Making the Executive ‘Function’ for the Foundations of Mathematics: the Need for Explicit Theories of Change for Early Interventions
Bibliographic record
Abstract
Abstract A vast body of work highlights executive functions (EFs) as robust correlates of mathematics achievement over the primary and preschool years. Yet, despite such correlational evidence, there is limited evidence that EF interventions yield improvements in early years mathematics. As intervention studies are a powerful tool to move beyond correlation to causality, failures of transfer from executive functions interventions are, we argue, highly problematic for both applied and theoretical reasons. We review the existing correlational and intervention literature at complementary neuroscientific, cognitive, developmental and educational levels. We appraise distinct theories of change underpinning the correlations between EF and early mathematics, as well as explicit or implicit theories of change for different types of EF interventions. We find that isolated EF interventions are less likely to transfer to improvements in mathematics than integrated interventions. Via this conceptual piece, we highlight that the field of EF development is in need of (1) a clearer framework for the mechanisms underpinning the relationships between early EF and other developing domains, such as mathematical cognition; (2) clearer putative theories of change for how interventions of different kinds operate in the context of EF and such domains; (3) and greater clarity on the developmental and educational contexts that influence these causal associations. Our synthesis of the evidence emphasises the need to consider the dynamic development of EFs with co-developing cognitive functions, such as early math skills, when designing education environments. [234 words].
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.009 | 0.024 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.003 | 0.008 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".