| Summary: | 碩士 === 國立臺南大學 === 應用數學系碩士在職專班 === 106 === The purpose of this thesis is to investigate the solving performance on logarithm operations of the senior high school students in Tainan City. By generalizing their error patterns and analyzing the possible reasons for making mistakes in order to know students' difficult part in learning. The results could be reference for teachers. To achieve the goal, we created a specific test, “Definition and operations of logarithm”, which covered two main subjects classified into four parts according to different concepts and types, 26 problems were included. There were 37 senior high school students in Tainan City being chosen to complete the test. Some of them were interviewed due to their performances without being against with their willingness. The quantitative data were analyzed via SPSS 21 and was compared with the results of interview to figure out the error patterns and analyze the possible reasons for making mistakes.
The results of the research was concluded as follows:
1. We classified the error patterns into 5 categories:
a. Be incapable or do not accomplish the problem.
b. Do not understand the definition of logarithm:
Be confused about the symbol’s meaning and limitations of logarithm.
c. Mistake logarithm operation:
Do not be skilled at logarithm formulas. Be confused about logarithm operation. Create wrong logarithm formulas. Use incorrect logarithm formulas.
d. Mistake index operation:
Easily make mistakes while dealing with the index problems and scientific notation problems.
e. The others:
Do not write down the correct answer. Make mistakes because of calculation error.
2. The main reasons for the mistakes in logarithm operations:
a. Lack some necessary background knowledge, especially in index problems and scientific notation problems.
b. Be poor at basic counting operations. Easily make mistakes while doing the basic counting operations and the decimal fraction problems.
c. Be confused about logarithm concept. Forget or mistake the symbol’s meaning and the limitations of logarithm. Easily make mistakes while switching between index and logarithm.
d. Be confused about the piths of logarithm formulas. Create wrong logarithm formulas. Be confused about logarithm pithy formulas.
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