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Pedagogical and curriculum potentials of homework: a case study about geometric proofs in Shanghai. (English)
Fan, Lianghuo (ed.) et al., How Chinese teach mathematics. Perspectives from insiders. Hackensack, NJ: World Scientific (ISBN 978-981-4415-81-1/hbk; 978-981-4415-83-5/ebook). Series on Mathematics Education 6, 185-210 (2015).
Summary: This study reports how an experienced secondary teacher in Shanghai explained student homework on geometric proofs. A discourse analysis reveals a structured set of her routine instructional actions in involving students in an IRE/F-patterned instructional discourse to get students to recall, reconnect and reconstruct their earlier learning. Marking student homework, ‘analyzing’ student thinking and tutoring individual students made the explaining detailed, multifaceted, structured and targeted at the mathematical substance. Analysis of curriculum materials and marked student work finds that difficulties in learning were with the fundamental norms to follow and habit of thinking required in writing geometric proofs. Finally, the tradition of design with variation was found to have students discern and master the fundamental deductive reasoning skills under diverse, carefully designed problem settings. These uncover the hidden dimensions of math teaching in Shanghai mediated through homework practice and help us rethink the role and potentials of homework.
Classification: D40 G40 E50 D70
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