As students have struggled to use the "chip model" (i.e., red and yellow chips representing positive and negative numbers) to model integer addition and subtraction and have found it confusing, the authors developed a series of activities based on adding and removing opposite objects to and from a boat to better help students in this…

Reimagining elementary mathematics pedagogy using a three-step process--See It, Say It, Symbolize It--author Patrick L. Sullivan provides a guide for developing a dynamic and flexible understanding of numbers and operations. By helping students develop a language that is consistent across concepts and connecting it to what is seen and symbolized,…

According to National Council of Teachers of Mathematics (NCTM), students must develop a conceptual understanding of place value by second grade to understand that mathematics processes are more than a set of procedural steps. Yet, students with learning disabilities in mathematics typically struggle to understand place value in a deeper,…

Argues that number concepts are not single-faceted ideas that children either have or do not have. Suggests that number concepts can be broadened by helping children develop a collection of relations. Examples of classroom activities are included. (PK)

Describes a number line activity based on students' individual timelines to help students understand the concepts of integers and rational numbers. Middle school students and their parents construct a number line using positive and negative rational numbers to represent dates of events before and after the student's birth. (KHR)

A series of nine activities that illustrate prime factorization and other elementary number theory ideas in concrete, representative, and symbolic form are described. (MNS)

Two major ways to view the numbers to 100 are counting by ones and grouping by tens and ones. Research suggests that early understanding of numbers comes from counting and that place value instruction cannot be hurried. (PK)

Demonstrates the consequences of teaching rules without understanding using examples from two 3rd grade children. Suggests alternative instructional strategies. (KHR)

Describes seven estimation and counting activities appropriate for an early childhood classroom. Includes suggested methods for going beyond the prescribed activities. (PK)

Suggests ways to increase students' computational fluency using concrete materials, engaging tasks, and reflection time to increase number automaticity, flexibility in thinking about numbers, and use of efficient problem-solving strategies to find sums and differences. (Author/NB)

The inertial balance is one device that can help students to quantify the quality of inertia--a body's resistance to a change in movement--in more generally understood terms of mass. In this hands-on activity, students use the inertial balance to develop a more quantitative idea of what mass means in an inertial sense. The activity also helps…

Children's literature can play a significant role in integrating math and science concepts into real-world applications. One particularly delightful selection is "Cucumber Soup" (Krudwig, 1998). This book can create a context--making cucumber soup--for weighing and for a real-life on adding fractions. This kind of learning context takes children…

Specific suggestions for teaching young children (ages 5-7) mathematical principles are offered, covering such concepts as addition, subtraction, multiplication, division, arithmetical laws, and utilizing a story to teach various mathematical concepts and skills. (DB)

Extracts from "Experimenting with Numbers" by Margaret Stern demonstrate the use of Stern Blocks to develop the conceptual base on which learning disabled students can build further mathematical skills. (DB)

This paper provides some guidance as to what to listen for to help students make sense of expressions in ways that connect to their ideas and honestly address the mathematics of rational numbers. It offers a reasonable initial answer to the question, "Where do students' ideas about fractions and ratios come from, and how can we work productively…