幾何論證判讀歷程之個案研究

A case study on the validation process of geometric argumentation texts

「論證文本」經數學社群「判讀」後方稱為「數學證明」，判讀不只經由閱讀而理解文本，亦需判斷局部論點與整體論證的有效性。本研究目的在比較碩士生與高中生之幾何論證判讀歷程，並分析個案的判讀策略。研究對象為四位數學低成就高二學生、四位數學碩士班研究生，以放聲思考法輔以晤談，對判讀原案進行分析，主要發現如下：專家、生手在判讀歷程上的差異在於專家能覺察附圖的侷限性，具有充分的知識背景，能去除無關訊息的干擾；生手則依據「視覺直觀」或「順勢判斷」，來推測文本的證明有效性，而且生手的檢驗多流於表面；專家、生手的判讀策略主要不同點在於專家採用「推理導向」的判讀策略，生手傾向於「訴諸直覺」。

An argumentation text that has been validated by the mathematics community is called a mathematics proof. Validation does not only concern about understanding the text by reading， but also about judging the validity of the argumentation both locally as well as globally. The purpose of this research is to compare the validating processes between experts and novices with respect to a geometry argumentation and to analyze the validating strategies of the latter. The participating subjects are four second-year senior high students of low mathematical achievement and four mathematics graduate students. The analysis of the validating protocol was done by the method of think-aloud and interviews. The main findings are that experts can perceive the limitation of the attached figures and have enough knowledge background to remove the distractions of irrelevant information. Their strategies are reasoning-oriented. Novices tend to rely on their visual intuition or follow the trend to judge and extrapolate the validity of the proof text. Furthermore， their examinations tend to be superficial.