Presents solutions to the Have a Heart problem that appeared in the February 2002 issue of this journal. (Author/NB)

Presents the March Mathness problem which allows students to mathematically analyze familiar situations. Uses sports as the analogy. (Author/NB)

Responses to rate-of-change problems were collected during and after 24 hours of conceptual calculus instruction given to first-year university students. Analysis revealed three categories of error in which variables were treated as symbols to be manipulated rather than quantities to be related. Contains test questions. (Author/MKR)

Uses rectangular models for illustrating products of numbers to solve mixture word problems. (MKR)

Three studies involving 198 undergraduates asked to construct mathematics word problems show that inferred semantic relations between objects help people decide when and how to apply their abstract formal knowledge of mathematics. The same mechanism that mediates analogical reasoning leads to interpretive content effects in reasoning about word…

Investigates how different problem presentations promote the construction of different cognitive models in school students (N=268) aged 14 to 16. Concludes that the lack of correspondence between a cognitive model of the situation and an algebraic representation of relationships in a problem is a powerful obstacle to the use of algebraic methods.…

Reports observations of the use of mental aerobics with 48 adults whose median age was 70. Provides examples of the group puzzles and logic, math, and word problems used to enhance cognitive functioning and creative thinking. (SK)

Presents a teaching experiment to turn students from external observers into active participants in a game of algebra learning where students use graphs to build meaning for equivalence of algebraic expressions. Concludes that the graphic-functional approach seems to make the introduction to algebra much more meaningful for the learner. (ASK)

Word problems have several purposes in mathematics education. Concentrates on two of these purposes--word problems as applications and word problems as mental manipulatives--and compares them with each other. (ASK)

Analyzed the role of explanations students provide themselves (self-explanation) in solving word problems. Results from six female ninth graders show how students' categorical self-explanations mediate their transfer from the sequential representation of the problem to the tabular one. (SLD)

Attempts to establish a description of mathematical word problems as a linguistic genre, particularly considering its pragmatic structure. Through a description of the pragmatics and discourse features of the genre, and through comparison of the word problems genre to other spoken and literary genres, finds clues to unspoken assumptions underlying…

Studied patterns of self-explanation that distinguish between good and poor problem solvers. Results with 32 ninth graders identify self-explanation patterns that show that poor problem solvers are more likely to produce clarifications after inferences and good problem solvers are more likely to produce justifications after regulations. (SLD)

Efforts are made to help students do better on mathematics problems without taking time from other class activities. An illustration of Mrs. Segura, a third-grade teacher at Sunflower Elementary School, is presented whose seventy percent students did not pass the fourth chapter test in mathematics.

The three studies presented here contrasted the problem-solving outcomes of university students when a break was provided or not provided during a problem-solving session. In addition, two studies explored the effect of providing hints (priming) and the placement of hints during the problem-solving session. First, the ability to solve a previously…

This paper applies APOS Theory to suggest a new explanation of how people might think about the concept of infinity. We propose cognitive explanations, and in some cases resolutions, of various dichotomies, paradoxes, and mathematical problems involving the concept of infinity. These explanations are expressed in terms of the mental mechanisms of…