Learning to Think Mathematically
The Learning to Think Mathematically series provides parents, teachers, and teacher educators with innovative resources and novel strategies to help young learners develop powerful mathematical insights and problem solving strategies. Based on contemporary mathematics education perspectives and research-based practices, these products are designed to help children reinvent significant mathematics. This series was written by Jeffrey Frykholm, Ph.D. Spanish translations by Alejandra Besa, Magíster.
Learning to Think Mathematically with the Rekenrek
Grade level: K–3
This book provides teachers with the theoretical basis, practical knowledge, and expertise to use a powerful mathematical tool called the Rekenrek (also known as the Arithmetic Rack). Building on the idea that children must be able to “see” numbers within other numbers (e.g., 7 might be thought of as “5 and 2 more”), this book helps children recognize number combinations of five and ten, develop a rich sense of numbers between 0 and 20, and build a powerful set of intuitive strategies for addition and subtraction of both single and double digit numbers.
Learning to Think Mathematically with the Rekenrek, Supplemental Activities
Grade level: K–3
This compilation of student-ready activities builds upon the contexts and learning objectives in Learning to Think Mathematically with the Rekenrek. Students solve imaginable, accessible problems motivating the key mathematical principles accessed through the rekenrek model, including cardinality, one-to-one-relationships, part-part-whole relationships, and subitizing.
Learning to Think Mathematically About Multiplication
Grade level: 3–5
This book engages different multiplication contexts and suggests various strategies and models (e.g., the area model, the lattice method, the ratio table) that resonate with those contexts. These models are offered as alternative strategies to the traditional multi-digit multiplication algorithm, which, while efficient, is not inherently intuitive to young learners. The intent of this book to provide students with a wealth of strategies for multiplication and division that can be called upon depending on the problem contexts they may be facing.
Learning to Think Mathematically with the Number Line
Grade level: K–5
This book provides teachers with the theoretical basis, practical knowledge, and expertise to effectively use the number line as a powerful model for mathematical learning in K–5 education. The number line is a common artifact in elementary school classrooms, but is seldom used to its potential. This book helps teachers to implement lesson activities through which children can develop confidence, fluency, and facility with numbers. It also will enable children to develop powerful intuitive strategies for both single and multiple digit addition and subtraction.
Learning to Think Mathematically with the Ratio Table
Grade level: 3–8
This book provides teachers with the theoretical basis, practical knowledge, and expertise to effectively use the ratio table as a powerful model for mathematical learning in K–8 education. The ratio table promotes proportional reasoning, makes use of equivalent fractions, can be a model for percents, functions as a double number line, and also can be an elegant computational tool in contexts that require either multiplication or division.
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