虛擬教具應用於國中學生學習多項式展開與因式分解之影響

Abstract

本研究以NLVM的Algebra Tiles為教學輔具，設計國中一年級多項式展開與因式分解活動，並進一步探討將此教學輔具應用於教學的成效。 本研究採不等組前後測準實驗研究設計，以桃園縣一所國中的兩個班級學生為研究樣本，隨機抽取一班為實驗組，一班為控制組。實驗組學生接受以NLVM的Algebra Tiles作為教學輔具的教學，而控制組的學生接受以具體教具作為輔具的教學，並以研究者自編的多項式展開與因式分解測驗、學習單、心得及感想問卷、教學過程中的觀察記錄與影片為工具，進行學習成效資料之收集。實驗研究主要發現如下： 一、不同性別與使用不同的教學輔具，對學生學習多項式展開概念有顯著的交互作用： 1.就教學輔具的使用而言，使用具體教具的女生在多項式展開測驗的成績顯著優於男生。 2.就性別而言，使用虛擬教具組的男生在多項式展開測驗的成績顯著優於使用具體教具的男生。 二、不同能力程度與不同的教學輔具，對學生學習多項式展開概念沒有顯著的交互作用： 1.高分組、中分組與低分組的學生，在多項式展開測驗的成績並無顯著差異。 2.使用虛擬教具的實驗組學生與使用具體教具的控制組學生，在多項式展開測驗的成績並無顯著差異。 三、不同性別與使用不同的教學輔具，對學生學習因式分解概念沒有顯著的交互作用： 1.不管使用虛擬教具或具體教具於因式分解概念的教學，女生在因式分解測驗的成績顯著優於男生。 2.使用虛擬教具的實驗組學生與使用具體教具的控制組學生，在因式分解的測驗成績並無顯著差異。 四、不同能力程度與不同的教學輔具，對學生學習因式分解概念沒有顯著的交互作用： 1.高分組、中分組與低分組的學生，在因式分解測驗的成績有顯著差異。 2.使用虛擬教具的實驗組學生與使用具體教具的控制組學生，在因式分解的測驗成績並無顯著差異。 五、使用虛擬教具與具體教具於數學的教學，對學生學習數學動機的提升並沒有顯著的差異。

This study used Web-based virtual manipulatives, Algebra Tiles, as aids to design instructional materials for the use of teaching junior high school students expanding polynomials and factorization. The effect of applying the instructional materials on students’ learning was also explored in this study. A pretest-posttest quasi-experimental design was used. The study involved 56 students in two different classes of a junior high school in Taoyuan county of Taiwan. The classes were randomly assigned to two methods of instruction; a virtual manipulative group and a physical manipulative group. The posttest developed by the researcher was conducted to measure effect. For an in-depth comparison between the two groups, the classroom climate and interactions among students and teachers were also investigated. Research results were as following: 1.Gender and the use of different manipulatives for students to learn the concept of expanding polynomials have significant interaction: (1)For the use of manipulatives, the expanding polynomials test results of the girls using physical manipulatives are significantly better than boys. (2)For gender, the expanding polynomials test results of the boys using virtual manipulatives are significantly better than boys using physical manipulatives. 2.Different ability levels and different manipulatives for students to learn the concept of expanding polynomials have no significant interaction: (1)For high level group, middle level group and low level group of students, there was no significant difference in the test scores of expanding polynomials. (2)For virtual manipulatives in the experimental group and the use of physical manipulatives in the control group, there was no significant difference in the test scores of expanding polynomials. 3.Gender and the use of different manipulatives for students to learn the concept of factorization have no significant interaction: (1)Whether to use virtual manipulatives or physical manipulatives in the factorization concept, girls in the test results are significantly better than boys. (2)For virtual manipulatives in the experimental group and the use of physical manipulatives in the control group, there was no significant difference in the test scores of the factorization. 4.Different ability levels and different manipulatives for students to learn the concept of factorization have no significant interaction: (1)For high level group, middle level group and low level group of students, the scores of the factorization are significant different. (2)For virtual manipulatives in the experimental group students and the use of physical manipulatives in the control group, the scores in the factorization test are not significant different. 5.Using virtual manipulatives and physical manipulatives in mathematics teaching, there is no significant difference in enhancing students’ motivation to learn mathematics.