Is math anxiety always bad for math learning? The role of math motivation
Open accessAbstract
The linear relations between math anxiety and math cognition have been frequently studied. However, the relations between anxiety and performance on complex cognitive tasks have been repeatedly demonstrated to follow a curvilinear fashion. In the current studies, we aimed to address the lack of attention given to the possibility of such complex interplay between emotion and cognition in the math-learning literature by exploring the relations among math anxiety, math motivation, and math cognition. In two samples—young adolescent twins and adult college students—results showed inverted-U relations between math anxiety and math performance in participants with high intrinsic math motivation and modest negative associations between math anxiety and math performance in participants with low intrinsic math motivation. However, this pattern was not observed in tasks assessing participants’ nonsymbolic and symbolic number-estimation ability. These findings may help advance the understanding of mathematics-learning processes and provide important insights for treatment programs that target improving mathematics-learning experiences and mathematical skills.
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TL;DR
In two samples (262 adolescent twin pairs and 237 college students), math anxiety related to math performance differently depending on intrinsic math motivation: high motivation showed an inverted-U relation, while low motivation showed modest negative linear associations. This pattern held for computation/problem tasks but not for symbolic or nonsymbolic number estimation.
Key findings
- In both samples, students with high intrinsic math motivation showed an inverted-U relation between math anxiety and math performance, peaking at intermediate anxiety; students with low intrinsic math motivation showed modest negative associations across anxiety levels.
- In Study 1, after covariates, the quadratic math-anxiety term was significantly associated with Problem Verification and Calculation performance; the moderated quadratic term (MA² × MM) was significantly related to four tasks—Composing and Decomposing Numbers, Problem Verification, Calculation, and Applied Problems—but not to the Dots or Number-Line tasks. Total variance explained by predictors ranged from .02 to .25 across the six tasks.
- In Study 2, hierarchical regression found the moderated quadratic interaction between math anxiety and math motivation significantly predicted Problem Verification performance after covariates and lower-order terms; post-hoc analyses replicated the Study 1 pattern.
- In Study 1, math anxiety was negatively associated with all tasks after covariates, and math motivation was positively associated with all math tasks in the moderated models; in Study 2, math anxiety was negatively associated with math performance and math motivation positively associated with it.
Methods
- Study 1: 262 pairs of same-sex adolescent twins from the Western Reserve Reading and Math Projects, mean age 12.25 years (SD = 1.20; range = 8.75–15.33). Participants self-reported math anxiety (MARS-E), math motivation (3 items from Chiu & Zeng, 2008), and general anxiety; math cognition was assessed with six tasks (Dots, Number-Line, Composing and Decomposing Numbers, Problem Verification, WJ-III Calculation, WJ-III Applied Problems). Structural equation modeling with interchangeable dyads was used, with bootstrapping on 1000 samples.
- Study 2: 237 undergraduates (56% female; 18 excluded for technical problems or random responses), mean age 19.53 years (SD = 2.01; range = 18–39), recruited from Introductory Psychology via Qualtrics. Measures included MARS-B math anxiety, STAI trait anxiety, the same 3-item math motivation scale, and the hard items of the Problem Verification Task; hierarchical regression tested the moderated quadratic interaction.
- Math anxiety, math motivation, and general anxiety were standardized and centered before computing interaction and higher-order terms; outcome variables were standardized.
Limitations
- Stated in the paper: the findings should not be interpreted as evidence of a unidirectional causal relation between math-related emotion and math cognition, and longitudinal studies spanning multiple developmental stages are needed.
- Stated/evident in the text: the three-way interaction was complex and effect sizes were small, with affect variables adding only incremental predictive effects beyond covariates.
- Evident from the text: Study 1’s sample was 91% White and consisted of twins, and Study 2 used volunteer Introductory Psychology undergraduates, limiting generalizability; both studies were cross-sectional and relied on self-report affect measures.
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Claims the paper makes
0 of 34 cited sources checked · 0 supported · 0 flagged
- Findingown data
General anxiety was minimally correlated with math task performance.
“Additionally, general anxiety was minimally correlated with math task performance whereas MA was modestly negatively correlated with math performance.”
Quote in the paperNot a substantial claim - Findingown data
Math anxiety was modestly negatively correlated with math performance.
“Additionally, general anxiety was minimally correlated with math task performance whereas MA was modestly negatively correlated with math performance.”
Quote in the paperSubstantial claim - Findingown data
In students with high intrinsic math motivation, math anxiety and math performance show an inverted-U relation.
“In both samples, results showed inverted-U relations between math anxiety and math performance in students with high intrinsic math motivation, and modest negative associations between math anxiety and math performance in students with low intrinsic math motivation.”
Quote in the paperSubstantial claim - Findingown data
In students with low intrinsic math motivation, math anxiety and math performance show modest negative associations.
“In both samples, results showed inverted-U relations between math anxiety and math performance in students with high intrinsic math motivation, and modest negative associations between math anxiety and math performance in students with low intrinsic math motivation.”
Quote in the paperSubstantial claim - Findingown data
The inverted-U and negative association pattern between math anxiety and math performance was not observed in tasks assessing nonsymbolic and symbolic number estimation.
“However, this pattern was not observed in tasks assessing student’s nonsymbolic and symbolic number estimation.”
Quote in the paperSubstantial claim
- Findingown data
At high levels of MM, there was an inverted-U curvilinear relation between MA and task performance.
“At high levels of MM, there was an inverted-U curvilinear relation between MA and task performance.”
Quote in the paperSubstantial claim - Findingown data
MM was positively associated with all math tasks.
“MM was positively associated with all math tasks.”
Quote in the paperNot a substantial claim - Findingown data
At high levels of MM, there was an inverted-U curvilinear relation between MA and each of the four tasks, such that performance peaked at an intermediate level of MA and decreased as levels of MA deviated from this optimal intermediate level.
“At high levels of MM, there was an inverted-U curvilinear relation between MA and each of these four tasks, such that performance peaked at an intermediate level of MA and decreased as levels of MA deviated from this optimal intermediate level”
Quote in the paperSubstantial claim - Findingown data
Total variance (total R2) in each of the six tasks explained by this set of predictors ranged from .02 to .25.
“total variance (i.e., total R2) in each of the six tasks explained by this set of predictors ranged from .02 to .25”
Quote in the paperNot a substantial claim - Findingown data
At low levels of MM, MA was modestly negatively associated with task performance across all levels of MA.
“At low levels of MM, MA was modestly negatively associated with task performance across all levels of MA”
- Also stated in: § Results · plain
“At low levels of MM, MA was modestly negatively associated with task performance across all levels of MA.”
Quote in the paperSubstantial claim - Also stated in: § Results · plain
- Findingown data
MA was increasingly negatively associated with math performance on the Problem Verification and Calculation tasks as levels of MA increased.
“MA was increasingly negatively associated with math performance on these two tasks as levels of MA increased”
Quote in the paperSubstantial claim - Findingown data
MA negatively predicted math performance after controlling for the effects of the covariates.
“MA negatively predicted math performance after controlling for the effects of the covariates.”
Quote in the paperSubstantial claim - Findingown data
MA was negatively associated with math performance.
“MA was negatively associated with math performance”
Quote in the paperSubstantial claim - Findingreasoning
MA was not related to the nonsymbolic number estimation task (Dots).
“MA was not related to the nonsymbolic number estimation task (i.e., Dots task).”
Quote in the paperSubstantial claim - Findingown data
MM was positively associated with math performance.
“MM was positively associated with math performance.”
Quote in the paperSubstantial claim - Findingown data
MA was negatively correlated with performance on the symbolic number estimation task (Number-Line).
“the current findings showed that MA was negatively correlated with performance on the symbolic number estimation task (i.e., Number-Line task)”
Quote in the paperSubstantial claim - Findingown data
The 64 easy items were far too easy for undergraduate students (mean accuracy = .93, SD = .06).
“Because the 64 easy items were far too easy for undergraduate students (mean accuracy = .93, SD = .06)”
Quote in the paperSubstantial claim - Findingown data
Less variance was explained in the Dots and Number-Line tasks compared to the other math tasks.
“with less variance explained in the Dots and Number-Line tasks compared to the other math tasks”
Quote in the paperNot a substantial claim - Findingown data
After controlling for the effects of the covariates, MA was negatively associated with all tasks.
“After controlling for the effects of the covariates, MA was negatively associated with all tasks.”
Quote in the paperSubstantial claim - Findingown data
After controlling for the linear effects of MA, the quadratic term was significantly associated with performance on the Problem Verification and Calculation tasks.
“after controlling for the linear effects of MA, the quadratic term was significantly associated with the performance on the Problem Verification and Calculation tasks.”
Quote in the paperSubstantial claim - Findingown data
Performance on the Applied Problems task peaked at relatively lower levels of MA compared to the other tasks.
“performance on the Applied Problems task peaked at relatively lower levels of MA.”
Quote in the paperNot a substantial claim - Premisecitation
Items measuring math anxiety and math motivation load on separate factors.
“MA and MM are distinct constructs in that items measuring MA and MM are shown to load on separate factors (Bai, Wang, Pan, & Frey, 2009; Krinzinger, Kaufmann, & Willmes, 2009).”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Bai, Wang, Pan, & Frey, 2009
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- cites Krinzinger, Kaufmann, & Willmes, 2009
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- Premisecitation
Relations between anxiety and performance on complex cognitive tasks follow a curvilinear fashion.
“However, the relations between anxiety and performance on complex cognitive tasks have been repeatedly demonstrated to follow a curvilinear fashion.”
- Also stated in: § Abstract · boosted
“This inverted-U law has since been extended to the relation between negative emotions such as anxiety and performance in complex memory and attention tasks that rely heavily on prefrontal cortex functioning in primates (Andreano & Cahill, 2006; Aston-Jones, Rajkowski, & Cohen, 2000; Mendl, 1999).”
Quote in the paperSubstantial claim0 of 3 sources checked- cites Yerkes & Dodson, 1908
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- cites Andreano & Cahill, 2006
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- cites Aston-Jones, Rajkowski, & Cohen, 2000
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- Also stated in: § Abstract · boosted
- Premisecitation
Math anxiety and math motivation together improve prediction of math learning behaviors and achievement outcomes as compared to either one alone.
“Importantly, MA and MM together improves prediction of math learning behaviors and achievement outcomes as compared to either one alone (Lyons & Beilock, 2012; Wigfield & Meece, 1988).”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Lyons & Beilock, 2012
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- cites Wigfield & Meece, 1988
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- Premisecitation
Math anxiety and math motivation are modestly negatively correlated.
“MA and MM are related in the sense that they both capture some hedonic (i.e., negative vs. positive) aspects of math experience, and are shown to be modestly negatively correlated (Chiu & Henry, 1990).”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Chiu & Henry, 1990
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- Study design and conductown data
The significant moderated quadratic effects persisted with the sequential Bonferroni correction.
“These significant moderated quadratic effects persisted with the sequential Bonferroni correction.”
Quote in the paperSubstantial claim - Interpretationown data
Moderate levels of MA seem to be beneficial rather than detrimental to intrinsically motivated children.
“The current findings suggest that moderate levels of MA seem to be beneficial rather than detrimental to intrinsically motivated children.”
Quote in the paperSubstantial claim - Premisecitation
The effects of stress response on math performance depend on whether individuals interpret math situations as positive and challenging or negative and threatening.
“the effects of stress response on math performance depend on whether individuals interpret math situations as positive and challenging or negative and threatening”
Quote in the paperSubstantial claim0 of 1 sources checked- cites Mattarella-Micke, Mateo, Kozak, Foster, & Beilock, 2011
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- Interpretationown data
It is only in students with high MM that moderate MA had a facilitative effect on performance.
“It is only in students with high MM that moderate MA had a facilitative effect on performance.”
Quote in the paperSubstantial claim - Interpretationown data
The current study demonstrated that the transactions between math-related emotions and cognitions were far more complex than simple linear and additive relations.
“demonstrated that the transactions between math-related emotions and cognitions were far more complex than simple linear and additive relations.”
Quote in the paperSubstantial claim - Interpretationcitation
MA may not universally impair the development of math abilities.
“MA may not universally impair the development of math abilities”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Lyons & Beilock, 2012
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- cites Wigfield & Meece, 1988
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- Interpretationown data
This pattern emerged among both adolescents and adults.
“This observation emerged among both adolescents and adults.”
Quote in the paperSubstantial claim - Interpretationreasoning
In individuals with low MM, higher MA consistently demonstrated a debilitative effect on math performance.
“In individuals with low MM, higher MA consistently demonstrated a debilitative effect on math performance.”
Quote in the paperSubstantial claim
- Classified as probably not a substantial claim. 31
- May combine two claims. 16
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Findingown dataPerformance on all math tasks was positively correlated.
“Finally, performance on all math tasks was positively correlated.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataMath motivation was positively correlated with the Calculation and Applied Problems tasks, but was not correlated with performance on other math tasks.
“MM was positively correlated with the Calculation and Applied Problems tasks, but was not correlated with performance on other math tasks.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataAfter controlling for covariates, linear effects of MA and MM, and all lower-order interaction terms, the moderated quadratic term (MA2*MM) was significantly related to four math tasks but not to the Dots and Number-Line tasks.
“After controlling for the covariates, linear effects of MA and MM, and all lower-order interaction terms, the moderated quadratic term (i.e., MA2*MM) was significantly related to four math tasks but were not significantly related to the Dots and Number-Line tasks.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown dataAfter controlling for all linear and 2-way interaction effects, the moderated quadratic interaction between MA and MM was statistically significant and added incremental predictive effects on math performance.
“after controlling for all the linear and 2-way interaction effects, the moderated quadratic interaction between MA and MM was statistically significant, and added incremental predictive effects on math performance.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Findingown dataSex was negatively correlated with MA.
“and was negatively correlated with MA.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataThe covariates as a set explained a major proportion of variance in the math outcome variables, whereas the main effects of MA and MM and their interactive effects together only added incremental effects in predicting math performance.
“Overall, the covariates as a set explained a major proportion of variance in these math outcome variables, whereas the main effects of MA and MM and their interactive effects together only added incremental effects in predicting math performance.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataAge and sex both negatively predicted task performance, indicating that younger and male participants performed better on average, with a larger effect size for sex.
“Overall, age and sex both negatively predicted task performance, indicating that younger and male participants performed better on average, with a larger effect size for the latter.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Findingown dataNone of the main study variables vary as a function of age.
“None of the main study variables vary as a function of age.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataGeneral anxiety was not related to or predictive of math performance.
“general anxiety was not related to math performance.”
- Also stated in: § Results · plain
“General anxiety did not predict math performance.”
Quote in the paperSubstantial claim- Also stated in: § Results · plain
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Findingown dataSex was positively associated with performance on the Problem Verification task.
“Sex (0 = female, 1 = male) was positively associated with performance on the Problem Verification task”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim.
PremisecitationHigh activations in brain regions involved in motivating behaviors dampen the negative effects of high math anxiety on math performance.
“In particular, one recent study showed that high activations in brain regions involved in motivating behaviors dampen the negative effects of high MA on math performance, suggesting that math performance not only varies as a function of MA, but also on how individuals approach math-related situations (Lyons & Beilock, 2012).”
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Study design and conductown dataLog transformations successfully produced variables that more closely approximated normal distributions.
“Subsequently, log transformations were performed on the skewed variables. Transformation successfully produced variables that more closely approximated normal distributions.”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim.
PremisecitationTwo previous studies provided preliminary evidence suggesting facilitative effects of moderate levels of math anxiety on math performance in adults and mathematically gifted children.
“Two previous studies have provided some preliminary evidence suggesting facilitative effects of moderate levels of MA on math performance in adults and mathematically gifted children (Evans, 2000; Tsui & Mazzocco, 2006).”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Evans, 2000
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- cites Tsui & Mazzocco, 2006
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Study design and conductcitationThe Number-Line Estimation Task measures individuals' ability to represent and estimate numerical quantities spatially.
“Number-Line Estimation Task captures individuals’ ability to represent and estimate numerical quantities spatially (Siegler & Opfer, 2003).”
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Study design and conductown dataResults remained essentially the same when missing data were handled using both listwise deletion and full information maximum likelihood estimation.
“Results remained essentially the same when missing data were handled using both listwise deletion and full information maximum likelihood estimation.”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim.
Study design and conductreasoningThe linear and quadratic effects of general anxiety were entered as covariates to control for the possibility that the relations between math performance and math anxiety are due to general anxiety, not specific anxiety about math.
“The linear and quadratic effects of general anxiety (i.e., general anxiety and its squared term) were entered as manifest covariates in the model for each sibling to control for the possibility that the relations between math performance and MA are due to general anxiety, not specific anxiety about math.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductown dataThe general anxiety subscale of the Spence Children's Anxiety Scale has adequate internal consistency with a Cronbach's α of .71.
“This scale has adequate internal consistency with a Cronbach’s α of .71.”
Quote in the paperNot a substantial claimMay combine two claims.
PremisecitationSome highly math anxious individuals are more avoidant in math, whereas others invest more efforts and recruit more cognitive resources in math problem solving.
“Some highly math anxious individuals are more avoidant in math, whereas others invest more efforts and recruit more cognitive resources in math problem solving (Lyons & Beilock, 2012; Wigfield & Meece, 1988).”
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- cites Wigfield & Meece, 1988
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Study design and conductcitationThe Calculation subtest of the Woodcock Johnson III Tests of Achievement is a test of mathematical computation ability.
“The Calculation subtest of the Woodcock Johnson III Tests of Achievement (Woodcock, McGraw, & Mather, 2001) is a test of mathematical computation ability.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Woodcock, McGraw, & Mather, 2001
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PremisecitationMath performance varies not only as a function of math anxiety but also on how individuals approach math-related situations.
“In particular, one recent study showed that high activations in brain regions involved in motivating behaviors dampen the negative effects of high MA on math performance, suggesting that math performance not only varies as a function of MA, but also on how individuals approach math-related situations (Lyons & Beilock, 2012).”
Quote in the paperSubstantial claim0 of 1 sources checked- cites Lyons & Beilock, 2012
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PremisecitationCentral neurochemical activities (e.g., catecholamine release and signaling) may underlie the observed curvilinear relationship between anxiety and complex cognitive performance.
“More recent studies have demonstrated that central neurochemical activities (e.g., catecholamine release and signaling) may underlie the observed curvilinear relationship between anxiety and complex cognitive performance (Arnsten, 2009; Diamond, Campbell, Park, Halonen, & Zoladz, 2007).”
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- cites Diamond, Campbell, Park, Halonen, & Zoladz, 2007
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Study design and conductcitationThe Problem Verification Task measures math calculation fluency.
“Problem Verification Task was developed as a measure of math calculation fluency and metacognition (Rinne & Mazzocco, 2014). We relied on the calculation fluency component of this measure in the present study.”
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Study design and conductcitationSignificance tests for the correlations were adjusted according to the method outlined by Griffin & Gonzalez (1995) to account for biased standard errors arising from sibling non-independence.
“To account for the biased standard errors arising from sibling non-independence, significance tests for the correlations were adjusted according to the method outlined by Griffin & Gonzalez (1995).”
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Study design and conductcitationThe Composing and Decomposing Numbers Task is a timed measure of the automaticity of composing and decomposing numbers.
“Composing and Decomposing Numbers Task (CDNT) is a timed measure of the automaticity of composing and decomposing numbers (Mazzocco & Hanich, 2010).”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Mazzocco & Hanich, 2010
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Study design and conductown dataThe MARS-E has good internal consistency with a Cronbach's α of .94.
“The MARS-E has good internal consistency with a Cronbach’s α of .94.”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim. May combine two claims.
PremisecitationAn intermediate level of stress produces optimal learning efficiency of complex tasks in rats, whereas both extremely low and high levels of stress produce poor learning efficiency.
“These studies revealed that an intermediate level of stress produced optimal learning efficiency of complex tasks in rats, whereas both extremely low and high levels of stress produced poor learning efficiency (Yerkes & Dodson, 1908).”
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Study design and conductnone givenW-scores are obtained based on item response theory and have equal measurement intervals.
“W-scores are obtained based on item response theory, and all scores have equal measurement intervals.”
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Study design and conductcitationSEM with interchangeable dyads was preferred over multiple regression because it can analyze data from both siblings within the same family together to enhance statistical power while controlling for biased standard errors arising from sibling non-independence.
“SEM with interchangeable dyads was preferred over multiple regression because the former approach was more flexible, such that it is possible to analyze data from both siblings within the same family together to enhance statistical power while controlling for biased standard errors arising from sibling non-independence at the same time (Olsen & Kenny, 2006).”
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Study design and conductcitationThe Dots Task measures individual differences in the approximate number system and the ability to represent numerical quantities nonverbally.
“The Dots Task captures individual differences in the approximate number system. It measures individual’s ability to represent numerical quantities nonverbally (Halberda, Mazzocco, & Feigenson, 2008).”
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Study design and conductown dataMost variables were distributed normally, with the exception of Dots task, Number-Line task, and Problem Verification task.
“Most variables were distributed normally, with the exception of Dots task, Number-Line task, and Problem Verification task.”
Quote in the paperNot a substantial claimMay combine two claims.
PremisecitationA moderate level of anxiety heightens alertness and focused attention, facilitating complex cognitive functioning, whereas high anxiety impairs performance by diverting resources away from cognitive performance.
“At the behavioral level, a moderate level of anxiety is believed to heighten alertness and focused attention, which facilitates complex cognitive functioning, whereas high anxiety impairs performance by diverting resources away from cognitive performance.”
Quote in the paperSubstantial claim0 of 3 sources checked- cites Andreano & Cahill, 2006
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- cites Aston-Jones, Rajkowski, & Cohen, 2000
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- cites Mendl, 1999
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Study design and conductcitationThe Applied Problems subtest of the Woodcock Johnson III Tests of Achievement measures the ability to integrate math knowledge, quantitative reasoning, and calculation skills in problem solving.
“The Applied Problems subtest of the Woodcock Johnson III Tests of Achievement (Woodcock et al., 2001) measures participant’s ability to integrate math knowledge, quantitative reasoning, and calculation skills in problem solving.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites Woodcock et al., 2001
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Study design and conductown dataThe math motivation scale has adequate internal consistency with a Cronbach's α of .78.
“The Cronbach’s α for this scale is .78, indicating adequate internal consistency.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductown dataThe trait subscale from the State-Trait Anxiety Inventory has adequate internal consistency with a Cronbach's α of .94.
“This scale has adequate internal consistency with a Cronbach’s α of .94.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThe pattern is consistent with contemporary fMRI research that highlights the links between brain activations involved in motivating behaviors and cognitive control in improving performance in math anxious adults.
“is consistent with contemporary fMRI research that highlights the links between brain activations involved in motivating behaviors and cognitive control in improving performance in math anxious adults”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites Lyons & Beilock, 2012
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Interpretationown dataAn inverted-U relation between MA and math performance was observed in students who are more intrinsically motivated in math, whereas a negative linear relation was observed in those who are less motivated.
“Consistent with our hypothesis, an inverted-U relation between MA and math performance was observed in students who are more intrinsically motivated in math, whereas a negative linear relation was observed in those who are less motivated.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductown dataThe math motivation scale has a Cronbach's α of .82, indicating adequate internal consistency.
“The Cronbach’s α for this scale is .82, indicating adequate internal consistency.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductnone givenThe MARS-B has good internal consistency with a Cronbach's α of .94.
“The MARS-B has good internal consistency with a Cronbach’s α of .94.”
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Interpretationown dataThe findings of Study 2 were consistent with results from Study 1.
“The findings were consistent with results from Study 1.”
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Study design and conductnone givenAll main study variables were distributed widely and normally across their respective scales.
“All main study variables were distributed widely and normally across their respective scales.”
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Study design and conductown dataThe 24 hard items had wider performance variability (mean accuracy = .85, SD = .13) and were a more proper measure of individual differences in math calculation fluency in college students.
“we chose to focus on the 24 hard items which had wider performance variability (mean accuracy = .85, SD = .13), and was therefore a more proper measure of individual differences in math calculation fluency in college students.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductown dataEighteen participants were excluded from the analyses due to either technical problems (2) or random responses (16).
“Eighteen participants were excluded from the analyses due to either technical problems (2) or random responses (16).”
Quote in the paperNot a substantial claimMay combine two claims.
PremisecitationModerate levels of anxiety help enhance focused attention and working memory whereas extremely high or low levels of anxiety are associated with insufficient cognitive resources allocated to the tasks.
“The general cognitive literature has shown that moderate levels of anxiety help enhance focused attention and working memory whereas extremely high or low levels of anxiety are associated with insufficient cognitive resources allocated to the tasks”
Quote in the paperSubstantial claim0 of 2 sources checked- cites Arnsten, 2009
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- cites Diamond et al., 2007
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Interpretationown dataThe pattern was observed in the four math tasks that required generating or evaluating number combinations (CDNT, PVT, Calculations, Applied Problems), but not in the symbolic or nonsymbolic number estimation tasks (Dots and Number-Line).
“Importantly, this pattern was observed in the four math tasks that required generating or evaluating number combinations (i.e., CDNT, PVT, Calculations, Applied Problems), but not in the symbolic or nonsymbolic number estimation tasks (i.e., the Dots and the Number-Line tasks).”
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Moderate levels of stress can enhance learning by increasing attentional vigilance.
“For example, in some situations, moderate levels of stress can enhance learning by way of increasing attentional vigilance [29].”
From The neuroscience of emotion regulation development: Implications for education (2016) · cites this paper as [29]
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Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Study 2 sex coefficient conflicts with its interpretation
MinorSex is coded 0 for female and 1 for male. A negative coefficient for sex therefore indicates lower predicted performance for males, not that males performed better.
“Overall, age and sex both negatively predicted task performance, indicating that younger and male participants performed better on average, with a larger effect size for the latter.”
“Sex (0 = female, 1 = male) was positively associated with performance on the Problem Verification task and was negatively correlated with MA.”
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- Authors
- Wang, Z., Lukowski, S. L., Hart, S. A., Lyons, I. M., Thompson, L. A., Kovas, Y., Mazzocco, M. M. M., Plomin, R., & Petrill, S. A.
- Affiliations
- Virginia Tech (US)
- The Ohio State University (US)
- Florida State University (US)
- Western University (CA)
- Case Western Reserve University (US)
- King's College London (GB)
- University of Minnesota (US)
- Corresponding author
- Wang, Zhe
- ORCID
- Venue
- Psychological Science
- Publisher
- SAGE Publications
- Published
- 2015-10-30
- Volume
- 26
- Issue
- 12
- Pages
- 1863-1876
- ISSN
- 0956-7976 (ISSN-L)
- 1467-9280
- PMC
- PMC4679544
- OpenAlex
- W2262152752
- Cited by
- 225
- References
- 41
- Citations by year
- 2026: 22 · 2025: 13 · 2024: 30 · 2023: 31 · 2022: 31 · 2021: 33 · 2020: 18 · 2019: 10 · 2018: 18 · 2017: 12 · 2016: 7
- FWCI
- 18.58
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Psychological Science (publishedVersion)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- Research Portal (King's College London) (submittedVersion)
- Funders
- Eunice Kennedy Shriver National Institute of Child Health and Human Development (HD038075, R01HD068728, R01HD059215, R01HD038075, R24HD075460, HD075460, HD059215)
- Topics
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Education, Achievement, and Giftedness
- Physical Sciences › Mathematics › Statistics and Probability › Cognitive and developmental aspects of mathematical skills
- Physical Sciences › Mathematics › Applied Mathematics › Mathematics Education and Pedagogy
- Keywords
- mathematics anxiety, math motivation, intrinsic motivation, mathematics achievement, curvilinear relationship, inverted U-shaped relationship, numerical estimation, non-symbolic number processing, symbolic number processing, emotion-cognition interaction, mathematics learning, adolescents, university students
- MeSH terms
- Achievement, Adolescent, Adult, Anxiety, Child, Emotions, Female, Humans, Male, Mathematics, Problem Solving, Regression Analysis, Students, Comprehension, Young Adult
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