The What Works Clearinghouse (WWC) looked at elementary school math curricula designed to promote math knowledge and skills among elementary school students (average ages 5 to 10 years). Curricula included in this review are replicable, materials-based instructional programs that cover one or more of the following content areas: numbers,…

In this article, the authors offer three definitions of dyscalculia, then describe the background and initial progress of the Harrow Dyscalculia Project. Their project in Harrow is associated with ongoing research into numeracy and brain development led by Brian Butterworth, Professor of Cognitive Neuropsychology at UCL. Pupils from Harrow schools…

Problem-posing abilities of 54 third graders who displayed different patterns of achievement in number concepts and novel problem solving were investigated in this paper. The children were administered a problem-posing pretest followed by an instructional program (for half the sample) and a delayed posttest. Among the findings are the limited…

This book contains activities and projects designed to be congruent with three underlying philosophies: the National Council of Teachers of Mathematics' Curriculum and Evaluation Standards; Howard Gardner's multiple intelligences; and manipulatives, activities, and projects. The introduction contains information about educational reforms; multiple…

Defining better implicit models of children's actions in a series of situations is of paramount importance to understanding how knowledge is constructed. The objective of this study was to analyze the implicit mental models used by children in complex change problems to understand the stability of the models and their evolution with the child's…

Equivalent fractions are usually introduced in fourth grade and reviewed repeatedly in the subsequent grades as the four arithmetical operations are taught. In spite of this repeated instruction, the results are disappointing. This paper reviews some data from previous research documenting the difficulty of equivalent fractions, explains this…

A series of puzzle-type activities combining arithmetic reasoning and geometric figures is described and illustrated. (SD)

The first four chapters of a 14-chapter, three-volume work on arithmetical applications are contained in this document. Each chapter details the "use classes" of one broad arithmetical concept. (A "use class" of a concept is a set of examples of real world uses of the concept which share a common structure). Each chapter…

Chapters 11 through 14 of a 14-chapter, three-volume work on arithmetical applications are contained in this document. Each chapter details the "use classes" of one broad arithmetical concept. (A "use class" of a concept is a set of examples of real world uses of the concept which share a common structure). Each chapter…

On the basis of implications drawn from Piagetian theory, an approach to first-grade arithmetic which eliminated instruction and used only two kinds of activities (situations in daily living and group games) was implemented in an experimental context. Situations in daily living and group games, in contrast to "mechanical" worksheet…

A study was conducted to: (1) observe through a case study approach the exploratory behavior exhibited by 8-year-old boys and girls when calculators were made available in problem-solving situations; (2) investigate changes that occur in the kinds of arithmetical problems children construct following the introduction of calculators; and (3)…

Guidelines are presented for modifying basic instruction of subtraction facts for elementary level learning disabled students. A detailed case study is used to illustrate a five-step structured program: (1) find a way to work it out; (2) add to check; (3) learn the partner facts; (4) study families of facts; (5) review and practice. The selection…

In the fall of 1966, the School Mathematics Study Group embarked upon a four-year longitudinal study of mathematical learning in the primary grades, the Elementary Mathematics Project (ELMA). The primary purpose of the study was to assess children's progress in learning particular mathematical ideas during the beginning school years. This volume…