The Influence Of Fading Worked-out Steps,Self-Explanation And Instruction Explanation On Mathematical Problem Solving Transfer Among Studying Examples

Based on lots of references of the role of self-explanation in mathematical problem-solving, this article summarizes the development on the concepts, research methods, theories, as well as the status of the role of self-explanation in mathematical problem-solving research in these days. We then try to adopt instruction explanation to resolve the shortage of the self-explanation. The purpose of this research lies in examining the present of the worked example of the fading worked-out steps whether is better than the "example- problem pairs" or not to promote the student's problem solving. There is the self-explanation of hint whether is better than didn't hinting self-explanation to promote the student's problem solving. The presence of the worked example whether has the interaction with the self-explanation or not. The instruction explanation whether is better than no instruction explanation to promote the student's problem solving.There are two experiments in this text. There are 165 students in the first experiment random assortment four classes students of grade three in the middle school to four experiment scenes according to their natural classes: example-problem pairs (40),example-problem pairs + self-explanation (40), fading worked-out steps (44), fading worked-out steps+ self-explanation(41).In the second experiment we offered the instruction explanation to anther class about 35 students whose self-explanations were wrong in fading worked-out steps+ self-explanation experiment scene. Its scores were compared with the group of fading worked-out steps+ self-explanation experiment scene in the first experiment. The results show:1. In the way of the example present, the fading worked-out steps is better than"example-problem pairs"in the score of study and transfer: the group of fading worked-out steps is better than example-problem pairs in the score of study and near-transfer, but there has not difference in the score of far-transfer; the group of fading worked-out steps+ self-explanation is better than"example-problem pairs"+ self-explanation in the score of study and transfer.2. Under the condition of having the self-explanation or not, the self-explanation is better than no self-explanation in transfer scores: the experiment scores and transfer scores of the group of"example-problem pairs"+ self-explanation are better than the group of"example-problem pairs"; the experiment scores and transfer scores of the group of fading worked-out steps +self-explanation are better than the group of fading worked-out steps.3. The presence of the worked example hasn't the interaction with the self-explanation.4. Under the situation that have the instruction explanation or not, the instruction explanation is better than no instruction explanation in the transfer scores: the transfer scores of the group of fading worked-out steps+ self-explanation + instruction explanation is better than the group of fading worked-out steps + self-explanation.