Reports a study to investigate the extent to which research experience of designing and conducting their own study could enhance five preservice teachers' understanding of children's knowledge of the mathematical concept of fractions. Results indicated that research experience is fruitful in developing an inquisitive disposition in preservice…

Provided is an analysis of Turtle Geometry using van Hiele levels of development and understanding. The author also relates a language use framework, suggested by the work of Fry (1982), to the language activities of Turtle Geometry. Research supporting the analysis is discussed. (RH)

Proposes that although the past 30 years have seen increasing efforts to make mathematics more relevant and useful, schools continue to fail. Argues that forced rote learning is the direct cause of this failure and that improved teaching methods must be developed. Urges that shifts in methodology be phased in gradually. (TW)

The geometry curriculum at the elementary school level is discussed. Details of five different units on geometry, each stressing space orientation, are given. (DT)

Examined is what radical constructivism in connection with Intuitionism might mean to mathematics instruction. Implications for mathematics education, especially the potential consequences for the teaching of mathematics of a relativist view of mathematical knowledge, are suggested. (YP)

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)

An instructional program is described involving six booklets on descriptive statistics and four computer programs on statistical tests. (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)

Topics discussed include: reasons for strategies; the use of a hierarchy of spaces from topological to Euclidean in teaching; structural strategies; pedagogical strategies; and mathematical strategies. (MP)

Six units of instruction, each including a variety of activities involving ratios, are presented. (DT)

The idea of mathematical camps for bright pupils is discussed. Some activities in such a camp include meetings with scientists, mathematical evenings, brain-teachers, semi-seminars, brainstorming, guiding texts, Olympian club, consultations, adventures, marches, and various games and competitions. These were evaluated by camp participants in…

The behavior of one child as she constructed knowledge about fractions over a nine-month period is presented. The intent is to explain behavioral patterns for which certain mental processes, called schemes, seem responsible. (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 relationship between arithmetical concepts and solution methods is discussed. A case study illustrates the contention that some children with relatively sophisticated concepts express those concepts with primitive methods. (MNS)