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Teaching through Variation: A European Perspective

Kapitel i bok
Författare Ference Marton
Johan Häggström
Publicerad i R. Huang & Y. Li (Eds.), Teaching and Learning Mathematics through Variation – Confucian Heritage Meets Western Theories
Sidor 389–406
ISBN 9789463007818
Förlag Sense Publishers
Förlagsort Rotterdam
Publiceringsår 2017
Publicerad vid Institutionen för didaktik och pedagogisk profession
Nationellt Centrum för matematikutbildning, NCM
Sidor 389–406
Språk en
Länkar https://www.sensepublishers.com/cat...
Ämnesord Mathematics Education, Matematikdidaktik, Variationsteori, Lärarutbildning
Ämneskategorier , Lärande, Internationell pedagogik


This book is about variation and invariance in the teaching of mathematics, that is, about what instances, examples, tasks are used and in which order, to make it possible for students to make concepts, principles, methods their own. Although we can find cases of individual teachers and individual textbook authors paying special attention to such aspects of the teaching of mathematics in different places in the world and at different points in time, such focused attention on the pattern of similarities and differences-especially on the latter-between tasks, instances, examples seems have been particularly common in China for a long time. Moreover, this character of Chinese practice of teaching mathematics has been made explicit by Gu (1991) who called it Bianshi (i.e. teaching with variation) and who tried to relate it to theoretical and empirical research on the learning and teaching of mathematics (in the following the acronym “BS” is used to widely refer to the Chinese tradition of systematically using variation and invariance in the teaching of mathematics). This is the major impetus of most chapters of the present book. We also find another influence, not quite comparable in importance, with the former. It is our own research specialization, called the Variation theory of learning. This research specialization originates from a phenomenological interest in differences in how various phenomena appear to people, i.e., an interest in which different meanings the same phenomenon might have for different people. The reason for this interest is the assumption that people act in relation to things as they appear to them. Hence learning to handle situations in powerful ways takes learning to see them in powerful ways. As one particular contrast between Bianshi (BS) and the Variation theory of learning (VTL) is our focus in the present chapter, and as the former is elaborated in other chapters, we will deal with the latter at some length in the present chapter. There are shorter, but by no means less accurate, introductions to the theory in other chapters. First, when we have established the contrasts between BS and VTL, will we use it very briefly in the very last section as a perspective on the previous chapters. Doing so may appear odd, unconventional, and even disappointing. We have, however, found a problem that – we believe – has to be addressed for the field (the teaching of mathematics through variation) to move forward. Being the authors of one of the last chapters of the book, we were eager to make it pertinent beyond itself.

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