Lists questions and answers for mathematical investigations that teachers should ask when they consider using alternative approaches to teach new content. Presents an example of a mathematical investigation on concepts of area, symmetry, pattern, function, algebraic rules, and Pythagorean theorem. Argues that investigations offer opportunities for…

Presents activities on estimation, scaling, area of nonstandard shapes, algebraic thinking, and real-life situations using the United States of America. These activities make it possible to integrate mathematics and social studies. Uses technology by employing geometry software packages such as The Geometer's Sketchpad, Cabri, and Geometric…

Describes several short geometry tasks that go beyond the simple recognition of figures and properties. Presents scoring rubrics and questions that might be useful to middle school teachers developing short open-ended questions that encourage and assess students' thinking. (ASK)

Mathematics in textbooks and indeed in conventional classrooms is often presented as exercises or worksheets in which the mathematics itself has been processed into a form that is easily digested. This McDonald's version of mathematics ensures that the mathematical skill or technique is laid bare and typically the sole focus of attention. In this…

This book reviews alternative assessment. Suggestions include portfolios, interviews, observations, journals, and tests utilizing various rubrics. This book contains suggestions and materials that teachers can use to assess students' progress in problem solving, reasoning, and communication. Many performance tasks and problem-specific rubrics for…

In a cooperative research program, classroom teachers and university researchers developed and implemented a contextualized performance-based assessment in mathematics. The assessments were intended to model what students may do in the course of daily activity and designed to assess problem solving, and conceptual and procedural understanding.…

Describes typical student strategies for counting cubes in cube buildings and explains why these problems are difficult for students. Suggests instructional tasks that can help students develop more powerful ways of thinking about such problems. Lists two action research ideas related to this issue. (ASK)

The National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards puts great stress on the mathematical processes of problem solving, communication, reasoning, and making connections. NCTM standards also emphasize new and emerging content areas for middle school students such as algebra, data analysis, and probability.…

In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the "Butter Beans Problem" and the "Airplane Problem"). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data,…

The first volume of the 29th annual conference of the International Group for the Psychology of Mathematics Education contains plenary lecture and research forum papers as listed below. Short oral communications papers, poster presentations, brief summaries of discussion groups, and working sessions are also included in the volume. The plenary…