線型函數不同表徵問題對國三學生解題表現、性別 與數學能力間關係之研究

A Study on the Relationship Among Problem-Solving Performance, Gender and Mathematical Ability of the Ninth Grade Students by Different Representations of Linear Functions

本研究旨在探討國三學生在線型函數不同表徵問題的解題表現及不同性別、不同數學能力間的關係。本研究採紙筆測驗蒐集量化資料，依據國三學生在研究者自編的線型函數解題能力測驗上的解題表現。研究者取高雄市某一介於城鄉之間的國民中學三年級學生作為樣本，完成研究者自編的線型函數解題能力測驗，透過描述性統計、獨立樣本 t 檢定、單因子變異數分析、二因子變異數分析及Pearson 積差相關等統計方法，將所蒐集到的量化資料去分析國三學生在線型函數不同表徵問題之解題表現、不同性別及不同數學能力是否會對解題表現造成差異、不同表徵型式與不同性別或不同數學能力二者之間是否存在交互作用的關係以及表徵概念互逆問題之轉換能力是否有顯著的相關。研究結果如下：

一、不同性別的國三學生在線型函數解題表現沒有顯著差異

二、不同數學能力的國三學生在線型函數解題表現有顯著差異

三、線型函數不同表徵型式和不同性別二者之間不存在顯著交互作用

四、線型函數不同表徵型式和不同數學能力二者之間存在顯著交互作用

五、國三學生在表徵概念互逆問題之轉換能力的解題表現有顯著正相關

 

The purpose of this study was to investigate the problem-solving performance of the different representations of the ninth grade students and the relationship between different genders and different mathematical abilities. In this study, data was collected through examinations. Participants were ninth grade students from one suburb school in Kaohsiung City. Problem-solving performance of those ninth grade students was measured using the linear function examination designed by the researcher. Statistical methods of Descriptive statistics, Independent-Sample t test, One-way ANOVA, Two-factor ANOVA and Pearson-product moment Correlation, etc. were then employed to analyze the problem-solving performance of the different representations of the ninth grade students, the relationship between different genders and different mathematical abilities, whether there were interactions between different genders or different mathematical abilities and whether the ability to represent conceptual reciprocal problems has a significant correlation.

The research results were as follows:

1. There was no significant difference between genders among the ninth grade students in the performance of linear function examination.

2. There were significant differences among the ninth-grade students with different mathematical ability in the performance of linear function examination.

3. There were no remarkable interaction effects between different representations of the linear function and different genders.

4. There were remarkable interaction effects between different representations of the linear function and different mathematical abilities.

5. There was significant positive correlation between the performance of the ninth-grade students in the representation of the transforming ability of the concept reciprocal question.