Number of canonical components in students' PF solutions correlates with conceptual knowledge, but the range of distinct components does not¶

Claim · All claims
Evidence · 1 study (2 entries) · causal r2 · q3 · i3 large
Currency · newest study 2025 · checked against its sources 2026-10-20 (automated, 2 of 2 entries) · not reviewed by a person

Subclaims¶

q3 i3 Overall quality measured as canonical components present in PF solutions showed a strong positive correlation with conceptual knowledge scores (r =.418, p =.009). → Thomas C. Braas 2025 q3 i? The range of distinct components present (maximum four points) did not significantly relate to conceptual knowledge (r =.211, p =.204). → Thomas C. Braas 2025 (2)

Evidence¶

Thomas C. Braas 2025¶

Thomas C. Braas, Christian Hartmann, Vincent Hoogerheide, Nikol Rummel, Tamara van Gog. (2025). When is observing failure productive? Investigating the role of solution diversity in vicarious failure. Instructional Science. https://doi.org/10.1007/s11251-025-09706-x

q3 · i3 · causal · r2

Correlational analysis within the PF condition (n = 37 scored) of solutions generated in the problem-solving phase; the article reports "a strong positive correlation with conceptual knowledge scores (r =.418, p =.009)".

"The overall quality of solutions, measured through the number of canonical components that were present in the students’ solutions, showed a strong positive correlation with conceptual knowledge scores (r =.418, p =.009)."

Thomas C. Braas 2025 (2)¶

Thomas C. Braas, Christian Hartmann, Vincent Hoogerheide, Nikol Rummel, Tamara van Gog. (2025). When is observing failure productive? Investigating the role of solution diversity in vicarious failure. Instructional Science. https://doi.org/10.1007/s11251-025-09706-x

q3 · i? · causal · r2

Secondary correlational analysis in the PF condition using the range of distinct canonical components (maximum four points); the correlation with conceptual knowledge was not significant (r =.211, p =.204).

"However, this finding was not iterated when viewing the range of which components were present (i.e., max. four points, indicating all canonical components used regardless of the number of components used overall, as done in both VF-examples) (r =.211, p =.204)."

Discussion¶

Related Claims¶

• Neither the quantity nor the quality of PF students' own solution attempts correlated with their conceptual knowledge acquisition — related
• Inventing-phase failure was unproductive: invented solutions did not correlate with transfer, but suboptimal inventions related to lower interest and learning time — related
• Success in developing the canonical solution is not a necessary condition for learning from generation, but failure is not claimed to be indispensable either — related
• Solution quality correlates with conceptual knowledge and gap awareness only for individual problem solvers — related
• Vicarious failure with high solution diversity is as effective as engaging in Productive Failure oneself for conceptual knowledge acquisition — related
• Diversity of student-generated representations and solution methods is significantly correlated with learning from PF — reports the opposite