Supplemental Material for A Multilevel Meta-Analysis on the Causal Effect of Approximate Number System Training on Symbolic Math Performance

The Approximate Number System (ANS) is hypothesized to play a foundational role in humans’ development of symbolic numerical representations and even the symbolic mathematical ability. However, studies attempting to investigate the causal relation between ANS and symbolic mathematical performance by training the latter and measuring the former have produced mixed findings. We systematically review the ANS training literature to investigate the strength of the effects of practicing ANS related tasks on symbolic math performance. Across 31 effect sizes from 9 studies involving 595 participants, for which neither the treatment nor control group received symbolic training, we found a small non-significant effect of ANS training on symbolic math task performance (g = .10, CI[-0.03, 0.22]). Some heterogeneity was accounted for by participant age, with larger estimates for adults than for children. Estimates did not vary significantly by ANS training type, training duration, and control group type. An exploratory analysis on the transfer effects of ANS training on untrained non-symbolic tasks suggests weak support for the key auxiliary assumption that ANS training has substantial effects on a general ANS, indicating that the training literature may not adequately represent theories on how ANS influences symbolic number performance.

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Changing the precision of preschoolers’ approximate number system representations changes their symbolic math performance

Journal of Experimental Child Psychology ◽

10.1016/j.jecp.2016.03.002 ◽

2016 ◽

Vol 147 ◽

pp. 82-99 ◽

Cited By ~ 45

Author(s):

Jinjing (Jenny) Wang ◽

Darko Odic ◽

Justin Halberda ◽

Lisa Feigenson

Keyword(s):

Number System ◽

Math Performance ◽

Approximate Number System

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Intensive math training does not affect approximate number acuity: Evidence from a three-year longitudinal curriculum intervention

Journal of Numerical Cognition ◽

10.5964/jnc.v2i2.19 ◽

2016 ◽

Vol 2 (2) ◽

pp. 57-76 ◽

Cited By ~ 13

Author(s):

Jessica Sullivan ◽

Michael C. Frank ◽

David Barner

Keyword(s):

Number System ◽

Math Performance ◽

Cognitive Tasks ◽

Approximate Number System ◽

Math Intervention ◽

Math Success ◽

Large N ◽

Curriculum Intervention ◽

Induced Changes ◽

Longitudinal Dataset

Does nonverbal, approximate number acuity predict mathematics performance? Some studies report a correlation between acuity of representations in the Approximate Number System (ANS) and early math achievement, while others do not. Few previous reports have addressed (1) whether reported correlations remain when other domain-general capacities are considered, and (2) whether such correlations are causal. In the present study, we addressed both questions using a large (N = 204) 3-year longitudinal dataset from a successful math intervention, which included a wide array of non-numerical cognitive tasks. While we replicated past work finding correlations between approximate number acuity and math success, these correlations were very small when other domain-general capacities were considered. Also, we found no evidence that changes to math performance induced changes to approximate number acuity, militating against one class of causal accounts.

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The relationship between children’s approximate number certainty and symbolic mathematics

Journal of Numerical Cognition ◽

10.5964/jnc.v6i1.220 ◽

2020 ◽

Vol 6 (1) ◽

pp. 50-65

Author(s):

Carolyn Baer ◽

Darko Odic

Keyword(s):

Large Body ◽

Number System ◽

Math Performance ◽

Approximate Number System ◽

Mathematical Skills ◽

Math Ability ◽

Positive Correlations ◽

Number Perception ◽

The Relationship ◽

Symbolic Number

Why do some children excel in mathematics while others struggle? A large body of work has shown positive correlations between children’s Approximate Number System (ANS) and school-taught symbolic mathematical skills, but the mechanism explaining this link remains unknown. One potential mediator of this relationship might be children’s numerical metacognition: children’s ability to evaluate how sure or unsure they are in understanding and manipulating numbers. While previous work has shown that children’s math abilities are uniquely predicted by symbolic numerical metacognition, we focus on the extent to which children’s non-symbolic/ANS numerical metacognition, in particular sensitivity to certainty, might be predictive of math ability, and might mediate the relationship between the ANS and symbolic math. A total of 72 children aged 4–6 years completed measures of ANS precision, ANS metacognition sensitivity, and the Test of Early Mathematical Ability (TEMA-3). Our results replicate many established findings in the literature, including the correlation between ANS precision and the TEMA-3, particularly on the Informal subtype questions. However, we did not find that ANS metacognition sensitivity was related to TEMA-3 performance, nor that it mediated the relationship between the ANS and the TEMA-3. These findings suggest either that metacognitive calibration may play a larger role than metacognitive sensitivity, or that metacognitive differences in the non-symbolic number perception do not robustly contribute to symbolic math performance.

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The effect of gender stereotypes on young girls’ intuitive number sense

PLoS ONE ◽

10.1371/journal.pone.0258886 ◽

2021 ◽

Vol 16 (10) ◽

pp. e0258886

Author(s):

Antonya Marie Gonzalez ◽

Darko Odic ◽

Toni Schmader ◽

Katharina Block ◽

Andrew Scott Baron

Keyword(s):

Gender Stereotypes ◽

Number Sense ◽

Number System ◽

Math Performance ◽

Approximate Number System ◽

Math Ability ◽

Young Girls ◽

And Gender ◽

Math Test ◽

The Impact

Despite the global importance of science, engineering, and math-related fields, women are consistently underrepresented in these areas. One source of this disparity is likely the prevalence of gender stereotypes that constrain girls’ and women’s math performance and interest. The current research explores the developmental roots of these effects by examining the impact of stereotypes on young girls’ intuitive number sense, a universal skill that predicts later math ability. Across four studies, 762 children ages 3–6 were presented with a task measuring their Approximate Number System accuracy. Instructions given before the task varied by condition. In the two control conditions, the task was described to children either as a game or a test of eyesight ability. In the experimental condition, the task was described as a test of math ability and that researchers were interested in whether boys or girls were better at math and counting. Separately, we measured children’s explicit beliefs about math and gender. Results conducted on the combined dataset indicated that while only a small number of girls in the sample had stereotypes associating math with boys, these girls performed significantly worse on a test of Approximate Number System accuracy when it was framed as a math test rather than a game or an eyesight test. These results provide novel evidence that for young girls who do endorse stereotypes about math and gender, contextual activation of these stereotypes may impair their intuitive number sense, potentially affecting their acquisition of formal mathematics concepts and developing interest in math-related fields.

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Number knowledge and the approximate number system are two critical foundations for early arithmetic development.

Journal of Educational Psychology ◽

10.1037/edu0000426 ◽

2020 ◽

Vol 112 (6) ◽

pp. 1167-1182 ◽

Cited By ~ 1

Author(s):

Stephanie A. Malone ◽

Kelly Burgoyne ◽

Charles Hulme

Keyword(s):

Number System ◽

Approximate Number System ◽

Number Knowledge

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Do Commodity Price Shocks Cause Armed Conflict? A Meta-Analysis of Natural Experiments

American Political Science Review ◽

10.1017/s0003055420000957 ◽

2021 ◽

pp. 1-8

Author(s):

GRAEME BLAIR ◽

DARIN CHRISTENSEN ◽

AARON RUDKIN

Keyword(s):

Causal Effect ◽

Meta Analysis ◽

Resource Curse ◽

Civil Conflict ◽

Commodity Price ◽

Future Research ◽

Natural Experiments ◽

Price Changes ◽

Price Increases ◽

Commodity Price Shocks

Scholars of the resource curse argue that reliance on primary commodities destabilizes governments: price fluctuations generate windfalls or periods of austerity that provoke or intensify civil conflict. Over 350 quantitative studies test this claim, but prominent results point in different directions, making it difficult to discern which results reliably hold across contexts. We conduct a meta-analysis of 46 natural experiments that use difference-in-difference designs to estimate the causal effect of commodity price changes on armed civil conflict. We show that commodity price changes, on average, do not change the likelihood of conflict. However, there are cross-cutting effects by commodity type. In line with theory, we find price increases for labor-intensive agricultural commodities reduce conflict, while increases in the price of oil, a capital-intensive commodity, provoke conflict. We also find that price increases for lootable artisanal minerals provoke conflict. Our meta-analysis consolidates existing evidence, but also highlights opportunities for future research.

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Causal effect of renal function on venous thromboembolism: a two-sample Mendelian randomization investigation

Journal of Thrombosis and Thrombolysis ◽

10.1007/s11239-021-02494-4 ◽

2021 ◽

Author(s):

Shuai Yuan ◽

Maria Bruzelius ◽

Susanna C. Larsson

Keyword(s):

Renal Function ◽

Venous Thromboembolism ◽

Mendelian Randomization ◽

Causal Effect ◽

Meta Analysis ◽

Genome Wide Association Studies ◽

Uk Biobank ◽

Genome Wide ◽

Increased Risk ◽

Mr Study

AbstractWhether renal function is causally associated with venous thromboembolism (VTE) is not yet fully elucidated. We conducted a two-sample Mendelian randomization (MR) study to determine the causal effect of renal function, measured as estimated glomerular filtration rate (eGFR), on VTE. Single-nucleotide polymorphisms associated with eGFR were selected as instrumental variables at the genome-wide significance level (p < 5 × 10−8) from a meta-analysis of 122 genome-wide association studies including up to 1,046,070 individuals. Summary-level data for VTE were obtained from the FinnGen consortium (6913 VTE cases and 169,986 non-cases) and UK Biobank study (4620 VTE cases and 356,574 non-cases). MR estimates were calculated using the random-effects inverse-variance weighted method and combined using fixed-effects meta-analysis. Genetically predicted decreased eGFR was significantly associated with an increased risk of VTE in both FinnGen and UK Biobank. For one-unit decrease in log-transformed eGFR, the odds ratios of VTE were 2.93 (95% confidence interval (CI) 1.25, 6.84) and 4.46 (95% CI 1.59, 12.5) when using data from FinnGen and UK Biobank, respectively. The combined odds ratio was 3.47 (95% CI 1.80, 6.68). Results were consistent in all sensitivity analyses and no horizontal pleiotropy was detected. This MR-study supported a casual role of impaired renal function in VTE.

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