Describes how elementary linear algebra can be taught successfully while introducing students to the concept and practice of mathematical proof. Suggests exploring the concept of solvability of linear systems first via the row echelon form (REF). (Author/KHR)

Reports on the development of a mathematics course in fractals and dynamic processes for volunteer students in the second phase of secondary education in the Netherlands. Presents findings on the correct way for teachers to coach students in investigations. (Author/MM)

Argues that mathematics education in virtual culture should strive to give students generative fluency to learn varieties of representational systems, provide opportunities to create and modify representational forms, develop skill in making and exploring virtual environments, and emphasize mathematics as a fundamental way of making sense of the…

Describes a teaching experiment in grade three based on (Adrian) Treffers' idea of vertical mathematization. Discusses the central components of the developed course. The teaching experiment is illustrated by means of children's own productions and put into broader context as contributing to the design science approach of mathematics education.…

Suggests a theoretical framework to address some phenomena of mathematical behavior. Defines the terms "pseudo-conceptual" and "pseudo-analytical" and analyzes examples from classrooms, exams, and homework within the framework. (Author/AIM)

Focuses on culture examined in the unique context of South Africa. Makes visible both conceptual difficulties in its formulation and also difficulties with respect to its interpretation into educational practice. Also explores a critique of ethnomathematics using the South African situation and conceptual tools of a critical mathematics education.…

Presents the results of a case study which looked at the mathematics classroom of one teacher trying to teach mathematics with meaning to pupils or lower ability at the secondary level. Contrasts methods of teaching linear equations to a variety of ability levels and uses the Pirie-Kieren model to account for the successful growth in understanding…

Reports on a study that focused on three teachers and their ways of teaching problem solving. Findings indicate that the participants unconsciously constructed personal metaphors that became the basis of their conceptualization of problems. "Community", "adventure" and "game" were the key metaphors. The outcome suggests that such metaphors could…

Investigates students' conceptions and misconceptions relating to the construction of graphs. Qualitative analysis of students' responses identified three main alternative conceptions. Quantitative analyses of the data indicated that overall students did not enter the learning situation as a tabula rasa. Discusses the theoretical and practical…

Analyzes students' productions, taking affective and social factors into account. Uses the technique of virtual monologue to reproduce the student's voice in order to describe as vividly as possible what might be going on in the student's mind during such situations. (AIM)

Presents a framework for assessing probabilistic thinking based on validated data obtained from eight third grade children who served as case studies. Major constructs were sample space, probability of an event, probability comparisons, and conditional probability. Levels of thinking appear to agree with the levels of cognitive functioning…

Discusses the difficulties observed in the transition from teaching arithmetic to teaching algebra. Future teachers (n=164) were questioned regarding to what extent they were able to shift back and forth between teaching methods within the context of problem solving. Interviews were conducted individually and in a dyad format. (AIM)

Presents to second graders the concept of an n-gon, characterized by a commutative diagram which is composed of four ways of judging a given figure. Observes that some children gave persuading arguments containing a critical idea and the concept formation corresponding to a structure-preserved transformation in the diagram. (AIM)

Elementary combinatorial problems may be classified into three different combinatorial models: (1) selection; (2) partition; and (3) distribution. The main goal of this research was to determine the effect of the implicit combinatorial model on pupils' combinatorial reasoning before and after instruction. Gives an analysis of variance of the…

An account is given of the introduction of multiple-choice and other forms of objective testing into the assessment of a first-year university elementary analysis class. (MP)