Category Archives: History of Math: A tool or a goal?

Should we use history as a goal or as a tool, or maybe in both ways?

Descartes meditation: What can we know?

What can we know? 

Descartes and the Matrix

Very interesting analogy

In recent years, important works on the relationship between history and mathematics
education have appeared:
(a) The Proceedings of the “European Summer University on History and Epistemology in
Mathematics Education” (Montpellier, France, 1993, Braga, Portugal, 1996, and
Leuven/Louvain-la-Neuve, Belgium, 1999),
(b) Two books based on the elaboration of papers which were presented during the satellite  meetings of HPM (History and Pedagogy of Mathematics, one of the ICMI affiliated
international groups), the first edited by R. Calinger (MAA 1996), and the second edited
by V. Katz (MAA 2000),
(c) The ICMI Study book on “History in Mathematics Education”, edited by J. Fauvel and J.
van Maanen.
(d) Journals for Mathematics Teachers and/or Mathematics Education Researchers have
published special issues on the History of Mathematics in Mathematics Teaching (e.g. For
the Learning of Mathematics in 1991, Mathematics in school in 1998 and Mathematics
teacher in 2000). The re-born newsletter of HPM (International Study Group on the
Relations between History and Pedagogy of Mathematics) is becoming (we hope) a forum
where piece of information and ideas are shared.
These material and the experiments carried out all over the world make further discussion on the role of the History of Mathematics in Mathematics Teaching both possible and necessary. In recent discussions the expression “integration of History in Mathematics Teaching” appears frequently. Which ideas are behind this expression? The main idea is that of using History as a mediator to pursue the objectives of Mathematics Education. This means that, these objectives, together with the study of the historical evolution of concepts should be analysed. This work has to be carried out by educators and historians in a collaborative way. Among the benefits, which are expected to result from this work, is the new perspective offered by History to consider students’ difficulties in learning Mathematics. To make teacher active actors in this process we need to give a convenient place to the History of Mathematics in pre-service and in-service teacher education.

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Technology rich innovative environments


Our rapidly changing world has posed the long-standing question to education,
―How can today’s schools be transformed so as to become environments of
teaching and learning that makes individuals lifelong learners and prepare them
for the 21st Century?” 

The response to this question is the focus of the OECD project, Innovative Learning
Environments, and has produced a sampling of the rich array of new visions for education around the  world. As one might imagine, many learning environments have looked to technology in their efforts  to redesign teaching and learning. While technology integration has long been a key area of concern in education, the intersection of technology with our rapidly transforming educational landscape is framing the nature of technology in education in profound, new ways. New and emerging technologies are provoking a re-conceptualisation of teaching and learning, while also serving as catalysts for transformation and innovation.
Successfully preparing all learners with the skills and capacities for 21st century citizenship
global awareness, creativity, collaborative problem-solving, self-directed learning—is no small order,  and many educational leaders are finding that the traditional forms of education that have evolved through the end of the last century are simply inadequate for achieving these goals. At the same time,  while our outer world was transforming, considerable advances have been made in the learning sciences, forcing educators to reconsider how they approach learning, instruction, and the environments created to foster these. Finally, dramatic advances in educational technology have inspired powerful new ways for learners to engage with all kinds of content and activities in their own
self-direct learning experiences. The juxtaposition of these three events creates a very interesting  challenge and opportunity—a space to reconsider, re-imagine, and re-invent learning environments able to prepare and excel each individual for effective life-long learning.

The drive of technology for school change…Read more

Oxford Mathematics and Mathematicians


This is the text of a lecture by the late I. W. Busbridge, who was appointed to a lecturership in mathematics at St Hugh’s College in 1938, and who was a fellow of the College from 1945 to 1970. She died in 1988. It is reproduced here without revision, as it was printed in a Mathematical Institute pamphlet in 1974. Much has happened in Oxford since then, but her account is still of great interest.

Notes from Lawrence , SMaking Sense of Newtons’ Math

It was considered that some historical insight into the study of curves by Newton, his persistent attempts to ‘resolve problems by motion‘ and his study of the curves via the readings of Descartes and van (1615-1660), and their description of dynamic generation of curves was crucial to his later work on fluxions and subsequently his formulation of calculusImage

Jeremy Gray

Mathematics, motion and truth: The earth goes round the sun

The reality of the Earth’s motion, as proclaimed by Copernicus, quickly proved contentious. Accepted by Kepler, disputed by theologians (Lutheran and Catholic alike), veiled in suggestions of mere convenience, adopted and explained by Newton as a consequence of universal gravitation, parent of the notion of force – What is involved in accepting as true that the Earth goes round the Sun? This lecture traces these debates from the early 1600s to the time of Poincare