关键词: 算术应用题, 表面特征, 结构特征, 变异样例, 迁移

Abstract: There is disagreement with regard to the transfer effects of learning through varied worked examples. Ross (1989) found that multiple examples should be made very similar to each other; even a small difference in the surface feature could make the learner pay more attention to solving the problem. Gentner (2003) discovered that comparing examples with the same structure could prompt the learners’ transition to problem solving. Holyoak (1987) pointed out that deeper structural differences had an impact on the transfer. Based on these researches, the present study hypothesized that the variability of the surface feature of two examples could have some effect on the near transfer of pupils’ word-problem solving, and the proper variability of the structural feature of the two examples could have an impact on the far transfer of pupils’ word-problem solving.
A total of 210 second-grade students from a primary school were selected using a pretest and were divided into six experimental groups and a control group. Each group learnt a word problem example. Then, the pupils of three experimental groups learned one kind of word problem example that varied from the first example with regard to the surface feature: the pupils in the first group learned a number and substance varied example; the pupils in the second group learned a story varied example; and those in the third group learned an expression varied example. The pupils in the other three experimental groups learned another kind of worked example that varied from the first problem with regard to the structural feature. The first group learned a rule varied example, the second group learned a rule repeated example; the third group, learned a rule of speed composed example. The pupils in the control group did not learn any worked example. Finally, all the pupils of the six experimental groups and the control group were given a test with 15 word problems. Three of them varied from the first example with regard to the surface feature, three of them varied from the first example with regard to the structural feature, and the others varied from the first example with regard to the surface and structural features. The experimenters recorded the pupils’ test scores.
The results were as follows. First, the pupils in the control group who learned the first word problem example could solve the word problems whose example varied with regard to the surface feature, but could not solve the other word problems. Second, the pupils in the three experimental groups who learned the word problem example that varied with regard to the surface feature could solve the word problems that varied from the first example with regard to the surface feature, but could not solve the other word problems. Third, a different effect was observed for the pupils in the three experimental groups who learned the word problem example that varied with regard to the structural feature. The pupils who learned the rule parallel combined example solved more word problems than the pupils in the other groups. The pupils who learned the rule varied example solved more word problems than those who learned the rule embedding combined example. The pupils who learned the rule embedding combined example solved the fewest number of word problems.
The variability of the surface feature of the two examples could have some impact on the near transfer of pupils’ word-problem solving. The rule parallel combined example had the best effect on the far transfer of the pupils’ word-problem solving. The rule varied example had a more positive effect than the rule embedding combined example on the pupils’ word-problem solving far transfer. Finally, the rule embedding combined example had the poorest effect on the far transfer of the pupils’ word-problem solving

Key words: word problem, surface feature, structural feature, varied worked example, transfer