基於認知成分之代數推理測驗自動化命題模式之發展

Development of a Cognitive Component-Based Computerized Algebraic Reasoning Test

蘇義翔(I-Hsiang Su) ； 洪碧霞(Pi-Hsia Hung)

《國立臺灣科技大學人文社會學報》 11卷2期 (2015/06) Pp. 133-162

摘要

本研究的目的在提出認知成分依據自動化命題模式，研究中針對國小高年級學生常見的代數推理作業，分析解題的核心認知成分，選取運算子、表徵轉換、計算複雜度等三項認知成分，操作性定義其內涵與編碼方式。依據認知成分的定義，自動化產出代數推理能力測驗共36題，並針對國小五、六年級177名學生進行施測，實徵檢視模式的適用性。本研究採用Rasch模式進行難度參數校準，再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。結果顯示運算子和表徵轉換對試題實徵難度參數的解釋量約為78%。本研究所提出認知成分及自動化命題模式，初步試用結果呈現合理的生產性，可作為未來代數推理測驗自動命題的基礎，因應代數學習落後學生補救教學的需求。

關鍵字

代數推理測驗 ； 認知成分 ； 試題難度參數 ； 試題模型 ； 自動化命題

並列摘要

The purpose of this study is to propose a plausible cognitive component based automatic item generation model to assure the psychometric quality of items generated. A three-component model was adopted accordingly to develop the computerized algebraic reasoning test (CART). The three cognitive components included are; arithmetic operator, representation transformation, and computational complexity. Thirty-six items were automatically generated according the operational definition of the cognitive components. The CART was administered to 177 5th and 6th graders. The IRT item difficulty parameters of the CART were obtained by Rasch model calibration. Multiple regression analysis was employed to predict the impact of the three components on the IRT difficulty parameters. The results suggest that the first two cognitive components can account for around 78% of variances of the IRT difficulty parameters. The results also reveal that the proposed model may serve as a reasonable quality checking monitor. The components investigated in this study may also serve as a basis for implementation of an automatic item generation of algebraic reasoning test and for further compensatory instructional intervention for students with low algebraic reasoning ability.

並列關鍵字

algebraic reasoning test ； cognitive component ； item difficulty parameter ； item model ； automatic item generation

參考文獻

丁振豐(1997)。認知分析與心理計量分析對解平衡桿問題認知發展層次與解題運作成份測量之比較。初等教育學報。10，81-125。

李岳勳(2004)。國小電腦化空間感測驗難度來源之成份分析(碩士論文)。國立台南師範學院測驗統計研究所。

林世華、葉嘉惠(1999)。數字系列完成測驗試題認知成分分析之研究。教育心理學報。31(1)，139-165。

洪碧霞、林素微、林娟如(2006)。認知複雜度分析架構對TASA-MAT 六年級線上測驗試題難度的解釋力。教育研究與發展期刊。2(4)，69-86。

洪碧霞、蕭嘉偉、林素微(2009)。PISA 數學素養認知成份分析對補救教學的意涵。課程與教學。13(1)，47-66。