Linking inhibitory control to math achievement via comparison of conflicting decimal numbers

Parameterizing Individual Differences in Fraction and Decimal Arithmetic

Math problem solving frequently involves choices among alternative strategies. Strategy choices, and effects of problem features on strategy choices, both vary among individuals. We propose that individual differences in strategy choices can be well characterized in terms of parametric variation in three types of influence: global bias, relevant feature effects, and irrelevant feature effects. We test this framework by applying it to children's strategy choices in fraction and decimal arithmetic. We describe a simple mathematical model of strategy choice in this domain that is based on a recent theory of arithmetic development and includes parameters representing the three types of influence above. We estimate these parameters in a sample of 120 fifth to ninth graders and find that all of them vary substantially among children. Further, we find that different parameters relate differently to other domain-specific and domain-general abilities, supporting the utility of distinguishing among the parameters and estimating them separately for individuals. We discuss implications of the results regarding the nature and origins of individual differences in strategy choice in fraction and decimal arithmetic and math more broadly.

The relationship between executive functions and mathematics achievements in early-grade elementary students

Mathematics, along with reading and writing, is a core academic subject in the school curriculum. The development of mathematical skills is influenced by various cognitive factors, with executive functions (EF) playing a central role. EF, which encompasses working memory, inhibitory control, and cognitive flexibility, is critical for supporting complex cognitive processes required for problem-solving and mathematical reasoning. Research consistently shows that children with stronger EF tend to achieve better academic outcomes, including in mathematics. The goal of the present study was to examine the relationships between the global EF and its three core components - working memory, inhibitory control, and cognitive flexibility - and their impact on mathematics achievement. The sample for this study consisted of 180 children, aged 8-11 years (mean age: 9.6, SD: 1.0 year; 83 girls, 97 boys). EF was assessed using the Yellow-Red test, while mathematics achievement was evaluated based on teachers' evaluations of the child's mathematics performance. The results indicated a statistically significant effect of global EF and its three components on mathematics achievement. Given the potential malleability of EFs, we conclude with recommendations for strategies to enhance EF development at an early school age.

Neural Associations between Inhibitory Control and Counterintuitive Reasoning in Science and Maths in Primary School Children

Emerging evidence suggests that inhibitory control (IC) plays a pivotal role in science and maths counterintuitive reasoning by suppressing incorrect intuitive concepts, allowing correct counterintuitive concepts to come to mind. Neuroimaging studies have shown greater activation in the ventrolateral and dorsolateral pFCs when adults and adolescents reason about counterintuitive concepts, which has been interpreted as reflecting IC recruitment. However, the extent to which neural systems underlying IC support science and maths reasoning remains unexplored in children. This developmental stage is of particular importance, as many crucial counterintuitive concepts are learned in formal education in middle childhood. To address this gap, fMRI data were collected while fifty-six 7- to 10-year-olds completed counterintuitive science and math problems, plus IC tasks of interference control (Animal Size Stroop) and response inhibition (go/no-go). Univariate analysis showed large regional overlap in activation between counterintuitive reasoning and interference control, with more limited activation observed in the response inhibition task. Multivariate similarity analysis, which explores fine-scale patterns of activation across voxels, revealed neural activation similarities between (i) science and maths counterintuitive reasoning and interference control tasks in frontal, parietal, and temporal regions, and (ii) maths reasoning and response inhibition tasks in the precuneus/superior parietal lobule. Extending previous research in adults and adolescents, this evidence is consistent with the proposal that IC, specifically interference control, supports children's science and maths counterintuitive reasoning, although further research will be needed to demonstrate the similarities observed do not reflect more general multidemand processes.

Transfer of congruency effects between Stroop and multiplication tasks: Evidence that retrieval of multiplication facts requires inhibitory control

Inhibitory control is classically considered a domain-general process, yet recent findings suggest it may operate in context-specific ways. This has important implications for theories in other cognitive domains, such as mathematics, in which inhibitory control is proposed to play a key role. Inhibitory control has been implicated in resolving interference between competing number facts when retrieving them from memory, yet clear evidence for this is lacking. Here we report two pre-registered experiments with adults that investigated transfer of inhibitory control between interleaved Stroop and multiplication fact retrieval trials. Experiment 1 (n = 450) measured the congruency sequence effect, where transfer of inhibitory control between trials leads to a reduced congruency effect following an incongruent trial. Experiment 2 (n = 370) measured transfer of the list-wide proportion congruency effect, where the congruency effect is reduced when incongruent trials are more frequent. We found evidence of transfer of the congruency sequence effect between Stroop and multiplication. This did not differ depending on whether the Stroop task used number or animal stimuli. There was no transfer of the list-wide proportion congruency effect. These results suggest that reactive, transient domain-general inhibitory control processes are involved in retrieving multiplication facts from memory. Our findings have implications for theories of cognitive control and mathematical cognition, but caution should be taken in interpreting implications for educational interventions.

Children's estimates of equivalent rational number magnitudes are not equal: Evidence from fractions, decimals, percentages, and whole numbers

Integration of rational number knowledge with prior whole number knowledge has been theorized as critical for mathematical success. Fractions, decimals, and percentages are generally assumed to differ in difficulty based on the degree to which their structure is perceptually similar to whole numbers. Specifically, percentages are viewed as most similar to whole numbers with their fixed unstated denominator of 100. Decimals are often assumed to be easier than fractions because their place-value structure is an extension of the base-ten system for whole numbers, unlike fractions, which have a bipartite structure (i.e., a/b). However, there has been no comprehensive investigation of how fraction, decimal, and percentage knowledge compares with whole number knowledge. To assess understanding of the four notations, we measured within-participants number line estimation of equivalent fractions and decimals with shorter string lengths (e.g., 8/10 and 0.8) and longer string lengths (e.g., 80/100 and 0.80), percentages (e.g., 80%), and proportionally equivalent whole numbers on a 0-100 scale (e.g., 80.0). Middle school students (N = 65; 33 female) generally underestimated all formats relative to their actual values (whole numbers: 3% below; percentages: 2%; decimals: 17%; fractions: 5%). Shorter string-length decimals and fractions were estimated as smaller than equivalent longer string-length equivalents. Overall, percentages were estimated similarly to corresponding whole numbers, fractions had modest string-length effects, and decimals were the most underestimated, especially for single-digit decimals. These results highlight the strengths and weaknesses of children's understanding of each notation's magnitudes and challenge the assumption that decimals are easier than fractions.

Neural Mechanisms of Inhibition in Scientific Reasoning: Insights from fNIRS

This study examines the impact of response and semantic inhibition on scientific reasoning using fNIRS data from 30 students (15 male, 15 female). Utilizing Go/Nogo and Stroop-like tasks within a modified speeded-reasoning task, it was found that inhibition significantly influences scientific reasoning. Specifically, slower responses and lower accuracy on incongruent statements were linked to increased activity in bilateral dorsolateral prefrontal cortex (DLPFC) and pre-supplementary motor area (pre-SMA). The research shows that both DLPFC and pre-SMA are associated with overcoming misconceptions in scientific reasoning. The findings suggest that understanding inhibitory mechanisms can enhance educational strategies to improve critical thinking and scientific literacy.

The mechanism of inhibition control in mathematical reasoning: a functional near-infrared spectroscopy study

BACKGROUND AND OBJECTIVES

The ability to comprehend and engage in mathematical reasoning is a fundamental cognitive skill, central to problem-solving and critical thinking. However, the intricate cognitive processes underlying mathematical reasoning, particularly in relation to inhibitory control, have garnered increasing attention in recent research. While previous studies have explored this connection, there remains a need for a more comprehensive understanding of the interplay between inhibitory control and mathematical reasoning. This study explored the contribution of response inhibition and semantic inhibition to scientific reasoning by comparing the brain activation of the speeded-reasoning task of mathematical subdomain concepts with that of the Go/Nogo and Stroop tasks.

METHOD

Using functional near-infrared spectroscopy, oxygenated hemoglobin (oxy-Hb) was recorded in 28 subjects performing Go/Nogo tasks, Stroop tasks and speeded-reasoning tasks. The study was divided into two parts. In one part, subjects performed the Go/Nogo task and the Stroop task, and in the other part, subjects performed speeded-reasoning tasks.

RESULTS

The results showed that the subjects had slower responses and lower accuracy when judging incongruent statements. The concentration of oxy-Hb in the brain region related to inhibition was increased. In addition, the oxy-Hb in reasoning incongruent nonmathematical statements was correlated to the Go/Nogo task, whereas the oxy-Hb in reasoning incongruent mathematical statements was correlated to the Stroop task.

CONCLUSION

This result supports the hypothesis that inhibitory control plays a role in the scientific reasoning of mathematical subdomain concepts, and both response inhibition and semantic inhibition are involved in suppressing the interference of mathematical misconceptions.Supplementary Video Abstract, Supplemental digital content 1, http://links.lww.com/WNR/A732.

Competing numerical magnitude codes in decimal comparison: Whole number and rational number distance both impact performance

A critical difference between decimal and whole numbers is that among whole numbers the number of digits provides reliable information about the size of the number, e.g., double-digit numbers are larger than single-digit numbers. However, for decimals, fewer digits can sometimes denote a larger number (i.e., 0.8 > 0.27). Accordingly, children and adults perform worse when comparing such Inconsistent decimal pairs relative to Consistent pairs, where the larger number also has more digits (i.e., 0.87 > 0.2). Two explanations have been posited for this effect. The string length congruity account proposes that participants compare each position in the place value system, and they additionally compare the number of digits. The semantic interference account suggests that participants additionally activate the whole number referents of numbers - the numbers unadorned with decimal points (e.g., 8 < 27) - and compare these. The semantic interference account uniquely predicts that for Inconsistent problems with the same actual rational distance, those with larger whole number distances should be harder, e.g., 0.9 vs. 0.81 should be harder than 0.3 vs. 0.21 because 9 < < 81 whereas 3 < 21. Here we test this prediction in two experiments with college students (Study 1: n = 58 participants, Study 2: n = 78). Across both, we find a main effect of consistency, demonstrating string length effects, and also that whole number distance interferes with processing conflicting decimals, demonstrating semantic interference effects. Evidence for both effects supports the semantic interference account, highlighting that decimal comparison difficulties arise from multiple competing numerical codes. Finally, for accuracy we found no relationship between whole number distance sensitivity and math achievement, indicating that whole number magnitude interference affects participants similarly across the spectrum of math achievement.

Different cognitive mechanisms used for solving open and closed math problems

Problem-solving skills are very important in our daily life. Almost all problem-solving studies have addressed the cognitive correlates of solving closed problems, but only limited studies have investigated the cognitive mechanisms of solving open problems. The current study aimed to systematically examine differences between the cognitive mechanisms used for solving open and closed problems. In total, the abilities of 142 high school students to solve open and closed problems were assessed, as were a series of general cognitive abilities as controlled variates. Analogical reasoning uniquely contributed to solving both open and closed math problems, after controlling for age, gender, and inductive reasoning. Reactive cognitive flexibility (measured using the Wisconsin card sorting test) and spatial working memory uniquely correlated only with solving open and closed math problems, respectively. These findings suggest that the cognitive processes used to solve open and closed math problems differ. Open and closed math problems appear to require more reactive cognitive flexibility for generation and more memory for retrieval, respectively.

Middle-schoolers' misconceptions in discretized nonsymbolic proportional reasoning explain fraction biases better than their continuous reasoning: Evidence from correlation and cluster analyses

Early emerging nonsymbolic proportional skills have been posited as a foundational ability for later fraction learning. A positive relation between nonsymbolic and symbolic proportional reasoning has been reported, as well as successful nonsymbolic training and intervention programs enhancing fraction magnitude skills. However, little is known about the mechanisms underlying this relationship. Of particular interest are nonsymbolic representations, which can be in continuous formats that may emphasize proportional relations and in discretized formats that may prompt erroneous whole-number strategies and hamper access to fraction magnitudes. We assessed the proportional comparison skills of 159 middle-school students (mean age = 12.54 years, 43% females, 55% males, 2% other or prefer not to say) across three types of representations: (a) continuous, unsegmented bars, (b) discretized, segmented bars that allowed counting strategies, and (c) symbolic fractions. Using both correlational and cluster approaches, we also examined their relations to symbolic fraction comparison ability. Within each stimulus type, we varied proportional distance, and in the discretized and symbolic stimuli, we also manipulated whole-number congruency. We found that fraction distance across all formats modulated middle-schoolers' performance; however, whole-number information affected discretized and symbolic comparison performance. Further, continuous and discretized nonsymbolic performance was related to fraction comparison ability; however, discretized skills explained variance above and beyond the contributions of continuous skills. Finally, our cluster analyses revealed three nonsymbolic comparison profiles: students who chose the bars with the largest number of segments (whole-number bias), chance-level performers, and high performers. Crucially, students with a whole-number bias profile showed this bias in their fraction skills and failed to show any symbolic distance modulation. Together, our results indicate that the relation between nonsymbolic and symbolic proportional skills may be determined by the (mis)conceptions based on discretized representations, rather than understandings of proportional magnitudes, suggesting that interventions focusing on competence with discretized representations may show dividends for fraction understanding.

Relationship Between Inhibitory Control and Arithmetic in Elementary School Children With ADHD: The Mediating Role of Working Memory

OBJECTIVES

To test if inhibitory control was a significant predictor for arithmetic in children with ADHD and if the relationship between inhibitory control and arithmetic was mediated by working memory.

METHODS

Eighty-four children (ADHD, n = 54; Non-ADHD, n = 30) were tested on their interference control, behavioral inhibition, working memory, and arithmetic. Regression analysis was used to test the predictive role of inhibitory control in arithmetic. Moreover, mediation analysis was done to test whether working memory mediated the relationship between inhibitory control and arithmetic memory.

RESULTS

Interference control but not behavioral inhibition was a significant predictor for arithmetic. In addition, interference control had direct and indirect effects via working memory on arithmetic.

CONCLUSIONS

Results demonstrated that inhibitory control contributed to arithmetic in children with ADHD. Furthermore, interference control had direct and indirect effects via working memory on arithmetic, suggesting interventions for arithmetic difficulties should involve training on both inhibition and working memory.

Children's gesture use provides insight into proportional reasoning strategies

Children struggle with proportional reasoning when discrete countable information is available because they over-rely on this numerical information even when it leads to errors. In the current study, we investigated whether different types of gesture can exacerbate or mitigate these errors. Children aged 5-7 years (N = 135) were introduced to equivalent proportions using discrete gestures that highlighted separate parts, continuous gestures that highlighted continuous amounts, or no gesture. After training, children completed a proportional reasoning match-to-sample task where whole number information was occasionally pitted against proportional information. After the task, we measured children's own gesture use. Overall, we did not find condition differences in proportional reasoning; however, children who observed continuous gestures produced more continuous gestures than those who observed discrete gestures (and vice versa for discrete gestures). Moreover, producing fewer discrete gestures and more continuous gestures was associated with lower numerical interference on the match-to-sample task. Lastly, to further investigate individual differences, we found that children's inhibitory control and formal math knowledge were correlated with proportional reasoning in general but not with numerical interference in particular. Taken together, these findings highlight that children's own gestures may be a powerful window into the information they attend to during proportional reasoning.

Teasing apart the unique contributions of cognitive and affective predictors of math performance

Math permeates everyday life, and math skills are linked to general educational attainment, income, career choice, likelihood of full-time employment, and health and financial decision making. Thus, researchers have attempted to understand factors predicting math performance in order to identify ways of supporting math development. Work examining individual differences in math performance typically focuses on either cognitive predictors, including inhibitory control and the approximate number system (ANS; a nonsymbolic numerical comparison system), or affective predictors, like math anxiety. Studies with children suggest that these factors are interrelated, warranting examination of whether and how each uniquely and independently contributes to math performance in adulthood. Here, we examined how inhibitory control, the ANS, and math anxiety predicted college students' math performance (n = 122, mean age = 19.70 years). Using structural equation modeling, we find that although inhibitory control and the ANS were closely related to each other, they did not predict math performance above and beyond the effects of the other while also controlling for math anxiety. Instead, math anxiety was the only unique predictor of math performance. These findings contradict previous results in children and reinforce the need to consider affective factors in our discussions and interventions for supporting math performance in college students.