Describes the book 'Wonder, the Rainbow and the Aesthetics of Rare Experiences' which is not ostensibly connected to mathematics education but which turns out to have deep connections with mathematics, education, and mathematics education. (MM)

Draws on a range of Japanese work and unifies it under an integrating theme of 'surprise' to help gain insight into a characteristic of mathematics lessons which make students interested in mathematical ideas. (MM)

Presents a study to describe and understand the thinking processes of students in a computer environment while undertaking mathematical tasks related to the differentiation of functions defined on real numbers. Describes two different approaches, the visual and the algebraic approach, in the thinking processes of calculus students. (Contains 19…

Highlights some general difficulties that emerge in justifying the learning of mathematics on the strength of its supposed utility. Discusses the view that mathematics is of crucial importance in every pupil's education. Focuses on use and cognition, use and compulsion, and use and self-consciousness. (Contains 26 references.) (ASK)

Discusses the role of play in the learning of mathematics. Describes a play for the third grade mathematics classroom that focuses on negative numbers and number concepts, and revisits Vygotsky from this point of view. Concludes that mathematically imaginative play can contribute greatly to mathematics learning in elementary school. (Contains 20…

Addresses the definitions of several mathematical concepts and the relationships between them based on a theoretical framework presented in the first part. Presents two examples of mathematical activities on equivalent and non-equivalent definitions constructed in the context of professional development workshops for mathematics teachers.…

Presents a case study that aimed to obtain information on students' mathematical comprehension levels and on whether students may or may not make use of visualization processes in solving mathematical problems. Discovers students' beliefs about teaching and learning processes in general, and mathematics in particular. (Contains 25 references.)…

Discusses whether verbal interaction is recognized as the source from which co-operative groups draw their power to facilitate mathematical learning. Reflects on a group in a mathematics course for prospective secondary teachers focused on problem solving where silence was commonplace. (ASK)

Explores a theory of 'politeness' which claims to describe and explain some universal features of dialogue, and considers what new insights it might give into teacher-pupil dialogue. Uses it to analyze two interviews between a teacher and pupil in order to assess the implications of any new interpretations. (Contains 20 references.) (ASK)

Explores some of the issues behind mathematical modeling for technology with reference to undergraduate teaching and professional practice. Discusses theory and practice in mathematical modeling and its place and uses of modeling in engineering. (ASK)

Proposes an entirely different perspective and challenges both the current para-dogmatic character of constructivism in some quarters of mathematics education and the dismissive attitude towards 'humanist non-sense' in others. Discusses the linguistic aspects of mathematical knowledge through a language acquisition device and a language…

Focuses on the problems of diagnosis and remediation of dyscalculia. Explores whether there is justification for believing that specific difficulty with mathematics arises jointly with a specific language problem, or whether a specific difficulty with mathematics can arise independently of problems with language. Uses a case study to illuminate…

Interviews students majoring in mathematics who had passed a required introductory course on algebraic structures on students' difficulties with basic concepts in group theory as part of a research project. Reports data concerning cyclic groups. (ASK)

Provides five short commentaries from attendees of the 9th International Congress on Mathematical Education (ICME) held in Japan, July 30-August 6, 2000. (ASK)

Reflects on four years of teaching a course called Principle of Major Teachers for pre-service elementary school teachers. Identifies and describes the discord between their formal mathematical knowledge and their informal language used in the context of elementary number theory. Presents encouraging results from a code-switching experiment.…