特質階層法於臺灣PISA 2006 數學評量之認知診斷分析

The Application of Attribute Hierarchy Method to Taiwan Students’ Cognitive Diagnosis on the PISA 2006 Mathematics Assessment

本研究旨在透過認知診斷技術了解臺灣15歲學生於PISA 2006數學評量表現的 優勢與弱點。本研究為臺灣15歲學生在PISA 2006數學評量的表現提出二種認知模 式，並以結構方程模式（structural equation modeling， SEM）與階層一致性指標 （Hierarchy Consistency Index， HCI）驗證之。依據驗證結果選定認知模式二，運用 特質階層法（Attribute Hierarchy Method， AHM）對臺灣學生在PISA 2006 數學評量 的表現進行認知診斷分析。具體言之，本研究企圖：(1)辨識（建構）臺灣學生在 PISA 2006 數學評量表現的認知模式，並驗證該模式的適配度；(2)探討以特質階層 法分析臺灣PISA 2006數學評量資料的適切性；(3)提供臺灣學生在PISA 2006 數學 評量不同表現水準的診斷訊息。 研究結果發現，本研究提出之認知模式與臺灣PISA 2006數學評量資料適配良 好，SEM 與HCI 均支持此論述，即PISA 2006 數學評量所測量之特質並非獨立運 作，而為一組具有階層性關聯的網絡特質。此外，依據AHM 對PISA 2006 數學評 量各表現水準學生的典型特質組型分析，顯示表現水準一以下的臺灣學生最多僅能 精熟階層一的特質，表現水準三的臺灣學生則可精熟階層二的特質，因此，若從教育 決策與補救教學考量，實應針對不同表現水準的臺灣學生強化其尚未精熟之特質。

The aim of this study is to understand Taiwan students’ strength and weakness on PISA 2006 mathematics assessment. In the study， two cognitive models underlying 15- year-old Taiwan students’ performance on the PISA 2006 mathematics assessment was identified.Meanwhile， the cognitive models were validated by using structural equation modeling (SEM) and the hierarchy consistency index (HCI). On the basis of the chosen cognitive model， a Q-matrix was developed for the PISA 2006 mathematics assessment. The attribute hierarchy method (AHM) was applied to the Taiwan PISA 2006 mathematics assessment for diagnostic analyses. In detail， this study attempts to (a) identify and validate the cognitive models， (b) examine the feasibility of the AHM for cognitive diagnostic analyses， and (c) provide the diagnostic information for Taiwan students at different PISA proficiency levels. The findings show that the cognitive model of the seven hierarchically structured attributes fits the Taiwan PISA data well. That is， the seven attributes do not function independently on the PISA 2006 mathematics assessment but form a hierarchically related network. Besides， Taiwan students performed on the proficiency level one and below level one could only master the first level attributes at most. Those who performed on the proficiency level three could master the attributes on the first two levels. Thus， the remedial instruction should be in accord with students’ proficiency levels to enforce the attributes that students have not mastered.