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The extent to which processing of abstract numerical concepts depends on perceptual representations is still an open question. In four experiments, we examined the association between contrast polarity and mental arithmetic, as well as its possible source. Undergraduate psychology students verified the correctness of single-digit arithmetic problems such as 2 + 5 = 7 or 9 - 6 = 5. Problems appeared either in white or black on a grey background, thus creating positive or negative contrast polarity, respectively. When the correct response was Yes (No), participants were faster (slower) in verifying positive than negative addition problems and in verifying negative than positive subtraction problems. Experiment 2 confirmed that the same result also held for written word problems (e.g., SEVEN + SIX = THIRTEEN). However, Experiment 3 found that the effect of contrast polarity observed in Experiments 1 and 2 disappeared in a blocked design where arithmetic operation was a between-participant factor. In addition, Experiment 4 revealed that the effect of contrast polarity does not generalise to multiplication and division. Overall, available evidence suggests that participants spontaneously associate the abstract relation between addition and subtraction (more-less) with a similar relation between contrast polarities (bright-dark).

In the domain of cognitive arithmetic, the size effect corresponds to an increase in solution times as a function of the size of the operands involved in the problems. In this study, we tracked the evolution of size effects associated with tie and non-tie addition problems across development. We scrutinized the progression of solution times for very small problems involving operands from 2 to 4, larger problems, and 1-problems (problems involving 1 as one of the operands) in children from Grade 1 to Grade 5 and adults. For the first time, we document the presence of a size effect for tie problems with a sum up to 8 in Grade 1 children. In contrast, from Grade 3 until adulthood, this size effect could not be evidenced. Crucially, for non-tie problems, whereas a general size effect is observed when contrasting small one-digit additions with large additions, we show that, from Grade 1 until adulthood, a continuous size effect as a function of the sum of the problems is not observed. In fact, for all age groups, medium problems with sums of 8, 9, and 10 do not present a size effect at all. Given that the problem size effect is sometimes referred to as one of the most robust and reliable effects in the numerical cognition literature, our results necessarily challenge its theoretical interpretation., (Copyright © 2020 The Author(s). Published by Elsevier Inc. All rights reserved.)

In some languages the order of tens and units in number words is inverted compared with the symbolic digital notation (e.g., German 23 → " dreiundzwanzig ," literally: " three-and-twenty "). In other languages only teen-numbers are inverted (e.g., English 17 → " seventeen "; Polish 17 → " siedemnaście " literally " seventeen "). Previous studies have focused on between group comparisons of inverted and non-inverted languages and showed that number word inversion impairs performance on basic numerical tasks and arithmetic. In two independent experiments, we investigated whether number word inversion affects addition performance within otherwise non-inverted languages (Exp. 1: English, Exp. 2: Polish). In particular, we focused on the influence of inverted ( I ; English: teen-numbers ⩾ 13, Polish: numbers 11-19) and non-inverted ( N ) summands with sums between 13 and 39. Accordingly, three categories of addition problems were created: N + N, N + I , and I + I with problem size matched across categories. Across both language groups, we observed that problems with results in the 20 and 30 number range were responded to faster when only non-inverted summands were part of the problems as opposed to problems with one or two inverted summands. In line with this, the cost of a carry procedure was the largest for two inverted summands. The results support the notion that both language-specific and language-invariant aspects contribute to addition problem-solving. In particular though, regarding language-specific aspects, the results indicate that inverted number word formation of teens influences place-value processing of Arabic digits even in otherwise non-inverted languages.

Previous research indicates that interactive arithmetic tasks may alleviate the deleterious impact of maths anxiety on arithmetic performance. Our aim here was to further test the impact of interactivity on maths-anxious individuals and those with poorer numeracy skills. In the experiment reported here participants completed sums in two interactivity contexts. In a low-interactivity condition, sums were completed with hands down. In a second, high-interactivity condition, participants used moveable number tokens. As anticipated, accuracy and efficiency were greater in the high compared to the low-interactivity condition. Correlational analyses indicated that maths anxiety, objective numeracy, measures of maths expertise and working memory were stronger predictors of performance in the low- than in the high-interactivity conditions. Interactivity transformed the deployment of arithmetic skills, improved performance, and reduced the gap between high- and low-ability individuals. These findings suggest that traditional psychometric efforts that identify the cognitive capacities and dispositions involved in mental arithmetic should take into account the degree of interactivity afforded by the task environment.

Acute stress responses are known to include increases in heart rate and blood pressure, as well as increases in the number of circulating immune cells, all of which are governed by the autonomic nervous system. This laboratory practical measures cardiovascular and circulating immune cell responses to a passive (cold pressor) and active (mental arithmetic) acute stress task in student participants. The results allow them to examine the different patterns of autonomic response they elicit (approximated by heart rate and blood pressure responses), and knowledge of these responses can then be used to infer the governing autonomic aspect of the increases in circulating immune cells from the results. This activity can be either adapted from teacher-led methods to inquiry, asking students to design the details of the acute stress tasks, or developed by asking students to design a follow-up experiment that could be used to provide direct evidence for their conclusions. Data collected provide a platform for teaching data analysis and interpretation, as well as critical thinking.

Processing numbers induces shifts of spatial attention in probe detection tasks, with small numbers orienting attention to the left and large numbers to the right side of space. This has been interpreted as supporting the concept of a mental number line with number magnitudes ranging from left to right, from small to large numbers. Recently, the investigation of this spatial-numerical link has been extended to mental arithmetic with the hypothesis that solving addition or subtraction problems might induce attentional displacements, rightward or leftward, respectively. At the neurofunctional level, the activations elicited by the solving of additions have been shown to resemble those induced by rightward eye movements. However, the possible behavioural counterpart of these activations has not yet been observed. Here, we investigated overt attentional shifts with a target detection task primed by addition and subtraction problems (2-digit ± 1-digit operands) in participants whose gaze orientation was recorded during the presentation of the problems and while calculating. No evidence of early overt attentional shifts was observed while participants were hearing the first operand, the operator or the second operand, but they shifted their gaze towards the right during the solving step of addition problems. These results show that gaze shifts related to arithmetic problem solving are elicited during the solving procedure and suggest that their functional role is to access, from the first operand, the representation of the result.

Working memory allows complex information to be remembered and manipulated over short periods of time. Correlations between working memory and mathematics achievement have been shown across the lifespan. However, only a few studies have examined the potentially distinct contributions of domain-specific visuospatial and verbal working memory resources in mental arithmetic computation. Here we aimed to fill this gap in a series of six experiments pairing addition and subtraction tasks with verbal and visuospatial working memory and interference tasks. In general, we found higher levels of interference between mental arithmetic and visuospatial working memory tasks than between mental arithmetic and verbal working memory tasks. Additionally, we found that interference that matched the working memory domain of the task (e.g., verbal task with verbal interference) lowered working memory performance more than mismatched interference (verbal task with visuospatial interference). Findings suggest that mental arithmetic relies on domain-specific working memory resources.

Mangarevan traditionally contained two numeration systems: a general one, which was highly regular, decimal, and extraordinarily extensive; and a specific one, which was restricted to specific objects, based on diverging counting units, and interspersed with binary steps. While most of these characteristics are shared by numeration systems in related languages in Oceania, the binary steps are unique. To account for these characteristics, this article draws on-and tries to integrate-insights from anthropology, archeology, linguistics, psychology, and cognitive science more generally. The analysis of mental arithmetic with these systems reveals that both types of systems entailed cognitive advantages and served important functions in the cultural context of their application. How these findings speak to more general questions revolving around the theoretical models and evolutionary trajectory of numerical cognition will be discussed in the ., (Copyright © 2016 Cognitive Science Society, Inc.)

When solving mental arithmetic problems, one can easily be distracted by someone speaking in the background and this distraction is greater if the speech comprises numbers. We explored the basis of this disruption by asking participants to solve mental addition problems (e.g., "45 + 17 = ?") in three different conditions: background speech comprising numbers in ascending order (e.g., "61, 62, 63, 64, 65"), background speech comprising numbers in descending order (e.g., "65, 64, 63, 62, 61"), and quiet. Performance was best in quiet, worse in the descending numbers condition, and poorest in the ascending numbers condition. In view of these findings, we suggest that disruption arises as a by-product of preventing the primed, but inaccurate, candidate responses from assuming the control of action. Alternative explanations are also discussed.

The processing of numbers has been shown to induce shifts of spatial attention in simple probe detection tasks, with small numbers orienting attention to the left and large numbers to the right side of space. Recently, the investigation of this spatial-numerical association has been extended to mental arithmetic with the hypothesis that solving addition or subtraction problems may induce attentional displacements (to the right and to the left, respectively) along a mental number line onto which the magnitude of the numbers would range from left to right, from small to large numbers. Here we investigated such attentional shifts using a target detection task primed by arithmetic problems in healthy participants. The constituents of the addition and subtraction problems (first operand; operator; second operand) were flashed sequentially in the centre of a screen, then followed by a target on the left or the right side of the screen, which the participants had to detect. This paradigm was employed with arithmetic facts (Experiment 1) and with more complex arithmetic problems (Experiment 2) in order to assess the effects of the operation, the magnitude of the operands, the magnitude of the results, and the presence or absence of a requirement for the participants to carry or borrow numbers. The results showed that arithmetic operations induce some spatial shifts of attention, possibly through a semantic link between the operation and space.

Mental arithmetic shows systematic spatial biases. The association between numbers and space is well documented, but it is unknown whether arithmetic operation signs also have spatial associations and whether or not they contribute to spatial biases found in arithmetic. Adult participants classified plus and minus signs with left and right button presses under two counterbalanced response rules. Results from two experiments showed that spatially congruent responses (i.e., right-side responses for the plus sign and left-side responses for the minus sign) were responded to faster than spatially incongruent ones (i.e., left-side responses for the plus sign and right-side responses for the minus sign). We also report correlations between this novel operation sign spatial association (OSSA) effect and other spatial biases in number processing. In a control experiment with no explicit processing requirements for the operation signs there were no sign-related spatial biases. Overall, the results suggest that (a) arithmetic operation signs can evoke spatial associations (OSSA), (b) experience with arithmetic operations probably underlies the OSSA, and (c) the OSSA only partially contributes to spatial biases in arithmetic.

Patients with mild cognitive impairment (MCI) are by definition still autonomous in daily life and therefore make their own decisions, for example, concerning their own or their partners' health care. Health care information typically contains complex mathematical constructs like proportions, probabilities, and survival rates. The purpose of this study was to investigate whether patients with MCI have difficulties with understanding health numeracy questions and to explore the impact of declining cognitive functions. The performance of 25 patients with MCI in a health numeracy questionnaire was compared with the performance of a control sample including 164 healthy older adults, matched in age and educational level. Participants were asked to convert percentages, assess different probabilities, or understand the dosage of a short patient information leaflet. Additionally, neuropsychological background tests were administered. Patients with MCI answered fewer items correctly than controls in the health numeracy questionnaire. A correlation analysis showed statistically significant associations between performance in the health numeracy task and mental arithmetic, executive functions (psychomotor speed, conceptualization), and global cognitive status, respectively. Patients with MCI show problems in understanding numerical information concerning health care. Since patients with MCI are confronted with several health care decisions, special attention has to be paid to presenting information in an easily understandable way, to make additional sources of information available, and to provide adequate support.

Mathematics requires precise inferences about abstract objects inaccessible to perception. How is this possible? One proposal is that mathematical reasoning, while concerned with entirely abstract objects, nevertheless relies on neural resources specialized for interacting with the world-in other words, mathematics may be grounded in spatial or sensorimotor systems. Mental arithmetic, for instance, could involve shifts in spatial attention along a mental "number-line", the product of cultural artefacts and practices that systematically spatialize number and arithmetic. Here, we investigate this hypothesized spatial processing during exact, symbolic arithmetic (e.g., 4 + 3 = 7). Participants added and subtracted single-digit numbers and selected the exact solution from responses in the top corners of a computer monitor. While they made their selections using a computer mouse, we recorded the movement of their hand as indexed by the streaming x, y coordinates of the computer mouse cursor. As predicted, hand movements during addition and subtraction were systematically deflected toward the right and the left, respectively, as if calculation involved simultaneously simulating motion along a left-to-right mental number-line. This spatial-arithmetical bias, moreover, was distinct from-but correlated with-individuals' spatial-numerical biases (i.e., spatial-numerical association of response codes, SNARC, effect). These results are the first evidence that exact, symbolic arithmetic prompts systematic spatial processing associated with mental calculation. We discuss the possibility that mathematical calculation relies, in part, on an integrated system of spatial processes.

Recent research on spatial number representations suggests that the number space is not necessarily horizontally organized and might also be affected by acquired associations between magnitude and sensory experiences in vertical space. Evidence for this claim is, however, controversial. The present study now aims to compare vertical and horizontal spatial associations in mental arithmetic. In Experiment 1, participants solved addition and subtraction problems and indicated the result verbally while moving their outstretched right arm continuously left-, right-, up-, or downwards. The analysis of the problem-solving performances revealed a motion-arithmetic compatibility effect for spatial actions along both the horizontal and the vertical axes. Performances in additions was impaired while making downward compared to upward movements as well as when moving left compared to right and vice versa in subtractions. In Experiment 2, instead of being instructed to perform active body movements, participants calculated while the problems moved in one of the four relative directions on the screen. For visual motions, only the motion-arithmetic compatibility effect for the vertical dimension could be replicated. Taken together, our findings provide first evidence for an impact of spatial processing on mental arithmetic. Moreover, the stronger effect of the vertical dimension supports the idea that mental calculations operate on representations of numerical magnitude that are grounded in a vertically organized mental number space.

Previous research has shown that math anxiety can influence the math performance level; however, to date, it is unknown whether math anxiety influences performance on working memory tasks during neuropsychological evaluation. In the present study, 172 undergraduate students completed measures of math achievement (the Math Computation subtest from the Wide Range Achievement Test-IV), math anxiety (the Math Anxiety Rating Scale-Revised), general test anxiety (from the Adult Manifest Anxiety Scale-College version), and the three Working Memory Index tasks from the Wechsler Adult Intelligence Scale-IV Edition (WAIS-IV; Digit Span [DS], Arithmetic, Letter-Number Sequencing [LNS]). Results indicated that math anxiety predicted performance on Arithmetic, but not DS or LNS, above and beyond the effects of gender, general test anxiety, and math performance level. Our findings suggest that math anxiety can negatively influence WAIS-IV working memory subtest scores. Implications for clinical practice include the utilization of LNS in individuals expressing high math anxiety.

Early detection of and relevant information on children's mathematical difficulties is important to initiate targeted teaching and intervention. This study investigated the extent to which strategy use in single-digit addition provides additional predictive information about 61 grade one children's (6-year-old) mathematical achievement 3 years later that is not available from a standardised mathematics achievement test. Four predictors available in year one (arithmetic strategy use, mathematical achievement, non-verbal reasoning skills and sex) explained 54% of the variation in grade four mathematics achievement. Arithmetic strategy use was the most important single predictor of year four mathematics achievement (R2 = 30%) and explained an additional 12% variation if added to a model comprised by the three other year one predictors. This result suggests that systematically obtained measures of how young children solve single-digit arithmetic problems might provide useful information about their foundational number knowledge, which in turn may reveal how well they achieve later in school. [ABSTRACT FROM AUTHOR]

• Phonological awareness in kindergarten plays a crucial role in predicting later word problem-solving abilities in mathematics. • Visual-spatial skills, specifically the visual-spatial sketchpad, have an indirect influence on multi-digit arithmetic performance through their impact on simple addition skills. • Sustained attention in kindergarten contributes to word problem performance in later grades through its influence on number identification skills. This longitudinal study aimed to investigate the differential contributions of phonological processing and spatial attention skills to mathematical performance in Chinese children. The study involved the assessment of 184 children's phonological awareness, phonological memory, rapid automatized naming (RAN), visual-spatial sketchpad, and sustained attention during their kindergarten. Three years later, the same children were evaluated on tasks related to simple addition, non-symbolic comparison, number identification, complex word problems, and multi-digit arithmetic. Through path analysis, the study revealed that phonological awareness in kindergarten directly predicted later word problem-solving abilities. Additionally, simple addition mediated the relationship between visual-spatial working memory and multi-digit arithmetic performance, while number identification mediated the relationship between sustained attention and complex word problems. However, number processing skills did not mediate the relationship between phonological processing and mathematics performance. These findings contribute to our understanding of the complex interplay between visual-spatial skills, phonological processing skills, number processing, and mathematics performance. [ABSTRACT FROM AUTHOR]

The early prediction of math difficulties (MD) is important as it facilitates timely support. MD are multifaceted, and several factors are involved in their manifestation. This makes the accurate early prediction of MD particularly challenging. In the present study, we aim to predict MD in Grade 6 with kindergarten-age (age 6) measures by applying a neural networks model. We use a set of 49 variables assessed during kindergarten from the domains of early arithmetic skills, cognitive skills, the home learning environment, parental measures, motivation, behavioral problems, and gender, which have been shown to have associations with mathematical development and/or MD. A two-step approach was used: First, we examined whether the neural networks approach can provide a solution for the effective early identification of MD based on all 49 variables and, then, by using the most important predictors as identified by the initial model. The initial model achieved an area under the curve (AUC) of.818, demonstrating excellent performance. The most important predictors of Grade 6 MD came from the domains of arithmetic and cognitive skills (arithmetic skills, rapid automatized naming, number concepts, spatial skills, counting) and behavioral problems (attention-orientation). The model with only the most important predictors achieved an AUC of.776, indicating good performance. Our results provided proof of concept for using neural networks in MD prediction in Grade 6 using information already available in kindergarten. In schools, these results could be used to identify children at potential risk of developing MD and to provide access to early support. Educational Impact and Implications Statement: Approximately 4%–15% of children suffer from math difficulties (MD), and many more struggle with them without a formal diagnosis. MD have been shown to put children at increased risk of lower academic achievement, lower motivation, anxiety, depression, and even higher unemployment. Predicting MD accurately and early facilitates timely support. The current study demonstrates the potential of neural networks models to facilitate the early identification of those at risk of developing MD. The performance of our model provided proof of concept for using neural networks for the prediction of MD in Grade 6 using information already available in kindergarten. In a school setting, such prediction knowledge could be used to identify children at potential risk of developing MD and to provide access to early support. [ABSTRACT FROM AUTHOR]

Task-related change in physiological arousal is suggested to reflect active involvement with the task. While studies often examine such task-related changes in arousal as averaged across the entire task, the present study focused on temporal changes in arousal during a task. More specifically, we investigated changes in elementary school students' physiological arousal during an arithmetic task and associations between these changes and students' mindset, performance on the task, and math grades. We used a person-oriented approach to analyze the tonic electrodermal activity of 86 fourth graders, recorded while they were working on an arithmetic task. With model-based clustering of students' on-task electrodermal activity, we identified three groups of students with differing temporal dynamics of physiological arousal during the task: Increasing Arousal, Decreasing Arousal and Decreasing and Increasing Arousal. The Decreasing Arousal profile contained more students classified as holding a Fixed Mindset Tendency than would be expected if physiological profile membership and mindset tendency were independent. The Increasing Arousal profile performed better on the task than the Decreasing Arousal profile. No association was found with math grades. These results provide a new insight into individual differences in temporal patterns of on-task physiological arousal. [ABSTRACT FROM AUTHOR]

During the twentieth century, the meaning of successful Mathematics learning underwent several shifts in response to changes in both society and schooling. For roughly the first half of the century, success in learning the mathematics of pre-kindergarten to eighth grade usually meant facility in using the computational procedures of arithmetic, with many educators emphasizing the need for skilled performance and others emphasizing the need for students to learn procedures with understanding. To this end, the researchers is conducting a study to identify academic predictors of learning proficiency across strands of mathematics of grade 8 students of a public secondary school in Marikina City, the Marikina High School. The study is descriptive in nature and makes use of 6 groups of subjects: they were composed of 42 Grade 8 of Marikina High School, a secondary public school in the Schools Division of Marikina City, Metro Manila. From the research findings, it can be concluded that the majority of the respondents got a high rating in Algebra and Geometry, most of the student respondents fell above the passing rate of the subject Mathematics, and most of the student respondents accumulated a high score rating in Statistics and Probability. The null hypothesis is rejected; therefore, there is a significant difference between students' proficiency levels in Mathematics along with Algebra and Geometry. In academic characteristics related to the proficiency level of the students along study strategy in terms of Rehearsal, analyzing its contents again and again in studying math materials is strongly agreed by the student-respondents; Organization, reading through the class notes textbook and finding out the most important parts is strongly agreed; Self-regulation, listing down related formula first is strongly agreed; Study Environment, making it a hobby to study Math at a fixed time is agreed; Attitude towards Mathematics, student-respondents treat Mathematics difficult but an interesting subject. There is no significant difference in the Academic Characteristics of the respondents except in terms of Attitude towards Mathematics and Time and Study Environment, which have a strong positive/negative difference in the academic characteristics of the respondents. Moreover, a significant relationship exists between academic characteristics and students' proficiency levels. [ABSTRACT FROM AUTHOR]

Introduction: Neural exaptations represent descent via transitions to novel neural functions. A primary transition in human cognitive and neural evolution was from a predominantly socially oriented primate brain to a brain that also instantiates and subserves science, technology, and engineering, all of which depend on mathematics. Upon what neural substrates and upon what evolved cognitive mechanisms did human capacities for science, technology, engineering, and mathematics (STEM), and especially its mathematical underpinnings, emerge? Previous theory focuses on roles for tools, language, and arithmetic in the cognitive origins of STEM, but none of these factors appears sufficient to support the transition. Methods: In this article, I describe and evaluate a novel hypothesis for the neural origins and substrates of STEM-based cognition: that they are based in human kinship systems and human maximizing of inclusive fitness. Results: The main evidence for this hypothesis is threefold. First, as demonstrated by anthropologists, human kinship systems exhibit complex mathematical and geometrical structures that function under sets of explicit rules, and such systems and rules pervade and organize all human cultures. Second, human kinship underlies the core algebraic mechanism of evolution, maximization of inclusive fitness, quantified as personal reproduction plus the sum of all effects on reproduction of others, each multiplied by their coefficient of relatedness to self. This is the only "natural" equation expected to be represented in the human brain. Third, functional imaging studies show that kinship-related cognition activates frontal-parietal regions that are also activated in STEM-related tasks. In turn, the decision-making that integrates kinship levels with costs and benefits from alternative behaviors has recently been shown to recruit the lateral septum, a hub region that combines internal (from the prefrontal cortex, amygdala, and other regions) and external information relevant to social behavior, using a dedicated subsystem of neurons specific to kinship. Conclusions: Taken together, these lines of evidence suggest that kinship systems and kin-associated behaviors may represent exaptations for the origin of human STEM. [ABSTRACT FROM AUTHOR]

There is an emerging consensus that numerical, executive function (EF), and spatial skills are foundational to children's mathematical learning and development. Moreover, each skill has been theorized to relate to mathematics for different reasons. Thus, it is possible that each cognitive construct is related to mathematics through distinct pathways. The present study tests this hypothesis. One-hundred and eighty 4- to 9-year-olds (Mage = 6.21) completed a battery of numerical, EF, spatial, and mathematics measures. Factor analyses revealed strong, but separable, relations between children's numerical, EF, and spatial skills. Moreover, the three-factor model (i.e., modelling numerical, EF, and spatial skills as separate latent variables) fit the data better than a general intelligence (g-factor) model. While EF skills were the only unique predictor of number line performance, spatial skills were the only unique predictor of arithmetic (addition) performance. Additionally, spatial skills were related to the use of more advanced addition strategies (e.g., composition/decomposition and retrieval), which in turn were related to children's overall arithmetic performance. That is, children's strategy use fully mediated the relation between spatial skills and arithmetic performance. Taken together, these findings provide new insights into the cognitive foundations of early mathematics, with implications for assessment and instruction moving forward. [ABSTRACT FROM AUTHOR]

Spatial ability is an influential factor for academic performance in Science, Technology, Engineering, and Mathematics (STEM) education. However, the roles of spatial strategies are unclear. Therefore, coupling with virtual Starmaze developed by fields of cognitive neuroscience, this study aimed to explore spatial strategy among STEM students and its role in academic performance. A virtual Starmaze was constructed to test how students complete a navigation test. A total of 172 college students majoring in STEM participated in this study. Modeling analysis showed students tend to use allocentric strategy when the difficulty of spatial tasks increased. Results further showed students with high STEM academic performance tended to use allocentric strategy while ones with low STEM academic performance tended to use egocentric strategy. Specifically, academic performances in science and mathematics learning were associated with the allocentric strategy, while academic performances in technology and engineering learning were associated with proficiency and hands-on ability. [ABSTRACT FROM AUTHOR]

Active breaks (AB) are short periods of physical activity in the classroom. The purpose of this study was to compare the acute effects of 5-minute dance break with an aerobic and a sedentary group on the executive functions, math performance and enjoyment of elementary school children. A total of 67 children (10.41±.13 years) of three fifth grade classes were randomly assigned to the three groups: dance (21 children), aerobic (24 children) and control (22 children). At the beginning and at the end of the intervention, all participants completed the Flanker task, the Digit Span test, the tower of London and a math test (mental calculations). In addition, the dance and the aerobic group were evaluated on their enjoyment level and physical activity intensity. At the end of the intervention both the dance and the aerobic group showed significant improvement in inhibition compared to pre-test. Moreover, the dance group showed higher levels of enjoyment compared to the aerobic group. The findings of the study suggest that even 5-minute dance break may positively affect children's inhibition and enjoyment. Children's enjoyment is crucial for AB participation and affects their academic performance. Therefore, children's enjoyment should also be considered in AB planning, and dance could be a suitable alternative compared to other AB physical activities (aerobic/strength activities). [ABSTRACT FROM AUTHOR]

Algebra and geometry are important components of mathematics that are often considered gatekeepers for future success. However, most studies that have researched the cognitive skills required for success in mathematics have only considered the domain of arithmetic. We extended models of mathematical skills to consider how executive function skills play both a direct role in secondary-school-level mathematical achievement as well as an indirect role via algebra and geometry, alongside arithmetic. We found that verbal and visuospatial working memory were indirectly associated with mathematical achievement via number fact knowledge, calculation skills, algebra and geometry. Inhibition was also indirectly associated with mathematical achievement via number fact knowledge and calculation skills. These findings highlight that there are multiple mechanisms by which executive function skills may be involved in mathematics outcomes. Therefore, using specific measures of mathematical processes as well as context-rich assessments of mathematical achievement is important to understand these mechanisms. [ABSTRACT FROM AUTHOR]

The present study aimed at examining the effect of mental calculation and number comparison on motor performance measured as the movement time of a fast manual-pointing movement. Three experiments, involving a total number of 65 undergraduate subjects, examined the effect of mental subtraction (complex) and, respectively, of (a) mental addition (simple or complex), (b) mental multiplication (simple or complex), and (c) the comparison of dot sets and number comparison. Each number was written in Arabic. The movement times were analyzed by using a multilevel linear mixed-effect model. The results showed significant improvement of manual-pointing movement performance only after the complex calculations and after number comparison. Possible implication of attentional mechanisms specific to this arithmetical activity is further discussed. [ABSTRACT FROM AUTHOR]

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Estimation is a primary activity in everyday life, so getting it "right" in primary school provides a foundational basis in mathematical reasoning. This study focuses on numerosity estimation in primary mathematics, which is one of four types of estimation reported in literature. In numerosity estimation, a nonnumerical quantitative representation is typically translated into a number. While it is assumed that fostering numerosity estimation has a great impact on the development of mathematical skills, research indicates that math achievement is influenced by non-cognitive aspects such as students' math interests. So, math interest could also influence the accuracy in numerosity estimation. In this study, we investigate the relationship between accuracy in numerosity estimation, math achievement, and math interest in third-grade students. For capturing accuracy in numerosity estimation in a standardized way, we developed an online numerosity estimation test. For assessing the construct of math interest, we used an existing questionnaire. Math achievement was assessed by a standardized math test that includes two subtests focusing on arithmetic and application tasks. The sample was comprised of 185 third-grade students. We analyzed the data using correlation and multiple linear regression analysis. The results showed a significant positive correlation between math interest and math achievement. However, no relationship was found between accuracy in numerosity estimation and math interest nor between accuracy in numerosity estimation and math achievement. These partly unexpected findings suggest further studies dedicated to numerosity estimation and its relationship to other constructs. [ABSTRACT FROM AUTHOR]

Math learning programs were expected to revolutionize students' learning, but their effects so far have mostly been disappointing. Following the debate about why to continue research on math learning programs, we aimed to reformulate this question into how to continue this research. Investigations to date have neither considered a sufficiently wide set of outcome variables nor differentiated between performance measures (e.g., measuring addition and subtraction performance separately) and affective-motivational variables. Moreover, as students can only benefit from a program if they use it, researchers need to take practice behavior into account. Thus, we investigated whether the adaptive arithmetic learning program Math Garden fostered students' addition and subtraction performance, their math self-concept, and a reduction of their math anxiety. We also investigated how practice behavior (practiced tasks/weeks) affected these outcomes. We used a randomized pretest-posttest control group design with 376 fifth-grade students in Germany. Students in the experimental condition practiced with Math Garden for 20.7 weeks and had an increase in math self-concept. The more subtraction tasks the students practiced, the more they improved their subtraction performance. We found no effects on math anxiety. The results are discussed in terms of providing a starting point for new directions in future research. [ABSTRACT FROM AUTHOR]

Background: Studies have investigated the effects of achievement goals on learning interests and mathematics performance above the elementary-school level. However, few studies have explored this topic among kindergarteners based on sound theoretical frameworks. Methods: Through the enrollment of 15 kindergarten teachers and 180 kindergarteners, this study re-validated newly developed measurements of kindergarteners’ achievement goals and learning interests and used these measures to further clarify the effects of achievement goals on learning interests and mathematics performances using structural equation modeling. Results: The results indicate that (1) task-approach goals have positive effects on situational interest and advanced arithmetic performance, whereas task-avoidance goals have positive effects on individual interest. (2) Self-based goals have null effects on most learning interests and mathematics performance, but they have significant negative effects on numbering and counting performance. However, most of these null effects represent negative tendencies. (3) Other-approach goals have positive effects on situational interest and basic arithmetic performance, whereas other-avoidance goals have null effects on these outcomes but have an almost significant positive effect on numbering and counting performance. (4) Task-based goals and self-approach goals are generally beneficial for learning interests and mathematics performance. Conclusion: These results suggest that task-based goals and other-approach goals may be implemented with consideration of the potential long-term detrimental effects of social comparison on learning outcomes. Furthermore, possible negative effects of self-based goals must be monitored to prevent them from undermining learning outcomes. This study revealed consistent, inconsistent, and new evidence that, respectively, verifies, complements, and contradicts findings on the learning outcomes of students above the elementary-school level. [ABSTRACT FROM AUTHOR]

Previous studies suggest that task-irrelevant changing-state sound interferes specifically with the processing of serial order information in the focal task (e.g., serial recall from short-term memory), whereas a deviant sound in the auditory background is supposed to divert central attention, thus producing distraction in various types of cognitive tasks. Much of the evidence for this distinction rests on the observed dissociations in auditory distraction between serial and non-serial short-term memory tasks. In this study, both the changing-state effect and the deviation effect were contrasted between serial digit recall and mental arithmetic tasks. In three experiments (two conducted online), changing-state sound was found to disrupt serial recall, but it did not lead to a general decrement in performance in different mental arithmetic tasks. In contrast, a deviant voice in the stream of irrelevant speech sounds did not cause reliable distraction in serial recall and simple addition/subtraction tasks, but it did disrupt a more demanding mental arithmetic task. Specifically, the evaluation of math equations (multiplication and addition/subtraction), which was combined with a pair-associate memory task to increase the task demand, was found to be susceptible to auditory distraction in participants who did not serially rehearse the pair-associates. Together, the results support the assumption that the interference produced by changing-state sound is highly specific to tasks that require serial-order processing, whereas auditory deviants may cause attentional capture primarily in highly demanding cognitive tasks (e.g., mental arithmetic) that cannot be solved through serial rehearsal. [ABSTRACT FROM AUTHOR]

The representation format of math problems can manifest dissimilarly in people with varying levels of math performance. The aim of this study was to investigate the neurocognitive underpinnings of two-digit exact calculation tasks in different formats: numerical and word. Fifty-three students were divided into groups with high and low levels of math performance based on their ability to solve math problems. They were asked to calculate addition problems with two-digit numbers and to read math problems that did not require calculations. Brain activation was recorded using functional near-infrared spectroscopy (fNIRS). General linear model (GLM) analysis revealed that reading math problems without calculation led to increased activation in the inferior temporal and fusiform gyri in a group of high-level performers, while a group of low-level performers demonstrated increased activation in Broca's area and the inferior frontal gyrus in the same experimental condition, as well as during solving arithmetic problems in a word format of the exact calculation task. Analysis after bootstrapping revealed similar activation patterns in both groups. Both domain-specific and domain-general regions of the frontal and parietal brain areas were involved in the calculations. Right and left hemisphere activation was found both in low and high math performers. Comparing experimental conditions with resting state revealed significant activation in Broca's area in all conditions in a group of high-level performers and in a word format of arithmetic problems in a group of low-level performers. Thus, the observed brain patterns suggest the involvement of complex sentence comprehension, especially in high-performing students. These results could be used in future to improve educational practice for students with varying levels of math competence. [ABSTRACT FROM AUTHOR]

The aim of the research is to identify the effect of a scenariobased learning in the mathematics achievement and the mental motivation for fifth - scientific grade students in high school. To achieve it, the researchers adopted the experimental research method with two groups (experimental and control) with a post-test. The research community was identified, which represents the fifth scientific grade students from the first Karkh Education Directorate. The sample (60) students were chosen intentionally, and was divided into two groups: an experimental group that studied according to the scenario-based learning model; and a control group studied according to the usual method. For the purpose of collecting data for the experiment, the achievement test was built, in its final form, consisting of (10) test items of the type of essay, and the mental motivation scale, in its final form, consisting of (60) items. Appropriate statistical analyzes were conducted, and the psychometric properties of the test and scale were confirmed. The results indicated that the students of the experimental group who studied according to the scenario-based learning model outperformed the students of the control group who studied according to the traditional method. [ABSTRACT FROM AUTHOR]

We investigated the cognitive demand of the exercise problems that middle school students from Nepal are expected to complete. The middle school (grades 6, 7, and 8) mathematics textbooks examined in this study were published and distributed by the government of Nepal. Our data set consisted of textbooks that are currently in use in public schools of Nepal and used by majority of the middle school students in Nepal. Using the mathematical tasks framework to analyze the data, we found more than 92% tasks are of lower cognitive demands, and most tasks are at the level of procedures without connections. We also observed that the majority (more than 75%) of exercise problems are supplemented with similar worked examples. We discuss implications and suggest future studies. [ABSTRACT FROM AUTHOR]

The mathematician G.F.C. Griss is known for his program of negationless intuitionistic mathematics. Although Griss's rejection of negation is regarded as characteristic of his philosophy, this is a consequence of an executability requirement that mental constructions presuppose agents' executing corresponding mental activity. Restoring Griss's executability requirement to a central role permits a more subtle characterization of the rejection of negation, according to which D. Nelson's strong constructible negation is compatible with Griss's principles. This exposes a 'holographic' theory of negation in negationless mathematics, in which a full theory of negation is 'flattened' in a putatively negationless setting. [ABSTRACT FROM AUTHOR]

Effective K-12 integrated STEM education should reflect an intentional effort to adequately represent and facilitate each of its component disciplines in a meaningful way. However, most research in this space has been conducted within the context of science classrooms, ignoring mathematics. Also missing from the literature is research that examines the level of cognitive demand required from mathematical tasks present within integrated STEM lessons. In order to seek insight pertaining to this gap in the literature, we sought to better understand how science teachers use mathematics within K-12 integrated STEM instruction. We used an explanatory sequential mixed methods research design to explore the enactment of mathematics in integrated STEM lessons that focus on physical, earth, and life science content. We first examined 2030 sets of video-recorded classroom observation scores generated from the 10-item STEM Observation Protocol (STEM-OP) designed for observing integrated STEM education in K-12 classrooms. We compared the STEM-OP scores of classroom observations that included mathematics with those that did not. This quantitative analysis was followed by a closer, more in-depth qualitative examination of how mathematics was employed, focusing on the degree of cognitive demand. To do this, we coded and analyzed transcripts from video-recorded classroom observations in which mathematical content was present. Our study yielded two main findings about mathematics in integrated STEM lessons: (1) the presence of mathematical content resulted in higher STEM-OP scores on nearly all items, and (2) mathematical tasks within these lessons were categorized as requiring mainly low levels of cognitive demand from students. This study highlights the need for the increased inclusion of mathematical tasks in integrated STEM teaching. Implications for including higher-order mathematical thinking within integrated STEM teaching are discussed. [ABSTRACT FROM AUTHOR]

• This study examines the cognitive and language skill correlates of preschool children's performance in arithmetic, measurement and geometry. • Working memory, visual-spatial skills, and receptive vocabulary are related to arithmetic performance. • Receptive vocabulary is associated with measurement performance. • Short-term memory is related to geometry performance. Based on a sample of 138 children aged approximately 5 years in Hong Kong, this study examined how general cognitive and language skills, including working memory, short-term memory, visual-spatial skills, and receptive vocabulary, were associated with young children's performance in arithmetic, geometry, and measurement. The results showed that these cognitive and language skills yielded unique contributions to different domains of mathematical abilities after controlling for children's sex, age, maternal education, paternal education, and family income. Specifically, working memory, visual-spatial skills, and receptive vocabulary were related to arithmetic performance; receptive vocabulary was associated with measurement performance; and short-term memory was related to geometry performance. These findings' implications for theory and practice are discussed. [ABSTRACT FROM AUTHOR]

The first books in Croatia that teach the reader the basics of arithmetic, were written in the middle of the 18th century. Arithmetica Horvatszka (1758), written by Mihajlo Šilobod, and Aritmetika u slavni jezik ilirski (1766) by Mate Zoričić were published in separate parts of Croatia; the former was published in the part of Croatia that was under Austro-Hungarian rule and the latter under the Venetian rule. Although they were not directly intended for school work, the authors wanted to teach the general population the basics of numbers and arithmetic through these books. This paper provides a brief analysis of the calculation methods from that time, as well as the forms of instructions the authors gave to their readers. [ABSTRACT FROM AUTHOR]

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Hybrid EEG-fNIRS brain-computer interface (HBCI) is widely employed to enhance BCI performance. EEG and fNIRS signals are combined to increase the dimensionality of the information. Time windows are used to select EEG and fNIRS singles synchronously. However, it ignores that specific modal signals have their own characteristics, when the task is stimulated, the information between the modalities will mismatch at the moment, which has a significant impact on the classification performance. Here we propose a novel crossing time windows optimization for mental arithmetic (MA) based BCI. The EEG and fNIRS signals were segmented separately by sliding time windows. Then crossing time windows (CTW) were combined with each one segment from EEG and fNIRS selected independently. Furthermore, EEG and fNIRS features were extracted using Filter Bank Common Spatial Pattern (FBCSP) and statistical methods from each sample. Mutual information was calculated for FBCSP and statistical features to characterize the discrimination of crossing time windows, and the optimal window would be selected based on the largest mutual information. Finally, a sparse structured framework of Fisher Lasso feature selection (FLFS) was designed to select the joint features, and conventional Linear Discriminant Analysis (LDA) was employed to perform classification. We used proposed method for a MA dataset. The classification accuracy of the proposed method is 92.52 ± 5.38% and higher than other methods, which shows the rationality and superiority of the proposed method.

The current study presents the results of empirical research, which focuses on analyses of the solution of tasks containing the selected elements of propositional logic formulated in different subject-specific contexts. The focus group of our interest was the university students. As a research tool, we used a knowledge test. Our research aimed to investigate the results of the respondents (N = 497) depending on the selected aspects (students' performance according to the students' study programme and their success in solving individual tasks depending on the subjectspecific context, gender, age, type of secondary school where they graduated). The results show that students' chosen orientation in higher education is typically related to the successful application of formal logic and its subject-specific contexts. Furthermore, the results confirmed that secondary grammar school education still provides better preparation in formal logic than other types of secondary schools. [ABSTRACT FROM AUTHOR]

We present arguments in favor of an interdisciplinary approach in mathematics education. As an instance, we briefly recall how cognitive neuropsychologists promoted intense finger gnosis acquisition, i.e., acquiring the ability to mentally represent one's fingers, at an early age. Mathematics educators definitely recommended the development of finger gnosis but examined its limits. They also presented arguments in favor of developing flexible mental calculation as a goal of arithmetical instruction in elementary school. In this context we describe the training of "Zahlenblick" as a way to foster flexible mental calculation and connect it with concepts from the theory of metacognition. We illustrate how precisely this branch of metacognition demands further interdisciplinary research. In our analysis, "Zahlenblick" extends to acquiring an eye for proportions, beyond just whole numbers. We illustrate how useful it would be to better understand the neural underpinnings responsible for the advantages of so-called natural frequencies, compared with percentages or probabilities, and of icon arrays for representing them. Such natural frequencies are adequate formats for the early confrontation with decision-making under risk. [ABSTRACT FROM AUTHOR]

Many individuals, when faced with mathematical tasks or situations requiring arithmetic skills, experience exaggerated levels of anxiety. Mathematical anxiety (MA), in addition to causing discomfort, can lead to avoidance behaviors and then to underachievement. However, the factors inducing MA and how MA deploys its detrimental effects are still largely debated. There is evidence suggesting that MA affects working memory capacity by further diminishing its limited processing resources. An alternative account postulates that MA originates from a coarse early numerical cognition capacity, the perception of numerosity. In the current study, we measured MA, math abilities, numerosity perception and visuo-spatial working memory (VSWM) in a sample of neurotypical adults. Correlational analyses confirmed previous studies showing that high MA was associated with lower math scores and worse numerosity estimation precision. Conversely, MA turned out to be unrelated to VSWM capacities. Finally, partial correlations revealed that MA fully accounted for the relationship between numerosity estimation precision and math abilities, suggesting a key role for MA as a mediating factor between these two domains. [ABSTRACT FROM AUTHOR]

• Mother's math activities predicted children's math performance only in kindergarten • Fathers' home math activities were not related to children's math outcomes • Differences in math performance between students in high- vs low-SES schools increased with grade • Mothers' math fluency and school SES predicted children's math performance in Grades 1–3 We investigated whether home math activities were related to children's math performance in kindergarten and the first three years of primary school. Participants were Chilean parents and their children in kindergarten, Grade 1, Grade 2, and Grade 3 (n s = 101, 95, 87, and 84, respectively). Mothers and fathers independently answered questions about their math activities at home, provided sociodemographic information, and completed an arithmetic fluency task. Children completed measures of applied problem solving, calculation, and arithmetic fluency. For kindergarten children, we found that mothers' (but not fathers') reports of the frequency of operational (e.g., mental arithmetic) activities were positively related to children's math performance, whereas mothers' reports of the frequency of mapping (e.g., counting, number naming) math activities were negatively correlated with performance. For children in Grades 1–3, home math activities were not significant unique predictors of math outcomes. The socioeconomic status of children's schools and maternal math fluency predicted children's math performance in Grades 1–3. The implications of these findings are discussed for understanding how children's home environments are related to their mathematical development. [ABSTRACT FROM AUTHOR]

Mathematical skills are essential to mastering everyday activities, making professional choices, and exercising citizenship in a numerate society. There is extensive evidence of the relationship between math anxiety (MA) and working memory (WM) influencing math attainment. Studies have mainly considered adult samples, however, leaving primary school children almost unexplored. This study is a first attempt to examine how the complex interplay between MA and WM affects math achievement from a developmental perspective. A total of 148 third graders were assessed with WM, general anxiety (GA), MA, and math tasks. Anxiety and WM were assessed at the beginning of the school year when children started attending grade 3, while math achievement was tested twice at the start of grades 3 and 4. The findings seem to confirm that GA has both a direct and an indirect effect (mediated by WM) on math performance in third and fourth graders. MA has a direct effect on math performance in grade 4, but only an indirect effect in grade 3, suggesting MA has a developmental trajectory, becoming stronger over time. The implications in the educational setting are discussed, pointing to the importance of a combined intervention on MA and WM. [ABSTRACT FROM AUTHOR]