Adapt productive failure principles to large university lectures by having the lecturer discuss preparatory exercises and common misconceptions at the start of the lecture¶

Strategy · All strategies
Evidence · 4 claims (3 for, 1 mixed) · 1 study (1 design), q3 · 1 of 1 report an effect size · 4 claims rest on one study

Description¶

Because discussing student-generated solutions with hundreds of students is not feasible, the article adapted PF principles 2A and 2B: the lecturer "discussed the preparatory exercises at the beginning of the subsequent lecture and elaborated on potential pitfalls and common misconceptions", emphasizing critical features and referring frequently to the exercises. This enabled students "to compare and contrast their solutions to the canonical ones" without individual discussion of student work.

Design Implications¶

Context¶

Requirements¶

• The lecturer must review the preparatory exercises and highlight common misconceptions and critical features at the start of each PS-I cycle lecture

Constraints¶

• The lecturer was unable to build directly on students' solutions due to the vast number of students in the course; the approach was an adaptation, not a full implementation of PF principles 2A and 2B

Target Learners¶

• first-year university students in large lecture courses

Target Learning Goals¶

• conceptual understanding of targeted mathematical concepts

Affordances¶

• Productive Failure Two Phase Four Mechanisms Framework

Claims¶

• During the intervention, linear algebra exam performance rose distinctly above overall first-year performance, a pattern the authors interpret as intervention impact beyond cohort differences [+W]
• Participation in preparatory exercises predicted conceptual-understanding test performance in the first two iterations only, with no evidence in Years 3 and 4 [~W]
• Students' participation in preparatory exercises positively predicted their final exam grade in every intervention year (β = 0.16–0.31; R² = 0.03–0.16) [+W]
• The PS-I intervention significantly increased the percentage of students passing the linear algebra final exam in all four cohorts (Cohen's d = 0.21–0.42) [+W]

Related Strategies¶

• Invented Strategies Before Instruction
• Just In Time Teaching

Examples¶

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Key Sources¶

• Baumgartner, V., Daguati, S., Trninic, D., Akveld, M., Caspar, A., Hungerbühler, N., Kapur, M. (2025). Problem-solving before instruction for learning linear algebra in university mathematics. Instructional Science. https://doi.org/10.1007/s11251-025-09709-8