Skills and understanding of operations with negative numbers, which are typically taught in middle school, are crucial aspects of numerical competence necessary for all subsequent mathematics. To more swiftly and coherently develop the field's understanding of how to foster this critical competence, we need shared measures that allow us to compare…

According to social dilemma theory, students may be characterized as being indifferent to reciprocal behavior and disengaged from interacting with the board gaming process. Given a common goal, students' prosociality can affect the collective efficacy and goal achievement motivation that reflects their flow experience in a cooperative-competitive…

During a time when students are accessing instruction virtually because of COVID-19, reflecting on the sixth of the Standards for Mathematical Practice (SMP 6) is a vital step for educators to take. Although the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010) identifies SMP 6 as Attend to precision, associated expertise…

The author explains how "structured material such as the Colour-Factor Set can show all the properties, patterns and characters of numbers. Given the mastery over numbers with which these materials provide children, he condemns teachers who require children "to learn multiplication tables by rote and the so-called four rules by…

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.

The document presents a criterion referenced test of basic math skills, including division, multiplication, addition, subtraction, fractions, decimals, time, and measurement. (DLS)

This book explores how primary school children with dyslexia or dyspraxia and difficulty in math can learn math and provides practical support and detailed teaching suggestions. It considers cognitive features that underlie difficulty with mathematics generally or with specific aspects of mathematics. It outlines the ways in which children usually…

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…

Presented is a paradigm for teaching basic and semibasic arithmetic facts to children with arithmetic difficulties, in which the student progresses from the use of concrete materials such as blocks, to the use of diagrams such as tally marks, to a reasoning process, to responding in an automatic manner. (DLS)

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

This book provides regular classroom and special education teachers with alternative, individualized methods of teaching math computation skills. Learning activities are designed to appeal to auditory, visual, and kinesthetic learning modalities. Six mathematics topics addressed include modeling addition and subtraction, basic facts for addition…

The document presents the final report of the Initial Learning in Mainstreaming Project, which developed and tested instructional techniques in 14 specific mathematics skill areas with 429 handicapped and normal elementary school students in Grace and Soda Springs, Idaho. Skill areas included addition facts; subtraction facts; carrying…

This book is a compilation of recent research on the development of multiplicative concepts. The sections and chapters are: (1) Theoretical Approaches: "Children's Multiplying Schemes" (L. Steffe), "Multiplicative Conceptual Field: What and Why?" (G. Vergnaud), "Extending the Meaning of Multiplication and Division" (B. Greer); (2) The Role of the…