| Summary: | 碩士 === 國立臺南大學 === 數學教育學系教學碩士班 === 96 === The purpose of this study was to investigate the changes of compensation adjustment ability of number sense of high ability schoolchildren before and after the self-developed compensation adjustment teaching activity through experimental teaching.
The teaching activities include four multiplication exercises converted from reduction record, amount comparison, multiplication distribution rate, and division operation based on solution strategies of addition, subtraction, multiplication, and division of decimal and fraction. The research subjects were sixth grade elementary schoolchildren of high ability group in mathematics. Pre- and post tests for qualitative and quantitative analyses were administered before and after the experimental teaching as reference data to academic performance. Interviews were conducted on six schoolchildren who were selected in groups of high, medium, and low ability in the performance of decimal and fraction operations in order to understand the changes of compensation adjustment concept of number sense of schoolchildren before and after the experimental teaching. The results are as follows:
1. Schoolchildren did not perform well before the experimental teaching of compensation adjustment. The performance in addition and subtraction was better than that in multiplication and division, while that in decimal is better than that in fraction.
2. After the experimental teaching of compensation adjustment, the overall schoolchildren performance was improved. There was significant difference in addition, multiplication, and division, especially there was greatest improvement in multiplication and division. The performance in decimal was better than the performance in fraction, but the improvement rate in fraction was better than that in decimal. The improvement rate in fraction multiplication was the best, followed by fraction division.
3. Schoolchildren were not good at using reduction record to solve questions of addition and subtraction, especially in subtraction. They often failed in solving the questions due to displaced signs in reduction record.
4. Before experimental teaching, schoolchildren neglected errors between actual value and approximate value. They did not have ideas concerning solution strategies except for vertical calculation method. After experimental teaching, schoolchildren could differentiate errors between actual value and approximate value, and apply on solving questions. They could also create solution strategies for an addition operation converted by subtraction operation, or a subtraction operation transferred by addition operation; and further simplify the operation of multiplication distribution rate.
5. After experimental teaching, schoolchildren were able to properly use errors between actual value and approximate value to understand the phenomenon that when two numbers are greater in addition and subtraction operations, the results are greater and result changes when one of the number is greater and the other one is smaller.
Finally, this study proposed suggestions concerning curriculum, teaching, and future studies according to research results for references of curriculum design and teaching methods.
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