We introduce some concepts for analyzing proofs, including various structures, and for analyzing undergraduate and beginning graduate mathematics students' proving abilities. We then discuss how the coordination of these two analyses might be used to improve students' ability to construct proofs. For this purpose, we need a richer framework for…

The paper discusses the boundary in the frequency-amplitude plane for boundedness of solutions to the forced spring Duffing type equation x[umlaut] + x + [epsilon]x[cubed] = F cos[omega]t. For fixed initial conditions and for representative fixed values of the parameter [epsilon], the results are reported of a systematic numerical investigation…

A clinical task-based interview can be seen as a situation where the interviewer-interviewee interaction on a task is regulated by a system of explicit and implicit norms, values, and rules. This paper describes how documenting and mapping triadic interaction among the interviewer, the interviewee, and the knowledge negotiated can be used to…

The mean and variance of some continuous distributions, in particular the exponentially decreasing probability distribution and the normal distribution, are considered. Since they involve integration by parts, many students do not feel comfortable. In this note, a technique is demonstrated for deriving mean and variance through differential…

This article provides the rationale for using Fermi questions with eighth graders studying algebra. It describes the students' reaction to such questions as well as their thinking processes and solutions to questions posed to them by their teacher. (Contains 1 figure.)

In 3 experiments, the authors examined mathematical problem solving performance under pressure. In Experiment 1, pressure harmed performance on only unpracticed problems with heavy working memory demands. In Experiment 2, such high-demand problems were practiced until their answers were directly retrieved from memory. This eliminated choking under…

Results from an earlier study conducted by the researchers [Cai, J., & Cifarelli, V.V. (2005). "Exploring mathematical exploration: How two college students formulated and solved their own mathematical problems?" "Focus on Learning Problems in Mathematics," 27(3), 43-72] illustrated and explained several characteristics of the solvers'…

This article addresses the concept of participation in the mathematics classroom, especially as it relates to students from certain ethnic and language groups and economically disadvantaged students. The authors are primarily concerned with seeking ways to develop approaches to mathematics education that are sensitive to the contexts and lived…

Presents a geometric problem and illustrates four different ways to solve it: (1) a synthetic approach; (2) a coordinate approach; (3) a vector approach; and (4) a transformation approach. (KHR)

Contends that, although the introduction of problem solving, intended to involve students more actively in their learning and understanding of the nature of mathematics, is a positive factor, the need for proof, which is an integral part of mathematics, must not be overlooked. (25 references) (MKR)

For those instructors lacking artistic skills, teaching 3-dimensional calculus can be a challenge. Although some instructors spend a great deal of time working on their illustrations, trying to get them just right, students nevertheless often have a difficult time understanding some of them. To address this problem, the author has written a series…

This document consists of three issues of the journal "Seedbed," an outcome of the Teachers' Center Project at Southern Illinois University at Edwardsville (SIUE). Issue Number 29 contains 67 articles on teachers' ideas that they thought worth sharing with other teachers. Issue Number 30 consists of a single paper, "Children and…

Pascal's Triangle is an important numerical table; with its help, a number of computation problems may be solved. Some of these problems are examined and the question of what"solving a problem" can mean is generally considered. (Author/MK)

Describes the PrIME working group experience. Provides three problems on combination and typical answers from primary school students. Discusses some findings. (YP)

How children give meaning to problems solved by multiplying or dividing is considered. After showing two cases of children's understanding of multiplication problems, six recommendations for classroom practice are presented. (YP)