Younger students solve letter equations less accurately than number equations, but this difference disappears by age 16–17¶

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

Subclaims¶

q3 i2 Abstraction level (numbers vs. letters) affected accuracy, effect size η2 p = 0.126, with an Age × Abstraction interaction, η2 p = 0.043. → Susac A 2014 q3 i? In the 2nd grade of secondary school (age 16–17) there was no statistically significant accuracy difference between number and letter equations. → 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 · i2 · associational · r2

Two-way mixed-design ANOVA with between-subjects factor Age and within-subjects factor Abstraction level (numbers vs. letters) on accuracy; printed effect sizes η2 p = 0.126 (Abstraction level) and η2 p = 0.043 (interaction). "Participants were more accurate on equations with numbers, but only in primary school and in the 1st grade of secondary school."

"the statistically significant main effects of Age [F(3,327) = 8.37, p < 0.001, η2 p = 0.071] and Abstraction level [F(1,327) = 47.17, p < 0.001, η2 p = 0.126], as well as the interac­tion effect [ F(3,327) = 4.89, p < 0.01, η2 p = 0.043], were found"

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 · i? · associational · r2

Post-hoc pattern of the Age × Abstraction interaction: "no sta­tistically significant difference" in accuracy between number and letter equations for 2nd-grade secondary students; no effect size printed, and equivalence was not otherwise tested.

"In the 2nd grade of secondary school there was no sta­tistically significant difference in the accuracy of solving equations with numbers and letters."

Discussion¶

Learner Variables¶

• Age and Developmental Stage — moderator: an instructional effect differs with it

Related Claims¶

• Equations of the form a/x = b are the most difficult equation type, reflecting procedural complexity — related
• Younger students mostly use concrete strategies (e.g., inserting numbers) while older students use abstract rule-based strategies, with the transition around age 14–15 — related
• Accuracy and speed of simple equation rearrangement increase with students' age across grades 7–12 — related
• Students' difficulty rankings of equation types partly mismatch their measured performance, though metacognitive accuracy improves with age — related
• Students were reasonably accurate overall across the nine scored interview questions (M = 6.17, SD = 2.12), with accuracy varying by question type — related
• Ramp task levels are ordered by difficulty: performance declines as the number of variables to set increases — related