Study on the development of representations of grade eight students’ linear function concept

• Main Authors: Ping-Yueh Ting, 丁斌悅
• Other Authors: Po-Son D. Tsao
• Format: Others
• Language: zh-TW
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/36103319232684056150

碩士 === 國立臺灣師範大學 === 數學研究所 === 90 === The main purpose of this study is to investigate the conceptual development of three primary representations (“table”、 “formula”、 “graph”) and their relationships of “linear function” concept. In this study, 25 students in a regular class of a Taipei municipal junior high school were selected as subjects. Based on Anna Sfard’s theory (1991), two batteries of tests were created. Two instruments with pre-test focusing on linear equation with two variables, and post-test focusing on linear function were developed to investigate the conceptual development, strategies, misconception, and error patterns of three representations of “linear function” concept. We also used the interview techniques to collect related information. The foremost results are as following： 1.When students study the concept of linear function, the paces of the cognitive development of the three main representations are different.At the .05 level of significance： (1). The performance of “table” representation is better than “formula” representation. (2). The performance of “graph” representation is better than “formula” representation. (3). There is no significant difference between the performance of “table” representation and “graph” representation. 2.There are no significant differences of the developmental rate among three representations. 3.Since the name of the linear function concept is named after its graph representation, the graph representation plays an importation role in the other two representations when they are promoted to higher level. 4.After the topic of “linear function” was learned, the performance of post-test are better than the performance of the pre-test in all three representations at the .05 level of significance.