Teaching general problem-solving skills is not a substitute for teaching math [pdf] (2010)
Claims that general “problem‑solving skills” can replace explicit math instruction draw sharp scrutiny, with many pointing to cognitive science showing that domain‑specific knowledge, memorization, and worked examples are crucial for real competence. Commenters highlight weaknesses in education research, confusion over what “math proficiency” means, and the gap between how higher math is taught (theorem–proof, few examples) and what’s known about effective learning. The conversation broadens into whether most people need advanced math at all, how poor numeracy drives bad financial and life decisions, and how much mathematical ability is genuinely transferable beyond its own domain.
Education research & evidence quality
- Some argue randomized controlled trials in education are rare and often poorly designed, so “no RCT evidence” is weak criticism.
- Others counter that there are many RCTs and meta-analyses, but education research often has replication and p-hacking problems.
- View emerges that a small set of findings is solid, many are not, and incentives distort the field.
General vs domain-specific problem-solving
- Central debate: can teaching “general problem-solving skills” substitute for teaching specific mathematical content and techniques?
- Many commenters align with the paper: problem-solving ability is largely domain-specific; general training transfers poorly.
- Some want clearer definitions of “general problem-solving” and “math proficiency” (procedural fluency vs progress on novel problems).
Memorization, expertise, and “10,000 hours”
- Strong theme: expertise relies heavily on stored patterns, facts, and heuristics, not just abstract reasoning.
- Memorization is framed as “caching” that frees working memory and enables higher-level thinking; without it, you are too slow.
- Skepticism toward simplistic “10,000 hours to mastery”; practice must be deliberate, and individuals vary widely.
Worked examples & pedagogy
- Many endorse “worked example effect”: students learn faster from many well-chosen, scaffolded examples than from unguided problem solving.
- Critiques of higher math textbooks and classes: too much theorem–proof, too few motivating examples or step-by-step solutions.
- Some warn that examples can encourage mere mimicking if teachers don’t connect them to definitions, theorems, and concepts.
- Direct, guided instruction is argued to work better for novices; open-ended “productive struggle” may be more appropriate for advanced learners.
How much math & why
- Disagreement over how much formal math most people need.
- Some see most math beyond basic algebra/stats as rarely used and arguably “vestigial” for non-STEM careers.
- Others stress math’s role in financial decisions, avoiding scams, and understanding technology, and argue that ignorance is costly.
- Several note motivation is key: students often only engage when they see concrete applications (programming, graphics, engineering, finance).
Chess analogy & transfer limits
- Discussion of chess expertise supports the paper’s claim: masters excel via massive pattern memory, not magical general reasoning.
- Parallel drawn to math: high performance reflects deep, specific knowledge plus heuristics, not a generic problem-solving “muscle.”