Teaching general problem-solving skills is not a substitute for teaching math [pdf] (2010)

Original Article ↗ Hacker News Discussion ↗

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.”