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¶

Claim · All claims
Evidence · 1 study (2 entries) · causal r2 · q3 · i2 medium
Currency · newest study 2021 · checked against its sources 2026-10-18 (automated, 2 of 2 entries) · not reviewed by a person

Subclaims¶

q3 i2 PS-I students outperformed I-PS students on the 24-item isomorphic problem-solving test after controlling for mathematics grade and reasoning ability (η2p = 0.06). → Esther Ziegler 2021 q3 i? The advantage showed no main effect of time and no condition × time interaction, indicating a consistent advantage at both delays. → 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

Mixed-factorial ANCOVA on the 24-item isomorphic test (Cronbach's α = 0.89), with 41 PS-I and 40 I-PS sixth-graders and mathematics grade and reasoning ability as covariates; the article reports the condition main effect "F(1,72) = 4.35, p = 0.041, η2p = 0.06".

"There was a main effect of condition on students' isomorphic problem solving in favor of the PS-I condition after controlling for mathematics grade and reasoning ability, F(1,72) = 4.35, p = 0.041, η2p = 0.06"

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 · i? · causal · r2

Same ANCOVA with a time factor (one-day vs one-week posttest); the article reports no time effect and no condition × time interaction, calling it "a consistent advantage of the PS-I condition in the one-day and one-week delay."

"there was no main effect of time, F(1,72) = 0.25, p = 0.619, η2p = 0.00, and also no interaction of condition × time, F(1,72) = 0.13, p = 0.715, η2p = 0.00, indicating a consistent advantage of the PS-I condition in the one-day and one-week delay."

Discussion¶

Learner Variables¶

• Algebraic Thinking — outcome: instruction changes it
• Problem Solving — outcome: instruction changes it

Related Claims¶

• Micro productive failure showed no effect on conceptual explanation, but a condition × time interaction emerged as the I-PS mean advantage at one day reversed at one week — related
• Productive Failure Improves Conceptual Learning — a broader claim this one bears on
• The manipulation worked as intended: I-PS students largely succeeded on the problem-solving sheets while PS-I students largely failed — related
• Initial failure did not hurt subsequent learning during instruction: no condition differences on example generation or immediate learning tests — related
• Practice-problem performance favored PS-I overall, but the advantage was concentrated on the first two worksheets (d = 0.52) — related
• The self-study-before-discussion advantage persisted at one-week delayed tests, with lecture-condition scores declining over time while self-study-condition scores remained stable — related
• Order of worked examples and problem solving had no significant effect on application and transfer scores in experimental design or graphing — related
• Reflection on a prediction failure shifted students' isomorphism awareness from structural recognition to boundary awareness
• Merely delaying instruction until after problem solving does not improve conceptual understanding when no additional measures trigger knowledge-gap awareness or deep-feature discovery — reports the opposite
• Solving an isomorphic practice problem after studying a worked example improves prospective monitoring accuracy, with mixed effects on regulation accuracy — related
• Problem solving after acquisition outperformed example study at a one-week delayed posttest but not immediately — related