Analyzes from an historical perspective the extension of the natural-number domain to integers in students' transition from arithmetic to algebra in the context of word problems. Extracts four levels of acceptance of these numbers--subtrahend, relative number, isolated number and formal negative number--from historical texts. The first three…

Reports on a 3-year study of patterns of student-student social interaction that mediated metacognitive activity in senior secondary school mathematics classrooms. Unsuccessful problem solving was characterized by students' poor metacognitive decisions exacerbated by lack of critical engagement with each other's thinking while successful outcomes…

Investigates the differential effects of cooperative learning with or without metacognitive instruction on lower and higher achievers' solutions of mathematical authentic tasks. Results indicate that students exposed to metacognitive instruction within cooperative learning (COOP+META) significantly outperformed their counterparts exposed to…

Analyzes the context and status of mathematics education reform in Malawi through four developments in the reform of secondary education. Describes attempts to increase access to secondary education for the majority of Malawians. Suggests that limitations in the reform process are a function of inadequate understanding of the social-contextual…

Analyzes 11-12-year-old English children's responses to two 'realistic' problems. Through a comparison of responses to two items, suggests that, given suitable 'realistic' problems, many children may be more willing and able to introduce realistic responses in a testing context than earlier research might lead one to expect. (Author/MM)

Suggests a new framework for analyzing attitude and changes in attitude. Identifies four different evaluative processes as aspects of attitude: (1) emotions aroused in the situation; (2) emotions associated with the stimuli; (3) expected consequences; and (4) relating the situation to personal values. Illustrates the usefulness of this analytical…

Analyzes the pedagogical ideas underpinning teachers' accounts of the successful use of computer-based tools and resources to support the teaching and learning of mathematics. Organizes central themes to form a pedagogical model capable of informing the use of such technologies in classroom teaching and generating theoretical conjectures for…

Examines the question of the link between the heterogeneities that can characterize a didactic system and the teaching of mathematics. Defines three types of heterogeneity--exogenous, perididactic, and didactic--and posits teaching as a process that regulates these heterogeneities. Concludes that, unlike in language teaching, there is no link…

Presents evidence that there exists much confusion regarding the connection between the algebraic and geometric aspects of slope, scale, and angle. Participants responded to a simple but non-standard task concerning the behavior of slope under a non-homogeneous change of scale. Analysis of the responses reveals two main approaches termed…

Provides an historical account of how proving evolved in school geometry. Explains how the two-column proof format brought stability to the course of studies in geometry. Uncovers what the nature of school geometry came to be as a result of the emphasis on student learning. Draws connections between that century-old reform and current reform…

Suggests that trivialized versions of constructivism are promulgated due to misunderstandings of vocabulary adopted by its advocates. Discusses specifics of frustrations in an effort to communicate the insights and implications of radical and social constructivist theories to preservice and practicing teachers. Presents a classroom episode to show…

Examines the balance model and identifies the issues that divide scientists. Describes learning situations that were the subject of the empirical study which involved 40 students in two 8th-grade classes. Shows the presence of negative numbers gave rise to many errors. Discusses the relevance of the balance model and analyzes the arguments put…

Examines the emotional responses of three individuals to timed mathematics skills-tests. Uses a non-Newtonian view of time to interpret the individual reactions. Draws on Mandler's insights into the nature of emotional responses. Examines the implications of these emotional responses for equitable assessment practices. (Author/KHR)

Explores the attempts of a group of preservice elementary school teachers to generalize a repeating visual number pattern. Discusses students' emergent algebraic thinking. Indicates that students' ability to express generalities verbally was not accompanied by algebraic notation, but participants often perceived complete and accurate solutions…

This paper examines the results of a questionnaire on reading ability in English by Japanese college students, which was formerly analyzed using raw scores, from the viewpoint of Rasch measured scores. In the Rasch analysis, the basic requirements for measuring are the following: (1) reduction of experience to one dimensional abstraction; (2)…