6th Graders' Problem-solving Thinking Regarding Non-common Fractional Division Arithmetic Word Problems

• Main Authors: CHEN, YI-JU, 陳逸如
• Other Authors: HSIEH, KAI-JU
• Format: Others
• Language: zh-TW
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/55051008527824458848

碩士 === 國立臺中教育大學 === 數學教育學系在職專班 === 103 === The purpose of this study was to explore 6th graders' problem-solving thinking regarding non-common fractional division arithmetic word problems. Twenty-seven 6th graders were selected from one elementary school at Daya District, Taichung City to participate in this study. Self-constructed paper-and-pencil test was given to 27 participants. Based on their responses on the test, eighteen students were chosen for semi-structured interviews. The results were as follows: 1. 6th graders' performed better in measurement division than in determination of a unit rate . In measurement division, students did best on “mixed fraction dividing by proper fraction”, followed by “mixed fraction dividing by mixed fraction” , and “proper fraction dividing by proper fraction”. In determination of a unit rate, students did best on “mixed fraction dividing by mixed fraction”, followed by “mixed fraction dividing by proper fraction”, “proper fraction dividing by proper fraction”, and “proper fraction dividing by mixed fraction”. 2. There were two common factors influencing students problem-solving: key words and surplus information. Low-achievers solved problem at random if they couldn’t understanding the meaning of the problem, and they were disturbed by newly learning context; middle-achievers used trial-and-error and check answer strategy, and bigger number divided by smaller one strategy; high-achievers used multiple strategies, such as simplified problem, applied learning knowledge, and trial-and-error and made sure answer reasonably. 3. 6th graders would solve the problem successfully if they were guided by simplified problem strategy. 4. The reason why 6th graders had difficulties in fractional division were followings: they couldn’t understanding the meaning of the problem; they were affected by numbers and words; they couldn’t make an equation; they couldn’t know whether the answer was correct or not; they couldn’t solve problems by using keywords; and they didn’t have enough patience.