本研究從認知負荷的觀點，分析認知成分對於國中代數試題難度的解釋力。研究蒐集近十年國中基測與教育會考數學代數測驗試題共 65 題，對九年級 982 名學生施測。並以數的種類、表徵轉化、運算複雜度與方程式資訊等四項認知成分，實徵檢視認知成分編碼的適用性。測驗結果採用 Rasch 模式進行難度參數校準，以多元迴歸進行認知成分編碼對試題難度參數的預測分析。結果顯示表徵轉化、運算複雜度、方程式資訊對試題難度參數的解釋量約為 82%。整體而言，本研究所提出代數認知成分，初步試用對於試題的難度呈現合理解釋，可作為試題發展者及教師在代數測驗和教學之設計基礎，以及學生學習補充教材的規劃。

This study analyzes the explanatory power of cognitive components for the difficulty of national algebra test items. According to four cognitive components including the type of number, representation transformation, computational complexity, and equation information, a total of 65 algebra test items were drawn from the Basic Competence Test and the Comprehensive Assessment Program for Junior High School Students administered in Taiwan over the past ten years. A total of 982 students in the ninth grade were tested. The Rasch model is used to adjust the difficulty parameters, and the multivariate regression is used to predict and analyze the difficulty parameters of the test components. The results show that representation transformation, computational complexity, and equation information explain the difficulty parameter of the test items by about 82%. The initial trial indicates that the proposed algebraic cognitive components provide a reasonable explanation for the difficulty of the test items. Researchers and teachers can apply these components as the basis for algebra teaching and the testing design and planning for the supplementary algebra learning materials.