Word problems, schema instruction, and the conceptual-vs-procedural question

Verdict

Three findings, each deflating a piece of folk pedagogy:

1. Math sub-skills are modular. The cleanest demonstration (Fuchs 2014, 1,102 students): calculation instruction transfers zero to word problems, and word-problem instruction transfers zero to calculation. Both folk theories — "get the facts down and problem-solving follows" and "problem-solving builds computation" — fail. Each strand needs explicit teaching. (Notably, word-problem/schema instruction was also the only route to pre-algebraic knowledge.)
2. Explicit schema instruction is what teaches word problems. Teach the underlying problem structures, represent them with diagrams, and explicitly train transfer across surface features. Replicated across two labs (Fuchs grades 1–3, and the Jitendra series), retained at 6–9 weeks. The 42-classroom efficacy trial gave g=1.24 (1.27 at 6 weeks, transfer test null); the 82-classroom scale-up gave ~0.32 (0.25 at 9 weeks). Honest at-scale magnitude: ~0.25–0.45 SD on trained content (the g>1.2 small-trial and g=1.57 meta headlines are aligned-measure/improper-pooling inflation — the modern meta confirms the inflation within itself). The open weakness: the one independent standardized outcome the series ever administered (the GMADE Process and Applications subtest, in the scale-up) showed no effect.
3. Concepts-first dogma has no experimental warrant. The authoritative both-sides review (Rittle-Johnson, Schneider & Star): conceptual and procedural knowledge develop bidirectionally, and the only direct sequencing experiments favor iterating between them over concepts-first blocks. (The related compare-solution-methods technique is a worked-examples variant with the same novice boundary — and a sobering year-long scale-up null when teachers didn't use it.)

Hereditarian-lens assessment

Risk: low (large RCTs). Schema instruction is not contraindicated for strugglers — in the 806-student subgroup analysis of the scale-up, students with mathematics problem-solving difficulties gained about as much as their classmates and held the gain at nine weeks — and the modularity finding is itself lens-consistent: what look like "general problem-solving abilities" in correlational data decompose, under experimental control, into separately teachable narrow skills plus g-loaded residual.

Practical guidance

• Organize word-problem instruction around problem types (additive: change/combine/compare; multiplicative: ratio/proportion/percent), with a diagram per schema and a solve-check routine.
• Explicitly train transfer: same schema, varied surface stories — transfer taught is transfer got; transfer hoped-for doesn't happen (the efficacy trials' own transfer tests were null).
• Run computation fluency (fact fluency) and word-problem strands in parallel; iterate concepts ↔ procedures within each.
• Expect trained-content gains, not standardized-test miracles; durability beyond ~2 months is unmeasured.