Explores the nature of language from a linguistic viewpoint and describes how mathematics can be seen to be a foreign language by students. Describes how natural language reading strategies provide language-specific problems to mathematics teachers. (MDH)

Discusses how student errors can be utilized to understand the nature of the conceptions that underlie students' mathematical activity. Looks at why errors are made in mathematics, how teachers and students perceive errors, and how to use errors in the classroom. (MDH)

Discusses the problem-solving heuristics of examining for special cases, utilizing dimensions to make sense of proposed solutions, and symmetry. Presents examples to illustrate the use of one or combinations of these heuristics. (MDH)

Describes five skills underpinning the understanding of geometry for primary and lower secondary mathematics students. Skill categories identified include (1) visual; (2) verbal; (3) drawing; (4) logical; and (5) application. Gives examples of skills appropriate for Van Hiele levels 1-3. (MDH)

Argues that the basis for communications between teachers and between teacher and student lies in the beliefs that teachers hold about mathematics and problem solving. Proposes a framework for teacher education curricula that describes seven dimensions on which primary mathematics education can be developed. (MDH)

Proposes the utilization of graph theory to solve optimization problems. Defines the notion of spanning trees and presents two algorithms to determine optimization of a spanning tree. Discusses an example to connect towns by power transmission lines at minimum cost. (MDH)

Discusses the differences between teaching for procedural understanding and teaching for conceptual understanding by asking several penetrating, open-ended questions, directed at teachers, about the type of mathematical understanding students are achieving within several examples of classroom situations. (JJK)

Outlines various methods for constructing cardboard polyhedra that can be helpful in the learning of geometric concepts and relationships and can also provide the student with a rewarding, inspiring, and colorful output for display. Includes selected illustrations of suitable construction techniques, as well as finished products. (seven…

Described is the use of story telling as a context to introduce mathematical concepts by providing a model, offering problem-posing situations, stimulating investigation, and illustrating concepts. Examples of appropriate stories are given for the primary and low secondary levels. (MDH)

The actuarial profession is described to provide secondary school mathematics teachers insights into how actuaries use mathematics in solving real life problems. Examples are provided involving compound interest, the probability of dying, and inflation with computer modeling. (MDH)

It is difficult for students to unlearn misconceptions that have been unknowingly reinforced by teachers. The examples "multiplication makes bigger,""pi equals 22/7," and the use of counter examples to demonstrate the numerical property of closure are discussed as potential areas where misconceptions are fostered. (MDH)

Three activities are presented to assess the level of students' geometric understanding according to van Hiele learning model. The activities--Descriptions, Minimum Properties, and Class Inclusion--are applied to the example of classifying quadrilaterals as squares, rectangles, rhombi, or parallelograms. Implications of this assessment are…

A survey study asked Australian experienced teachers during workshops to rate what they believed to be the most difficult aspects of mathematics in grades seven and eight. Problem solving, number sense, and rational numbers were rated as most difficult. The research question provided a catalyst for action in professional development programs. (MDH)