Mindsets and Neural Mechanisms of Automatic Reactions to Negative Feedback in Mathematics in Elementary School Students

Neuroscientific research regarding mindsets is so far scarce, especially among children. Moreover, even though research indicates the importance of domain specificity of mindsets, this has not yet been investigated in neuroscientific studies regarding implicit beliefs. The purpose of this study was to examine general intelligence and math ability mindsets and their relations to automatic reactions to negative feedback in mathematics in the Finnish elementary school context. For this, event-related potentials of 97 elementary school students were measured during the completion of an age-appropriate math task, where the participants received performance-relevant feedback throughout the task. Higher growth mindset was marginally associated with a larger P300 response and significantly associated with a smaller later peaking negative-going waveform. Moreover, with the domain-specific experimental setting, we found a higher growth mindset regarding math ability, but not general intelligence, to be associated with these brain responses elicited by negative feedback regarding errors in math. This suggests that it might be important to address domain-specific and even academic-domain-specific beliefs in addition to general mindsets in research and practice.

Proactive Control Mediates the Relationship Between Working Memory and Math Ability in Early Childhood

Based on the dual mechanisms of control (DMC) theory, there are two distinct mechanisms of cognitive control, proactive and reactive control. Importantly, accumulating evidence indicates that there is a developmental shift from predominantly using reactive control to proactive control during childhood, and the engagement of proactive control emerges as early as 5–7 years old. However, less is known about whether and how proactive control at this early age stage is associated with children’s other cognitive abilities such as working memory and math ability. To address this issue, the current study recruited 98 Chinese children under 5–7 years old. Among them, a total of 81 children (mean age = 6.29 years) contributed useable data for the assessments of cognitive control, working memory, and math ability. The results revealed that children at this age period predominantly employed a pattern of proactive control during an AX-Continuous Performance Task (AX-CPT). Moreover, the proactive control index estimated by this task was positively associated with both working memory and math performance. Further regression analysis showed that proactive control accounted for significant additional variance in predicting math performance after controlling for working memory. Most interestingly, mediation analysis showed that proactive control significantly mediated the association between working memory and math performance. This suggests that as working memory increases so does proactive control, which may in turn improve math ability in early childhood. Our findings may have important implications for educational practice.

Effects of Visual Training of Approximate Number Sense on Auditory Number Sense and School Math Ability

Research with children and adults suggests that people's math performance is predicted by individual differences in an evolutionarily ancient ability to estimate and compare numerical quantities without counting (the approximate number system or ANS). However, previous work has almost exclusively used visual stimuli to measure ANS precision, leaving open the possibility that the observed link might be driven by aspects of visuospatial competence, rather than the amodal ANS. We addressed this possibility in an ANS training study. Sixty-eight 6-year-old children participated in a 5-week study that either trained their visual ANS ability or their phonological awareness (an active control group). Immediately before and after training, we assessed children's visual and auditory ANS precision, as well as their symbolic math ability and phonological awareness. We found that, prior to training, children's precision in a visual ANS task related to their math performance - replicating recent studies. Importantly, precision in an auditory ANS task also related to math performance. Furthermore, we found that children who completed visual ANS training showed greater improvements in auditory ANS precision than children who completed phonological awareness training. Finally, children in the ANS training group showed significant improvements in math ability but not phonological awareness. These results suggest that the link between ANS precision and school math ability goes beyond visuospatial abilities and that the modality-independent ANS is causally linked to math ability in early childhood.

Individual Differences in Math Ability Determine Neurocognitive Processing of Arithmetic Complexity: A Combined fNIRS-EEG Study

Some individuals experience more difficulties with math than others, in particular when arithmetic problems get more complex. Math ability, on one hand, and arithmetic complexity, on the other hand, seem to partly share neural underpinnings. This study addresses the question of whether this leads to an interaction of math ability and arithmetic complexity for multiplication and division on behavioral and neural levels. Previously screened individuals with high and low math ability solved multiplication and division problems in a written production paradigm while brain activation was assessed by combined functional near-infrared spectroscopy (fNIRS) and electroencephalography (EEG). Arithmetic complexity was manipulated by using single-digit operands for simple multiplication problems and operands between 2 and 19 for complex multiplication problems and the corresponding division problems. On the behavioral level, individuals with low math ability needed more time for calculation, especially for complex arithmetic. On the neural level, fNIRS results revealed that these individuals showed less activation in the left supramarginal gyrus (SMG), superior temporal gyrus (STG) and inferior frontal gyrus (IFG) than individuals with high math ability when solving complex compared to simple arithmetic. This reflects the greater use of arithmetic fact retrieval and also the more efficient processing of arithmetic complexity by individuals with high math ability. Oscillatory EEG analysis generally revealed theta and alpha desynchronization with increasing arithmetic complexity but showed no interaction with math ability. Because of the discovered interaction for behavior and brain activation, we conclude that the consideration of individual differences is essential when investigating the neurocognitive processing of arithmetic.

Using Hierarchical Linear Models to Examine Approximate Number System Acuity: The Role of Trial-Level and Participant-Level Characteristics

The ability to intuitively and quickly compare the number of items in collections without counting is thought to rely on the Approximate Number System (ANS). To assess individual differences in the precision of peoples' ANS representations, researchers often use non-symbolic number comparison tasks in which participants quickly choose the numerically larger of two arrays of dots. However, some researchers debate whether this task actually measures the ability to discriminate approximate numbers or instead measures the ability to discriminate other continuous magnitude dimensions that are often confounded with number (e.g., the total surface area of the dots or the convex hull of the dot arrays). In this study, we used hierarchical linear models (HLMs) to predict 132 adults' accuracy on each trial of a non-symbolic number comparison task from a comprehensive set of trial-level characteristics (including numerosity ratio, surface area, convex hull, and temporal and spatial variations in presentation format) and participant-level controls (including cognitive abilities such as visual-short term memory, working memory, and math ability) in order to gain a more nuanced understanding of how individuals complete this task. Our results indicate that certain trial-level characteristics of the dot arrays contribute to our ability to compare numerosities, yet numerosity ratio, the critical marker of the ANS, remains a highly significant predictor of accuracy above and beyond trial-level characteristics and across individuals with varying levels of math ability and domain-general cognitive abilities.

Convergent Evaluation of Working Memory and Arithmetic Ability in a Child with Autism Spectrum Disorder without Intellectual Impairment

Studies focusing on a joint evaluation of both Working Memory (WM) and Math Ability (MA) in autism are far from abundant in literature, possibly due to inadequate methodological approaches and reported inconsistencies between results obtained in each separate field of research, resulting in contradictory conclusions. The specific aim of this case report is therefore evaluating and integrating results on these two cognitive abilities in a child with autism spectrum disorder without intellectual impairment. Our data on an autistic 10-year-old child (M.N.) show that the levels of functional (active vs. passive), rather than structural (phonological vs. visual), data manipulation are quite relevant in the way the child scored differently in the various tasks. Furthermore, M.N. generally displayed average to good ability levels in math calculation, except for oral multiplication, and division activities. By way of conclusion, data are discussed in terms of strengths and weaknesses in relation to special learning trajectories in education and the relevant achievements.

Deficits in Approximate Number System Acuity and Mathematical Abilities in 6.5-Year-Old Children Born Extremely Preterm

Preterm children are at increased risk for poor academic achievement, especially in math. In the present study, we examined whether preterm children differ from term-born children in their intuitive sense of number that relies on an unlearned, approximate number system (ANS) and whether there is a link between preterm children’s ANS acuity and their math abilities. To this end, 6.5-year-old extremely preterm (i.e., <27 weeks gestation, n = 82) and term-born children (n = 89) completed a non-symbolic number comparison (ANS acuity) task and a standardized math test. We found that extremely preterm children had significantly lower ANS acuity than term-born children and that these differences could not be fully explained by differences in verbal IQ, perceptual reasoning skills, working memory, or attention. Differences in ANS acuity persisted even when demands on visuo-spatial skills and attention were reduced in the ANS task. Finally, we found that ANS acuity and math ability are linked in extremely preterm children, similar to previous results from term-born children. These results suggest that deficits in the ANS may be at least partly responsible for the deficits in math abilities often observed in extremely preterm children.

The Approximate Number System Acuity Redefined: A Diffusion Model Approach

While all humans are capable of non-verbally representing numerical quantity using so-called the approximate number system (ANS), there exist considerable individual differences in its acuity. For example, in a non-symbolic number comparison task, some people find it easy to discriminate brief presentations of 14 dots from 16 dots while others do not. Quantifying individual ANS acuity from such a task has become an essential practice in the field, as individual differences in such a primitive number sense is thought to provide insights into individual differences in learned symbolic math abilities. However, the dominant method of characterizing ANS acuity-computing the Weber fraction (w)-only utilizes the accuracy data while ignoring response times (RT). Here, we offer a novel approach of quantifying ANS acuity by using the diffusion model, which accounts both accuracy and RT distributions. Specifically, the drift rate in the diffusion model, which indexes the quality of the stimulus information, is used to capture the precision of the internal quantity representation. Analysis of behavioral data shows that w is contaminated by speed-accuracy tradeoff, making it problematic as a measure of ANS acuity, while drift rate provides a measure more independent from speed-accuracy criterion settings. Furthermore, drift rate is a better predictor of symbolic math ability than w, suggesting a practical utility of the measure. These findings demonstrate critical limitations of the use of w and suggest clear advantages of using drift rate as a measure of primitive numerical competence.

The role of self-math overlap in understanding math anxiety and the relation between math anxiety and performance

Recent work has demonstrated that math anxiety is more than just the product of poor math skills. Psychosocial factors may play a key role in understanding what it means to be math anxious, and hence may aid in attempts to sever the link between math anxiety and poor math performance. One such factor may be the extent to which individuals integrate math into their sense of self. We adapted a well-established measure of this degree of integration (i.e., self-other overlap) to assess individuals’ self-math overlap. This non-verbal single-item measure showed that identifying oneself with math (having higher self-math overlap) was strongly associated with lower math anxiety (r = -0.610). We also expected that having higher self-math overlap would leave one especially susceptible to the threat of poor math performance to the self. We identified two competing hypotheses regarding how this plays out in terms of math anxiety. Those higher in self-math overlap might be more likely to worry about poor math performance, exacerbating the negative relation between math anxiety and math ability. Alternatively, those higher in self-math overlap might exhibit self-serving biases regarding their math ability, which would instead predict a decoupling of the relation between their perceived and actual math ability, and in turn the relation between their math ability and math anxiety. Results clearly favored the latter hypothesis: those higher in self-math overlap exhibited almost no relation between math anxiety and math ability, whereas those lower in self-math overlap showed a strong negative relation between math anxiety and math ability. This was partially explained by greater self-serving biases among those higher in self-math overlap. In sum, these results reveal that the degree to which one integrates math into one’s self – self-math overlap – may provide insight into how the pernicious negative relation between math anxiety and math ability may be ameliorated.

Is Approximate Number Precision a Stable Predictor of Math Ability?

Previous research shows that children's ability to estimate numbers of items using their Approximate Number System (ANS) predicts later math ability. To more closely examine the predictive role of early ANS acuity on later abilities, we assessed the ANS acuity, math ability, and expressive vocabulary of preschoolers twice, six months apart. We also administered attention and memory span tasks to ask whether the previously reported association between ANS acuity and math ability is ANS-specific or attributable to domain-general cognitive skills. We found that early ANS acuity predicted math ability six months later, even when controlling for individual differences in age, expressive vocabulary, and math ability at the initial testing. In addition, ANS acuity was a unique concurrent predictor of math ability above and beyond expressive vocabulary, attention, and memory span. These findings of a predictive relationship between early ANS acuity and later math ability add to the growing evidence for the importance of early numerical estimation skills.

Not lack of ability but more choice: individual and gender differences in choice of careers in science, technology, engineering, and mathematics

The pattern of gender differences in math and verbal ability may result in females having a wider choice of careers, in both science, technology, engineering, and mathematics (STEM) and non-STEM fields, compared with males. The current study tested whether individuals with high math and high verbal ability in 12th grade were more or less likely to choose STEM occupations than those with high math and moderate verbal ability. The 1,490 subjects participated in two waves of a national longitudinal study; one wave was when the subjects were in 12th grade, and the other was when they were 33 years old. Results revealed that mathematically capable individuals who also had high verbal skills were less likely to pursue STEM careers than were individuals who had high math skills but moderate verbal skills. One notable finding was that the group with high math and high verbal ability included more females than males.