大學數學教師在微積分教室使用的教學例與論述

Discourses of Derivative - University Mathematics Teaching Through a Commognitive Lens

黃志賢(Chih-Hsien Huang)

《通識教育學報》 7期 (2019/12) Pp. 143-172

https://doi.org/10.6517/MCUT.201912_(7).0005

摘要

由於研究教學基本上是一個困難的過程，儘管大學數學教學研究的需求一再被提出，仍然很少有實徵性的研究描述和分析大學數學教師的教學實踐。本文採用強調認知與溝通的Commognitive理論作為研究大學數學教學的理論架構，以教學例及其伴隨的數學論述做為分析的單位，描述三位大學教師在導數教學中的數學論述。本研究採用非參與觀察及訪談做為資料蒐集的方法，檢驗教學情境所建構、發生的脈絡。結果顯示：雖然三位教師的講課形式是相似的，他們的數學論述卻有著明顯的差異，特別是在他們使用的教學例與數學論述常規；教師使用的教學例類型包括啟動例、探究例、定義與定理的實例、反例及延伸例；教師呈現了「命名」、「動機」、「相同」、「探究」及「輔助證明」等特殊的論述常規；從教師使用的教學例及論述常規類別的不同，可以區辨出不同的教學取向。本文另就未來大學數學教學及研究，提出省思與建議。

關鍵字

教學例 ； 數學論述 ； 微積分 ； 導數

並列摘要

This paper addresses a topic within university mathematics education which has been somewhat underexplored: the teaching practices actually used by university mathematics teachers when giving lectures. The study investigates the teaching practices of three university teachers on the topic of derivative using a discursive approach, the commognitive framework of Sfard. In the paper a categorization of the construction and substantiation routines used by the teachers is presented, for instance various routines for constructing definitions and examples, and for verifying whether an example satisfies a given definition. The findings show that although the overall form of the lectures is similar, with teachers using 'chalk talk', and overt student participation limited to asking and answering questions, there are in fact significant differences in the way the teachers present and do mathematics in their lectures. These differences present themselves both on the level of discursive routines and on a more general level in how the process of doing mathematics is made visible in the teachers' teaching practices. Moreover, I believe that many of the results of the study could be relevant for investigating the teaching of other mathematical topics.

並列關鍵字

instructional example ； mathematical discourse ； calculus ； derivative

參考文獻

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