Practice-problem performance favored PS-I overall, but the advantage was concentrated on the first two worksheets (d = 0.52)¶

Claim · All claims
Evidence · 1 study (2 entries) · causal r2 · q3 · i2 medium
Currency · newest study 2021 · checked against its sources 2026-10-20 (automated, 2 of 2 entries) · not reviewed by a person

Subclaims¶

q3 i2 On practice problems during instruction, PS-I significantly outperformed I-PS (η2p = 0.10). → Esther Ziegler 2021 q3 i2 Sub-analyses showed the practice advantage was significant only on the first two worksheets (d = 0.52), possibly influenced by the pretest. → Esther Ziegler 2021 (2)

Evidence¶

Esther Ziegler 2021¶

Esther Ziegler, Dragan Trninic, Manu Kapur. (2021). Micro productive failure and the acquisition of algebraic procedural knowledge. Instructional Science 49, 313–336. https://doi.org/10.1007/s11251-021-09544-7

q3 · i2 · causal · r2

Univariate ANOVA on the ratio of correctly solved practice problems (process measure 3) across the six worksheets, from the same MANCOVA; the article reports F(1,77) = 8.22, p = 0.005, η2p = 0.10 in favor of PS-I.

"On subsequent practice problems, the effect reversed to a significant effect in favor of the PS-I condition, F(1,77) = 8.22, p = 0.005, η2p = 0.10, but no significant effect on immediate learning tests"

Esther Ziegler 2021 (2)¶

Esther Ziegler, Dragan Trninic, Manu Kapur. (2021). Micro productive failure and the acquisition of algebraic procedural knowledge. Instructional Science 49, 313–336. https://doi.org/10.1007/s11251-021-09544-7

q3 · i2 · causal · r2

Sub-analysis comparing the first two worksheets with the later four; the article reports t(79) = 2.35, p = 0.021, d = 0.52 on the first two worksheets and suggests there might have been an influence of the pretest on initial practice problems only.

"we found a significant difference between the PS-I and the I-PS conditions on the first two worksheets, t(79) = 2.35, p = 0.021, d = 0.52, distinct from later worksheets and the above reported practice problem outcomes."

Discussion¶

Learner Variables¶

• Algebraic Thinking — outcome: instruction changes it
• Proportional Reasoning — outcome: instruction changes it

Related Claims¶

• Initial failure did not hurt subsequent learning during instruction: no condition differences on example generation or immediate learning tests — related
• Productive Failure Improves Conceptual Learning — a broader claim this one bears on
• Micro productive failure (problem solving before instruction) improved sixth-graders' isomorphic algebraic procedural problem solving, with the advantage stable across one-day and one-week delays — related
• CPS students proposed better problem-solving solutions and allocated more time to solutions, evidence-based reasoning, and simulation/data recording than IPS students — related
• PF design fidelity predicts larger PS-I effects, with four fidelity criteria showing significant subgroup differences — related
• The manipulation worked as intended: I-PS students largely succeeded on the problem-solving sheets while PS-I students largely failed — reports the opposite
• Order of worked examples and problem solving had no significant effect on application and transfer scores in experimental design or graphing — related
• In Experiment 1, I-PS students solved the initial problem better but PS-I students learned more from the subsequent instructional video — related
• Productive failure before instruction outperforms instruction followed by problem-solving — related
• Peer-expert modeling videos interspersed with instructional guidance produce significant medium-to-large positive effects on IPS performance compared to practice-only groups — related