This research study presents the PGBE model for teaching and learning percentages with students of Grade 7 when their cognitive development enables the conceptual understanding of percentages as proportional statements, and offers the possibility for more effective matching of them with fractions and decimal numbers. The abbreviation PGBE presents…

In a 1-hour teaching interview, 20 children (aged 7 to 11) discovered how to tell whether objects might be made of the same material by using ratios of measures of weight and size. We examine progress in the children's reasoning about measurement and proportional relations, as well as design features of instruments, materials, and tasks crafted to…

Ben, a good mathematics student, participated in a seven-week study. Describes three tasks that reflect impact of textbooks, real-life connections, and mathematical symbols. Shows that Ben's notion of one-half was task-dependent, concrete, and based on physical actions. (NI)

Mathematical concepts presented within disciplines outside mathematics are either assumed to be already familiar to the students, or else, they are regarded as being peripheral to the appreciation of the content of the nonmathematical lesson. Because it is routinely included without regard for possible students' interpretations, the mathematical…

This study sought to determine the basis for young children's understanding of fundamental addition and subtraction processes, and to expose any limitations on such arithmetic reasoning. Thirty-six two-year-olds and 36 three-year-olds participated in six experiments which examined children's relational quantity judgments about pairs of arrays in…

Analyzed are the different stages in the conceptual evolution of infinity as developed historically through the work of Bolzano and Cantor. Results of a study of 18 to 20 year old's concept of infinity prior to instruction produced aspects of the passage between conceptual levels of infinity. (MDH)

Presents computer approach formulated within a framework of versatile thinking designed to overcome obstacles to understanding algebra. Results from related studies comparing the computer and traditional approaches taught to 11, 12, and 13 year olds showed that the computer approach significantly improved the understanding of higher order concepts…

Matrix tasks designed to assess the logical properties of multiple classification and multiple seriation were administered to 105 first, third, and fifth grade children. The tasks included cross-class and double series matrices, each of which had a reproduction and a transposition instructional set, and a revised set of cross-class and double…

This practicum addresses the need to organize a structured problem solving program for fifth and seventh grade students. The improvement of the students' problem solving skills and the enhancement of students' attitudes toward problem solving in mathematics were the main goals. The program implemented consisted of a structured problem solving…

The researcher conducted a six-month ethnographic study as an apprentice carpenter in Cape Town, South Africa, to document the valid mathematical ideas that are embedded in the everyday woodworking activities of a group of carpenters. A secondary objective was to examine and to give a firsthand account of the teaching and learning of mathematical…

Recent calls for mathematics instruction reform recommend that a problem-solving inquiry-oriented (PSIO) classroom environment be established. Students, however, may view mathematics as a static, ruled-based discipline that runs counter to the PSIO approach. A study examined the student/teacher interactions as seen from the viewpoint of five…