國小數學創造力診斷與認知歷程工具研發

Developing Test Tools to Analyze and Diagnose Mathematical Creativity in Elementary Students

10.6251/BEP.20060503

陳李綢(Lee-Chou Chen)

數學創造力 ； 認知成分 ； 領悟力 ； 自動化 ； 創新力 ； 類比推理 ； 後設認知 ； 數學解題 ； mathematical creativity ； cognitive component ； insight ； automaticity ； novelty ； analogical reasoning ； meta-cognition ； mathematical problem-solving

教育心理學報

38卷1期（2006 / 09 / 01）

1 - 17

繁體中文

本研究主要在探討國小高年級數學創造力診斷與認知歷程分析，並研發適合國小高年級生使用的診斷工具。本研究以國小五、六年級學生為研究對象，根據史騰柏格的創造三面模式理論及國小高年級數學教材編製「國小高年級學生數學創造力診斷與認知歷程分析工具」；其中包括；『算術與邏輯字量表』、『自動化解題行為量表』、『圖形推理量表』、『概念映射量表』、『後設認知成份量表』以及『創造性行為量表』等工具，以此工具分析診斷國內國小高年級學生數學創造力，並找出具代表性的數學創造力診斷指標。研究結果顯示：1.本研究編製的「國小高年級學生數學創造力診斷與認知歷程分析工具」係為一套有效且可靠的數學創造力及數學解題歷程的衡量指標。2.本研究編製之工具成分包括創新力、領悟力、自動化能力、推理能力與後設認知能力。3.後設認知場地獨立與創造性行為高低學生，國小高年級學生數學創造力，如領悟力、創新力、自動化能力及後設認知能力都有顯著差異。4.數學能力與數學創造力有密切關係，而兩者共同的成分是數學解題所具備的後設認知能力、自動化能力、創新力與推理能力。

The main purpose of this study was to develop a set of test tools to analyze and diagnose mathematical creativity of elementary students. The subjects were 5th and 6th graders from an elementary school. Based on Sternberg's Three-factor Model of Creativity and the mathematical learning materials for elementary students, a test battery of mathematical creativity was developed which included Mathematics and Logical Words Scale, Automatic Mathematical Problem-Solving Scale, Figure Analogical Reasoning Scale, Mathematics Mapping Scale, Meta-Cognitive Ability Scale, and Creativity Behavior Scale. These tools were used to analyze and diagnose the mathematical creativity of elementary students. The findings indicate that: (1) the devised test battery was good in reliability and validity in analyzing and diagnosing the mathematical creativity of elementary students; (2) this battery is comprised of the cognitive components of novelty, insight, automaticity, analogical thinking and meta-cognitive ability; (3) high meta-cognition students and field-independents scored higher than low meta-cognition students and field-dependents, respectively, in all components of mathematical creativity, while high creativity students scored higher than low creativity students in several components of it; and (4) mathematical achievement was closely related to mathematical creativity, due to common components in mathematical problem-solving such as meta-cognitive ability, automaticity, novelty and analogical reasoning.

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