2007年4月

比例理解測驗資料之解題規則的模糊分類
Fuzzy Clustering for Rules Usage on Proportional Reasoning Test with Raw Rule Score

研究論文 Article

林原宏 
Yuan-Horng Lin

59-85

 根據Noelting(（1980）的研究顯示，學童解決「柳橙汁濃度測驗」（Orange Juice Test,OJT）的比例理解問題時，會使用五種解題規則（rule of problem-solving），此五種解題規則呈現學童對於比例理解概念的不同認知層次。然而，Noelting（1980）的研究屬於樣本數較少的質性晤談調查，而且其測驗設計中，不同的解題規則可能會造成相同的選項答案，這在傳統二元計分與機率觀點中，較難有適當的解題規則分類方法。所以，本研究進行大樣本的施測調查以及利用模糊統計方法進行解題規則的模糊分類（fuzzy clustering）。

本研究對象869名國小四至六年級學童（其中男生439名，女生430名），基於Noelting（1980）的OJT解題規則，研究者自編25題「柳澄汁濃度測驗」，在五種解題規則的計分準則下，每位受試者有五個解題規則分數。研究者以Bezdek（1981）所提出的fuzzy c-means分類方法，就解題規則分數將受試樣本分類。

資料分析結果顯示最佳分類群數為五群，而且根據各群中心向量，可知各群確能代表某一種解題規則類型，此分類結果頗能符合Noelting（1980）的理論。以分群結果與年級和性別進行人數的卡方檢定（Chi-square test），檢定結果顯示不同年級的受試者，在解題規則類型使用次數上有顯著差異；而不同性別的受試者，在解題規則類型使用上並無不同。

本研究分析可提供規則評量方法論（rule assessment methodology）之參考，最後，研究者根據分析結果提出進階研究的相關建議。

The purpose of this study is to analyze the rule usage of OJT by fuzzy clustering with multiple rule score. According to the findings of G. Noelting, pupils will adopt five rules in order to solve problems of OJT. The OJT is a proportional reasoning test and there are five rules of solving strategies. These five rules display different cognition capability on proportional reasoning. However, as to the research of G. Noelting, it was a qualitative approach and inferences was limited. Moreover, only dichotomous scoring was used and there were some difficulties when it went to classify the rule usage. Therefore, in this study, large sample size is acquired and classification method of fuzzy theory approach is adopted in order to classify the rule usage of pupils.

There are 869 pupils of fourth, fifth and sixth graders in this study. The score of OJT depends on these five rules so that each subject has five raw rule scores as to rule usage. The scoring of the OJT differs from most related research. Moreover, the author applies fuzzy clustering algorithm in the data analysis. Thanks to the fuzzy clustering , subjects will be properly classified. Therefore, patterns of rule usage for each group display the cognitive capability of those who belong to that group. In the empirical study, it shows five groups are the best classifications of rules usage. Besides, each group represents one rule or mixture of rules with which fits the theoretic foundation of rule usage provided by G. Noelting. It also shows that patterns of rule usage vary with different grade of subjects, but not with gender. Finally some suggestions for future research and rule assessment methodology are provided.

比例理解, 解題規則, 模糊分類
fuzzy clustering, proportional reasoning, rule of problem-solving

教育學
Education

https://doi.org/10.7014/SRMA.2007040003

全文下載