Equations of the form a/x = b are the most difficult equation type, reflecting procedural complexity¶

Claim · All claims
Evidence · 2 studies · 1 causal r2, 1 associational r2 · q3 · i2–i3
Currency · newest study 2014 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q3 i3 Equation type affected accuracy, effect size η2 p = 0.169, with all participants less accurate on C equations (a/x = b) than A and B equations. → Susac A 2014 q3 i2 Equation type affected RTs, effect size η2 p = 0.113, and inverse efficiency indicated C equations were the most difficult. → 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 · i3 · causal · r2

Two-way mixed-design ANOVA, Age × Equation type (A vs. B vs. C), on accuracy; printed effect size η2 p = 0.169 for Equation type. "All participants were less accurate on the C equations compared to both the A and B equations."

"a significant main effects of both Age [ F(3,327) = 8.37, p < 0.001, η2 p = 0.071] and Equation type [ F(2,654) = 66.59, p < 0.001, η2 p = 0.169] were found, as well as their interac­tion [ F(6,654) = 2.53, p < 0.05, η2 p = 0.023]"

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 · i2 · associational · r2

Inverse-efficiency ANOVA (Age × Equation type) on equations with letters: Equation type main effect F(2,650) = 43.72, printed effect size η2 p = 0.119; "the C equations were the most dif­ficult" and A and B did not differ significantly.

"the results suggest that the C equations were the most dif­ficult. There was no statistically significant difference between the A and the B equations."

Discussion¶

Related Claims¶

• Students' difficulty rankings of equation types partly mismatch their measured performance, though metacognitive accuracy improves with age — related
• Younger students solve letter equations less accurately than number equations, but this difference disappears by age 16–17 — related
• Students become faster and more accurate in equation rearrangement over a short practice session even without feedback — related
• Girls were on average more accurate than boys in equation rearrangement, with no significant difference in speed — related
• High school teachers' rankings of algebra problem difficulty were uncorrelated with student performance, while middle school teachers' rankings were accurate