The study of Tangram integrated into mathematics teaching of six graders: The example of fractional teaching

• Main Authors: Zhi-Xu Huang, 黃志敘
• Other Authors: Der-Ching Yang
• Format: Others
• Language: zh-TW
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/85708824046691259468

碩士 === 國立嘉義大學 === 數學教育研究所 === 93 === 32 students from a middle-sized elementary school of Yunlin county joined this study. The purposes of this study were to investigate sixth graders’ misconceptions on fraction, problem solving strategies, and the change of misconceptions and strategies after teaching when tangram integrated into fractional activities (continuous and discrete quantities). Results indicated that three different fractional misconceptions on continuous quantity were found which included: 1).without understanding the meanings of fractions; 2).without recognizing the relationship between part and whole and 3).lacking the concept of equal parts. At the same time, four different strategies were used in the class. They are 1).using benchmark appropriately; 2).using the smallest grid as a unit; 3).selecting the appropriate unit as a benchmark and 4).using real measuring method to solve problems. About 50% of these students had misconceptions on fraction before teaching, however, only 18.9% of these students without change after instruction. At the same time, about 1/3 of sixth graders could not solve or used the incorrect strategies to solve problem before teaching. After instruction, less than 1/5 students could not applied correct strategies to solve problems. This indicates that the teaching has positive help on children’s learning of fractions and the use of strategies. Data also showed that four different fractional misconceptions on discrete quantity were found which included: 1).without understanding the meanings of fractions; 2).without recognizing the relationship between part and whole; 3).lacking the concept of units and 4).lacking the concept of equal parts. At the same time, five different strategies were used in the class. They are 1).using pictorial representations; 2).selecting the appropriate unit to compose fractions; 3).using the division method; 4).using the multiplication method and 5).using the method of equivalent fraction. About 69% of sixth graders had misconceptions on fraction before teaching, yet about 38% of students do not change after instruction. Although many students improved, but the change is not obvious.