The undergraduate curriculum in differential equations has undergone important changes in favor of the visual and numerical aspects of the course primarily because of recent technological advances. Yet, research findings that have analyzed students' thinking and understanding in a reformed setting are still lacking. This paper discusses an ongoing…

The questions addressed in this paper are: how do students interpret the non-solution problems as a mathematical practice in the classroom? What kinds of arguments do the students offer? To deal with these questions the utterances of students working in the classroom with problems in which they had to look for general relations in order to argue…

We report a study of 10-14 year old children's use of additive strategies while solving ratio and proportion tasks. Rasch methodology was used to develop a diagnostic instrument that reveals children's misconceptions. Two versions of this instrument, one with "models" thought to facilitate proportional reasoning and one without were…

According to the National Science Education Standards, science curricula should emphasize understanding, reasoning, and problem solving. In order to align with the standards, the learning environment should be an active learning environment rather than a lecture-centered format in postsecondary education. This study evaluates a new format for an…

This paper discusses a two-semester integrated mathematics content and methods course for preservice elementary school teachers taught for the past twenty years at Saint Xavier University. The course material is presented in a problem solving format in a laboratory context with students working with manipulative materials as part of cooperative…

This paper addresses components of a 3-year longitudinal study in which 9th and 10th grade students in Australia, Canada, and Zambia participated in data-handling programs through networked learning communities. Of interest here are the students' responses to a selection of "ends-in-view" problems, which formed the major part of the…

Math Sense consists of five books that develop from basic to more advanced math skills. This document contains a placement test used with Math Sense to help students and their teachers decide into which Math Sense book to begin working. The placement test is divided into six parts, each consisting of 10 to 22 problems, and is based on exit skill…

This book reports on the first wave of the Mosaic Project which investigates the effects of educational change and teaching practices in mathematics and science on student achievement. The Mosaic project was supported by the National Science Foundation (NSF) and featured two waves. The states that participated in the first wave were State Systemic…

This yearbook sharpens the views of mathematical reasoning and its development at all grade levels. Various perspectives about the nature of reasoning and addresses the many issues and concerns involving mathematical reasoning such as how learners reason in mathematics, how communication promotes reasoning, how teachers gather evidence of student…

Massively parallel programming languages, like StarLogo, provide a rich environment for introducing differential equations to students with an unsophisticated mathematical background. This paper describes the basic software for stimulating and monitoring various population dynamics. Simple differential equations that describe the observed dynamics…

The Program for International Student Assessment (PISA) is a system of international assessments that measures 15-year-olds? capabilities in reading literacy, mathematics literacy, and science literacy every 3 years. PISA was first implemented in 2000 and is carried out by the Organization for Economic Cooperation and Development (OECD), an…

Using data and analyses gathered from multiple sources, this article discusses how students learn in reading, writing, and mathematics. A section on reading concentrates on methods and materials that motivate, a writing section concentrates on content, and a mathematics section discusses procedures for problem solving. A bibliography is included.…

A study of differences in the problem-solving skills of Black, Anglo, and Chicano adolescents from rural Texas found that: (1) Reading achievement played a major role in problem-solving; and (2) No significant sex or ethnic differences were revealed. (PP)