关键词: 代数运算规则, 样例学习, 解释法, 解释−标记法, 分步呈现

Abstract:

Previous research (Lin & Zhang, 2007) indicated that 6th grade pupils failed to master the algebraic operation rules of the “sum of perfect squares” and “square difference” by worked examples. The reason could be that pupils did not understand the meanings of the new algebraic operators or operation rules. So that the authors proposed two kinds of worked-example designing methods and their presentation modes, named “method of explanation,” “method of explanation-labels,” “stepwise presentation mode” and “whole presentation mode,” and took place three experiments as follow. In experiment 1, a 2 (methods of design: the “method of explanation” or the ordinary method) × 2 (algebraic operation rules: “sum of perfect square” or “square difference”) between-subjects factorial design was adopted. One hundred and twenty 6th grade primary school students chosen from pre-test were randomized into four groups to learn different kinds of worked examples. At last, all participants were received near and far transfer tests to test their learning effects. They further compared the “method of explanation” and the “method of explanation-labels” in learning the two algebraic operation rules in experiment 2. The procedure was same as in experiment 1. In experiment 3, the “method of explanation-labels” was presented by stepwise mode or whole mode to explore the effect of presentation mode in learning two algebraic operation rules. The procedure was same as in experiment 1. The results revealed that: (1) Mean performance of near and far transfer tests was better for the “the method of explanation” than ordinary method in learning the two algebraic operation rules. (2) There was no significant difference between the “method of explanation-labels” and “method of explanation,” except that the mean performance of the near transfer test was better for the “method of explanation-labels” than the “method of explanation” in learning the “square difference” rule. (3) Mean performance of near and far transfer tests was better for the “stepwise presentation mode” than the “whole presentation mode” in learning the two algebraic operation rules. In conclusion, these results demonstrated that the “method of explanation” was helpful to improve pupils’ learning of algebraic operation rules relative to ordinary method. Operation labels should be appropriately added to the worked examples when designed the “method of explanation,” otherwise, it would increase the pupils’ cognitive load, and reduce the positive effect of labels. In the case of the worked examples, which involved too many operation labels or operation steps, the learning effect was better for the “stepwise presentation mode” relative to the “whole presentation mode.”

Key words: algebraic operation rule, worked-example learning, method of explanation, method of explanation- labels, stepwise presentation mode