A science fiction approach is used to explore some unusual properties associated with the concept of infinity. (MP)

A mathematical system based on six functions is illustrated. (MP)

The creation of "false laws" of mathematics by many pupils as they attempt to rephrase new ideas and make them understandable and useful is discussed. The reasons for these mistakes and some ways teachers can help students adopt correct rules are reviewed. (MP)

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)

Problems related to representing mathematical concepts with computer models are discussed. The pros and cons of computer assisted instruction (CAI) in aiding students is discussed in relation to a pilot study at the University of Edinburg, Scotland. (MP)

An approach to teaching the principle of mathematical induction that could make more sense to introductory-level pupils is given. (MP)

A way of exploring the concept of rational and irrational numbers with calculators is outlined. The numbers and routines suggested are designed to lead to additional extensions and provide an area for student exploration. (MP)

The authors develop the idea of Niven numbers and discuss their potential usefulness in the classroom. A computer program to generate Niven numbers is provided. (MK)

Discussed is the tendency of students to equate the concepts of continuity and connected graphs based on their lack of an understanding of such concepts as limit points, closed sets, and connected sets. Included is a theorem with three lemmas with their proofs. (KR)

Discussed is the problem of inscribing a rectangle of maximum area in a given right triangle. Answered is whether there is an advantageous orientation and whether a corner of the rectangle of maximum area can lie on the midpoint of a leg of the triangle. (KR)

The main features of the theoretical framework of French research in didactical mathematics are presented. An example is given that presents the rationale for the construction of a didactical situation and its analysis. (CW)

Investigated are three misconceptions of probability and the differential effect of two activity-based instructional units. Response categories (law of averages, law of small numbers, and availability) are identified. Treatment differences (evaluation or no evaluation) appear to influence subjects' interpretations of the information. (YP)

There may be a social and an intellectual aspect to the process of development of mathematical knowledge. This paper describes quadratic equations as intellectual mathematics and as colloquial mathematics. Provides some historical data. (YP)

Provides several problems and their solutions for a descriptive statistics course. Included are problems related to measurement, data collection, sample construction, applications, and computation. Discusses the misleading nature of statistics. (YP)

Introduces an introductory module for analysis. Describes stock of basic functions and their graphs as part one and three methods as part two: transformations of simple graphs, the sum of stock functions, and upper and lower bounds. (YP)