Problem solving is presented as a resource for creating curriculum through reflections on intuition such as: exploring available intuitions, making explicit the intuitions used, and using intuition to generalize. (MP)

Identifies key questions concerning children's intuitions and conceptions of probabilistic notions. Research on the theoretical framework for probability studies, misconceptions and strategies, and pupil attainment is reviewed, and the methodology is evaluated. Finally, implications for classroom practice are discussed. (MNS)

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

Two teaching studies were conducted, based on a descriptive framework and diagnostic interviews described previously. In the pilot study, low-achieving students were taught individually; in the main study, they were taught in a group. Performance improved in both cases. (MNS)

How the computer as a metaphor affects our understanding of the processes of learning and teaching is explored. After describing reflection and recursion in mathematics and their roles in thinking and learning, models of the mind and teaching effects are discussed, with self-awareness as a theme. (MNS)

The teaching objectives and curriculum content of the secondary school mathematics program in China are discussed. Public examination papers and classroom teaching methods are described, with specific examples. (MNS)

A didactic principle of operative concept formation is described and explained. It is argued that this principle meets current demands for practical geometric activities with concrete forms and for the exploration of the primordial relation between geometry and reality. (MK)

Mathematical modeling is defined. Examples are used to show that there are models available which illustrate both the traditional use of mathematics in the physical science and its newer use in nonphysical disciplines, and which are at a suitable level for teaching in schools. (Author/MK)

Ratio and proportion are discussed by giving examples of a child's view of the concept. Instructional suggestions are given. (MK)

Ideas on a teaching-learning theory of ratio are presented. Views of children and of members of an international panel are presented, and five questions and their responses are compared with real classroom experience. (MNS)

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)

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)

Reports on a study into the problem solving abilities of students in a Jamaican high school who were intentionally taught problem solving strategies during one-sixth of their mathematics instruction for one academic year. Results indicated no significant increases in their performance on a problem solving test. (TW)

Discusses the educational value of engaging mathematics students in writing a journal. Provides a table showing the relationship between writing topics and the potential benefits. (Author/YP)

Developed is a working definition of the concept of preformal proof through the analyses of an action proof, a geometric-intuitive proof, and a reality-oriented proof of a differential equation. Instructional problems for teachers and learners in connection with preformal proofs are pointed out. (MDH)