phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text| phenomenon | cognitive correlates of advanced mathematics learning— “The goal of the current study was to investigate cognitive correlates of learning advanced mathematics.” | |
| claim-type | existence— “The results showed that spatial abilities were significantly correlated with performance in advanced mathematics after controlling for other factors.” | |
| method — evidence | — “The current study investigated the associations between students’ performance on a test of advanced mathematics and a battery of 17 cognitive tasks on basic numerical processing, complex numerical processing, spatial abilities, language abilities, and general cognitive processing.” | |
| mechanism | 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— “For advanced mathematics, it is crucial to have accurate mental spatial layout of mathematical symbols.” | mechanisms[0] |
| mechanism | 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— “Subjects in the current study needed to understand the 18 mathematical terminologies, just as they would with words included in the word semantics task.” | mechanisms[1] |
| mechanism | 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— “One explanation for this is that elementary mathematics involves numerosity and numbers, but advanced mathematics is too far removed from basic numerical processing.” | mechanisms[2] |
| builds-on | Shepard & Metzler (1971) mental rotation task— “The three-dimensional mental rotation task was based on Shepard’s mental rotation task (Shepard & Metzler, 1971).” | claim_relations[0] |
| builds-on | Halberda et al. (2008) coloured-dot numerosity comparison task— “This task was adapted from Halberda et al. (2008).” | claim_relations[1] |
| builds-on | Delazer et al. (2005) artificial arithmetic learning paradigm— “This test was based on Delazer and colleagues’ study (Delazer et al., 2005).” | claim_relations[2] |
| sense | 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— “the tests for numerical processing were not highly correlated among themselves. It is not clear whether they reflect different types of number sense.” | senses[0] |
| sense | 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— “Other studies, however, found that performance on non-symbolic quantity tasks was not associated with mathematics performance.” | senses[1] |
| sense | 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— “For example, the tests for numerical processing were not highly correlated among themselves. It is not clear whether they reflect different types of number sense. In contrast, the spatial processing tests were highly intercorrelated” | senses[2] |
| control | about four hours between the two testing sessions — held — rules out that second-session performance is depressed by fatigue carried over from the first— “The interval between the two sessions was about 4 hr to ensure that the participants had adequate rest.” | controls[0] |
| control | the position of the stimulus on screen was randomly determined within 15 degrees of visual angle — held — rules out that performance depends on a fixed retinal location rather than on the cognitive demand— “The position where the stimulus occurred on the screen was randomly determined, in a range of 15◦ of visual angles.” | controls[1] |
| control | instructions and practice trials preceded every task — held — rules out that early performance on each task reflects unfamiliarity rather than ability— “Before each task, participants were given instructions and practice trials.” | controls[2] |
| audit | spatial processing —causes→ advanced mathematics — 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.— “The results showed that spatial abilities were significantly correlated with performance in advanced mathematics after controlling for other factors. In addition, certain language abilities (i.e., comprehension of words and sentences) also made unique contributions. In contrast, basic numerical processing and computation were generally not… | concept_edges[0] |
| differs in | spatial processing —causes→ advanced mathematics — 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— “The results showed that spatial abilities were significantly correlated with performance in advanced mathematics after controlling for other factors. In addition, certain language abilities (i.e., comprehension of words and sentences) also made unique contributions. In contrast, basic numerical processing and computation were generally not… | concept_edges[0] |
| weight | spatial processing —causes→ advanced mathematics — 0.8— “The results showed that spatial abilities were significantly correlated with performance in advanced mathematics after controlling for other factors. In addition, certain language abilities (i.e., comprehension of words and sentences) also made unique contributions. In contrast, basic numerical processing and computation were generally not… | concept_edges[0] |
| audit | number sense —operationalised-as→ numerical processing — 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.— “For example, the tests for numerical processing were not highly correlated among themselves. It is not clear whether they reflect different types of number sense. In contrast, the spatial processing tests were highly intercorrelated” | concept_edges[1] |
| note | number sense —operationalised-as→ numerical processing — 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.— “For example, the tests for numerical processing were not highly correlated among themselves. It is not clear whether they reflect different types of number sense. In contrast, the spatial processing tests were highly intercorrelated” | concept_edges[1] |
| weight | number sense —operationalised-as→ numerical processing — 0.7— “For example, the tests for numerical processing were not highly correlated among themselves. It is not clear whether they reflect different types of number sense. In contrast, the spatial processing tests were highly intercorrelated” | concept_edges[1] |
| outcome (stated by the tagger, no quotation) | control — held | controls[0] |
| outcome (stated by the tagger, no quotation) | control — held | controls[1] |
| outcome (stated by the tagger, no quotation) | control — held | controls[2] |
| for which use | limitation — what 'advanced mathematical ability' means here: A RELATIVELY SMALL RANGE OF HIGH-LEVEL MATHEMATICAL ABILITIES WERE ASSESSED— “First, a relatively small range of high-level mathematical abilities were assessed in the current study.” | limitations[0] |
| for which use | limitation — the cognitive measures: THE TESTS INCLUDED FOR EACH TYPE OF COGNITIVE FACTORS CAN BE FURTHER IMPROVED— “Second, the tests included for each type of cognitive factors can be further improved.” | limitations[1] |
| for which use | limitation — the population the result speaks for: THE RANGE OF PARTICIPANTS WAS ALSO LIMITED - adults not majoring in mathematics or allied disciplines— “Third, the range of participants was also limited.” | limitations[2] |
| for which use | limitation — 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— “the tests for numerical processing were not highly correlated among themselves. It is not clear whether they reflect different types of number sense. In contrast, the spatial processing tests were highly intercorrelated.” | limitations[3] |
| for which use | limitation — conclusions about advanced mathematics performance in general: only the ability to acquire new advanced concepts and to solve problems was assessed— “First, a relatively small range of high-level mathematical abilities were assessed in the current study. That is, we only investigated the ability to acquire new advanced mathematical concepts and to solve mathematical problems.” | limitations[4] |
| for which use | limitation — 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— “Third, the range of participants was also limited. The participants were adults who did not major in mathematics or allied disciplines. Future research needs to include participants with mathematical difficulties as well as those with high-level mathematical abilities.” | limitations[5] |
| replication | untested | |
| no type for this | 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.— “The results showed that spatial abilities were significantly correlated with performance in advanced mathematics after controlling for other factors. In addition, certain language abilities (i.e., comprehension of words and sentences) also made unique contributions. In contrast, basic numerical processing and computation were generally not… | unhoused_relations[0] |
| limitation | Only a narrow slice of advanced mathematical ability was measured, namely acquiring new concepts and solving problems about them.— “First, a relatively small range of high-level mathematical abilities were assessed in the… | limitations[0] |
| limitation | The cognitive tests themselves are improvable; the numerical-processing tests were not well correlated with each other. | limitations[1] |
| limitation | The participant range was limited to adults who did not major in mathematics or allied disciplines. | limitations[2] |
| limitation | 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. | limitations[3] |
| limitation | The headline construct was assessed over a narrow range, which the authors name first among their limitations. | limitations[4] |
| limitation | The sample excludes both ends of the ability range the conclusions are about. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[5] |
| limitation | 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 — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[6] |
finding · quantity · variable · definition · key-term — grounded in the full text| finding | Mental rotation, spatial working memory and figure analysis had significant partial correlations with advanced mathematics. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[0] |
| finding | None of the four number-sense tasks had a significant partial correlation with advanced mathematics. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[1] |
| finding | After controlling for general cognitive, spatial and basic numerical processing, word semantics still correlated with advanced mathematics. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[2] |
| finding | 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 — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[3] |
| finding | The combined z-score for basic numerical processing showed no correlation with advanced mathematics (r = .021). Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[4] |
| quantity | 80 — number of undergraduate participants recruited Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[0] |
| quantity | 21.9 years — mean age of the sample Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[1] |
| quantity | 18 — total number of tasks administered (17 computerised cognitive tasks plus the advanced mathematics test) Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[2] |
| quantity | r = .540, p = .000 — partial correlation between the composite spatial-processing score and advanced mathematics performance Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[3] |
| quantity | r = .021, p = .852 — partial correlation between the composite basic-numerical-processing score and advanced mathematics performance Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[4] |
| quantity | 17 — number of cognitive tasks in the battery correlated with the advanced mathematics test Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[5] |
| variable | deviation of estimated quantity (dependent) Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.variables[0] |
| variable | reaction time (dependent) Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.variables[1] |
| evidence status note | variable — 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'. | content_tags.variables[1] |
| variable | spatial working memory (dependent) Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.variables[2] |
| variable | general cognitive processing (control) Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.variables[3] |
| variable | language processing (control) Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.variables[4] |
| variable | basic numerical processing (control) Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.variables[5] |
| definition | advanced mathematics Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.definitions[0] |
| definition | mental number line Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.definitions[1] |
| definition | number sense hypothesis Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.definitions[2] |
| concept | number sense Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[0] |
| concept | numerical processing Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[1] |
| concept | spatial processing Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[2] |
| concept | advanced mathematics Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[3] |
| correlation r | as written: correlation coefficients Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[0] |
| partial correlation r | as written: partial correlations Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[1] |
| split-half reliability | as written: split-half reliabilities Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[2] |
| standardization (z-scores) z | as written: averaging standardized scores Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[3] |
| mean and standard deviation SD | as written: means and standard deviations Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[4] |
| p-value p | as written: r = .313, p = .011 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[5] |
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