後設認知架構與執行性數學寫作對微積分變化率應用問題解題的影響

Metacognitive Instruction and Transctional Mathematical Writing in Calculus Related-rates Problem-solving

辛靜宜(Ching-I Hsin)

《高雄師大學報：自然科學與科技類》 25期 (2008/12) Pp. 65-86

https://doi.org/10.7060/KNUJST.200812.0065

摘要

Many students of technological universities cannot solve problems on the secondary educational level, and even have no intention to try. To help them deal with the problem, the researcher implemented metacognitive instruction and transactional mathematical writing, The researcher also conducted an experimental research with the aid of interviewing. The research findings are as follows. When solving not-so-difficult applied problems, most of the students could solve the problems. However, there is a by-peak phenomenon in post-testing. Some students were almost ignorant, but the others were almost excellent. By ANCOVA, the researcher found that the performance of the comparative group was worse than the other two groups in the post-test (p＜.001), because the students in the comparative group could set up unknown variables than those in the other two groups. But the learning sheets help students indirectly. The learning sheets display each process of problem-solving clearly, so students could memorize the problem-solving processes easily, and then they earned some credits. However, the learning sheets cannot help students learn more except for mastering the processes of problem-solving. This finding is consistent with Burks' research finding (1993) for junior high school students' experiences of mathematical writing in Calculus related-rates problem-solving.

關鍵字

後設認知架構 ； 執行性數學寫作 ； 微積分 ； 應用問題解題

並列摘要

Many students of technological universities cannot solve problems on the secondary educational level, and even have no intention to try. To help them deal with the problem, the researcher implemented metacognitive instruction and transactional mathematical writing, The researcher also conducted an experimental research with the aid of interviewing. The research findings are as follows. When solving not-so-difficult applied problems, most of the students could solve the problems. However, there is a by-peak phenomenon in post-testing. Some students were almost ignorant, but the others were almost excellent. By ANCOVA, the researcher found that the performance of the comparative group was worse than the other two groups in the post-test (p＜.001), because the students in the comparative group could set up unknown variables than those in the other two groups. But the learning sheets help students indirectly. The learning sheets display each process of problem-solving clearly, so students could memorize the problem-solving processes easily, and then they earned some credits. However, the learning sheets cannot help students learn more except for mastering the processes of problem-solving. This finding is consistent with Burks' research finding (1993) for junior high school students' experiences of mathematical writing in Calculus related-rates problem-solving.

並列關鍵字

Metacognitive instruction ； transactional mathematical writing ； calculus ； problem-solving

參考文獻

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林清山、張景媛(1993)。國中生後設認知、動機信念與數學解題策略之關係研究。教育心理學報。26，53-74。