The great gorilla jump is an activity designed to allow calculus students to construct an understanding of the structure of the Riemann sum and definite integral. The activity uses the ideas of position, velocity, and time to allow students to explore familiar ideas in a new way. Our research has shown that introducing the definite integral as…

This article describes how sixth-grade students developed concrete models to solve division of fractions story problems. Students developed separate two-step procedures to solve measurement and partitive problems, drawing on invented procedures for division of whole numbers. Errors also tended to be specific to the type of division problem…

In its empirical part this paper establishes a general weak understanding of the process of applying a mathematical model. This is also evident in the way teachers regard the application of alternative sharing in their own problem solving and in relating to children's answers. The theoretical part analyses problems that are considered as…

Presents student solutions to real-world problems that allow students to develop and defend their mathematical models of the situations. Elicits proofs and offers recommendations for the potential of real-world problems as contexts for proof. (KHR)

Investigated the effect of the choice of a model's medium (algebraic expression or computer program) on the performance of students. Student programers did not transfer the qualities of a computer program approach to their algebraic models. Provides items for five tests. (YP)

This paper analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem soving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent subjects. Analyses…

An exploratory study assessed the degree to which 13- and 14-year olds (n=100) adjusted assumptions of direct proportionality suggested by surface structure of word problems. Virtually no errors were made on "straightforward" items, but many students showed no adjustment for realistic constraints on complex items. (Contains 21…