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…

Competence in dealing with mathematical model building requires mathematical knowledge, technological knowledge about how to develop a model, and reflective knowledge relevant for evaluation of the model building process. A general conceptual framework for identification of reflective knowledge is presented by a structural and a developmental…

A study of geometric convexity, where the emphasis is on the gradual organization of a field by mathematizing, is outlined. (DT)

Describes two methods to resolve common difficulties in solving problems. The first is used when the solver becomes stuck with a problem and no idea seems to come to mind. The second is suitable when the solver is trapped in a loop and goes in circles around the problem. (JN)

This study, based on individual interviews with 100 students (aged 16 to 22 years), was designed to investigate understanding of elementary calculus (particularly integration and differentiation). Results indicated that items related to understanding integration as the limit of a sum were difficult even for good students. (Author/MP)

Describes a typical pattern in American colleges and universities in preparing mathematics teachers (at Indiana University), suggests reasons for the inadequacy of the pattern, and proposes a solution to the problem. Four reasons for the inadequacy of such programs are noted and discussed. (Author/MP)

This study took place among undergraduates enrolled in first-year university courses and graduates enrolled in teacher-training courses. The test used is presented in full. Results indicated that misconceptions received in secondary-level courses tend to remain and factors relating to presenting and learning mathematics dominate all other…

A number of general ideas intended to be helpful in analyzing differences in concept images among individuals are formulated. These ideas are applied to the specific concepts of continuity and limits, as taught in the secondary school and university. (MP)

The introduction of certain topics in the theory of machines and languages into school and college mathematics courses in place of the more usual discussion of groups and formal logic is proposed. Examples of machines and languages and their interconnections suitable for such courses are outlined. (MP)

The use of graph paper is traced from its origins in research reports in the early 19th century to massive use in the early 1900s. Reflected in this report is the impact of "squared paper" on instructional practices and courses in technical, scientific, and mathematical areas. (MP)

A questionnaire was given to 129 high school students taking college-prep mathematics and to 63 college students taking a pre-calculus course. Students were to identify sentences as axioms, postulates, facts, definitions, or theorems. Findings showed students did not have the formalist point-of-view about the structure of mathematics. (DT)

Examines the possibility that at times imagery might be a disadvantage in certain tasks. For example, the notion of a persistent image may be so vivid as to actually block other creative thought. Describes one calculus student's images supporting high levels of mathematical functioning which occasionally became so powerful as to obscure more than…

In an article from the July 1995 issue of Educational Studies in Mathematics, Even and Tirosh claim that the quantity (-8)1/3 is undefined. This article presents arguments as to why the reasoning of Tirosh and Even is flawed. Attempts to convince educators of the importance of applying a mathematical definition precisely. (AIM)

Discusses two possible approaches to (-8)1/3. Considers the pros and cons of each of these approaches and specifies some implications to teacher education. (AIM)

Describes aspects of research conducted with two secondary mathematics teachers and seven senior students, which explored their perceptions of mathematics from their experiences and beliefs about personal excellence in school mathematics. Identifies three categories of excellent students: the student excellent-in-mathematics, the student…