Examines several uses of the word cancel and suggests alternative terminology. In particular, arithmetic and algebraic examples are used to illustrate problems associated with the term cancel. (PK)

Defines and discusses number sense. Suggests a variety of activities appropriate for primary students that will help develop number sense. (PK)

Defines and supports investigative mathematics for schools. Presents several results of an investigation of Fermat's Last Theorem. (PK)

Classroom ideas for teaching area and perimeter concepts are presented. Squares, circles and other shapes are examined. Further explorations are suggested. (PK)

Proportion problems were given to pupils in grades 3-5. Success rates were high, with elementary strategies based on addition often used. Familiarity with the use of ratios in the context, the presence of a mixture, and the use of manipulatives were variables that influenced performance. (Author/MNS)

Outlines two mathematics teaching strategies: the exploration/discovery approach to mathematical concepts, and the use of pair group problem-solving. These require teachers to shift from the traditional role of lecture/demonstrator to a role demanding new skills in planning and facilitating student work. Includes 10 references. (MD)

Suggestions for using microcomputers in statistics instruction are described, with programs that a seven-year-old could write using LOGO. (MNS)

This sampler presents assessment tasks that are appropriate for use with students from age 4 through age 8. The book provides teachers of primary grades mathematics with examples of assessment tasks that reflect the various ways assessments can be used prior to, during, and following mathematics instruction. Teachers can then consider the …

A glyph--short for hieroglyphic--is a form of picture writing that conveys information. This book uses 10 glyphs to teach math concepts that are linked to the new NCTM Standards. There are four key parts to each glyph: (1) a legend (or survey questions); (2) directions for the teacher that tell students what to draw, color, or write based on…

We compare the activity of young children using a microworld and a JavaScript relational calculator with the literature on children using traditional calculators. We describe how the children constructed different meanings for the equal sign in each setting. It appears that the nature of the meaning constructed is highly dependent on specificities…

The broad goal of this report is to describe a form of knowing and a way of participating in mathematics learning that contribute to and further alternative views of transfer of learning. We selected an episode with an undergraduate student engaged in a number of different tasks involving a physical tool called "water wheel". The embodied…

This study reports the cognitive processing of a Year 8 female student (Kerri) during a test, and during her subsequent homework as she consolidated as part of abstracting; a topic of recent research interest. This case adds to the body of knowledge about how constructing and consolidating can occur simultaneously. The analysis captured the…

This paper adds to the research studies on prospective elementary school teachers' mathematics knowledge with findings on proportional reasoning. In addition to analyzing prospective elementary school teachers' solution strategies for solving a missing value proportion task, it also examines the nature of the drawings and writing they used to…

In this paper we report on a case study of a university student (third year of Mathematics course). She was engaged in proving a statement of elementary number theory. We asked her to write the thoughts that accompanied her solving process. She was collaborative and her protocol is suitable to study the interrelation between affect and cognition.…

As part of a research project on students' understanding of variability in statistics, 272 students, (84 middle school and 188 secondary school, grades 6-12) were surveyed on a series of tasks involving repeated sampling. Students' reasoning on the tasks predominantly fell into three types: additive, proportional, or distributional, depending on…