S0157 · geary_mathematical_development_1994 · registry identity

Children's Mathematical Development

Geary · 1994

study independent4 occurrences across 1 book · load 4

Bears on

Canonical propositions this source was matched as evidence for.

P03 — Intellectual skill and expertise are domain-specific and transfer poorly across domains; so-called higher-order abilities are relevant kn…

P17 — There is no innate developmental blueprint determining what children can learn when: literacy and academic competence are cultural acquis…

How Hirsch uses it

Every occurrence, grouped by book and chapter, with the claim it was linked to support and (where the extraction regenerated one) the underlying warrant.

1996 · The Schools We Need

Cross-national comparison of math curricula showing French and Japanese children mastering 5-digit subtraction and multiplication tables by third grade.

direct Children in nations like France and Japan successfully master multi-digit arithmetic and place value by the end of first and second grade without strain.

ch 4 · international_comparison · swn:ch4_E24

Warrant (implicit): The successful implementation of a rigorous curriculum in one country proves that the same curriculum is developmentally appropriate and psychologically harmless for children of that age globally.

could fail ifReporting bias or lack of longitudinal data on the long-term burnout or 'hidden' psychological stress of children in high-pressure East Asian or European systems.

Research on 'skip counting' as a domain-specific strategy for learning multiplication.

direct Teaching domain-specific metacognitive strategies is more effective for problem-solving than teaching broad, general problem-solving strategies.

ch 5 · empirical_study · swn:ch5_E15

Warrant (implicit): When specialized techniques for a specific task yield better results than general heuristics, the brain's problem-solving capacity should be viewed as a collection of domain-specific tools.

could fail ifThe success of domain-specific strategies like 'skip counting' might actually rely on underlying general cognitive abilities (like working memory) that go unmeasured.

Research on math skill development identifying schemas and rules as independent processes.

direct Mathematics consists of two distinct elements: content-oriented aspects (schemas) and grammar-like operations (rules).

ch 5 · empirical_study · swn:ch5_E40

Warrant (implicit): The cognitive structure of a discipline like mathematics is defined by the psychological mechanisms used to acquire and execute its different components.

could fail ifThis reduces a formal system of logic to a biological process, ignoring that 'rules' and 'schemas' are often logically inseparable in advanced mathematical proofs.

Cognitive science models of schema theory applied to mathematical development.

direct Intellectual competencies are described, at least operationally, by schema theory.

ch 7 · empirical_study · swn:ch7_E19

Warrant (implicit): If a cognitive model successfully explains specific domains of learning like mathematics, it serves as a valid general description for all intellectual competencies.

could fail ifDomain specificity, where the mechanisms for mathematical development do not necessarily generalize to linguistic or social competencies.

Endnote numbers seen

Raw book:chapter:endnote references collected during endnote backfill.

swn:4:16swn:5:19swn:5:44swn:7:13

Raw source_reference strings seen

As they appeared before normalization/consolidation into this source identity.

Geary, Children’s Mathematical Development
Geary, Children’s Mathematical Development (1994)
Geary, Children’s Mathematical Development, 72–78
National curriculum guides for France and Japan; Geary, Children’s Mathematical Development