Appreciating the power and beauty of mathematical thought should be an integral component of a student's mathematical education. The meaning of aesthetics in the realm of mathematical reasoning, the relationship of aesthetics to problem solving, the results of two studies, and recommendations for developing aesthetics are included. (MNS)

How the author moved from concern about research to development of prescriptive models of heuristic problem solving and the exploration of metacognition and belief systems is discussed. Student beliefs about problem solving, and their corollaries, are included. (MNS)

A one-semester course at the third-year level at York University is described. It tries to legitimize in students' eyes that it makes sense to talk about mathematics as well as do mathematics. Seven course themes are discussed, followed by nine problems used in the course. (MNS)

Historical issues concerning the role of mathematics in the school curriculum are considered, with numerous examples illustrating varying emphases. (MNS)

How students are convinced that they have the correct solution to a problem, free of contradiction, is discussed. The role of counterexamples and the need for a situational analysis of problem-solving behaviors are each included. (MNS)

How children perceive doubling and halving numbers is discussed, with many examples. The use of calculators is integrated. The tendency to avoid division if other ways of solving a problem can be found was noted. (MNS)

Reflecting the author's experiences in Mozambique, some conditions and strategies for mathematics education in underdeveloped countries are suggested. How mathematics education can be used for emancipation is discussed, with extensive comments on problemising reality in classroom situations and creating confidence. (MNS)

Described are the difficulties in translating word sentences between English and Algebra. Two classic sentences that typically produce student errors are presented with explanations that can be shared with the students on overcoming these translation difficulties. (MDH)

Describes a classroom experience in which the teacher experiments with integrating mathematics history into a calculus class by presenting a historical problem taken from L'Hopital to be solved by the students. Extracts the role that history can play in teaching mathematics from the experience. (MDH)

The roles and uses of symbols in mathematical thinking are discussed. The thinking process is further subdivided into specialization, generalization, and reasoning. (MP)

Investigates children's behaviors and conceptual achievements in the transition from informal calculation strategies to a written division algorithm. Describes five different strategies observed in the solution of division problems. Discusses the implications of the children's behavior. (YP)

Describes basic problem-solving skills and presents a protocol of a student solving a problem. Discusses some of the difficulties in obtaining a correct solution. Lists basic prompts for problem solving. (YP)

Described and critiqued are two ideas which have proven valuable in teaching programming at the introductory level, the mental model and the programming plan. (PK)

Suggests that student errors in mathematics be used as motivational devices and starting points for mathematical explorations, involving problem solving and problem posing activities. It is further suggested that errors can foster a deeper and more complete understanding of mathematical content and nature of mathematics itself. (PK)

Presents activities that integrate story telling, history, and problem solving as a stimulus for discussion and creativity in the elementary mathematics classroom, and a way to relieve children's anxiety in an escalating curriculum. (MDH)