关键词: 新算符, 指-对数转换规则, 对数运算规则, 转换标记法, 解释法

Abstract: Most of the previous researches indicated that, after students had learned worked-examples including certain rules, they could master the rules involved to solve problems. However, recent researches have shown that students were able to discover and master new rules through well-designed worked-examples, based on their prior knowledge. Zhang Qi and Lin Hongxin (2005) and Lin Hongxin and Zhang Qi (2007) found that primary school students could learn new mathematic rules with proper design, but these students failed to master algebra rules. One possible reason of this finding was that the students did not understand the meaning of new algebra operators. Therefore, we designed worked-examples of conversion from index to logarithmic form by applying the “method of converting label” and worked examples of logarithmic operations by applying the “method of explanation”. The main objective of our study was to examine the effectiveness of each design method on worked-example learning. In order to explore the effect of “method of converting label (design with method of converting label or normal design)” and “number of worked-examples (3 or 6)” on learning conversion from index to logarithmic form, a 2×2 between-subjects factorial design was used in Experiment 1. One hundred twenty 9th grade students participated the experiment in which they were divided into 4 groups to take part in different procedures. Experiment 2 used a 2 (method of design: design with the method of explanation or normal design) ×2 (learned the conversion rules: yes or no) between-subjects factorial design, in which there were also 120 9th grade students took part and carried on different procedures in 4 separate groups to learn logarithmic operation rules. There was a significant main effect of “method of converting label”, which is, students who have learned worked-examples with this method performed better than those who haven’t. However, there was no significant main effect of the number of examples or interaction between the method of converting label and the number of examples; In addition, the main effects of both factors (design with method of explanation or normal design; learned conversion from index to logarithmic form or not) were significant. There was also a significant interaction between these two factors. For students who learned the conversion rules, their performance on worked-examples designed with the method of explanation was better than those who learned normal-designed examples. For students without the knowledge of the conversion rules, there was no significant difference between the two groups. The present study implied that most of the 9th grade students could master the conversion rules from index to logarithmic form and the logarithmic operation rules. Worked-examples designed with the method of converting label significantly improve students’ learning. Worked-examples designed with the method of explanation facilitate transferring, which is related to participants’ previous knowledge.

Key words: new algebra operators, conversion rules from index to logarithmic form, logarithmic operation rules, method of converting label, method of explanation