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.