以認知診斷模型分析台灣與亞洲四國（地區）八年級學生在TIMSS 2007的數學學習成就表現：以DINA模型為例

Abstract

本研究旨在針對TIMSS 2007的八年級數學成就測驗試題之解題所需認知屬性，透過認知診斷模型中的DINA模型進行分析，以了解並比較臺灣與亞洲四國（地區）之八年級學生在認知屬性的精熟情形。本研究依據測驗的題本四之試題分析出內容、歷程、技能／試題類型等三大類共20項認知屬性的Q矩陣架構，研究樣本共包含臺灣290名、韓國301名、新加坡306名、香港243名與日本301名等受測學生。研究主要發現如下： 一、臺灣與亞洲四國（地區）在大部分的認知屬性皆至少有一半的學生能精熟，其中臺灣在「數」、「代數」、「應用數、量與形的知識於計算或判斷」、「機率、統計與閱讀理解」、「數學思維」與「試題特徵」等面向皆有屬性的精熟情形顯著優於部分國家（地區），但在「機率、統計與閱讀理解」面向的部份屬性之精熟表現顯著不如日本與韓國。 二、將認知屬性分組檢視屬性組型的分布情形後發現：(1) 在「數」、「代數」與「機率、統計與閱讀理解」方面，皆有相對多數的學生精熟所有相關屬性；(2) 在「幾何」方面，相對多數的學生皆精熟或是皆未精熟所有相關屬性，表現具雙峰化現象；(3) 在「數學思維」方面，相對多數的學生在所有相關屬性皆精熟、皆未精熟或是僅未精熟屬性「解析的思維」；(4) 在「試題特徵」方面，相對多數的學生在所有相關屬性皆精熟、皆未精熟或是僅精熟屬性「開放式的題目」；(5) 臺灣表現最好的面向為「代數」與「試題特徵」，最不佳的為「機率、統計與閱讀理解」；(6) 臺灣在幾何面向的表現有些微雙峰化現象，即所有相關屬性皆精熟與皆未精熟的學生皆較大部分國家（地區）多。 三、精熟試題所需所有屬性的情形方面，臺灣在數與代數兩維度的情形較幾何和機率與統計維度試題都要好；亞洲四國（地區）在數、代數以及機率與統計等維度的情形皆較幾何維度好。此外，臺灣與韓國學生的精熟情形相近，而在代數維度試題的表現優於新加坡、香港與日本的情形最佳，數與幾何兩個維度次之，機率與統計維度的優異情形最不明顯。

This study focuses on cognitive attributes that required for solving the mathematical items of the TIMSS 2007 eighth-grade. It conducts analysis through the DINA model of the cognitive diagnostic model in order to understand and to compare the mastery of cognitive attributes among students of the eighth grade in Taiwan and other four countries in Asia (region). This study based on the questions in Test Booket Four to analyse a Q matrix framework covering 20 cognitive attributes, which are cataglorized into three major camps including “content”, “process”, and”skill / item type”. The sampling of this study takes up 290 examinees from Taiwan and 301 from Korea, 306 from Singapore, 243 from Hong Kong, and 301 from Japan. The major findings are as follows: 1) More than half of students in Taiwan and four other Asian countries (region) show masteries in most cognitive attributes. Taiwan students particularly outperform in dimentions including "number", " algebra”, " computational and judgmental applications of knowledge in number, quantity, and the geometry", "probability and the basic statistics”, “mathematical thinking” and “characteristics of items” while Taiwan students underperformed Japan and Korean in “probability, statistics, and reading comprehension”. 2) This study examined the distribution of attribute patterns via grouping attributes and found out: (1) Relatively a larger number of students master in attributes such as "number", "algebra" and "probability, statistics, and reading comprehension"; (2) relatively a larger number of students master all or master none of the related attributes in “ geometry ", showing a bimodal phenomenon; (3) in “mathematical thinking ", relatively a larger number of students master all or master none of the related attributes, or only not master the attribute “analytical thinking”; (4) in ”characteristics of items” , relatively a larger number of students master all or master none of the related attributes, or only master the attribute “ open-ended items"; (5) Taiwan outperformed in "algebra" and " characteristics of items“ while underperformed in “probability, statistics, and reading comprehension”; (6) Taiwan shows slight bimodal phenomenon in “geometry” with most students all master or master none of the related attributes while compared with most countries (regions). 3) In item related attributes, Taiwan performs better in “number” and “algebra” than in “geometry” and “probability and statistics”; four Asian countries (regions) perform better in “number”, “algebra” and “probability and statistics” than in”geometry”. In addition, Taiwan students demonstrate similar mastery as Korean students, outperforming students from Singapore, Hong Kong and Japan in “algerbra”, the best situation followed by “number” and “geometry”, while the performance in “probability and statistical dimensions” is the least obvious.