本研究旨在應用概念詮釋結構模式 (concept advanced interpretive structural modeling, CAISM) 與相似性聚類分析演算法 (Similarity-Based Robust Clustering Method, SCM)，分析國小六年級學童之速率概念知識結構。研究者以自編的「速率概念測驗」為研究工具，針對台中地區596名國小六年級學童進行施測，並透過SCM將這些學童分成五個群組，以探討個人化的速率概念階層結構。為了分析受試者其概念詮釋結構圖之特徵與異同，本研究探討此五個群組間的概念詮釋結構圖及其與專家的概念詮釋結構圖之差異。研究結果臚列如下：(1)概念詮釋結構模式可有效表徵速率概念並進行概念結構分析；(2)不同群組的受試者其速率概念結構與試題內的解題策略都不盡相同；(3)根據個人化速率概念之概念詮釋結構圖其概念間連結指向的訊息，可提供教學者進行補救教學的參考；(4)總分相同但反應組型不同的受試者對概念的精熟度與所採取的解題策略皆有所差異；(5)不同群組間概念詮釋結構圖之相似度大多數都有明顯差異存在，教學者可針對相似度差異顯著的不同群組實施適當的分組教學；(6)不同群組與專家的概念詮釋結構圖之相似度都有顯著的差異存在，顯示六年級學童對速率概念的學習尚未達精熟階段。本研究之結果可進一步幫助教學者瞭解學童的速率概念知識結構，並提供關於補救教學或分組教學之資訊。

This paper aims to analyze the sixth-grade students’ knowledge structure of speed concepts by using the methods of Concept Advanced Interpretive Structural Modeling (CAISM) and Similarity-Based Robust Clustering Method (SCM). There are 596 sixth-grade students in Taichung were tested by self-designed speed concepts test, and these students were classified into 5 groups via SCM. Then the researcher explores the individualized speed conceptual structures and compares the CAISM graphs’ characteristics and differences between these groups and the examinees who got the same total scores but different response patterns. Furthermore, we explores the differences of the CAISM graph among 5 groups and between each group and expert. The results are listed as follows: (i) CAISM can efficiently represent the speed concepts and analyze the conceptual structures; (ii) the students’ speed conceptual structures and problem-solving strategies are different among these groups; (iii) according to the individualized CAISM graph of speed concepts, the information of the links among concepts can provide the references for remedial instruction; (iv) the examinees who got the same total scores but different response patterns are different on concepts' mastery degree and problem-solving strategies; (v) most of the CAISM graph among these groups are significantly different, and teachers can implement group teaching properly by utilizing the groups whose graphs are significantly different; (vi) the CAISM graphs between each group and expert are significantly different, and it shows that the sixth-grade students are unfamiliar with the speed concepts. Furthermore, these results can help teachers to realize the students’ knowledge structure of speed concepts and provide the information about remedial instruction or group teaching.

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