded by the National Science Foundation and the Department of Education. In 2000 she received the Lifetime Achievement Award from the National Council of Teachers of Mathematics.Larry Sowder is Professor Emeritus of Mathematics and Statistics at San Diego State University. He taught mathematics to preservice elementary school teachers for more than 30 years. His work in a special program in San Diego elementary schools also shaped his convictions about how courses in mathematics for preservice teachers should be pitched, as did his joint research investigating how children in the usual Grades 4-8 curriculum solve "story" problems. He served on teh National Research Council Committee that published Educating Teachers of Science, Mathematics, and Technology(NRC, 2001).Susan Nickerson is an Associate Professor in San Diego State University's Department of Mathematics and Statistics. Her research interest is long-term professional development of elementary and middle school teachers. In particular, her focus is describing, analyzing, and understanding effective contexts that promote teachers' knowledge of mathematics and mathematics teaching."
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