Learning symbolic modeling from incorrect examples

Previous research has shown that instruction followed by problem solving (I-PS) is an effective pedagogical approach in many procedural domains, but engaging students in problem solving before instruction (PS-I) can benefit conceptual learning and transfer. However, it is unclear which order of instruction is optimal for domains that rely heavily on both procedural and conceptual knowledge, such as symbolic modeling. This study investigates optimal order of instruction for learning modeling when instruction is based on incorrect examples. In an experiment with 97 eighth graders, we tested which order of instruction, I-PS or PS-I, was most beneficial for learning to create and evaluate mathematical models of rate-based situations, and for transferring learning to create models with different structures. The study also investigated whether optimal order of instruction depended on a student’s prior knowledge. Students in the I-PS condition performed better on model generation, regardless of prior knowledge, but no condition differences were found in model evaluation or transfer outcomes. Students in the PS-I condition reported more instances of confusion. Confusion negatively predicted transfer and showed a trend toward negatively predicting model evaluation. However, confusion did not mediate the relationship between condition and learning outcomes. This study extends the research on the role of instructional order in learning, and its impact on students’ affective experiences.