The study on item analysis-a research on elementary school sixth grades students’ conceptualization of divisor

• Main Authors: Shih, Mei-To, 施美多
• Other Authors: Sheu, Tian-Wei
• Format: Others
• Language: zh-TW
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/05186483666454456075

碩士 === 國立臺中教育大學 === 數學教育學系在職進修教學碩士學位班 === 95 === This study explores the differences between the knowledge construct of school-aged children and experts in learning the concept of divisor. It also discusses commonly-made mistakes and fallacious concepts of school-aged children in learning the concept of divisor. The research subjects are a class of sixth graders in Chang Hua County. elementary school Self-constructed tests of the concept of divisor are used as the research tool. SPSS/PC statistic software and the IRS computer program of the Theory of Item Relation Structure are used in the analysis. The following is a summary of the research results. 1. The knowledge construct of school-aged children in the concept of divisor is as follows: 1.1 The “concept of relatively prime” is a sub-concept of the “concept of prime.” 1.2 The “concept of composite” is a sub-concept of the “concept of prime.” 1.3 The “concept of common divisor” is a sub-concept of the “concept of decomposition of prime factor.” 2. The commonly-made mistakes and fallacious concepts of the concept of divisor of school-aged children are as follows: 2.1 It is more difficult for school-aged children to consider the characteristic of a number (i.e. prime number) than to consider the relationship between two numbers (i.e. relatively prime). 2.2 Many school-aged children have misconceptions as to whether one is relatively prime. 2.3 It is easier for school-aged children to accept the concept of divisor when introducing with the Division Algorithm than with the Multiplication Algorithm. 2.4 Almost 30% of the school-aged children are not equipped with thoroughly considered process concept. Without the concept of tacit knowledge, they are not able to ponder on the meaning of tacit knowledge in the process of problem solving. 2.5 Almost 20 % of the school-aged children are often oblivious of the basic member of divisor—one, when considering divisor. Based on the results of the study, several suggestions are offered as reference for educators and future research.