A concrete approach to prime numbers is presented using rectangles and triangles to construct a building for each number so that each story represents a pair of factors and the triangular-shaped roof represents the number. (MP)

The representation of equivalent fractions is traditionally illustrated by diagrams showing division of units into parts. A second approach using linear graphs is suggested. (SD)

Noitcarf numbers provide a simulation activity that allows teachers or education students to gain an understanding of the feelings of students who are taught mathematics by a "rules" method. They are actually an abstract presentation of operations with fractions. (MK)

National tests, an influential assessment practice in many countries in East Asia, are often blamed as obstacles to good instructional practices. In this paper, the positive impact of assessment, national tests in particular, is discussed using the case of Singapore. The first part of the paper includes an analysis of items from the primary grade…

This article describes the positive impact of Montessori manipulative materials on four seventh grade students who qualified for academic intervention services because of previous low state test scores in mathematics. This mathematics technique for teaching multi-digit multiplication uses a placemat-sized quilt with different color-coded squares…

Each year, more teachers learn about the successful intervention program known as Math Recovery (USMRC 2008; Wright 2003). The program uses Steffe's whole-number schemes to model, understand, and support children's development of whole-number reasoning. Readers are probably less familiar with Steffe's fraction schemes, which have proven similarly…

The present study focused on two main goals. One was to test the "representational mapping hypothesis": The greater the transparency of the mapping between physical materials and desired internal representations, the greater the learning of the desired internal representation. The implication of the representational mapping hypothesis in the…

This paper discusses some issues that arose in the context of a three-year research project on Indigenous mathematics teacher education in the Northern Territory of Australia. The project was based on the premise that Indigenous student numeracy outcomes are more likely to be improved where students can work on key number ideas and strategies in…

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…

Some benefits of helping learners think in prime numbers are detailed. Reasons for the decay of this ability are described, with short division presented as one activity which should be reintroduced in schools. (MNS)

Presented is an example of how a child adopted an incorrect method for solution to arithmetic sentences. Methods for detecting and correcting this behavior are discussed. (JP)

The teaching of numeral representations other than decimals is seen as a necessary and important step in the education of pupils in computing. Basic arithmetic procedures for binary, octal, and hexidecimal bases are discussed. (MP)