Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

This study aimed to create a constructivist learning environment wherein third-grade students talk to problem solve, which is different from traditional approaches to math learning. The study focused on the group talk and discussions to understand the students' actions and interactions during the process of problem-solving. Fifteen students and…

In the winter of 1965, an experimental course in Elementary Number Theory was presented to a 6th grade class in the Hosmer School, Watertown, Massachusetts. Prior to the introduction of the present material, students had been exposed in class to such topics from the University of Illinois Arithmetic Project as lattices, number lines, frame…

This textbook is a course in elementary arithmetic. It stresses mental as well as written exercises. Addition and subtraction are first presented together, and later multiplication and division.

Using various aspects of mathematical structure as unifying concepts is stressed. Specific examples are given based on the concept of equivalent fractions and on the addition property of equality. (LS)

Allowing students to examine different ways of performing an operation is suggested as a means of increasing their understanding. (MP)

This article focuses on the aspect of mental arithmetic that uses thinking strategies that are effective with large numbers as well as basic facts. Two activities are suggested for lack of the four operations. (MK)

Three game activities are detailed. Informal work with addition and subtraction on a number line and graphing concepts are achieved with two simple dice games, and the distribution of monetary tokens is used to illustrate the division algorithm. (JP)

Masters to be removed and copied are given. The worksheets are designed to reinforce computational skills and the concepts of largest or smallest numbers, as well as to provide practice is using a straightedge. (MK)

This study was an attempt to provide some evidence on the effects of calculator usage with primary-age children. Specifically, the study compared the performance of children who had access to calculators for an extended period of time, and whose teachers used calculators in specified instructional ways, with children who did not have access to…

Five reports from a 2-year study are presented. Frequencies and descriptions of systematic errors in the four algorithms in arithmetic were studied in upper-middle income, regular, and special education classrooms involving 744 children. Children were screened for adequate knowledge of basic facts and for receiving prior instruction on the…

Drill activities for addition, subtraction, multiplication, and division that are derived from the history of mathematics are suggested. (MK)

This textbook is designed to teach the principles of Arithmetical Science as far as they are involved in the elementary processes, and to secure a reasonable degree of accuracy and rapidity in expressing numbers and computing results. This work presents at first the idea of numbers connected with visual representations of objects; afterward, when…

Described are activities and games incorporating a technique of "one step" which is used with children with learning difficulties. The purpose of "one step" is twofold, to minimize difficulties with typical trouble spots and to keep the step size of the instruction small. (Author/TG)

A "flipping" clown figure can be used on a number line to help students conceptualize operations using negative numbers. (SJL)