Understanding Linear Function: a Comparison of Selected Textbooks from England and Shanghai

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• 作者：Yuqian Wang ; Patrick Barmby ; David Bolden
• 关键词：Comparative study ; Linear function ; Textbook analysis ; Understanding
• 刊名：International Journal of Science and Mathematics Education
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：15
• 期：1
• 页码：131-153
• 全文大小：
• 刊物类别：Humanities, Social Sciences and Law
• 刊物主题：Mathematics Education; Science Education;
• 出版者：Springer Netherlands
• ISSN：1573-1774
• 卷排序：15

文摘

This study describes a comparison of how worked examples in selected textbooks from England and Shanghai presented possible learning trajectories towards understanding linear function. Six selected English textbooks and one Shanghai compulsory textbook were analysed with regards to the understanding required for pure mathematics knowledge in linear function. Understanding was defined as being at five levels: Dependent Relationship, Connecting Representations, Local Properties Noticing, Object Analysis and Inventising. These levels were developed by examining the most prominent theories from the existing literature on understanding function. Findings suggested that the English textbooks constrained the structural aspect of understanding linear function due to a point-to-point view of function, while the Shanghai textbook which focussed on a variable view of function overemphasised the algebraic approach. The discussion explored the drawbacks to each approach and what teachers or textbook writers could do to balance these two approaches in order to facilitate students’ understanding towards a structural view of linear function.