「探究-發現」教學法之個案研究--以商高定理為例
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Date
2005
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Abstract
本研究的主要目的是探討在台灣現行的教育環境下,在數學教室中施行「探究-發現」教學法的可行性,使用不同的教學法對一位資深數學教師的衝擊與影響以及瞭解學生在「探究-發現」教學法的環境下的學習過程與表現。又因為以商高定理的教學為例,所以本研究也針對學生對學習數學定理的發現與產生作細部的描述與分析。
根據研究者的教學心得,教學的錄影資料與文字稿以及個別訪談資料,本研究得到的主要結果如下:
1. 學生在「探究-發現」教學法下的學習表現
(i) 經由本教學法學習「商高定理」的學生能對圖形作靈活的切割,組合,平移,旋轉以說明解釋正方形的面積。
(ii) 經由本教學法學習「商高定理」發現1.部分學生已經能應用如
若P Q與若非Q 非P的等價觀念。2.實驗對象中大約有2/3的學生能夠分辨若P Q中P與Q的因果關係。
(iii) 經由本教學法學習「商高定理」的學生能夠1.以直觀的視覺推理
和等量公理對圖形作演繹式的推理與說明。2.能夠從多元表徵達成以符號作演繹推理。
2. 「探究-發現」教學法對教師的衝擊與影響
(1)發現學生學習能力以及創造力的潛力深厚。(2)讓研究者從不同的角度反省平日的教學死角,增進教學技能。
3. 施行「探究-發現」教學法的優、缺點以及在現行數學教育環境下實行「探究-發現」教學法的可行性:
就整體而言,在「商高定理」的單元教學上,比起傳統講述式的教學法,「探究-發現」教學法的施行是可行的。建議往後的研究可以針對不同單元作教學實驗,以瞭解「探究-發現」教學法的適用單元。
關鍵字:「探究-發現」教學法,商高定理,演繹推理
The Case Study of “Inquiry and Discovery” Teaching Method -on Pythagorean Theorem Abstract The main purpose of this study is to understand: under the circumstances of the educational environment in Taiwan, if it is feasible to utilize a different teaching method-“Inquiry and Discovery” teaching method other than the traditional way of teaching, how it affects a senior teacher and what the impact is of trying a new teaching method on her ordinary daily teaching, and observe the students’ learning process and performance during the teaching. And because the Pythagorean Theorem is the main theme of the teaching context, students’ learning concerning generating conjecture, justification of the conjecture and reasoning and proving the result is also analyzed. The results of this study show that: 1. Students’ performance under the teaching method of “Inquiry and Discovery” (i) Students are able to manipulate the geometric figures through cutting, combining, translating and rotating in order to explain the area of different squares. (ii) Some of the students are able to apply the equivalence concept of if P then Q and if ~Q then ~P. And about 2/3 of the class can differentiate the relationship between P and Q among the proposition of if P then Q. (iii) Students are able to do the explanation and reasoning via multi-representation towards deductive reasoning with symbols. Study shows that teaching with “Inquiry and Discovery” teaching method is feasible in mathematics classroom in Taiwan.
The Case Study of “Inquiry and Discovery” Teaching Method -on Pythagorean Theorem Abstract The main purpose of this study is to understand: under the circumstances of the educational environment in Taiwan, if it is feasible to utilize a different teaching method-“Inquiry and Discovery” teaching method other than the traditional way of teaching, how it affects a senior teacher and what the impact is of trying a new teaching method on her ordinary daily teaching, and observe the students’ learning process and performance during the teaching. And because the Pythagorean Theorem is the main theme of the teaching context, students’ learning concerning generating conjecture, justification of the conjecture and reasoning and proving the result is also analyzed. The results of this study show that: 1. Students’ performance under the teaching method of “Inquiry and Discovery” (i) Students are able to manipulate the geometric figures through cutting, combining, translating and rotating in order to explain the area of different squares. (ii) Some of the students are able to apply the equivalence concept of if P then Q and if ~Q then ~P. And about 2/3 of the class can differentiate the relationship between P and Q among the proposition of if P then Q. (iii) Students are able to do the explanation and reasoning via multi-representation towards deductive reasoning with symbols. Study shows that teaching with “Inquiry and Discovery” teaching method is feasible in mathematics classroom in Taiwan.
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Keywords
「探究-發現」教學法, 商高定理, 演繹推理