國二資優生線型函數概念之研究

A Study of the Eighth Grade Gifted Students' Concepts of Linear Function

邱芳津(Fang-Jin Chiou) ； 林來居(Lai-Jiu Lin)

《科學教育》 2期 (1991/03) Pp. 275-291

https://doi.org/10.6767/JSE.199103.0275

摘要

本研究選取九十五名國二資優生為研究對象，實施兩次線型函數單元測驗，根據學生的作答逐題分析，歸納出學生使用的正確解題策略和錯誤類型；再針對解題表現特殊的十三名受試者進行個別面談，進一步探討受試者所具有的錯誤的線型函數概念和解線型函數單元問題時所涉及的數學能力與影響解題表現有開因素。
一、受試者常能從問題中觀察出一些隱含的數量關係，並由此關係作出一般化的推論因而能夠得到多種簡捷的解題策略。
二、受試者存在許多錯誤的線型函數概念，例如：線型函數的圖形就是線，包括直線和曲線；線型函數的關係式除了y=ax+b外，還有許多更複雜的形式等。
三、受試者解線型函數單元問題時，涉及多項數學能力。
四、影響受試者解線型函數問題表現的有關因素有許多種，最主要的是受試者有多方面的學習經驗。

並列摘要

Ninety-five eighth grade gifted students were selected as the subjects. Two tests about linear function in mathematics were given. The researcher analyzed all the student’ answer to each question for inducing student’ correct problem solving strategies and error patterns. Then, 13 subjects whose performances were very specific (for example higher scores, lower scores, and special problem solving strategies) were purposively chosen by the researcher and an individual interview was given for better understanding their mental processes in solving those problems. The results provided more information about the misconcepts of linear funtion. Furthermore, the subjects’ mathematical abilities as well as the relative effect factors on their problem solving performances were explored.
The major findings of this study were as follows:
1 The subjects could usually observe some hidden quantity relations from the questions, draw general deduction from this point and then obtain various brief problem solving strategies.
2. The subjects possessed many misconcept of linear function, for example: the graphs of linear function were lines including straight lines and curves the algebraic forms of liner function had much more complicated forms with the conception of y=ax+b.
3. When the subjects solved the questions of liner function, they used a variety of mathematical abilities.
4. There were many relative effect factors on the subjects’ problem solving performances and the major one was their past learning experience.