| Summary: | 碩士 === 中華大學 === 應用統計學系碩士班 === 99 === The main purpose of this research is to explore the types of mistakes made by senior high students when answering logarithm application questions and the reasons for making these mistakes.
The research is conducted with the methods of written examinations and the face-to-face talk together. The method of written examinations can help to investigate the types of mistakes when dealing with logarithm application questions; as for the face-to-face talk, it can help to further understand students’ thinking process when answering the questions and the reasons for making mistakes.
“The examination on logarithm application questions”, edited by the researcher, is first taken to evaluate the ability of the students in the freshman and the sophomore science-talented classes. Fifty-eight effective samples are regained in total.
The main reasons for the students’ mistakes in dealing with logarithm application questions, discovered by the research, are as follows:
1. Influenced by their former knowledge or the learning of the unit, the students make wrong inferences or have the wrong understanding.
2. The lack of the concepts about compound interests, the geometric series, the geometric progression and the half-life makes them make mistakes.
3. The students have the incorrect memory of the logarithmic formulas or the exponential law.
4. The students fail to employ the method of difference.
5. The students lack the background knowledge of processing logarithm value.
6. Their carelessness or obvious miscalculation causes the mistakes.
The suggestions in teaching mathematics offered by the research:
1. The teacher can offer more illustrations of the common application in life to enable students to associate their living situations with the application of logarithm. This can not only arouse students’ motivation and stimulate their thinking abut also avoid the negative study migration caused by the ossified study. Moreover, regular examinations should also be strengthened and improved by adding the designs of situations to the questions, thus cultivating students’ correct concepts in operating logarithm application.
2. As for the simplification of the solving process or the use of logarithm value provided in the questions, the teacher should often remind students to accumulate and memorize the logarithmic formulas with the constant practice in operating them so as to improve the fluency and accuracy of the solving process.
3. With regard to the obvious difference between the obtained answer and the correct answer, the teacher had better explain with examples the occasions and necessity to use the method of difference, and also reminds students to promote the fluency and accuracy in using the method of difference by accumulating the experiences in operating it in practice.
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