In this article I discuss an investigation of handwritten mathematics manuscripts known as navigation cyphering books. These manuscripts, which were prepared during the seventeenth and eighteenth centuries, are evidence of an educational tradition that was the primary means by which students in North America learned mathematics between 1607 and…

We review literature that discusses generic example proving and highlight ambiguities that pervade our research community's discourse about generic example arguments. We distinguish between pedagogical advice for choosing good examples that can serve as generic examples when teaching and advice for developing generic example arguments. We provide…

Reviews the book by Michel Serres, "Hermes: Literature, Science, Philosophy." Discusses Serres' ideas about the history of science and mathematics, mathematical discourse, the double writing of geometry, and the applications of mathematics in the human response to the world. (MDH)

Mathematics education is viewed as a process imbedded in social interaction. Alternatives to seven widely recognized modeling perspectives that provide conceptual foundations for mathematics learning are discussed. (MP)

A discussion of the history of error analysis in mathematics education research provides an overview of research published in German and Anglo-American publications since the early 1900s. (MP)

Failure of most children to solve word problems beyond the simplest is seen to stem from two causes: failure to understand applied arithmetic and failure to relate problems to the real world. Relevant research is reviewed, and a route for new research is proposed. (MP)

The kaleidoscope is presented as a suitable topic for a preservice mathematics teacher's first contact with a nontrivial mathematical phenomenon. Included are historical notes on the kaleidoscope, explanation of the inner mechanisms of various kaleidoscope designs, and suggestions for further student investigations. (JJK)

Presents a theoretical framework for mathematics teaching research based on a content analysis of Psychology of Mathematics Education proceedings since 1979 and a selection of work outside mathematics education. Discusses the relationship between teachers' beliefs and teacher practice, the relationship between teachers' beliefs and innovation, and…

A general model of teacher-student interaction is expanded specifically to mathematics. Mathematics appears to lead to idiosyncratic forms of language and communication in the classroom. (MP)

Discusses problem posing as a feature of creative activity or exceptional mathematical ability, inquiry-oriented instruction, mathematical activity, improving students' problem solving, a window into students' mathematical understanding, and improving students' disposition toward mathematics. (Contains 70 references.) (MKR)

Discusses "connectionism," an alternative learning model wherein meaning resides in the function of the whole state of a network, rather than being localizable in certain symbols or areas. Topics discussed include integration with other learning models; the culture of the mathematics classroom; and characteristics of alternative…

Discussed are categorization schema, with elaborations about attendant epistemological obstacles, concerning the twin notions of understanding and comprehension, per se, as well as the processes affecting their attainment. Included is an example of such a schema involving the concept of the limit of a numerical sequence. (JJK)

Discusses the impact that the relationship between people and mathematics could have on the development of pure and applied mathematics. Argues for (1) a growing interest in philosophy, history and sociology of science; (2) new models in educational and psychological research; and (3) a growing awareness of the human factor in technology,…