Instructional Science

Problem-solving before instruction has been shown to be a more effective learning design than traditional tell-and-practice for several mathematical concepts at the secondary school level. In particular, the more a problem-solving before instruction design follows the productive failure principles, such as comparing and contrasting student-generated solutions, the higher the effect on students’ conceptual understanding and transfer. University mathematics education poses several inherent constraints that complicate the implementation of these principles. In the present study, we implemented a problem-solving before instruction design in a university linear algebra course adhering to the productive failure principles as closely as possible. Participation in the preparatory problems was voluntary. We investigated the effect on students’ learning over four one-year iterations in a design-based research approach. Compared to the baseline (aggregate of cohorts prior to the intervention), we observed a significant increase in final exam performance for all four cohorts with effect sizes between Cohen’s d = 0.28 and d = 0.59. For students who agreed to further analyses, our results show that up to 16% of the variance in students’ performance can be explained by variance in their participation in the problem-solving before instruction design. As our design did not include a control group, we refrain from conclusions regarding any design components that might have caused these effects. However, these results are promising, given that our implementation involved only minor changes to the original course structure and required little extra time for students.

Illustrative examples demonstrate how abstract information can be applied in real-world. In the context of advancing evidence-informed teaching practice, the current intervention study investigated to what extent student teachers should be supported in learning educational theories and findings by different example-based approaches. Conducting a 1 × 3-factorial design, N = 105 student teachers were randomly assigned to three experimental groups: After a pre-test, all groups received the same learning instruction on the topic of cooperative learning. Then, (1) n = 35 students were prompted to generate own examples for the instructional text, (2) n = 35 students received examples along with the text, and (3) n = 35 students studied the text only, without any prompts or examples. In a post-questionnaire, it was retrospectively assessed how students perceived their learning control in engaging with the material; in a post-test, knowledge retention and knowledge transfer were measured. As assumed, findings revealed that generating examples enhanced perceived learning control and learning outcomes compared to studying provided examples. Students who learned with the instructional text only achieved lowest learning outcomes; but contrary to the expectations, these students perceived their learning control comparably high as those who generated examples. Mediation analyses indicated that for students who received illustrative examples or the instructional text only, a greater learning control perception was positively associated with knowledge retention, subsequently enhancing knowledge transfer. The study underscores the benefits of illustrative examples in teacher education, particularly when students engage in generating them. It suggests further examination of how and why example generation facilitates learning.