| Summary: | 碩士 === 臺北市立教育大學 === 數學資訊教育學系碩士班 === 97 === This research is to investigate how much decimal operation sixth graders understand by the operation process analysis, the graphical presentation, and the problem writing. The research was conducted in two stages－paper-and-pencil test and interviews. Firstly, the paper-and-pencil test is aimed to analyze preliminarily pupils’ problem-solving performance on decimal operations. 65 sixth graders of an elementary school in Taipei County participated in the research by taking the self-designed decimal test. Secondly, pupils who took the paper-and-pencil test were divided into two groups in which achievement on mathematics is categorized into high and low level for the interview. Two students were selected from each group to do a semi-structured interview in order to gain better understanding of the pupils’ decimal operation conceptions.
Based on the result of data analysis, the following is the crucial findings and conclusions of student's performance on solving math questions:
1. By analyzing operation results: The overall performance on decimal subtraction is better than additive terms while the division performance is relatively weak compared with other operators.Additionally, pupils’ least successful performance on opening-answer questions indicate that their learning stage remain instrumental understanding rather than relational understanding.
2. By analyzing graphical presentation performance: When learning decimal operation, the premises is that students are rather unfamiliar with graphing presented questions and haven’t been given much chance to practice . As a result, students generally score low in their graphing performances. However, they do show higher achievement on multiplication graphing. Besides, the quasi-understood concept of unit quantity is the main reason students have difficulties making graphical presentations.
3. By analyzing problem writing performance: Students have better performance on addition and subtraction problem writing. On the contrary, they have poorer performance on the decimal division problem writing. Due to the limited life experiences or linguistic skills, students could create sentences or situations deviate from norm during problem writing. Moreover, lacking of precise sense of quantity such as “1 kilogram”, “1 liter” or “1 centimeter” could result in illogical descriptions.
Based on the findings and results from this research, three proposals on future decimal teaching are made: 1) Reinforce students’ conception connection between decimals and fractions. 2) Discover the meaning of decimal operation. 3) Provide situational examples found in daily life in which decimal operations are related to individual or applied.
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