Explicit vs reform/constructivist math instruction

Verdict

The math wars resolve the same way the general explicit-vs-inquiry question did — into a guidance-dose gradient with an age/prior-knowledge interaction — but the math-specific causal evidence is unusually good, and it is asymmetric:

1. The minimal-guidance pole reliably loses. In the only multi-curriculum RCT ever run (Agodini, 111 schools, independent ECLS-K outcome), the strongly constructivist Investigations trailed all three rivals — scripted Saxon, blended Math Expressions, and a conventional basal — by 0.22 SD after two years. Independent UK trials of reform maths (ICCAMS/RME) came back null at scale.
2. Explicit instruction for strugglers is settled. Three federal review cycles (NMAP 2008 → Gersten 2009 g=1.22 aligned → WWC 2021 Strong on ~43 studies) certify the same finding — though the certifications share an overlapping research community, and the honest standardized magnitude is roughly half the aligned headline.
3. The high-guidance region has no single winner. Agodini's winner set spans scripted-to- conventional; the best reform-side RCT (CGI) is neither a failure nor a winner (g≈0.18 on problem-solving measures, negative on computation); and for older students, structured problem-solving before instruction beats instruction-first on conceptual/transfer outcomes (productive failure, g=0.36 — reversing for grades 2–5).
4. The global dichotomy is formally unresolved: NMAP found only 8 rigorous direct comparisons and ordered all-encompassing mandates for either pole rescinded.

Hereditarian-lens assessment

Risk: low — the verdict rests on RCTs. Notes: (a) the popular correlational support (Morgan/Farkas ECLS) is grade D with a visible reverse-causation tell (teachers deploy manipulatives/music where strugglers concentrate) — we cite it only as weak corroboration, applying symmetric standards to both camps; (b) per the genetics review, the novice interaction here is prior domain knowledge, not g (the expertise- reversal literature explicitly distinguishes them); the genuine ability interaction is that explicit instruction is most necessary for the struggling tail — which twin data show is the more environmentally malleable part of the distribution, not the least.

Practical guidance

• Explicit core instruction (model → worked examples → guided practice → extensive practice → feedback) as the default, non-negotiable for strugglers and new content.
• Never adopt minimal-guidance constructivist curricula — the one stable causal loser.
• Layer structured problem-first work (productive failure) into secondary math for conceptual depth once foundations are automatic.
• Judge any curriculum's claims on independent standardized outcomes; reform-side effects concentrate on researcher-built problem-solving measures and often go negative on computation.