The article focuses on engaging students in algebra through modeling real-world problems. The technique of least squares is explored, encouraging students to develop a deeper understanding of the method. (Contains 2 figures and a bibliography.)

Previous studies have found that children have difficulty solving proportional reasoning problems involving discrete units until 10 to 12 years of age, but can solve parallel problems involving continuous quantities by 6 years of age. The present studies examine where children go wrong in processing proportions that involve discrete quantities. A…

The purpose of this study is to apply the attribute hierarchy method (AHM) to a sample of SAT algebra items administered in March 2005. The AHM is a psychometric method for classifying examinees' test item responses into a set of structured attribute patterns associated with different components from a cognitive model of task performance. An…

Teachers need to monitor students' self-efficacy judgments, as well as their mathematics learning, to provide optimal instruction. First, inaccuracies in self-judgments appear to be a major liability for elementary and middle school children. Classroom practice must cultivate the knowledge to succeed and should nurture the belief that one can…

In this paper, we explore the use of isomorphic problem pairs (IPPs) to assess introductory physics students' ability to solve and successfully transfer problem-solving knowledge from one context to another in mechanics. We call the paired problems "isomorphic" because they require the same physics principle to solve them. We analyze written…

Groups of mathematically strong and weak second-, fourth- and sixth-graders were individually confronted with numerosities smaller and larger than 100 embedded in one-, two- or three-dimensional realistic contexts. While one third of these contexts were totally unstructured (e.g., an irregular piece of land jumbled up with 72 cars), another third…

The focus of the article is on the complex cognitive process involved in learning the concept of "straightness" in Non-Euclidean geometry. Learning new material is viewed through a conflict resolution framework, as a student questions familiar assumptions understood in Euclidean geometry. A case study reveals how mathematization of the straight…

We describe the implementation and effects of group problem solving in recitation sections associated with the general chemistry course at a small private science university. Recitation sections of approximately 45 students are used to supplement large (approximately 180 students) lecture sections. The primary goal of recitation is working in…

The relationship between working memory, intelligence and problem-solving is explored. Wittmann and Suss [Wittmann, W.W., & Suss, H.M. (1999). Investigating the paths between working memory, intelligence, knowledge, and complex problem-solving performances via Brunswik symmetry. In P.L. Ackerman, R.D. Roberts (Ed.), "Learning and individual…

The adaptive use of approximate calculation was examined using a verification task with 18 third graders with mathematics learning disabilities, 22 typically achieving third graders, and 21 typically achieving second graders. Participants were asked to make true-false decisions on simple and complex addition problems while the distance between the…

Researchers have examined inductive reasoning to identify different cognitive processes when participants deal with inductive problems. This article presents a prescriptive theory of inductive reasoning that identifies cognitive processing using a procedural strategy for making comparisons. It is hypothesized that training in the use of the…

The lack of national attention to preparing future faculty for their roles as citizen-scholars represents a significant missed opportunity. Whereas graduate student involvement in engaged teaching and research, such as service-learning or community-based research, likely has immediate benefits for retention and learning, this article focuses on…

David Schwartz's classic book "How Much Is a Million?" can be the catalyst for sparking many interesting mathematical investigations. This article describes five episodes in which children in grades 2-5 all heard this familiar story read aloud to them. At each grade level, they were encouraged to think of their own way to explore the concept of…

This study offers an analysis of the learning of practicing teachers as they acquire a deeper knowledge of mathematics. While some professional developers have shifted part of their focus to helping practicing teachers acquire a deeper knowledge of mathematics (e.g., Stein & Silver, 1996), the results from studies often describe what translates…

The Program for International Student Assessment (PISA) is an international assessment that measures the performance of 15-year-olds in reading literacy, mathematics literacy, and science literacy. Coordinated by the Organization for Economic Cooperation and Development (OECD), an intergovernmental organization of 34 member countries, PISA was…