| Summary: | 碩士 === 臺南師範學院 === 教師在職進修數學碩士學位班 === 90 === The present research investigates the effectiveness of cognitive conflict in correcting wrong concepts of arithmetic multiplication and division and consists of two studies conducted with sixth-grade students from Tzguan Elementary School in Kaohsiung County. In both studies, students were first screened for various implicit misconceptions about multiplication and division ("multiplication always makes a number larger," "division always makes a number smaller," "the larger number must be divided by the smaller number"). In the first study, students were divided into two equivalent groups, one group received instruction based on exposition of underlying principles (the conventional instruction method), while the other group received instruction based on cognitive conflict. The effectiveness of the two instruction methods was then compared by analyzing the problem-solving performance of the two groups for statistical covariance. In the second study, only one group received cognitive-conflict instruction and the study can not provide statistical inference for the reason of few students.
In the first study, remedial instruction based on cognitive conflict resulted in improved student performance both in the short-term and the long-term. However, instruction based on cognitive conflict failed to show any statistical advantages over principle-based instruction on either time-scale. After the results of the first study were analyzed, it was hypothesized that the failure of cognitive conflict to yield positive results might have been due to flaws in the methodology and teaching materials used in the experiment. Therefore, an attempt was made to correct possible shortcoming and a second study was conducted. In the second study, group instruction was replaced with small-group discussion, in order to provide stronger learning support. In addition, a more straightforward approach based on the "operational consistency" of multiplication and division was developed to replace the impractical processes of estimation, checking, and object operation which were used in the first study. In the second study, students receiving instruction based on cognitive conflict showed a more diversified and more flexible approach to problem-solving and were more willing to try problem-solving patterns used by others.
Both studies also demonstrated that student performance on multiplication and division problems was hindered not only by "implicit misconceptions" about these two operation, but also by a variety of other inadequate concepts about decimals, the relationship between parts and a whole, the relationships between fractions and decimals, the relationships between integers and decimals, and decimal conversions. The ability to deal with such "value conversions" appears to be a key factor which indirectly influences the ability of students to perform multiplication and division problems.
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