Effects of Rule Variant Reasoning in Far Transfer Problem Solving

Previous experimental results have shown that worked-example learning can promote the solution of near, but not far, transfer problems. However, according to Sweller, in order to promote the solution of the far transfer problem, it was necessary to learn a series of worked-examples of variant problems solutions. Furthermore, they must try to solve problems requiring variant rules. Thus, they will be assigned a large number of homework exercises. To avoid this, we developed a rule worked-example learning method to promote far transfer problem solving, in which students applied rules variant reasoning after prototype worked-example learning. We carried out four experiments to test the effectiveness of this method. In Experiment 1, 162 fourth- grade students were selected as participants. They were randomly divided into three groups. After learning the prototype worked-examples, the first group learned worked-examples of the four variant problem solutions. The second group applied rule variant reasoning to four problems presented to them. The third group solved four near transfer problems. Then, participants in all groups were evaluated by transfer tests. In Experiment 2, 54 mathematics high- performing students, 54 mathematics middle- performing students, and 54 mathematics low-performing students were selected as participants. After learning the prototype worked-examples, they all applied rule variant reasoning to four variant problems presented to them. Then, they all took transfer tests. In Experiment 3, 90 mathematics middle-performing students were randomly divided into three groups. Additionally, 90 mathematics low-performing students were randomly divided into three groups. After prototype worked-examples learning, two first groups made up the variant problems by self, and then they carried out rules variant reasoning for the variant problems; two second groups carried out rules variant reasoning for four variant problems presented to them; two third groups made four types division for eight variant problems presented to them, and then they carried out rules variant reasoning for the four kinds of the variant problems. Finally, they were all tested by transfer tests. In Experiment 4, 80 mathematics low-performing students were randomly divided into two groups. After learning prototype worked-examples, they all made four types division for eight variant problems presented to them. The first group carried out rules variant reasoning for the four kinds of the variant problems. The second group carried out rules variant reasoning using the variant problems of incomplete solving rules. Finally, they all took transfer tests. The results showed that (1) The far transfer scores of the first group were significantly better than those of the second and the third groups, and that the second group's scores were significantly better than those of the third group; (2) Significant differences were found in the far transfer test scores among three math performance levels; (3) The far transfer test scores of the third group were significantly better than those of the first and second groups; (4) The far transfer test scores of the second group were significantly better than those of the first. It can be concluded that rule variant reasoning after learning prototype worked-example significantly promotes far transfer problem solving.