Students become faster and more accurate in equation rearrangement over a short practice session even without feedback¶

Claim · All claims
Evidence · 2 studies · 2 associational r2 · q3 · i1–i3
Currency · newest study 2014 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q3 i1 Accuracy increased from the first to the second block (Block main effect, effect size η2 p = 0.015). → Susac A 2014 q3 i3 RTs decreased from the first to the second block (Block main effect, effect size η2 p = 0.489). → Susac A 2014 (2)

Evidence¶

Susac A 2014¶

Susac A, Bubic A, Vrbanc A and Planinic M (2014) Development of abstract mathematical reasoning: the case of algebra. Front. Hum. Neurosci. 8:679. https://doi.org/10.3389/fnhum.2014.00679

q3 · i1 · associational · r2

Two-way mixed-design ANOVA, Age × Block (first vs. second), on accuracy across the experiment's blocks; printed effect size η2 p = 0.015 for the Block main effect, a small effect.

"The results showed a statistically significant main effect of both factors, Age [F(3,327) = 8.37, p < 0.001, η2 p = 0.071] and Block [F(1,327) = 5.11, p < 0.05, η2 p = 0.015]"

Susac A 2014 (2)¶

Susac A, Bubic A, Vrbanc A and Planinic M (2014) Development of abstract mathematical reasoning: the case of algebra. Front. Hum. Neurosci. 8:679. https://doi.org/10.3389/fnhum.2014.00679

q3 · i3 · associational · r2

Same ANOVA design on RTs; printed effect size η2 p = 0.489 for the Block main effect, a large effect. "Participants of all ages became faster in equa­tion solving in the second block," even those with stable high accuracy.

"η2 p = 0.099] and Block [F(1,326) = 312.27, p < 0.001, η2 p = 0.489], while the interaction was not significant [ F(3,326) = 2.58, p > 0.05, η2 p = 0.023]. Participants of all ages became faster in equa­tion solving in the second block"

Discussion¶

Learner Variables¶

• Algebraic Thinking — outcome: instruction changes it

Related Claims¶

• Equations of the form a/x = b are the most difficult equation type, reflecting procedural complexity — related
• Students' difficulty rankings of equation types partly mismatch their measured performance, though metacognitive accuracy improves with age — related
• Accuracy and speed of simple equation rearrangement increase with students' age across grades 7–12 — related
• Alternating example-practice pairs produce faster and more accurate near-transfer solutions than blocked presentation of examples followed by practice — related
• During motor practice with knowledge of results, all groups reduced absolute error across blocks, and groups whose KR decision fell after the trial were more accurate during practice than groups whose decision fell before it, independent of choice. — related
• A second training session two days later further increases reasoning accuracy beyond the first session, though less strongly — related