本研究以國內學者許天維(民83)所引介的試題關聯結構(item relational structure,IRS)與鄭富森(民83)新近發展的「無參數試題反應理論」(item response theory of non-parameter)為分析工具,應用於國民小學數學教育領域,探討學生在乘除方面之概念。本研究以Fischbein et al.(1985)所提出的暗隱模式(implicit model)為基礎,利用此二種試題分析方法,期能進一步印證「暗隱模式」理論,並比較二者試題分析方法之特性,而研究結果期能對未來的相關研究提供參考。根據試題關聯結構、無參數試題反應理論的分析結果,大致能印證「暗隱模式」理論,並就此分析之結果,比較二者試題分析方法之特性。本研究提出暗隱模式的不同角度解釋,即此現象是學生無法以其既有的乘除概念解決「當量」問題;而試題關聯結構、無參數試題反應理論的分析則將可對「暗隱模式」理論提供更進一步的解釋。
The purpose of this study was to investigate students' performance in multiplication and division word problems. The ”Item relational structure” and ”Item response theory of non-parameter” were used to analyze the test items. The theoretical orientation of the research was based on ”implicit model”. By using these methods of analyzing test items, the author want to prove the ”implicit model” and compare the characteristics of these two methods. According to the results, the study could prove the ”implicit model”, and appear some different characteristics of these two methods. The study also proposed different and advanced explanation for ”implicit model”.