PISA數學素養認知成份分析對補救教學的意涵

Implications of Cognitive Component Analysis on PISA Mathematical Literacy Assessment for Supplemental Instruction Design

試題難度認知成份分析對教師教學與評量設計皆能提供實質參考資訊，PISA功能取向的嶄新評量理念，其試題認知成份的特徵尤其值得重視。本文針對PISA數學素養90個試題進行認知成份分析，探討該測驗不同難度層次試題認知成分特徵，同時藉由落後學生試題答對比率的差異，討論PISA數學素養內涵分析對落後學生補救教學設計的參考意涵。研究中以方程式資訊、圖形資訊與認知類別三項成份預測數學素養試題難度，該模式能精簡有效預測PISA數學素養試題難度參數變異。PISA數學素養層次零試題認知成份特徵可作為落後學生數學運思現況描述的依據，層次一試題認知成份特徵則可作為落後學生補救教學目標擬定的參考。整體而言，由於現有PISA數學素養題數的限制，落後學生認知特徵描述尚嫌單薄，而認知成份對試題難度預測的回歸係數在跨資料間也呈現些微浮動。PISA 2012將以數學素養為主軸，後續更豐富題庫的分析，將有助於補救教學和回歸係數意涵的解讀和推論。

The cognitive component analysis on item difficulty can provide useful information for instruction and assessment designs. In this study, we propose a cognitive component coding schema to predict the item difficulty parameters of PISA mathematical literacy assessment. Three cognitive components are included in this paper: the information of equation, the information of graph, and the competency cluster. The results suggest that these cognitive components can substantially predict the item difficulty parameters. The implications of these results for basic level definition and supplemental instruction design are also discussed.