Cognitive correlates of performance in advanced mathematics

Cognitive correlates of performance in advanced mathematics Wei Yuan Chen Zhou

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Cognitive correlates of performance in advanced mathematics 2012 British Journal of Educational Psychology 10.1111/j.2044-8279.2011.02049.x wei2012-cognitive-correlates-of-performanc wei2012-cognitive-correlates-of-performanc.txt, the project's staged copy 8b4435f56b241c03020faa3daf1d2f1b65e8d36c open-access psychology

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0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them existence Quotation withheld because this record is not cleared for redistribution. cognitive correlates of advanced mathematics learning 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 Advanced mathematical notation must be laid out and held in a mental spatial arrangement, so spatial ability constrains how well the symbols, numerals and letters of a formula can be represented and manipulated Quotation withheld because this record is not cleared for redistribution. mechanisms Learning advanced mathematics requires comprehending unfamiliar technical terminology, the same semantic-comprehension process tapped by the word semantics task, which is why word semantics predicts advanced mathematics Quotation withheld because this record is not cleared for redistribution. mechanisms Basic number sense drops out as a predictor because advanced mathematics operates far away from numerosity and numbers, unlike elementary mathematics which directly involves them Quotation withheld because this record is not cleared for redistribution. Only a narrow slice of advanced mathematical ability was measured, namely acquiring new concepts and solving problems about them. what this limits: what 'advanced mathematical ability' means here: A RELATIVELY SMALL RANGE OF HIGH-LEVEL MATHEMATICAL ABILITIES WERE ASSESSED Quotation withheld because this record is not cleared for redistribution. The cognitive tests themselves are improvable; the numerical-processing tests were not well correlated with each other. what this limits: the cognitive measures: THE TESTS INCLUDED FOR EACH TYPE OF COGNITIVE FACTORS CAN BE FURTHER IMPROVED Quotation withheld because this record is not cleared for redistribution. The participant range was limited to adults who did not major in mathematics or allied disciplines. what this limits: the population the result speaks for: THE RANGE OF PARTICIPANTS WAS ALSO LIMITED - adults not majoring in mathematics or allied disciplines Quotation withheld because this record is not cleared for redistribution. The tests for one construct do not agree with each other, and the authors state it is unclear whether that means the construct has several types — while the comparison construct behaves as one. what this limits: a numerical-processing score in this study as a measure of number sense: the tests were not highly correlated among themselves and the authors state it is unclear whether they reflect different types of number sense Quotation withheld because this record is not cleared for redistribution. The headline construct was assessed over a narrow range, which the authors name first among their limitations. what this limits: conclusions about advanced mathematics performance in general: only the ability to acquire new advanced concepts and to solve problems was assessed Quotation withheld because this record is not cleared for redistribution. The sample excludes both ends of the ability range the conclusions are about. what this limits: generalising to mathematicians or to people with mathematical difficulties: the participants were adults who did not major in mathematics, and the authors name both excluded groups as future work Quotation withheld because this record is not cleared for redistribution. THE NULL WAS PREDICTED, NOT DISCOVERED, and the authors say so before reporting it: 'we EXPECTED TO DISCONFIRM this number sense hypothesis because advanced mathematics is far removed from basic numerical processing', adding that in a college sample the variation in basic number processing should be limited. So the finding is confirmatory of the authors' expectation and partly explained in advance by their sampling, which is a different epistemic object from a surprising null. Quotation withheld because this record is not cleared for redistribution. about four hours between the two testing sessions eliminates: that second-session performance is depressed by fatigue carried over from the first · outcome (stated by the tagger, no quotation): held Quotation withheld because this record is not cleared for redistribution. the position of the stimulus on screen was randomly determined within 15 degrees of visual angle eliminates: that performance depends on a fixed retinal location rather than on the cognitive demand · outcome (stated by the tagger, no quotation): held Quotation withheld because this record is not cleared for redistribution. instructions and practice trials preceded every task eliminates: that early performance on each task reflects unfamiliarity rather than ability · outcome (stated by the tagger, no quotation): held Quotation withheld because this record is not cleared for redistribution. number sense number sense Quotation withheld because this record is not cleared for redistribution. numerical processing numerical processing Quotation withheld because this record is not cleared for redistribution. spatial processing spatial processing Quotation withheld because this record is not cleared for redistribution. advanced mathematics advanced mathematics Quotation withheld because this record is not cleared for redistribution. basic numerical processing → advanced mathematics A RELATION TESTED AND NOT FOUND: 'basic numerical processing and computation were generally NOT correlated with performance in advanced mathematics'. No edge type can assert an absent relation, and this one is the paper's stated aim - it set out to disconfirm the number-sense hypothesis. Third instance in this session's reading after arthur2022 and pan2023. Quotation withheld because this record is not cleared for redistribution. number sense - POSSIBLY SEVERAL TYPES: the tests intended to measure it were not highly correlated, and the paper leaves open whether that reflects distinct types or poor measures Quotation withheld because this record is not cleared for redistribution. the association between non-symbolic quantity tasks and mathematics - REPORTED IN BOTH DIRECTIONS in the literature this paper reviews, with studies finding it and studies finding none Quotation withheld because this record is not cleared for redistribution. number sense - a construct whose own tests do not converge here, leaving open whether they measure several different things; the spatial tests in the same battery do converge Quotation withheld because this record is not cleared for redistribution. builds-on → Shepard & Metzler (1971) mental rotation task Quotation withheld because this record is not cleared for redistribution. builds-on → Halberda et al. (2008) coloured-dot numerosity comparison task Quotation withheld because this record is not cleared for redistribution. builds-on → Delazer et al. (2005) artificial arithmetic learning paradigm Quotation withheld because this record is not cleared for redistribution. spatial processing —causes→ advanced mathematics spatial processing advanced mathematics differs in: WHICH COGNITIVE FACTOR SURVIVES CONTROLLING FOR THE OTHERS: spatial abilities and comprehension of words and sentences do; basic numerical processing and computation do not. The battery's job is to make the factors compete, and the one the field expected to win is the one that drops out · strength of the relation: 0.8 Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span writes 'spatial abilities' and reports a CORRELATION with performance; endpoint variant, association typed as cause. Quotation withheld because this record is not cleared for redistribution. number sense —operationalised-as→ numerical processing number sense numerical processing strength of the relation: 0.7 · note: THE INSTRUMENTS FOR ONE CONSTRUCT DO NOT AGREE WITH EACH OTHER, and the authors draw the right conclusion from it: the numerical-processing tests did not correlate highly with each other, and '…It is not clear whether they reflect…' different types of number sense. The contrast is inside the same battery - the spatial tests were '…highly intercorrelated' - so this is not a general problem with the method but a fact about this construct. Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span says it is NOT CLEAR whether the tests reflect different types of number sense; hedged. Quotation withheld because this record is not cleared for redistribution. correlation correlation Quotation withheld because this record is not cleared for redistribution. partial correlation partial correlation Quotation withheld because this record is not cleared for redistribution. split-half reliability split-half reliability 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. mean and standard deviation mean and standard deviation Quotation withheld because this record is not cleared for redistribution. p-value p-value Quotation withheld because this record is not cleared for redistribution. Mental rotation, spatial working memory and figure analysis had significant partial correlations with advanced mathematics. Quotation withheld because this record is not cleared for redistribution. None of the four number-sense tasks had a significant partial correlation with advanced mathematics. Quotation withheld because this record is not cleared for redistribution. After controlling for general cognitive, spatial and basic numerical processing, word semantics still correlated with advanced mathematics. Quotation withheld because this record is not cleared for redistribution. Complex numerical processing - number series completion and artificial arithmetic learning - stayed significantly correlated with advanced mathematics after all four other cognitive categories were controlled. Quotation withheld because this record is not cleared for redistribution. The combined z-score for basic numerical processing showed no correlation with advanced mathematics (r = .021). Quotation withheld because this record is not cleared for redistribution. advanced mathematics advanced mathematics Quotation withheld because this record is not cleared for redistribution. mental number line mental number line Quotation withheld because this record is not cleared for redistribution. number sense hypothesis number sense hypothesis Quotation withheld because this record is not cleared for redistribution. deviation of estimated quantity deviation of estimated quantity Quotation withheld because this record is not cleared for redistribution. reaction time reaction time about this quote: THE QUOTE CONTINUES A SENTENCE THAT THIS COPY CUTS IN TWO - a running head stands between it and the words it follows, which read 'The average percentage of correct'. Quotation withheld because this record is not cleared for redistribution. spatial working memory spatial working memory Quotation withheld because this record is not cleared for redistribution. general cognitive processing general cognitive processing Quotation withheld because this record is not cleared for redistribution. language processing language processing Quotation withheld because this record is not cleared for redistribution. basic numerical processing basic numerical processing Quotation withheld because this record is not cleared for redistribution. 80 — number of undergraduate participants recruited Quotation withheld because this record is not cleared for redistribution. 21.9 years — mean age of the sample Quotation withheld because this record is not cleared for redistribution. 18 — total number of tasks administered (17 computerised cognitive tasks plus the advanced mathematics test) Quotation withheld because this record is not cleared for redistribution. r = .540, p = .000 — partial correlation between the composite spatial-processing score and advanced mathematics performance Quotation withheld because this record is not cleared for redistribution. r = .021, p = .852 — partial correlation between the composite basic-numerical-processing score and advanced mathematics performance Quotation withheld because this record is not cleared for redistribution. 17 — number of cognitive tasks in the battery correlated with the advanced mathematics test 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/10.1111/j.2044-8279.2011.02049.x.