探討不同推理能力的國一個案形成與檢驗猜想的認知特徵

Cognitive Characteristics of Formulating and Verifying Conjectures of 7th Grade Cases with Different Reasoning Abilities

本研究的目的是在探討不同區辨敘述有效性及類比推理能力的國一個案形成與檢驗猜想的認知行為與主動性有何差異，藉此提供數學臆測教學和未來研究的建議。\r本研究採立意取樣，透過區辨敘述有效性推理問卷和類比推理問卷將學生區分成不同的推理能力，並各在其中挑選出一位幾何知識量相近的學生，總共四位國一學生為研究對象。透過晤談的方式，蒐集學生在四個幾何圖形中形成與檢驗猜想的思考過程。\r研究結果發現，四種不同推理能力的學生都曾以視覺所觀察的圖形表徵為基礎或聯想到跟上一題圖形的類似性質而主動形成猜想。高區辨敘述有效性推理能力還能夠利用演繹推理或一般化前提的策略形成猜想，而且檢驗猜想的正確性也比較高。文中將進一步討論實例的重要性與對教學的啟示。

This research aims to investigate cognitive characteristics of formulating and verifying conjectures of 7th grader cases with different reasoning abilities.This research selected four seven-grade-cases who have similar geometric knowledge and different reasoning ability. Through interviews， students’ formulation and verification of conjectures were collected and analyzed with modifying a code scheme of cognitive behaviors.The result shows that four cases with different reasoning ability were able to actively formulate conjectures by observing figures or connecting with similar figures. Students with high ability of distinguishing a statement and its inverse could use deductive reasoning or a strategy of generalizing the premise to formulate conjectures， and the correctness of their verifications was higher. The discussion and implication of this study would be presented in this paper.