One activity concerned with describing data about students in the class and a second activity based on students' original story problems are discussed. (DT)

This article presents, in the context of solving a specific mathematical problem, an argument to indicate how problem posing can lead to a deeper understanding of what is involved in the act of problem solving. (DT)

Four problems concerning the maximum number of regions determined by circles and polygons are explored. (DT)

An algebra problem is analyzed, and several variations are suggested for further student inquiry. Practical applications of the problem are discussed. (DT)

Differences in mathematics performance between boys and girls were investigated. Tests with content appropriate for boys or for girls were given randomly to 163 boys and 147 girls from ten high schools. Differences in performance favored the boys. Students' performance tended to be better on questions with sex-appropriate contextual settings. (DT)

Nonroutine problem-solving, too, involves elements of routine. Often, elementary routines such as solving for a variable are not carried out without error. In this paper, we use new findings from neuroscientific research to explain why even excellent students make mistakes in elementary routines. [For complete proceedings, see ED489597.]

This paper presents an analysis of high school and starting college students' work with algebraic expressions and problems involving parameters. We suggest that parameters should be considered as general numbers that are used to make second order generalizations. The Three Uses of Variable model (3UV model) is then used as theoretical framework to…

This paper consists of a learning unit for college algebra in which the problem presents three different payment plans for a tuition plan to pay for college expenses. The details of each payment plan are presented, each followed by several exercises so that comparisons of the results can be made across payment plans. (MM)

This paper presents a developmental model of students' acquisition of competence in quantitative and algebraic problem solving. A key notion underlying the developmental model is a distinction between grounded and abstract representations. Grounded representations, like story problems, are more concrete and familiar, closer to physical objects and…

This report describes a program for improving elementary school students ability to solve mathematical word problems. The targeted population consisted of primary, middle, and junior high students attending two different kindergarten through eighth grade schools. Both schools were located within blue collar neighborhoods in a large metropolitan…

This book features a guide to teaching mathematics more effectively. Examining the different ways students acquire mathematical skills, it helps teachers develop flexible teaching methods that suit these varied ways of learning. Common areas of learning difficulty in mathematics and why students fail, ways for teachers to determine gaps in…