Department of Psychology, University of Wisconsin-Madison, Madison, WI 53706, USA.
J Exp Child Psychol. 2010 Sep;107(1):15-30. doi: 10.1016/j.jecp.2010.03.004. Epub 2010 May 21.
This study investigated whether instruction that involves comparing the equal sign with other relational symbols is more effective at imparting a relational interpretation of the equal sign than instruction about the equal sign alone. Third- and fourth-grade students in a comparing symbols group learned about the greater than, less than, and equal signs and had the opportunity to compare the inequality symbols with the equal sign. Students in an equal sign group learned about the equal sign only. A third group of students served as a control group. Three aspects of students' knowledge were assessed before and after the lesson: (a) conceptual understanding of the equal sign, (b) equation encoding, and (c) problem solving. Students in the comparing symbols group showed greater gains in conceptual understanding from pretest to posttest than students in the other two groups, and students in the comparing symbols group also scored higher on a posttest that assessed knowledge about inequality symbols and inequality problem solving. Thus, they learned about three symbols in the same amount of time as other students learned about the equal sign alone or not at all. Therefore, an instructional approach involving comparison can be an effective tool for learning about concepts in mathematics.
本研究探讨了相较于单独教授等号，教授学生将等号与其他关系符号进行比较的教学方法是否更能帮助学生理解关系符号的含义。在本研究中，比较符号组的三、四年级学生学习了大于号、小于号和等号，并被提供了将不等号与等号进行比较的机会。等号组的学生仅学习了等号。第三组学生作为对照组。在课程前后，对学生的三个方面的知识进行了评估：（a）对等号的概念理解，（b）方程编码，以及（c）解决问题。与其他两组学生相比，比较符号组的学生在概念理解方面的测试中表现出了更大的进步，并且在测试中评估了学生对不等号符号和不等号问题解决的知识后，比较符号组的学生也获得了更高的分数。因此，他们在相同的时间内学习了三个符号，而其他学生只学习了等号或者完全没有学习。因此，涉及比较的教学方法可以成为学习数学概念的有效工具。
