Compares sixth-grade American students to three samples of (Chinese, Japanese, and Taiwanese) sixth-grade Asian students to determine if the well-documented mathematical achievement of students from these Asian nations might be due in part to a greater understanding of mathematical representations. Indicates that all Asian samples scored…

Studied the effects of item content and stereotypic threat to gender differences in mathematical problem solving through two experiments, one with 63 seventh and eighth graders and the other with 174 college students. Results suggest that gender-stereotype threat could be a big factor in gender differences in mathematical problem solving. (SLD)

During the years 2000-2003, a course on Exploring Quantitative Relationships (EQR) was created at Queens College under the support of the U.S. Department of Education Fund for the Improvement of Post-Secondary Education (DOE-FIPSE Grant No. P116B000772). Exploratory in nature, the course goals were to acquaint liberal arts students with…

This article describes how three algebra problems involving systems of equations can be modeled and solved with manipulative materials or pictorial representation, then the solutions are compared with standard solutions using algebraic symbols. As students begin to use manipulatives and represent their pictures with number sentences, they are…

The National Research Council has suggested that science classes need to become more active and authentic. To help with this effort, Thayer Model Engineering was created several years ago as an inquiry science course at Champlain Valley Union High School in Hinesburg, Vermont. In this school, the students apply the Thayer Model--a four-step…

In this article, the author describes a week of "timely" open-ended lessons with a high ability Y9 group of boys. He gives lessons that would give the students some sense of purpose, as they try to generate a mathematical entity to represent something they used regularly. He states that understanding metric time is something his students…

Traditionally, students learn arithmetic throughout their primary schooling, and this is seen as the ideal preparation for the learning of algebra in the junior secondary school. The four operations are taught and rehearsed in the early years and from this, it is assumed, "children will induce the fundamental structure of arithmetic" (Warren &…

Mathematical problem solving is a transfer challenge requiring children to develop schemas for recognizing novel problems as belonging to familiar problem types for which they know solutions. Schema-based transfer instruction (SBTI) explicitly teaches transfer features that change problems in superficial ways to make them appear novel even though…

This study explored the problem-solving schemas developed by 7th-grade pre-algebra students as they participated in a teaching experiment that was designed to help students develop effective schemas for solving algebraic problem situations involving contexts of (1) growth and change and (2) size and shape. This article describes the qualities and…

Development in the ability of 11-year-olds to solve numerical problems of addition, multiplication, and proportion was analysed by means of three Rasch models of change. The students, who had participated in a New Zealand numeracy project in 2002, comprised two groups that differed in socio-economic status: 1,274 students came from low…

The purpose of the present article is to give an account of the emergence of knowledge pertaining to the transition from arithmetic to algebra in the course of a debate in a grade 7 classroom. This debate follows two other instances of work: (1) the adidactic interaction between each student and a given problem, (2) the adidactic interaction of…

In this article, the author discusses the perils of adhering to a data-driven model of instruction, and discusses how writing center coaches can become involved with all academic disciplines represented at their schools--even those with which they are not familiar--in order to help students learn how to think about the things they are studying and…

Objective: Compare observed and forecasted efficacy of mixed amphetamine salts extended release (MAS-XR; Adderall) with atomoxetine (Strattera) in ADHD children. Method: The authors analyze data from a randomized, double-blind, multicenter, parallel-group, forced-dose-escalation laboratory school study of children ages 6 to 12 with ADHD combined…

This paper reports an example of a situation in which university students had to solve geometrical problems presented to them dynamically using the interactive computerized environment of the "MicroWorlds Project Builder". In the process of the problem solving, the students used ten different solution strategies. The unsuccessful…

In 1986 the United States (U.S.)-Japan Seminar on Mathematical Problem Solving convened to compare the state of problem solving in the classroom and in research in the two countries. The data and results given in this paper are the results of research conducted in the United States in response to the 1986 seminar. The U.S. and Japanese research…