探究九年級生推論形式之邏輯結構的建構與轉化

Construction and Transformation of Logical Structures in Ninth-graders´ Inferring Types

本研究基於EP-spectrum，將學生的數學證明之演繹推理發展視為是從探索、論證，再到證明的過程。本研究的基本立場是，學生對於幾何的探索與論證活動能提供學生證明所需邏輯結構之預先經驗，因而透過探索與論證活動學生對於證明的學習可用回想與轉化以取代重新建構。因此，本研究主要目的是探討學生在參與幾何探索和論證活動時展現的推論形式，從而分析、比較學生在探索、論證和證明區段所展現之推論形式推測學生的邏輯結構之建構與轉化。為了能考察學生如何理解與學習數學幾何證明過程，本研究設計一系列幾何性質的探索教學活動，並實際進入課堂對35位九年級學生進行教學形式演繹，透過這樣的教學試驗，本研究發現學生在一系列的學習活動中，從探索到證明所呈現出的推論形式其背後反映之邏輯結構彼此的連續性與不連續性，研究結果也顯示，學生透過這樣的探索與論證活動有助於學生演繹推理發展和數學證明的學習。

This study followed the Exploration-Proof Spectrum, [EP-Spectrum], by observing the development of deductive reasoning to provide evidence of the spectrum from exploration to argumentation and then to proof production. The aim of this study was toevaluate students’ performance at making inferences during explorative and argumentative activities. The teaching experiment, employing the exploration approach, was conducted with a class of 35 ninth-graders in Taiwan. We compared the different types of inferences made during exploration, argumentation, and proof. Through a teaching experiment concerning one specific geometric property, the study discovered that the continuity and discontinuity of a logical structure exists in each stage prior to the proof stage, and some results demonstrated that exploration and argumentation are useful to students’ deductive reasoning.