Abstract:

It is a primary way for students to learn mathematical rules by worked-examples. But there was inconsistent agreement on the effects of non-complete worked-example learning. Pass（1992） found that there were not significant different effects between non-complete worked-example learning and complete worked-example learning, while Stark（1999）got that the effects of complete worked-example learning were better than non-complete worked-example learning. Therefore, the present study focused on the pupils’ worked-example learning effects of the algebraic operation rules, and compared the effects of non-complete worked-example learning with complete worked-example leaning in different conditions.
Method
180 sixth Grade pupils were chosen with a pre-test from one primary school. During the experiment, the experimenters presented worked-examples of three different algebraic operation rules to every subject, and recorded their learning results on the post-test. The subjects’ learning rate was analyzed with Nonparametric Tests at last.
Results
Most of the subjects had difficulty to learn the arithmetic operation rules of square error by worked-example learning, and some subjects could learn the arithmetic operation rules of perfect square by worked-example learning; Feedback had positive effects on non-complete worked-example learning, and the effects were related with the number of the deleted operation steps of the worked-examples. Feedback had significant positive effects on the algebraic operation rule learning by worked-examples deleted one operation step, and hadn’t significant positive effects on the algebraic operation rule learning by worked-examples deleted two operation steps; Different difficult arithmetic operation rules had different learning effects by the non-complete worked-example learning. The non-complete worked-example learning effects of the more difficulty algebraic operation rules were poor, and the non-complete worked-example learning effects of the easier algebraic operation rules were well; The complete worked-example learning effects were all better than the non-complete worked-example learning effects when there wasn’t feedback, and the learning effects of the worked-example deleted one step operation were better than the complete worked-example learning effects when feedback was provided.
Conclusions
The present study further tested that feedback had significant positive effects on the algebraic operation rule learning by worked-examples deleted one operation step, and hadn’t significant positive effects on the algebraic operation rule learning by worked-examples deleted two operation steps; The non-complete worked-example learning effects of the more difficulty algebraic operation rules were poor, and the easier algebraic operation rules were well; The complete worked-example learning effects were all better than the non-complete worked-example learning effects when feedback wasn’t provided, and the learning effects of the worked-example deleted one step operation were better than the complete worked-example learning effects when feedback was provided. Based on the present study, teachers should give students feedback in time during teaching; When learn the difficult algebraic operation rules, it will be better to present complete work-examples or non-complete worked-examples kept key operation steps, when learn the easier algebraic operation rules, presented non-complete worked-examples will be better

Key words: pupil, worked-example learning, algebraic operation rule, feedback