Investigation of Cognitive Component Analysis on Mathematics Achievement Assessment for 7th and 8th Graders in Hualien

• Main Authors: Hui-Fang Chang, 張惠芳
• Other Authors: Jung-Chao Ban
• Format: Others
• Language: zh-TW
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/92627967192228460778

碩士 === 國立東華大學 === 數學系 === 98 === The purpose of this study was to analyze the sources of mathematic achievement item difficulty for junior high school students. Therefore, probing the adaptability of the coding framework on cognitive components proposed in this study was processed afterward. A coding framework conceptualized from previous related studies and references was developed to predict the item difficulty parameters after processing the 116 questions, which could be sorted into number and measurement, algebra, and geometry. The cognitive components proposed in this study were the complexity of problem solving, the information of equation, the cognitive level, the novelty of context, the information of graph, and the variety of math knowledge”. The statistic results were obtained by adopting stepwise multi-regression techniques, and the main findings of this study were: 1. “Condition variability”, “cognitive level”, “solving math problems” and ” the variety of math knowledge” can predict 65% of the difficulty variance. 2. “Condition variability” and “solving math problems” can predict 70% of the difficulty variance on “number and quantity” items. 3. “Condition variability”, “cognitive level”, “solving math problems” , “the information of graph” and “equation information” can predict 69% of the difficulty variance on “algebra” items. 4. “Solving math problems” can predict 52% of the difficulty variance on “geometry” items. The results suggested the six cognitive components proposed in this study can predict over 52% of the difficulty variance. With further analysis of the items of number and measurement, algebra, and geometry, each cognitive component shows different levels of importance; some can even predict up to 70% of the difficulty variance. The results suggested that these cognitive components can substantially predict the item difficulty parameters. The implications of these results for teachers to advance their teaching efficiency and to design more appropriate items were also discussed..