台南地區高中學生在「對數」單元之錯誤類型分析

An Analysis of Error Patterns of Logarithm Operations by Senior High School Studentsin Tainan City

研究的目的在探討台南地區某高中學生在「對數」單元中的學習狀況，並整理出 學生在運算中發生的錯誤類型及分析可能的錯誤原因，藉此了解學生在本單元學習的困難點，以提供教師作為教學參考。為了達到這個目的，研究者自編「對數的意義與對數的運算」測驗，該測驗由兩大主題，其中依照不同觀念、題型，分成四個部分，共有26 個題目。研究者選取台南市某所公立高中學生共37 人完成紙筆測驗，再依照學生意願及答題反應，選取部分學生進行晤談。研究以SPSS 21 分析量化資料並比對晤談內容，整理出錯誤類型及可能發生的錯誤原因。分析研究結果如下：

一、 研究者將台南地區某高中學生在「對數」單元之錯誤情形分為五類：

(一) 不會或未完成。

(二) 對數基本意義與符號不清楚：

對對數的符號意義及定義不清楚；對對數底數及真數的限制不清楚。

(三) 對數運算問題：

對數運算及公式的運用不熟悉，計算時容易混淆、誤用公式或自創錯誤公式。

(四) 指數運算問題：

指數的換算（包含科學記號的轉換）容易出錯。

(五) 其他：

計算結果未化簡完成、計算粗心錯誤等。

二、 台南地區某高中學生在「對數」單元發生錯誤的主要原因為：

(一) 先備知識不足：主要在指數及科學記號轉換上能力不足，容易出錯。

(二) 計算能力弱：在做基本四則運算，或小數計算時，容易粗心計算錯誤。

(三) 對數概念不清：對對數的條件、限制不清楚或忘記，對對數符號存在意義不清楚，指對數轉換易出錯。

(四) 對數公式混淆：先後學的公式互相混淆，自創錯誤公式，亦混淆背公式口訣。

 

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.

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.