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¶

Claim · All claims
Evidence · 2 studies · 2 associational r2 · q2
Currency · newest study 2014 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q2 i? The most frequent concrete strategy was inserting numbers (37% of participants); the most common rule-based strategy was standard multiplication/division operations (38%). → Susac A 2014 q2 i? The proportion using concrete strategies decreased and rule-based strategies increased with age, a gradual transition. → 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

q2 · i? · associational · r2

Categorization of post-hoc questionnaire answers using a general inductive approach; "The most frequently used concrete strategy (37% of all participants) was inserting numbers instead of letters." Other concrete strategies included a "triangle" technique (11%).

"The most frequently used concrete strategy (37% of all participants) was inserting numbers instead of letters."

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

q2 · i? · associational · r2

Figure 5 shows strategy-type proportions by grade: "the proportion of concrete strategy usage decreases at the same time as the propor­tion of rule-based strategies increases with the age of participants," a gradual progression likely continuing past age 16–17.

"the proportion of concrete strategy usage decreases at the same time as the propor­tion of rule-based strategies increases with the age of participants. This progression is gradual"

Discussion¶

Learner Variables¶

• Age and Developmental Stage — predictor: learners who differ on it differ in outcomes

Related Claims¶

• Younger students solve letter equations less accurately than number equations, but this difference disappears by age 16–17 — related
• Cool executive function measures show ascending age-related growth across adolescence, with a growth spurt around age 14–15 — related
• Students' difficulty rankings of equation types partly mismatch their measured performance, though metacognitive accuracy improves with age — related