ISSN 0439-755X
CN 11-1911/B
主办：中国心理学会
　　　中国科学院心理研究所
出版：科学出版社

心理学报 ›› 2015, Vol. 47 ›› Issue (8): 1013-1027.doi: 10.3724/SP.J.1041.2015.01013

• 论文 • 上一篇    下一篇

通过对比进行学习：多重样例变异性与先前知识的作用

郭建鹏1;杨凌燕2   

  1. (1厦门大学教育研究院, 厦门 361005) (2美国爱荷华大学教育学院, 爱荷华 52242)
  • 收稿日期:2014-07-18 发布日期:2015-08-25 出版日期:2015-08-25
  • 通讯作者: 郭建鹏, E-mail: guojianpeng@gmail.com
  • 基金资助:

    中央高校基本科研业务费专项资金(2013221021)。

Learning from Comparison: The Effects of Example Variability and Prior Knowledge

GUO Jianpeng1; YANG Lingyan2   

  1. (1 Institute of Education, Xiamen University, Xiamen 361005, China) (2 College of Education, University of Iowa, Iowa 52242, USA)
  • Received:2014-07-18 Online:2015-08-25 Published:2015-08-25
  • Contact: GUO Jianpeng, E-mail: guojianpeng@gmail.com

PDF (PC)

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摘要：

基于解一元一次方程两个关键特征(问题类型和解法)的单独变异和同时变异设计4种变异类型的多重样例。251名初一年级学生对比类型和解法的单独变异再对比两者的同时变异、对比解法或类型的单独变异再对比两者的同时变异、或者对比类型和解法的单独变异但没有对比两者的同时变异。结果显示变异类型与先前知识具有显著的交互作用：对于在前测中没有使用简便方法的学生, 类型和解法先单独变异再同时变异的方法最能提高他们的变通性知识和概念性知识。相反对于在前测中有使用简便方法的学生, 这种方法的学习效果最差。先前知识不同的学生学习时感知到不同的关键特征, 多重样例的对比要基于学生学习的关键特征。

关键词: 样例变异性, 对比, 关键特征, 变异范式, 数学教育

Abstract:

There is an enormous body of example-based research consistently showing that comparing multiple examples supports greater learning than does studying one single example or studying examples separately. Not all comparisons, however, may be equally effective. The impact of comparison on learning depends on the example variability and students’ prior knowledge; but the findings are contradictory. The current study investigated the effects of example variability and students’ prior knowledge on learning multistep linear equation solving.
In this study, problem type and solution method were identified as two critical aspects for learning how to solve linear equations, and four comparison conditions were designed accordingly. 251 seventh-grade students were randomly assigned to learn equation solving by (1) first comparing separate variation of problem types and solution methods and then comparing simultaneous variation of these two aspects, abbreviated as Type_Method_Type+Method, (2) first comparing separate variation of solution methods and then comparing simultaneous variation of problem types and solution methods, abbreviated as Method_Method_Type+Method, (3) first comparing separate variation of problem types and then comparing simultaneous variation of problem types and solution methods, abbreviated as Type_Type_Type+Method, or (4) comparing separation variation of problem types and solution methods but not comparing simultaneous variation of these two aspects, abbreviated as Type_Method_Type/Method. Students’ procedural knowledge, flexibility knowledge, and conceptual knowledge were assessed at pretest and posttest to evaluate the effectiveness of different comparisons.
To examine the possible interaction effect between students’ prior knowledge and experimental condition, students were categorized as using shortcuts or not using shortcuts based on their pretest performance. Results showed significant interaction effects between prior knowledge and condition. Comparing the two critical aspects of problem type and solution method first separately and then simultaneously (Type_Method_Type+ Method) led to more flexibility knowledge and conceptual knowledge than other methods for students who did not use shortcuts at pretest. The effectiveness of this method, however, was reverse for students who used shortcuts at pretest. In addition, Type_Method_Type/Method was the least beneficial condition for students who did not use shortcuts at pretest; Method_Method_Type+Method was the most beneficial condition for students who used shortcuts at pretest.

Example design should focus on aspects and features that are critical for student learning, and use the distinction of critical/uncritical instead of the distinction of surface/structural adopted by existing cognitive studies. Students with different levels of prior knowledge perceived different aspects of examples as critical for their learning. On the basis of these critical aspects, certain patterns of variation and invariance should be adopted to systematically determine the variability of examples, and to help students discern critical aspects first separately and then simultaneously. Suggestions for future research are provided.

Key words: example variability, comparison, critical aspect, patterns of variation and invariance, mathematics education