Jan van Maanen

The political context

People have studied, learned and used mathematics for over four thousand years. Decisions on what is to be taught in schools, and how, are ultimately political, influenced by a number of factors including the experience of teachers, expectations of parents and employers, and the social context of debates about the curriculum. The ICMI study is posited on the experience of many mathematics teachers across the world that its history makes a difference: that having history of mathematics as a resource for the teacher is beneficial.

The refutation of Longomontanus' quadrature by John Pell

Summary John Pell worked in the Netherlands from 1643 until 1652. He therefore deserves a place in a survey of mathematics c. 1650 in the Netherlands. During his stay he was mainly concerned with refuting a quadrature of the circle that was published in 1644 in Amsterdam by the Danish astronomer and mathematician Longomontanus. We therefore make Pells refutation the main theme of this paper, but other aspects of Pells work and some biographical information will be discussed within this framework. This paper includes a discussion of the refuted quadrature, and the first publication of a copy of the original one-leaf refutation, which was thought to be lost. In addition, we survey Pells correspondence about the affair and in that connection discuss some unknown letters from Mersenne.

CERME7 Working Group 12: History in mathematics education

At CERME7, WG12 embraced papers and posters, concerned both with including history in mathematics education and with the history of mathematics education, that have an implication for (future) practice. Among the papers of the first kind, some concern mainly theoretical or methodological aspects of HPM, a term referring to the ICMI-affiliated International Study Group on the Relations between History and Pedagogy of Mathematics, whereas others are to be considered empirical studies on the inclusion of history. Despite these differences in foci, one main theme in the work of WG12 was the influence of other related fields when searching for theoretical constructs to apply in our research. In their theoretical paper, Tzanakis and Thomaidis work towards providing a general framework for including history in mathematics education by combining two theoretical constructs; one from the history of mathematics by Grattan-Guinness (2004), who differentiates between the history and heritage of mathematics, and one from HPM by Jankvist (2009), who provides a categorisation of the different purposes and approaches for including history in mathematics education. Kjeldsen, in her study of the development of learning strategies and historical awareness, is influenced by theories from the history of mathematics, history in general, HPM and general mathematics education. In particular, she applies Sfard (2008) and Niss (2003) in the educational aspects of her research. Jankvist also refers to these two theoretical constructs from mathematics education in his methodological paper on designing and teaching modules on the history, application and philosophy of mathematics. The paper by Alpaslan, Isiksal and Haser is also on methodology, and concerns the development of a questionnaire for determining pre-service teachers’ attitudes to, and beliefs about, using history in school mathematics courses. Besides drawing on mathematics education research on attitudes and beliefs, the paper also makes use of various statistical constructs. The majority of the empirically-oriented papers on history in mathematics education make frequent references to chapters in, and apply constructs from, Fauvel and van Maanen (2000), the ICMI study on history in mathematics education. Examples are: OReilly’s study of students’ journals to explore their affective engagement in a module on history of mathematics; the study by Kotarinou, Stathopoulou and Chronaki using a historical role-play setting to develop students’

Diagrams and mathematical reasoning: some points, lines, and figures

A well-composed diagram can explain more than thousand words. This holds especially for ‘Proofs without words’. This article puts such proofs into a historical perspective and pays special attention to two examples proposed by the early seventeenth-century Dutch geometer Sybrandt Hansz Cardinael.