小学生代数运算规则的样例学习

Effects of Worked Example Learning on Learning Algebraic Operations

采用完整或不完整样例,对180名六年级小学生用样例学习两种代数运算规则进行了实验研究。结果显示多数被试难以学会“平方差”运算规则,只有少数被试学会了“完全平方和”运算规则;反馈对不完整样例的学习效果有促进作用;用不完整样例学习难度不同的规则,其效果不同;在无反馈条件下,完整样例的学习效果都好于不完整样例;在有反馈的情况下,只有删除一步运算步骤样例的学习效果比完整样例的学习效果好。

Introduction Following worked examples is fundamental for students to learn mathematical rules.But there is disagreement concerning the effect of incomplete worked example learning. Pass（1992） found that there was no significant difference between incomplete and complete worked example learning, while Stark（1999） suggested that complete worked example learning was better than incomplete worked example learning. The purpose of the present study was to examine the effect of worked example learning in learning algebraic operations, and to compare the effect of complete and incomplete worked example learning in different conditions. Method A total of 180 sixth-grade students from a primary school were chosen with a pie-test. During the experiment, the experimenters presented worked examples of three different algebraic operations to the subjects, and then recorded their learning rate as the post-test. The subjects＇ learning rate was analyzed with nonp arametric tests. Results Most of the subjects had difficulty learning the algebraic operations of square error using worked example learning and some subjects succeeded in acquiring the algebraic operations of perfect square after learning through worked examples. The technique of feedback had positive effect on incomplete worked example learning, and the effect was related to the number of deleted operation steps in worked examples; a significant positive effect on algebraic operations learning by worked examples was found when one operation step was deleted. But no significant effect was found when two operation steps were deleted. Arithmetic rules with different levels of difficulty obtained different learning rates in incomplete worked example leaming. The learning rates under incomplete worked example learning were poor in difficult algebraic operations, but good in easier algebraic operations. When there was no feedback, complete worked example learning was better than incomplete worked example learning effect. On the other hand, when feedback was provided, worked examples with one step deleted were better than complete work examples. Conclusion The present study demonstrates that feedback has significant positive effect on learning algebraic operations using incomplete worked examples with one operation step deleted, but the same effect was not found when two steps were deleted. Also, the consequent learning rate of incomplete worked examples was poor in more difficult algebraic operations, but good in easier algebraic operations. The learning rate was higher with complete worked example learning than incomplete worked example learning when feedback was not provided, whereas,when feedback was provided and only one operation step was deleted, incomplete worked example learning was more effective than complete worked example leaming Based on the findings of the present study, it is suggested that teachers should always give feedback to students during teaching, Also, when learning difficult algebraic operations, it will be more effective to present complete work examples or incomplete worked examples with key operation steps. On the other hand, when learning easy algebraic operations, it will be more effective to present incomplete worked examples.