輕度認知障礙國中生乘法公式表徵與運算學習成效之探討

The Effects of Representation and Computation of Multiplicative Identities of Middle School Students with Mild Cognitive Disabilities

本研究目的在探討輕度認知障礙國中生乘法公式表徵與運算之學習成效，並深入分析研究參與者在乘法公式中和的平方公式與差的平方公式表徵與運算學習情形及錯誤類型。研究參與者為二位資源班輕度認知障礙國中生，包含一位學習障礙學生和一位輕度智能障礙學生。研究方法採「單一受試跨行為多探測設計」，研究結果以曲線圖以及目視分析法進行量的分析，並就測驗資料進行質的分析。研究結果發現：(1)二位研究參與者在和的平方公式及差的平方公式表徵與運算教學後，皆能有學習成效和維持成效；(2)二位研究參與者因個人認知特質不同，呈現錯誤類型不同，學習障礙學生出現空間對位錯誤、小數點錯位、運算錯誤等典型數學障礙行為特徵，而輕度智能障礙學生則是因對於「平方」不理解造成的錯誤。本研究採用診斷式評量，就公式表徵層面、運算程序層面和運算最終結果正確性分別計分，以明確反應研究參與者已學習與仍需學習之處。本研究亦根據研究結果對輕度認知障礙學生和的平方公式和差的平方公式教學實務及未來研究提出建議。

The aim of this study was to investigate the effects of representation and computation of multiplicative identities of middle school students with mild cognitive disabilities. Two students with mild cognitive disabilities including one student with learning disability and the other student with mild mental retardation participated in this study. The multiple probe design across behaviors was implemented in this study. The data were analyzed using line chart and visual analysis. In addition， data were analyzed using qualitative approach. The results of this study were as follows: First， after knowledge representation of multiplicative identities instruction， two participants changed their cognitive behaviors and also maintained their cognition behaviors. Second， the errors patterns of two participants were different. The error pattern of student with learning disability was typical pattern of behavior of students with math disability. The error pattern of student with mild cognitive disability was due to limited cognitive ability. Third， diagnostic assessment was applied in this study in order to better present the learning process of research participants. In addition to discussion of results， this study also provides suggestions for teaching and future research.