In this paper, a focus is made on defining processes at stake in an unfamiliar situation coming from discrete mathematics which brings surprising mathematical results. The epistemological framework of Lakatos is questioned and used for the design and the analysis of the situation. The cognitive background of Vergnaud's approach enriches the study…

In this paper, we explore the development of two grounded theories. One theory is mathematical and grounded in the work of university calculus students' collaborative development of mathematical methods for finding the volume of a solid of revolution, in response to mathematical necessity in problem solving, without prior instruction on solution…

It is widely recognized that purely cognitive behavior is extremely rare in performing mathematical activity: other factors, such as the affective ones, play a crucial role. In light of this observation, we present a reflection on the presence of affective and cognitive factors in the process of proving. Proof is considered as a special case of…

This article presents the partial results obtained in the first stage of the research, which sought to answer the following questions: (a) What is the role of intuition in university students' solutions to optimization problems? (b) What is the role of rigor in university students' solutions to optimization problems? (c) How is the combination of…

The use of the history of mathematics in teaching has long been considered a tool for enriching students' mathematical learning. However, in the USA few, if any, research efforts have investigated how the study of history of mathematics contributes to a person's mathematical knowledge for teaching. In this article, I present the results of…

Problems in mathematics education as a social activity are the major focus of this document. Paragraphs that describe major problems in mathematics education point out at least eleven major issues as seen from the author's perspective. (MP)

The secondary-tertiary transition has been studied in a great amount of research in mathematics education, adopting different focuses and theoretical approaches. I present here how these focuses led the authors to identify and study different students' difficulties and to develop different means of didactical action. Individual, social, but also…

The relation between Lakatos' theory and issues in mathematics education, especially mathematical problem solving, is investigated by examining Lakatos' methodology of a scientific research program. (AIM)

This paper considers the aspect of heuristic teaching in which theorems are introduced in the form of problems and the proofs of these theorems as solutions to problems. The traditional treatment along with an illustration of a heuristic approach is discussed for each of several well-known theorems. (MN)

Responds to F. Uhlig's article on linear algebra that appeared in an earlier edition of this journal. (KHR)

The functions of a mathematician in industry are analyzed and suggestions are given concerning the mathematical training that would be appropriate. (DT)

Investiges the mathematical behavior of graduate students and the experiences that contributed to their mathematical development and success. Students reported that a mentor facilitated the development of their problem solving abilities and continued mathematical study. When confronted with an unfamiliar task, students exhibited exceptional…

The development and use of a taxonomy for describing the way distance students plan work and use course materials to complete mathematics exercises is detailed. The taxonomy was developed from an exploratory study but the initial results are viewed as having implications for educational use in many situations. (Author/MP)

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

Studies the effects of a course encouraging cooperative problem solving and reflection on thinking activities on students' attitudes. Reports that a majority declared negative attitudes but during the problem-solving course, the changes were almost all in the desired direction. Contains 18 references. (Author/ASK)