Teaching fractions and ratios for understanding: essential content knowledge and instructional strategies for teachers
"Teaching Fractions and Ratios for Understanding" addresses the urgent need for curriculum materials that cross traditional boundaries to include ... Show synopsis "Teaching Fractions and Ratios for Understanding" addresses the urgent need for curriculum materials that cross traditional boundaries to include many of the elements that are integrated in the teaching/learning enterprise: mathematics content, teacher understanding, student thinking, teaching methods, instructional activities, and assessment. It is meant to push readers beyond the limits of their current understanding of rational numbers, to challenge them to refine and explain their thinking and to make sense--without falling back on rules and procedures they have relied on throughout their lives. All the activities are to be solved using reasoning alone. Although readers may find it difficult to abandon fraction rules and procedures, forcing themselves to work without them will unleash powerful ways of thinking. This is not a textbook as much as it is a resource book. An underlying assumption is that facilitating teacher understanding using the same questions and activities that may be used with children is one way to help teachers build the comfort and confidence they need to begin talking to children about complex ideas. Unlike a textbook that is used to study formal theory and then discarded when it comes to putting ideas into practice, the many problems and activities included to facilitate teacher learning are valuable resources for use in elementary and middle school classrooms. However, no prescriptions are given for incorporating these ideas into instruction. Rather, drawing on her own experience with teachers, which suggests that teachers are thoughtful practitioners, Lamon's premise in this book is that when teachers feel confident in their own understanding, they know how to use new knowledge to inform what they do in the classroom. Each chapter includes Self-Assessment sections that invite the reader to "stop and work these examples before going on;" Activities to help readers try out the new ideas presented and to use them in examples that are not exactly like those shown in the text; and Children's Strategies (excerpts of children's work to give readers a sense of some of the responses they can expect from elementary- and middle-grade students). This book is intended for researchers and curriculum developers in mathematics education, for pre-service and in-service teachers of mathematics, for those involved in the mathematical and pedagogical preparation of mathematics teachers, and for graduate students in mathematics education. The methods and activities it includes have been tested with students in grades 3-8 and with pre-service and in-service teachers and other adults. This text is accompanied by "MORE"--a supplement that is not merely an answer key but a resource that includes in-depth discussions of all the problems in the text; develops and extends discussion of the issues, teaching problems, and other considerations raised in the chapters; and contains additional problems with solutions that instructors may find helpful for assessment purposes and a set of problems that require both good reasoning and computational skills.