利用徑路搜尋法探討六年級學生的乘除概念知識結構圖

The Pathfinder Analysis of Integer Multiplication-Division Knowledge Structure for Sixth Graders

鐘世帆(Shih-Fan Chung) ； 林原宏(Yuan-Horng Lin) ； 王啓章(Chi-Chang Wang) ； 易正明(Jenq-Ming Yih)

《智慧科技與應用統計學報》 5卷2期 (2007/12) Pp. 66-85

https://doi.org/10.29807/JTITAS.200712.0006

摘要

本研究應用徑路搜尋法及整合試題反應理論和類似性係數之計分演算，探究國小學生乘除文字題的知識結構，研究者以國民小學六年級學生為研究對象，採用「數學乘除概念測驗」，進行資料蒐集。本研究主要研究發現為： 一、知識結構量化指數能有效預估不同乘除能力組學生之能力值，在高乘除能力組中，以PFC指數最佳；在中乘除能力組中，以PRX指數最佳；在低乘除能力組中，以GTD指數最佳；在全體學生中，以PRX指數最佳。 二、參照結構之知識結構圖形表徵中並未明顯存在以乘除四個類型形成之次網路，但呈現出Ⅰ、Ⅱ、Ⅲ三個群組之群集關係。 三、低乘除能力組學生之知識結構圖形表徵明顯存在以類型形成之次網路，而高、中乘除能力組學生則否，顯示低乘除能力組學生比高乘除能力組及中乘除能力組學生更容易受乘除類型的影響。 四、乘除測驗分數相同學生，其知識結構圖形並不相同，仍有些許差異。因此，不能只是以總分來代表學生之學習成果，應著重在乘除概念的知識結構。 依據本研究結果與發現，研究者提出有關國小學生乘除概念教學之參考，以及未來進一步研究之建議。

關鍵字

乘除概念 ； 知識結構 ； 徑路搜尋

並列摘要

The purpose of this study was to use pathfinder in investigating the knowledge structure of multiplication-division problems. This study analyzed the patterns of knowledge structure with which it provided the recommemdations for cognition diagnosis and teaching design.
The researchers designed the test of multiplication-division concept. The main findings and conclusions were as follows: (1) The knowledge structure indices could effectively predict ability of subjects with different patterns of multiplication-division. The most predictive index for high multiplication-division group is PFC index; secondly, the most predictive index for middle multiplication-division group is PRX index. Furthermore, the most predictive for low multiplication-division group is GTD index. And the PRX index was the most predictive index for all task-takers. (2) The knowledge structure indices could effectively discriminate subjects with different response patterns of multiplication-division. (3) For the knowledge structure graph with different multiplication-division ability, the low ability group is affected mainly by the types of the questions. However, the high ability group and mid ability group are not. (4) Task-takers with the same test score didn't necessarily have the same knowledge structure.
The results and findings can offer the consultation for cognitions diagnosis and teaching design. Some recommendations and suggestions for further research were provided by the researchers.

並列關鍵字

Concepts of multiplication and division ； knowledge structure ； pathfinder