An outline for the development of concepts of area is given for the pre-middle school to post-middle school level. Learning activities are suggested. (DT)

A method is explained for using right triangles on a geoboard for determining the greatest common factor and least common multiple of two numbers. (DT)

Instructions are given for making a solid from unit cubes joined face to face. Activities lead to design and construction of the SOMA cube, along with other cube puzzles. (DT)

Plans for an international survey examining the areas of mathematics curricula, classroom processes, and changes in mathematics education since 1964 are discussed. Several reasons for U.S. participation in this survey are suggested. (DT)

A Mira is described, then several uses of the Mira are suggested. (DT)

There are two purposes in this study. One is to compare how 7th and 8th graders reason on linear and quadratic geometric number patterns when they have not learned this kind of tasks in school. The other is to explore the hierarchical relations among the four components of reasoning on geometric number patterns: understanding, generalizing,…

Three hundred and twenty-four middle school students considered a group of three graphs in a newspaper article about boating deaths. The graphs contained discrepancies and the students were asked to "comment on unusual features." This form of questioning produced a distribution of responses surprising to the authors and perhaps…

In a previous study, we posited a link between Chinese sixth grade students' problem solving and problem posing based on a pattern-formation strategy (Cai & Hwang, 2002). A similar parallel structure between problem solving and problem posing did not obtain for the U.S. sixth graders in the study. The present study attempts to locate this type of…

Can textbook exercises be transformed into problem solving activities that encourage students to develop mathematical thinking? This study documents what high school students showed when they were explicitly asked to use technological tools to examine and solve a routine problem from different angles or perspectives. In this process, students…

A horizontal translation of a function is the focus of this study. We examine the explanations provided by secondary school students and secondary school teachers to a translation of a function, focusing on the example of parabola y = (x - 3)[superscript 2] and its relationship with y = x[superscript 2]. The participants' explanations focused on…

The secondary technical schools of the United States, because of their heterogeneity, present peculiar difficulties to an investigation along the lines laid down by the International Commission. While such schools have existed for many years, it is particularly within the last decade that a great increase in their numbers has taken place, for it…

Describes a system of grading and grade reporting adopted at the Chapel Hill-Chauncy Hall School, Massachusetts, for classes in science and mathematics. Attempts to make grades more truly indicators of a level of performance by pointing out an individual's strengths and weaknesses in a given subject area. (JR)

This article discusses the development and operation of a mixed-ability, individualized mathematics project. The report is divided into five sections: problems and successes, SMP workcards, continuing development, questions of method, and more workcards. The workcards form a major component of the program. (LS)