Abstract: Researchers have consistently shown that studying multiple examples is more effective than one example to promote learning because the comparison evoked by comparing multiple examples is generally good for learning. Not all comparisons, however, may equally be effective. Principles found in the literature for designing multiple examples remain ambiguous. This paper reviews experimental studies on learning from comparison of examples and identifies issues that have not been resolved: (a) how similar or different examples should be to facilitate learning, and (b) the role of students’ prior knowledge in example-based learning. First, contradictory findings have been reported regarding how similar or different multiple examples should be in order to facilitate learning. Examples are generally analyzed from surface (irrelevant) features and structural (relevant) features. Surface features, such as names, objects, numbers, and story lines, are irrelevant to goal attainment; structural features, such as underlying mathematical procedures, rules, solutions, and principles, are relevant to goal attainment. It is unclear regarding how similar multiple examples should be in terms of surface and structural features. On the one hand, examples with different surface features were shown to help the learner focus on structural features, increase germane cognitive load, and induce a schema; superficially similar examples might confuse structural features with surface features and thus spoil schema construction and future problem solving. On the other hand, providing superficially similar examples does not overburden the learners’ working memory and can help them discern and align the structural features; highly variable examples might make the underlying structural commonalities difficult to be noticed. Second, it is also unclear regarding the role of students’ prior knowledge in learning from comparing multiple examples. Researchers found that (a) students with low prior knowledge did not benefit from comparing multiple examples, especially the complex and unfamiliar examples; (b) students with high prior knowledge benefited from comparing any example variability whereas students with low prior knowledge benefited from comparing only highly variable examples; (c) students with higher prior knowledge benefited more from comparing high-variability examples whereas students with lower prior knowledge benefited more from comparing low-variability examples; and (d) there was no interaction between students’ prior knowledge and example variability. The review addresses these limitations of existing literature and provides recommendations for example design according to our empirical studies. First, example design should focus on aspects and features that are critical for student learning, and use the distinction of critical/uncritical instead of surface/structural adopted by existing cognitive studies. Second, students may need to separately discern each critical aspect before they can benefit from comparing simultaneous variation of these aspects. Simultaneous variation is likely to overwhelm students and thus to be harmful for learning if they have not separately discerned each critical aspect. Third, students with different levels of prior knowledge may perceive different aspects of examples as critical for their learning and thus benefit differently from the same instruction. Examples should be designed according to aspects that are critical to specific students. Suggestions for future research are provided.

Key words: multiple examples, variability, prior knowledge, comparison

摘要： 样例学习研究表明多重样例的学习效果好于单个样例。然而研究者关于如何有效设计多重样例得出了不同的发现。通过综述已有关于多重样例学习的实证研究，总结出两个尚未得到解决的问题：（1）多重样例之间的相似或相异程度应该如何；（2）学生的先前知识在多重样例学习中的作用如何。针对已有研究的局限性，本文指出，具有不同先前知识的学生学习时感受到不同的关键属性，多重样例应该基于学生学习时的关键属性设计特定的变易范式以帮助学生学习。

关键词: 多重样例, 变异性, 先前知识, 对比