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

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.