質性評價高中資優生數學解題思路之探討──以SOLO與修訂版Bloom分類法為工具

Investigating the Qualitative Evaluation of High School Gifted Student’s Mathematical Problem Solving Mental Path Using SOLO and Revised Bloom’s Taxonomies

本研究目的在於以可觀察學習成果結構(Structure of the Observed Learning Outcome, SOLO)分類法與修訂版Bloom分類法為評價工具，分析高中數學資優生之解題表現，探討其解題思路的結構層次與樣貌。本研究採用個案研究法與顯性特徵分析法之研究設計，立意選取六位高中數學資優學生，收集六位個案學生在數學競賽培訓課程的解題實作測驗資料，參照兩種分類法之理論架構，分別整合成用以分析學生解題表現的評價規準，探討其解題思路在兩種分類法的結構層次及其發展途徑之樣貌。研究結果有：(1)六位個案學生之整體數學解題表現的評價結果，在SOLO方面，均已達到擴展抽象結構層次；在Bloom修訂版方面，其知識向度均已達到後設認知層次，而認知歷程向度亦皆達到創造層次。(2)六位個案學生之數學解題表現，都出現個數不一之U-M-R迴圈或路徑的解題思路；同時，研究發現六位個案學生的解題表現在SOLO之結構層次愈高，其所展現的Bloom之知識與認知歷程層次也愈好。在學生評量應用的蘊涵上，其意義揭示透過SOLO與修訂版Bloom分類法之質性評價，可以讓高中數學資優生的數學解題思路變得更加可觀察。

 

The purpose of this study was to use the Structure of the Observed Learning Outcome (SOLO) taxonomy and the revised Bloom taxonomy as evaluation tools to analyze the prob-lem-solving performance of high school gifted students in the mathematical contest tests and to explore the structural levels of their problem-solving strategies and mental paths. The research design adopted the case study and explicit feature analysis method, by deliberately selecting six high school mathematics gifted students with collecting their problem-solving manuscripts of six contest tests in the mathematics competition training course. The study refered to the theo-retical framework of the two taxonomies to respectively integrate into evaluation criteria for analyzing the problem-solving performance of the six students and explored the manifestations of the structural levels and the developmental paths. The research results showed that: (1) The overall evaluation of these six case students’ mathematics problem-solving performances had reached the “extended abstract structure level” in terms of SOLO; in the revised version of Bloom, their knowledge dimensions have reached the “metacognitive knowledge” level, and their cognitive process dimensions have also reached the “create” level. (2) There were several U-M-R loops appearing in the six case students’ mathematics problem-solving mental paths. Meanwhile, it also showed that the higher the structure level of SOLO taxonomy, the better the level of the knowledge and cognitive process dimension of the revised version of Bloom in the case students’ problem-solving performances.