Showing papers by "Ference Marton published in 2017"

What is made possible to learn when using the variation theory of learning in teaching mathematics

Abstract: The variation theory of learning emphasizes variation as a necessary condition for learners to be able to discern new aspects of an object of learning. In a substantial number of studies, the theor ...

Chinese lesson study, Learning study and keys to learning

Abstract: Purpose The purpose of this paper is threefold. First, the authors set out to advance the thesis that lesson study should be considered as the signature pedagogy of teachers. Second, the authors want to argue that combining the core attributes of Chinese lesson study and Learning study will improve the practice of lesson study. Third, the authors attempt to demonstrate how teachers discover necessary aspects of the object of learning (here called “keys to learning”) through their engagement in Learning studies. Design/methodology/approach The paper conducted a contrastive analysis of two varieties of lesson studies: the Chinese lesson study and the Learning study. Findings Lesson studies form a field of varieties, but the commonality among them (i.e. the focus on the lesson) makes the lesson study a strong candidate for being “the signature pedagogy” of teachers. The most important attribute of the Chinese lesson study is its close connection to the daily work of teachers through its embeddedness in teacher research group (arguably the core organisational principle of the Chinese educational system). The most important attribute of the Learning study is its theoretical grounding which helps teachers create an environment for the students to discern and appropriate necessary aspects of the object of learning. Practical implications Different varieties may be enriched by including the two core attributes found in the Chinese lesson study and the Learning study. Originality/value Two empirical studies are used to exemplify how teacher might discover previously unknown necessary aspects of the object of learning (here called “keys to leaning”).

Teaching through Variation

Abstract: 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).