Presents an educational mathematical activity from Africa. Shows how one child explored the game of Julirde, a game of the mosque emphasizing problem solving and symmetry. Offers several suggestions for exploring the game from the central African country of Cameroon in the elementary school mathematics classroom. (ASK)

Presents research in which mathematics teachers and educational researchers ordered arithmetic and algebra problems according to their predicted problem-solving difficulty for students. Analysis of students' problem-solving strategies indicates specific ways that students' algebraic reasoning differs from that predicted by most teachers and…

Previous computer-assisted problem-solving systems have incorporated all the problem-solving steps within a single stage, making it difficult to diagnose stages at which errors occurred when a student encounters difficulties, and imposing a too-high cognitive load on students in their problem solving. This study proposes a computer-assisted system…

The electronic medium suitable for mathematics learning and teaching is often designed with a notebook interface provided in a computer algebra system. Such a notebook interface facilitates a workspace for mathematical activities along with an online help system. In this paper, the proposed feature is implemented in the Mathematica's notebook…

A method for teaching problem-solving skills to mathematics students is presented. By subtly incorporating engineering applications, the students are simultaneously exposed to an effective outreach programme. The process includes offering a complex problem that challenges students' abilities. Before allowing the students to become frustrated, the…

This article describes a set of problem-solving tasks that may provide opportunities for students to make sense of proportional reasoning. (Contains 1 figure.)

This article explores how differences in problem representations change both the performance and underlying cognitive processes of beginning algebra students engaged in quantitative reasoning. Contrary to beliefs held by practitioners and researchers in mathematics education, students were more successful solving simple algebra story problems than…

This note describes a method for evaluating the sums of the m -th powers of n consecutive terms of a general arithmetic sequence: { S[subscript m] = 0, 1, 2,...}. The method is based on the use of a differential operator that is repeatedly applied to a generating function. A known linear recurrence is then obtained and the m-th sum, S[subscript…

This study explores the problem-solving frameworks of twenty prospective secondary mathematics teachers. Twenty prospective secondary mathematics teachers were asked to complete in writing the statement "When I am given a mathematics problem to solve, this is what I do...." Prospective secondary mathematics teachers were found to rely on…

This article describes how teachers learn to implement problem solving in their classrooms through participation in an evolving problem-solving class. (Contains 3 figures.)

This paper reports on data from seventy-eight 9-11 year old children attending four schools that had participated in a national numeracy initiative in New Zealand. Children's responses to a multi-digit addition problem, including alternative solution strategies, and their ideas about the importance of getting the "right answer" were…

"Cognitive Tutor[R]", a full-year course, covers organizing single variable data, simplifying linear expressions, mathematical modeling, solving systems with linear equations, problem-solving using proportional reasoning, and powers and exponents. Students work at their own pace to develop problem-solving skills. The duration of each…

The purpose of this study was to introduce Enhanced Anchored Instruction (EAI) into Korean special education classrooms, research its effectiveness in student achievement and motivation, to find out what kind of adjustment is needed for successful implementation, and analyze the students' and teachers' experiences of using EAI. Enhanced anchored…

The purpose of this study was to determine (1) strategies students use when solving composition problems and the difficulties they encounter; (2) conceptions and/or misconceptions students have with respect to composition of functions; and (3) the effect of using dynamic visualization during instruction on students' understanding of composition of…

This report makes recommendations for the development of middle-school assessment in mathematics, based on a synthesis of scientific findings in cognitive psychology and mathematics education. The focus is on background research, rather than test specifications or example tasks. Readers interested in early development and pilot efforts associated…