A Focus on Fractions is a groundbreaking effort to make the mathematics education research on how students develop their understanding of fraction concepts readily accessible and understandable to pre- and in-service K– 8 mathematics educators. Using extensive annotated samples of student work, as well as vignettes characteristic of classroom teachers’ experiences, this book equips educators with the knowledge and tools to revealstudents’ thinking so that they can modify their teaching and improve student learning of fraction concepts. A Focus on Fractions 2nd edition includes sections on the Common Core State Standards for Mathematics and the Ongoing Assessment Project (OGAP) Fraction Framework integrated into each chapter as well as a new chapter on the OGAP Fraction Progression and how it can be used for formative assessment purposes. This updated edition assists teachers in translating research findings into their classroom practice by conveying detailed information about how students develop fraction understandings. Additional images and examples serve to flesh out and supplement the newly-introduced concepts in this updated and expanded edition.
"…Readers will find children's work presented in the book to be interesting and sometimes intriguing. The work provides insights into difficulties understanding fractions and ways to help children develop a better understanding of concepts. Primarily because of extensive samples of student work, this is a valuable book for mathematics educators involved in K-8 classrooms….Recommended."--CHOICE
"To watch teachers interact with the research and practical suggestions in this book is exhilarating. The real joy, however, is seeing them use this learned knowledge as they instruct their students. This is a book for all of us who have struggled to help students make sense of fractions."--Mary Montgomery Lindquist, Fuller E. Callaway Professor of Mathematics Education, Emeritus, Past President of the National Council of Teachers of Mathematics
"This book is a tour de force in relating research and practice in mathematics education, and as such it should also be of great interest to researchers and graduate students in the field."--Edward A. Silver, William A. Brownell Professor of Education, University of Michigan
1. Developing Understanding of Fractions through Visual Models
2. Fractions are Quantities
3. What is the Whole?
5. Comparing and Ordering Fractions
6. Number Lines and Fractions
7. The Density of Fractions
8. Equivalent Fractions and Comparisons
9. Addition and Subtraction of Fractions
10. Multiplication and Division of Fractions
11. The OGAP Fraction Framework