An analysis of math exam questions regarding the addition and subtraction of fractions with a common denominator at the fourth grade level

• Main Authors: Chang,Chia Tzung, 張家榮
• Other Authors: Sheu,Tian-Wei
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/72897326137286323083

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 === 99 === Abstract Constructing basic fraction concepts, such as fraction measurement, unit quantity, and proper fraction has been carelessly ignored, which has resulted in confusion when students learn fraction. The changes of concepts of students after learning can be important messages for the teachers to improve their teaching strategies. Therefore, the study, sampling ninety fourth-graders in Nantou County in fall semester 2010, designed a test sheet of additon and substraction of fraction with the same denominator and further analyzed the written test result by applying “Item Relational Structure (IRS)” analysis. A concept construction diagram was acquired after the analysis to present the concepts students had constructed after the learning. Findings from analyzing the test results were concluded as the following: I. Through the analysis of the test items being passed by students, it was found that students performed better in addition and substraction of fraction in comparison with based concept of fraction. II. Concepts of proper fraction, fraction measurement, and the combination of fraction measurement need to be enhanced. To students,there was no obvious ordinal sequence in learning addition and substraction of fraction with the same denominator. III. To solve addition and substration of fraction problems,it is necessary to be familiar with the transfer among proper fractions,improper fractions and mixed fractions. IV. From the analysis of test sheet of concepts,the mistakes students often made were:(1)Confusion of “TWO PHASES MEASUREMENT”and (2)false identification of unit quantity. Key words:Fraction Measurement,Unit Quantity,Item Relational Structure(IRS) analysis theory.