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Researchers have consistently demonstrated that multiple examples are better than one example in facilitating learning because the comparison evoked by multiple examples supports learning and transfer. However, research outcomes are unclear regarding the effects of example variability and prior knowledge on learning from comparing multiple examples. In this experimental study, the two critical aspects of problem type and solution method were used to design comparison conditions to teach equation solving. Randomly selected groups of 263 seventh-grade students learned to solve equations by comparing different example pairs. Results showed that students who did not use a shortcut method at pretest benefited least from comparing the two critical aspects first separately and then simultaneously. Students who used a shortcut method at pretest learned equally within conditions. Students may need to separately discern each critical aspect before they benefit from comparing simultaneous variation of these aspects. Examples should be designed according to aspects that are critical for specific students. [ABSTRACT FROM AUTHOR]

Although researchers have demonstrated that studying multiple examples is more effective than studying one example to facilitate learning, the principles found in the literature for designing multiple examples remain ambiguous. This paper reviews variation theory research on example design which sheds light on unclear issues regarding the effects of example variability. First, the distinction of surface/structural should be replaced by critical/uncritical in example study. Aspects and features that are critical to students' understanding should be identified and compared in example design. Second, variation as well as similarity among examples should be taken into consideration in example design. Certain patterns of variation and invariance should be adopted to systematically determine the variability of examples. Third, students with different levels of prior knowledge perceive different aspects of examples that are critical for their learning. Examples should be designed according to aspects that are critical to specific students. [ABSTRACT FROM AUTHOR]

In experiment 1, novice fourth-grade students ( N = 92) who compared multiple examples that separately varied each critical aspect and then simultaneously varied all critical aspects developed better conceptual knowledge about the altitude of a triangle than students who compared multiple examples that did not separately vary each critical aspect but simultaneously varied all critical aspects. In experiment 2, this pattern was the same for fourth-grade students ( N = 90) but not for sixth-grade students ( N = 94) who had greater prior knowledge about the concept. Aspects that are critical for learning should be varied first separately and then simultaneously, and students with different levels of prior knowledge may perceive different aspects as critical for their learning and thus benefit differently from the identical instruction. [ABSTRACT FROM AUTHOR]