Notes for a history of the teaching of algebra

Abundant literature is available on the history of algebra. However, the history of the teaching of algebra is largely unwritten, and as such, this chapter essentially constitutes some notes that are intended to be useful for future research on this subject. As well as the scarcity of the works published on the topic, there is the added difficulty of drawing the line between the teaching of algebra and the teaching of arithmetic—two branches of knowledge whose borders have varied over time (today one can consider the arithmetic with the four operations and their algorithms and properties taught in schools as nothing more than a small chapter of algebra). As such, we will be very brief in talking about the more distant epochs, from which we have some mathematics documents but little information on how they were used in teaching. We aim to be more explicit as we travel forwards into the different epochs until modern times. We finish, naturally, with some reflections on the present-day and future situation regarding the teaching of algebra.info:eu-repo/semantics/publishedVersio

Measurement as relational, intensive and inclusive: Towards a ‘minor’ mathematics

Minor mathematics refers to the mathematical practices that are often erased by state-sanctioned curricular images of mathematics. We use the idea of a minor mathematics to explore alternative measurement practices. We argue that minor measurement practices have been buried by a ‘major’ settler mathematics, a process of erasure that distributes ‘sensibility’ and formulates conditions of mathematics dis/ability. We emphasize how measuring involves the making and mixing of analogies, and that this involves attending to intensive relationships rather than extensive properties. Our philosophical and historical approach moves from the archeological origins of human measurement activity, to pivotal developments in modern mathematics, to configurations of curriculum. We argue that the project of proliferating multiple mathematics is required in order to disturb narrow (and perhaps white, western, male) images of mathematics—and to open up opportunities for a more pluralist and inclusive school mathematics