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)

Typical difficulties involved in solving combinatorial problems are examined and seven common pitfalls are discussed. (MP)

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.…

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)

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…

The idea of mathematical camps for bright pupils is discussed. Some activities in such a camp include meetings with scientists, mathematical evenings, brain-teachers, semi-seminars, brainstorming, guiding texts, Olympian club, consultations, adventures, marches, and various games and competitions. These were evaluated by camp participants in…

Surveys the use of poster sessions with undergraduates in a mathematical modeling course, outlines the rationale for using posters with mathematics students, and describes experiences and proposes criteria to use in the assessment of student posters. (12 references) (Author/MKR)

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)

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…

A range of estimation techniques are described, and a series of mental computation procedures based on concepts of measurement and real numbers are presented in detail. (MP)

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…

Presents a model of rational number using pairs of line segments which can embody ratios of numbers. Actions upon these segments can embody arithmetical operations. Discusses tasks in a computer environment for bringing out diverse algebraic and geometric meanings of rational numbers. (Contains 23 references.) (MKR/Author)

Freudenthal was the founder of realistic mathematics education, in which reality serves as a source of applications and learning. Takes a newspaper article about reproducing a Van Gogh painting using plants in a field to exemplify a rich context problem containing elements of all areas of elementary school mathematics. (MDH)

Develops properties of tasks that are pedagogically efficient and allow students to discover mathematical concepts for themselves. Illustrates the structure and philosophy of powerful tasks for the concept of angle. Presents seven examples of powerful tasks, including two involving two-dimensional graphic systems. (Contains 39 references.)…

An experiment is described which started with exploratory interviews, evolved to design and administration of diagnostic tests, and led to the preparation and use of calculator-enriched teaching materials. (MP)