Direct and indirect influences of executive functions on mathematics achievement

Direct and indirect influences of executive functions on mathematics achievement Cragg Keeble Richardson Roome Gilmore

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Direct and indirect influences of executive functions on mathematics achievement 2017 Cognition 10.1016/j.cognition.2017.01.014 cragg2017-direct-and-indirect-influences-of cragg2017-direct-and-indirect-influences-of.txt, the project's staged copy 0b2faa250924bc9bdfae5d3dfa865a2aca7b30d7 open-access cognitive-psychology

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0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them mechanism Quotation withheld because this record is not cleared for redistribution. executive function contributions to mathematics achievement Quotation withheld because this record is not cleared for redistribution. behavioural-experiment behavioural-experiment Quotation withheld because this record is not cleared for redistribution. mechanisms Achievement tests additionally require locating the mathematical problem inside a verbal or visual description and building a problem representation, and working memory maintains and manipulates that representation - which is why a direct working-memory path survives beyond the component skills Quotation withheld because this record is not cleared for redistribution. mechanisms Working memory activates and retrieves number facts from long-term memory while inhibition suppresses the neighbouring but incorrect answers that are co-activated during retrieval Quotation withheld because this record is not cleared for redistribution. mechanisms Conceptual information is stored in a verbal code whereas arithmetic facts also carry a visuospatial component from how sums are presented and encoded, so only verbal working memory supports conceptual retrieval while both domains support fact retrieval Quotation withheld because this record is not cleared for redistribution. Because age-appropriate mathematics content was chosen separately for each group, the study may have measured only the application of already-mastered material, which could explain the absence of age-related change. Quotation withheld because this record is not cleared for redistribution. The direct working-memory-to-achievement pathway has not been shown to survive control for working memory's role in performing the arithmetic operation itself. Quotation withheld because this record is not cleared for redistribution. IQ was not included, so its share of the variance in each mathematics component is unknown. Quotation withheld because this record is not cleared for redistribution. The field's existing evidence cannot be put side by side, because it comes from separate studies — which is the stated reason this study exists. what this limits: the accumulated literature on executive functions and arithmetic: the paper states the evidence is drawn across separate studies, so the contributions cannot be directly compared across the three core competencies Quotation withheld because this record is not cleared for redistribution. The three-part division of the central construct is inherited from one paper rather than derived here. what this limits: the executive-function components in this analysis: they follow the three-component division of Miyake et al. (2000) rather than being derived from these data Quotation withheld because this record is not cleared for redistribution. a DIFFERENT item set chosen for each age band - 8-9, 11-12, 13-14, and young adults eliminates: floor and ceiling effects as the explanation of an age difference - a task easy enough for adults compresses their scores at ceiling and would make the developmental difference an artefact of the scale rather than of the ability · outcome (stated by the tagger, no quotation): held Quotation withheld because this record is not cleared for redistribution. the full list of acceptable strategies - counting in the head, on fingers, decomposition, retrieval - stated explicitly to participants eliminates: younger children suppressing the strategy they actually used because they believed it was not allowed, which would bias the self-report measure precisely in the age group the study is about · outcome (stated by the tagger, no quotation): held Quotation withheld because this record is not cleared for redistribution. executive functions executive functions Quotation withheld because this record is not cleared for redistribution. inhibition inhibition Quotation withheld because this record is not cleared for redistribution. shifting shifting Quotation withheld because this record is not cleared for redistribution. updating updating Quotation withheld because this record is not cleared for redistribution. working memory working memory Quotation withheld because this record is not cleared for redistribution. updating → executive functions A CUE-LIST GAP, NOT A VOCABULARY GAP - 'part-of' IS THE RIGHT TYPE. 'ARE TYPICALLY DIVIDED…' The gate refused it because its containment cue list holds 'within / part of / comprises / consists of / includes / belongs to' and not 'divided into'. Measured over all 711 staged bodies: 'composed of' 262 occurrences in 151 bodies and 'divided into' 201 in 137 - each MORE COMMON than 'comprises' (68 in 51), which IS in the list; also 'made up of' 28 and 'subdivided into' 17. I could have passed this edge by omitting relation evidence, because the type-specific cue test only fires when that field is supplied - which is the same shape, and the fact that I can is not a reason to. The edge is filed here until the cue list is amended by whoever owns the gate, and should be promoted to 'part-of' when it is. Note also that this record was MISSING the third Miyake component entirely: it carried 'inhibition' and 'shifting' and not 'updating'. the project, 2026-08-26. Quotation withheld because this record is not cleared for redistribution. executive functions - AS DIVIDED HERE: three components following Miyake et al. (2000) — updating or working memory, inhibition, and shifting Quotation withheld because this record is not cleared for redistribution. working memory - the Baddeley and Hitch (1974) model, described as adopted by the MAJORITY of researchers in the field rather than as established Quotation withheld because this record is not cleared for redistribution. `updating` / `working memory` - AN ALIAS ASSERTED BY A BARE `OR`, AND IT IS THE LOOSEST JOIN IN THIS PAPER. `These are (i) updating or working memory, the ability to monitor and manipulate information held in mind`. Miyake's component is `updating`; `working memory` is a much older and much broader term that this sentence quietly equates with it. The paper's own later sections then distinguish VERBAL from VISUOSPATIAL working memory and report they behave differently - a distinction `updating` does not carry. The `or` does more work than it admits. Quotation withheld because this record is not cleared for redistribution. `executive functions` - DEFINED BY WHAT THEY ARE FOR, THEN IMMEDIATELY BY A THREE-WAY PARTITION. `Executive functions, the skills used to guide and control thought and action, Quotation withheld` The functional gloss is the paper's own; the partition is attributed, and `typically` marks it as convention rather than fact. Each component then gets a one-clause definition in the same sentence - updating, inhibition, shifting - so the whole construct is fixed in 60 words. Quotation withheld because this record is not cleared for redistribution. builds-on → Geary (2004); Geary & Hoard (2005) hierarchical framework of mathematics Quotation withheld because this record is not cleared for redistribution. extends → previous hierarchical multi-component models of mathematics Quotation withheld because this record is not cleared for redistribution. contradicts → Cowan and Powell (2014); Fuchs et al. (2005) Quotation withheld because this record is not cleared for redistribution. contradicts → Andersson (2010); Clark et al. (2010) Quotation withheld because this record is not cleared for redistribution. replicates → Hecht et al. (2003); Jordan et al. (2013) Quotation withheld because this record is not cleared for redistribution. EVIDENCE CORRECTED (RE-GROUNDED) · inhibition —part-of→ executive functions inhibition executive functions EVIDENCE CORRECTED: RE-GROUNDED. The old span had an elided subject - 'are typically divided into…' three components - so the term executive functions was never named. This sentence names both and places one inside the other: the contribution of executive functions, '…IN PARTICULAR INHIBITION…' and shifting, to procedural skill. — strength of the relation: 1 Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but endpoint by anaphora: the span continues the sentence whose subject is 'Executive functions' (immediately before the span). Quotation withheld because this record is not cleared for redistribution. inhibition —part-of→ executive functions inhibition executive functions strength of the relation: 1 · note: RE-GROUNDS another row of this record: the old span named ONE endpoint. Quotation withheld because this record is not cleared for redistribution. hierarchical regression hierarchical regression Quotation withheld because this record is not cleared for redistribution. bootstrap bootstrap Quotation withheld because this record is not cleared for redistribution. variance partitioning variance partitioning Quotation withheld because this record is not cleared for redistribution. Mahalanobis distance (outlier detection) Mahalanobis distance (outlier detection) Quotation withheld because this record is not cleared for redistribution. multiple imputation multiple imputation Quotation withheld because this record is not cleared for redistribution. standardization (z-scores) standardization (z-scores) Quotation withheld because this record is not cleared for redistribution. descriptive statistics descriptive statistics Quotation withheld because this record is not cleared for redistribution. mediation analysis mediation analysis Quotation withheld because this record is not cleared for redistribution. The domain-specific skills of factual knowledge, procedural skill and conceptual understanding only partially mediated the executive-function/achievement link, with numerical inhibitory control acting on achievement through factual knowledge and procedural skill. Quotation withheld because this record is not cleared for redistribution. Executive function measures explained far more variance in overall mathematics achievement (34%) than in any single component skill, and least of all in conceptual understanding (5%). Quotation withheld because this record is not cleared for redistribution. Verbal working memory uniquely predicted all four outcomes - factual knowledge, procedural skill, conceptual understanding and mathematics achievement. Quotation withheld because this record is not cleared for redistribution. Shifting and non-numerical inhibition independently predicted none of the outcomes, whereas numerical inhibition uniquely predicted factual knowledge and procedural skill. Quotation withheld because this record is not cleared for redistribution. Contrary to prediction, the relationships between executive functions and mathematics were the same from 8 years to adulthood. Quotation withheld because this record is not cleared for redistribution. Visuospatial working memory had a substantial direct effect on mathematics achievement (b = 0.25). Quotation withheld because this record is not cleared for redistribution. Verbal working memory influenced achievement indirectly through all three component skills, with the procedural-skill route the largest of the three indirect paths. Quotation withheld because this record is not cleared for redistribution. The predicted relationship of inhibition and shifting with overall mathematics achievement was not found. Quotation withheld because this record is not cleared for redistribution. executive functions executive functions Quotation withheld because this record is not cleared for redistribution. factual knowledge factual knowledge Quotation withheld because this record is not cleared for redistribution. working memory working memory Quotation withheld because this record is not cleared for redistribution. inhibition inhibition Quotation withheld because this record is not cleared for redistribution. shifting shifting Quotation withheld because this record is not cleared for redistribution. mathematics achievement mathematics achievement Quotation withheld because this record is not cleared for redistribution. factual knowledge, procedural skill and conceptual understanding factual knowledge, procedural skill and conceptual understanding Quotation withheld because this record is not cleared for redistribution. executive function measures executive function measures Quotation withheld because this record is not cleared for redistribution. verbal working memory verbal working memory Quotation withheld because this record is not cleared for redistribution. age contrasts age contrasts Quotation withheld because this record is not cleared for redistribution. total number of words correctly recalled total number of words correctly recalled Quotation withheld because this record is not cleared for redistribution. 293 — total participants tested, aged 8-25 years Quotation withheld because this record is not cleared for redistribution. 34% — variance in mathematics achievement explained by the executive function measures alone Quotation withheld because this record is not cleared for redistribution. b = 0.25, 95% CI: 0.15–0.34 — direct effect of visuospatial working memory on mathematics achievement after the mediators were included Quotation withheld because this record is not cleared for redistribution. 9% — unique variance in mathematics achievement attributable to the working memory tasks once storage and processing speed were controlled Quotation withheld because this record is not cleared for redistribution. 0.3% — proportion of missing data replaced by multiple imputation Quotation withheld because this record is not cleared for redistribution.

The full text of this article is not redistributable, so it is not included here. The evidence sentences are withheld with it; the tag layer and its grounding status remain. The article itself is at https://doi.org/10.1016/j.cognition.2017.01.014.