Publication Date: April 11, 2015
Although proportional reasoning is not formally introduced as a topic in the Common Core and other mathematics curricula until 6th grade, introducing its fundamental ideas in the early grades helps students develop essential skills in ratios, percentages, and other proportional representations when they reach the upper grades. The author takes this complex subject and crafts examples and questions that help teachers see the larger purpose in teaching concepts, such as unitizing, and how that understanding is essential for more complex ideas, such as ratios. Teachers and vertical teams can see how the concepts can build year after year. This new resource by well-known professional developer Marian Small suggests questions that are both interesting for students and useful for providing diagnostic information to teachers. Chapters are organized by grade level (K–8) around the Common Core State Standards for Mathematics to help teachers use the resource more easily.
Math teachers can use this resource to help students develop a solid foundation for more proficient and more confident work with multiplicative thinking and proportionality. It will also help math coaches as they assist teachers in their transition to teaching mathematics within the more demanding framework of the CCSS. This book will also help preservice teachers and their instructors as they prepare themselves and their students to understand and teach math with a deep level of understanding.
PROFESSIONAL DEVELOPMENT: Visit Marian Small’s website onetwoinfinity.ca for in-person and online professional development.
Marian Small is the former dean of education at the University of New Brunswick, longtime professor of mathematics education, and bestselling author of Good Questions, Second Edition, More Good Questions, Eyes on Math, Uncomplicating Fractions to Meet Common Core Standards in Math, K–7, and Uncomplicating Algebra to Meet Common Core Standards in Math, K–8. Visit her website onetwoinfinityca for in-person and online professional development.
“The book’s notable strengths are the connections it makes between the early grades and the development of proportional reasoning, the clarity of the writing and organization, and the variety of models it uses to illustrate ideas.”
—Mathematics Teaching in the Middle School
"Once again, Marian Small has created an outstanding resource for anyone working with elementary or middle grades mathematics students. With her trademark 'good questions to ask,' clear explanations of underlying ideas, and rich activities, Dr. Small gets at the heart of ways to correct often misunderstood and poorly taught concepts of proportional reasoning, starting with the rarely mentioned primary level."
—Linda Sheffield, Regents Professor Emerita, Northern Kentucky University