International Journal of Science Annals, Vol. 6, No. 2, 2023 рrint ISSN: 2617-2682; online ISSN: 2707-3637; DOI:10.26697/ijsa SOCIAL AND BEHAVIORAL SCIENCES. Education ORIGINAL RESEARCH Prediction of Arithmetic Abilities of Children Who Practice Sports: The Use of the Gamma Model Authors’ Contribution: Serra L. 1,2 ABCDEF , Guerreiro C. 3 BDF , Silva L. 4 ADE A – Study design; 1 B – Data collection; Autonomous University of Lisbon, Portugal 2 C – Statistical analysis; Centre of Statistics and its Applications of the University of Lisbon, Portugal 3 D – Data interpretation; Higher Institute of Intercultural and Transdisciplinary Studies of Almada – E – Manuscript preparation; Piaget Institute of Almada, Portugal 4 F – Literature search; NOVA School of Science and Technology – NOVA University Lisbon, Portugal G – Funds collection Received: 30.08.2023; Accepted: 27.09.2023; Published: 25.12.2023 Abstract Background and The physical performance that children exhibit when engaging in sports or any Aim of Study: form of physical activity will depend not only on their physical abilities but also on their psychological and cognitive attributes. The aim of the study: to analyze whether symptoms of anxiety, lie, attention, and age are predictors of arithmetic abilities in children practicing sports. Material and Methods: The study sample consisted of 108 children with an average age of 12.12 (±2.18) who practice various sports, with greater emphasis on futsal and soccer. The study protocol consisted of a sociodemographic questionnaire, the Revised Children’s Manifest Anxiety Scale, the d2 Test of Attention, and the Arithmetic subtest of the Wechsler Intelligence Scale for Children. Results: The results showed that through the adjusted model, we identify four significant explanatory variables that are predictors of arithmetic abilities, namely anxiety symptoms (β=-0.009, p=0.009); and the attention sub-factors: processed characters (β=0.002, p=3.44e-14), default errors (β=-0.005, p=0.000), errors by marking irrelevant characters (β=-0.016, p=0.003). Conclusions: The presence of anxiety symptoms and attentional cognitive abilities play a significant role in predicting the arithmetic aptitudes of young individuals. These variables should be taken into consideration within training programs for young athletes, as they hold relevance for sports engagement. Keywords: sports participants, anxiety, lie, attention, age, arithmetic skills Copyright: © 2023 Serra L., Guerreiro C., Silva L. Published by Archives of International Journal of Science Annals DOI and UDC DOI https://doi.org/10.26697/ijsa.2023.2.1 UDC 37.037.1:786 Conflict of interests: The authors declare that there is no conflict of interests Peer review: Double-blind review Source of support: This research did not receive any outside funding or support Information about Serra Lidia (Corresponding Author) – https://orcid.org/0000-0003-2612-3335; the authors: lmserra@autonoma.pt; Doctor in Neuropsychology, Professor, Autonomous University of Lisbon; Centre of Statistics and its Applications of the University of Lisbon, Lisbon, Portugal. Guerreiro Cristiana – https://orcid.org/0009-0007-4820-6269; Master’s degree in Clinical and Health Psychology, Higher Institute of Intercultural and Transdisciplinary Studies of Almada – Piaget Institute of Almada, Almada, Portugal. Silva Luís – https://orcid.org/0000-0001-9811-0571; Doctor in Human Kinetics – Motor Behavior, Investigator, NOVA School of Science and Technology – NOVA University Lisbon, Caparica, Portugal. 10 International Journal of Science Annals, Vol. 6, No. 2, 2023 рrint ISSN: 2617-2682; online ISSN: 2707-3637; DOI:10.26697/ijsa Introduction anxiety within children can elicit avoidance behaviors Physical activity and sports hold a pivotal role in the when confronted with arithmetic challenges (Orbach et promotion of health and overall well-being. The al., 2020). Consequently, it is hypothesized that the engagement of young individuals in physical activities presence of anxiety may disrupt the arithmetic and sports has been correlated with favorable impacts on proficiencies of the participants under examination. their mental health, encompassing emotional states, However, an alternative perspective posited by Wu et al. behavioral patterns, and cognitive proficiencies (Hosker (2017) contends that when mathematical anxiety et al., 2019). The cultivation of cognitive capacities, prevails, there might be an elevation in children’s levels particularly arithmetic abilities, equips children and of vigilance, potentially serving as a mitigating factor adolescents with enhanced precision in numerical against the adverse impact of attentional deficits on comprehension, mathematical operations, point mathematical performance. Steele et al. (2012) study, enumeration, and improved numerical estimations, analyzing the developmental trajectory of children’s among other competencies (Landerl, 2013; Reeve et al., attentional capacities, identified sustained-selective 2012). These proficiencies are notably nurtured through attention as a predictive indicator of fundamental participation in games (Butterworth, 2005). The mathematical abilities over a one-year observation refinement of such abilities necessitates the period. Evidently, tasks involving counting necessitate establishment of neural connections, exemplified by the engagement of serial attentional processes. In these linkages between visual and verbal networks, as well as contexts, discrepancies in attentional proficiency may visual and spatial networks (Rapin, 2016), both of which contribute to disparities in children’s performance hold equal significance in the context of sports concerning mathematical problem-solving (Wu et al., performance (Tamorri, 2004). Moreover, a discernible 2017). The mechanism of attention entails focusing on correlation has been substantiated between arithmetic stimuli of significance, thereby sieving a substantial skills and self-reported levels of physical activity, portion of sensory input and directing cognitive aerobic fitness, and motor prowess (Syväoja et al., processing toward selected components (Broadbrent, 2021). Notably, motor skills have been identified as 1958; Deutsch & Deutsch, 1963). Within the realm of integral to fundamental numerical abilities, sports, attention assumes a pivotal function for athletes encompassing aspects such as symbolic representation in identifying, selecting, or quantifying pertinent stimuli on the number line (number identification) and during both training sessions and competitive events nonsymbolic representation (object identification) (Carrascosa, 2003). This perspective prompts us to (Gashaj et al., 2019a). The predictive linkage between contemplate the possibility of attention serving as a fine motor skills and arithmetic competencies is also predictive determinant of arithmetic proficiencies highlighted in a study conducted by Michel et al. (2020) among children engaged in sports. Nevertheless, involving 173 children. The utilization of gestures or instances may arise wherein children, when grappling manual manipulations has been shown to confer benefits with task challenges, resort to deception. This utilization in the accuracy and swiftness of item counting (Carlson of deceit can manifest as a coping mechanism for et al., 2007). The presence of proficient fine motor skills evading tasks, concealing uncertainties, and masking additionally emerges as a predictor for mathematical weaknesses (Matias et al., 2015). Children frequently prowess among children aged 7 to 8 years, as evidenced deploy falsehoods as a means of navigating their by Gashaj et al. (2019b). In light of these insights, it recreational pursuits. In the sporting context, the becomes apparent that sports training and the dissemination of false information can also be construed augmentation of motor capabilities exert tangible effects as an intentional strategic maneuver that disadvantages upon the arithmetic aptitudes of children who are adversaries and strategically shapes opponents’ engaged in sports activities. Moreover, in accordance behavior (Sailors et al., 2017). According to with the investigation conducted by Wu et al. (2017), Ommundsen et al. (2003), children undergoing training cognitive faculties encompassing working memory and to enhance soccer performance often exhibit heightened attention, alongside affective constituents such as tendencies towards amoral conduct compared to their mathematical anxiety, emerge as pivotal contributors to peers demonstrating elevated sociomoral maturity and mathematical performance across both verbal and non- adherence to fair-play principles. The conceptual verbal tasks. Nevertheless, the presence of mathematical framework advanced by Bransford and Stein (1993) anxiety has been shown to impede the cognitive frames lying as a form of decision-making employed processes essential to proficient task execution within when resolving problems risks compromising this domain (Orbach et al., 2020). Mathematical anxiety achievement objectives. As children mature, their constitutes an adverse emotional response characterized cognitive capacities for fabricating falsehoods improve by feelings of unease and apprehension that students (Evans & Lee, 2011), thereby signifying that older experience when confronted with mathematical children tend to wield lies more adeptly (Maggioni & exercises (Hill et al., 2016), and this phenomenon can Rossignoli, 2020). In this vein, it is posited that age and exert a detrimental influence on their mathematical the engagement in deceit could potentially exert comprehension and problem-solving skills (Vukovic et influence over the arithmetic abilities of children. al., 2013). Such anxiety can instigate intrusive negative Nonetheless, the intricacies of these abilities continue to thoughts and engender a perception of environmental command substantial scholarly attention. Scientific stimuli as threatening. Consequently, instances of math inquiry has delved into the associations between 11 International Journal of Science Annals, Vol. 6, No. 2, 2023 рrint ISSN: 2617-2682; online ISSN: 2707-3637; DOI:10.26697/ijsa arithmetic skills and various cognitive constructs, which the participant must identify the letter “d” with including working memory, executive functions two upper quotation marks (Brickenkamp & Zillmer, (Orbach et al., 2020; Swanson & Beebe-Frankenberger, 2010). Through this instrument, it was possible to 2004), interactivity, mathematical anxiety (Vallée- calculate the Total Processed Characters, PC (that is the Tourangeau, 2013), performance (Salminen et al., number of stimuli indicated, taking into account the 2018), and even finger-counting practices (Barrocas et participant’s speed, productivity, or motivation); the al., 2020; Crollen & Noël, 2015). While Becker et al. Total Hits, TH (that is the effectiveness in performing (2018) have demonstrated a correlation between the task); the Total Effectiveness, TE (which measured engagement in team sports and enhanced mathematical the level of attentional control and the relationship problem-solving abilities, studies investigating the between speed and accuracy throughout the task); the interplay of attention, anxiety, deception, and age in the Concentration Index, CI (indicating the level of mathematical capacities of children and adolescents concentration in the task); the Variability Index, VI active in sports are conspicuously scarce. (which revealed whether the task was performed The aim of the study. To examine how symptoms of consistently or in a variable way); and Percentage of anxiety, lying, attention, and age are predictors of Errors, E% (which showed the accuracy and quality of mathematical abilities in children who practice sports. performance). The Portuguese version of the instrument revealed a Cronbach’s Alpha greater than 0.90 Materials and Methods (Brickenkamp & Zillmer, 2010). Finally, the Arithmetic Participants subtest of the Wechsler Intelligence Scale for Children This observational, cross-sectional study, based on a (Portuguese version by Simões, 2002) was applied to non-probabilistic sample, considered 108 Portuguese assess the participants’ calculus, logical-mathematical participants with a mean age of 12.12 years (±2.18), reasoning, and problem-solving skills through 24 items. ranging from a minimum of 8 years to a maximum of 16 The score varies between a minimum of 0 and a years. Most participants are male 66.7% and have maximum of 24 points, with high scores reflecting good completed the 3rd cycle of education (9 years of arithmetic and reasoning skills (Wechsler, 1991/2003; education) (43.5%). The most popular sports in the Simões, 2002). The Portuguese version of this subtest sample are futsal (37.0%), football (25.0%), taekwondo showed good internal consistency with a Cronbach’s (17.6%), rhythmic gymnastics (7.4%), and tennis Alpha of 0.84 (Simões, 2002). (7.4%). Participants have been practicing sports, on Procedure average, for 54.85 (±28.68) months and the average First, the directors of several sports clubs in the Lisbon weekly training time is 3.97 hours (±2.6). As inclusion region were contacted. The study objectives were criteria, young athletes from sports clubs for at least one presented to the directors and permission was sought to year were considered. Participation in the study was contact the athletes’ legal representatives. After getting only accepted after signing the informed consent of the approval, the athletes’ legal representatives were young person and their legal representative. They were contacted. They were informed about the study’s informed that their participation was completely objectives, the confidentiality of the information voluntary and harmless. Young people with collected, the voluntary nature of the investigation, and developmental disorders or other physical and mental the ethical and deontological duties of the investigators. conditions that did not allow them to respond to the They were then asked to sign their informed consent. study protocol were not considered in this study. All After authorization by the legal representatives, the ethical and deontological duties inherent to the athletes who were willing to participate were contacted. investigation were considered. After this period, sessions were scheduled with the Measures participants who were individually assessed. The For the present investigation, a sociodemographic protocol application site was a room belonging to the questionnaire was used to collect information about the sports clubs that collaborated in the investigation. The participants (e.g., age, sex, time of the sport, etc.). The researchers respected all ethical and deontological Revised Children’s Manifest Anxiety Scale (CMAS-R; duties and there was no risk of any kind to the Portuguese version by Dias & Gonçalves, 1999) was participants. applied. This scale evaluated the global anxiety index Data Analysis and the global lie index. Anxiety was assessed using 28 For the present investigation, the statistical software R, items ranging from a minimum of 0 to a maximum of 28 R-Studio, was used for data analysis. Descriptive points. The global lie index was evaluated using 9 items, statistics were used to characterize the sample, varying between a minimum of 0 and a maximum of 9 specifically the analysis of means and standard points. High values represent a high level of lying on the deviations for quantitative variables and the analysis of part of the participant. According to the authors, this frequencies and percentages for nominal variables. A instrument has good reliability as represented by a Gamma Regression Model was used to study the Cronbach’s alpha of 0.80 (Dias & Gonçalves, 1999). response variable, using a logarithmic link function. The The d2 Test of Attention was used to measure children’s step function of R was also used to automatically select selective attention and concentration, through 14 lines, the covariates that should be included in the gamma each with 47 stimuli (of the letters p and d accompanied model. The significance level assumed in this study was by either one or two quotation marks or comma) from p-value ˂0.05. 12 International Journal of Science Annals, Vol. 6, No. 2, 2023 рrint ISSN: 2617-2682; online ISSN: 2707-3637; DOI:10.26697/ijsa Results 2.766 for 100 degrees of freedom. The measure of the Prediction of Arithmetic Skills quality of this adjustment given by the Akaike The following table (Table 1) shows the coefficients of Information Criterion (AIC) is 501.05. the explanatory variables of the athletes’ arithmetic Then, the covariates that should be included in the skills. gamma model were automatically selected and a new At the usual significance levels (5%), this model reveals adjustment value of the resulting model was performed. that there is a significant covariate, namely anxiety According to the new adjusted model (Table 2), the new symptoms. Residual deviations range from -0.43 to 0.40 coefficients and covariates of the model are identified. and the calculated value of the residual deviation is Table 1 Variable Coefficients: Age, Anxiety Symptoms, Lie, Attention: Processed Characters, Attention: Hits, Attention: Default Errors, Attention: Errors by Marking Irrelevant Characters Coefficients Estimated value SE t-value p-value Intercept 2.139 0.122 17.423 ˂2e-16*** Age 0.007 0.009 0.77 0.44 Anxiety symptoms -0.007 0.004 -2.06 0.04* Lie 0.002 0.007 0.36 0.72 Attention, PC 0.001 0.002 0.45 0.66 Attention, Hits 0.002 0.006 0.25 0.80 Attention, DE -0.003 0.006 -0.56 0.58 Attention, EMIC -0.009 0.005 -1.91 0.06 Note. SE – standard error; p-value: *0.05; **0.01; ***0.001; PC – processed characters; DE – default errors; EMIC – errors by marking irrelevant characters. Table 2 Variable Coefficients: Anxiety Symptoms, Attention: Processed Characters, Attention: Default Errors, Attention: Errors by Marking Irrelevant Characters Coefficients Estimated value SE t-value p-value Intercept 2.222 0.082 27.161 ˂2e-16*** Anxiety symptoms -0.009 0.004 -2.48 0.015* Attention, PC 0.002 0.000 8.86 2.51e-14*** Attention, DE -0.005 0.001 -4.00 0.000*** Attention, EMIC -0.009 0.005 -1.92 0.057 Note. SE – standard error; p-value: *0.05; **0.01; ***0.001; PC – processed characters; DE – default errors; EMIC – errors by marking irrelevant characters. During the adjustment, three covariates were eliminated Figure 1 from the model, namely, age, lying, and the total number Representation of the Adjusted Model Residuals of hits of the attention task. On the other hand, there were more significant covariates, a total of three new significant covariates, for the usual significance levels (5%). These variables are anxiety symptoms, the characters processed in the attention task, and the omission errors in the attention task. Residual deviations range from -0.43 to 0.39, with a residual deviation value of 2.740 with 103 degrees of freedom. The AIC value is 496.0. The p-value calculation to verify the suitability of this model shows a p-value=1. Considering the value of 1 obtained, it is accepted that this model is adequate and proves to be better than the previous model. Through the calculation of Cook’s distances (Figure 2), Through the analysis of the residuals of the adjusted the observations effectively influencing the model were model (Figure 1), it is verified that the residuals are verified. Thus, 3 effectively influential observations distributed around 0, with an amplitude that seems were identified, namely observations 15, 81, and 104, constant for the different adjusted values, without that is, a slight modification or exclusion of these verifying any trend. This also indicates that this model observations from the model could cause significant fits this dataset well. changes in the estimates of the model parameters. 13 International Journal of Science Annals, Vol. 6, No. 2, 2023 рrint ISSN: 2617-2682; online ISSN: 2707-3637; DOI:10.26697/ijsa Figure 2 The sample now has 105 participants. Calculation Results for Cook’s Distances In this model, it appears that there are two significant covariates, namely, anxiety symptoms and errors by marking irrelevant characters. Residual deviations range from -0.42871 to 0.39180. The AIC value is 480.56 and the residual deviation value is 2.5263 for 97 degrees of freedom. The suitability analysis of this model shows a p-value=1. According to the value of 1 obtained, the hypothesis that this regression model is adequate is not rejected. Then, a new value of the adjustment of the model was carried out, from which the covariates to be included in the gamma model were automatically selected. Then, these three observations were removed from the The set of covariates and their coefficients obtained with model and the gamma model was adjusted again (Table 3). the newly adjusted model are shown in Table 4. Table 3 Variable Coefficients: Age, Anxiety Symptoms, Lie, Attention: Processed Characters, Attention: Hits, Attention: Default Errors, Attention: Errors by Marking Irrelevant Characters for Adjusted Sample Coefficients Estimated value SE t-value p-value Intercept 2.179 0.122 17.747 ˂2e-16*** Age 0.006 0.009 0.72 0.48 Anxiety symptoms -0.008 0.004 -2.26 0.03* Lie 0.002 0.007 0.31 0.76 Attention, PC 0.001 0.002 0.47 0.64 Attention, Hits 0.001 0.007 0.16 0.87 Attention, DE -0.003 0.006 -0.56 0.58 Attention, EMIC -0.016 0.005 -3.06 0.003** Note. SE – standard error; p-value: *0.05; **0.01; ***0.001; PC – processed characters; DE – default errors; EMIC – errors by marking irrelevant characters. Table 4 Variable Coefficients: Anxiety Symptoms, Attention: Processed Characters, Attention: Default Errors, Attention: Errors by Marking Irrelevant Characters for Adjusted Sample Coefficients Estimated value SE t-value p-value Intercept 2.25 0.081 27.824 ˂2e-16*** Anxiety symptoms -0.009 0.003 -2.664 0.009** Attention, PC 0.002 0.000 8.84 3.44e-14*** Attention, DE -0.005 0.001 -3.52 0.000*** Attention, EMIC -0.016 0.005 -3.088 0.003** Note. SE – standard error; p-value: *0.05; **0.01; ***0.001; PC – processed characters; DE – default errors; EMIC – errors by marking irrelevant characters. In this new adjustment, three covariates were eliminated, Figure 3 namely, age, lying, and the total number of hits of the Representation of the Residuals of the New Adjusted attention task. With this new adjustment, there were now Model four significant covariates: anxiety symptoms, characters processed in the attention task, errors by omission, and errors by marking irrelevant characters in the attention task. Residual deviations range from -0.43140 to 0.37738. The AIC value is 475.34 and the residual deviation value is 2.5450 with 100 degrees of freedom. The value of p-value=1 and, for this reason, it is accepted that this model is adequate. The analysis of the model’s residuals (Figure 3) shows that the residuals are distributed around 0, which indicates that this model fits well with this data set. Comparing this model with the previously adjusted model, this model turns out to be better than the previous one for this dataset. 14 International Journal of Science Annals, Vol. 6, No. 2, 2023 рrint ISSN: 2617-2682; online ISSN: 2707-3637; DOI:10.26697/ijsa Discussion mathematical aptitude and the discernment of numerical The primary aim of this investigation was to ascertain quantities. Wong and Liu (2020) similarly affirmed that whether indicators of anxiety symptoms, deceptive goal-directed visual attention correlated with children’s behavior, attentional capacity, and age could serve as arithmetic capabilities, with this connection being predictive factors for arithmetic proficiency among mediated by the subjects’ enumeration proficiencies. children engaged in sporting activities. Furthermore, our findings indicate that deceitful behavior Our findings demonstrated that manifestations of anxiety and age do not bear significant relevance as predictors of symptoms, processing of characters during the arithmetic abilities. Costa & Pinho (2010) did not attentional task, instances of omission errors, and errors establish a notable correlation between dishonesty and associated with marking irrelevant characters in the arithmetic performance. However, Maggioni & attention assessment all function as predictors for Rossignoli (2020) did discern such a relationship. As arithmetic aptitude in the child and adolescent children undergo cognitive maturation, they acquire the demographic. capacity to adopt inaccurate behaviors and engage in Drawing from the research conducted by Wu et al. deception for competitive advantage, as delineated by (2017), it was established that in eight-year-old children, Ding et al. (2018). In regard to age, despite Aragón et al. the presence of math-related anxiety exerted a (2018) contention that arithmetic skills tend to advance noteworthy and consistent indirect impact on nonverbal in tandem with educational progression and age, such a performance in numerical operations and mathematical sociodemographic parameter did not manifest as a reasoning. Furthermore, in tasks of heightened pertinent predictor variable for arithmetic performance in complexity, mathematical anxiety exhibited both direct our analyzed sample. While a certain nexus between and indirect effects (via working memory) on subjects’ age and their arithmetic aptitude might be mathematical reasoning abilities. Conversely, it was apparent (Nogues & Duro, 2016), other factors like the posited that the adoption of cognitive reappraisal intensity of physical demands inherent to training strategies for mathematical tasks, resulting in diminished regimens could exert a more salient influence upon negative affect and amygdala responses to anxiety- cognitive proficiencies, particularly within the realm of inducing situations, could lead to a reduction in anxiety arithmetic, as asserted by Coe et al. (2006). The levels, thereby potentially enhancing mathematical implications of this study extend to sports clubs and performance (Pizzie et al., 2020). In accordance with Wu similar organizations, offering insights for designing et al. (2017) findings, instances where children interventions aimed at bolstering cognitive capacities, experience anxiety pertaining to arithmetic tasks may particularly attentional and arithmetic proficiencies, paradoxically lead to heightened attentional investment while concurrently fostering emotional regulation among in the tasks, thereby substantiating the notion that athletes, given their pronounced impact on athletic anxiety’s presence may not invariably yield detrimental performance. However, it should be acknowledged that outcomes. However, it should be noted that the presence this study did not account for the potential effects of math-related anxiety may impede the exclusion of stemming from other cognitive variables, such as distracting environmental stimuli from one’s focus, working memory, which could impinge upon attentional irrespective of the mathematical content involved capabilities (Orbach et al., 2020), consequently (Hopko et al., 2002). This phenomenon, as elucidated by influencing the resolution of arithmetic tasks (Michel et our observations, could contribute to an increased al., 2020). Additionally, the potential influence of frequency of errors on the part of participants in the tasks, negative affect on task performance among participants specifically encompassing default errors and errors remained unexamined (Storbeck & Clore, 2007). arising from the misidentification of irrelevant characters Subsequent research endeavors should endeavor to during the attentional assessment. Instances of delineate more precise participant characteristics compromised focused attention, difficulties in the concerning this task domain, thereby enhancing control effective utilization of well-practiced information (e.g., over potentially influential variables within analytical basic addition or multiplication facts), or challenges in models, as well as probing the ramifications of the ability to deploy and switch between diverse psychological symptoms on the mathematical mathematical processes for problem-solving, collectively proficiencies of youth engaged in sports. illuminate the adverse influence of attentional limitations on arithmetic competencies (Wu et al., 2017). Regarding Conclusions the characters processed within the attention task, it has This study allows for the conclusion that the presence of been established that these also hold predictive value for anxiety and attentional characteristics such as processing the participants’ arithmetic proficiencies. A study of characters during the attentional task, instances of conducted by Anobile et al. (2013) involving a cohort of omission errors and errors by marking irrelevant 68 children aged between 8 and 11 years revealed that characters hold predictive power over the arithmetic attentional and perceptual competencies pertaining to abilities of the youth. numerical concepts emerged as predictive indicators for This type of variables is important for the sports the participants’ mathematical scores. Even subsequent performance of young individuals and should be to controlling for the influence of other pertinent integrated into training and development programs for variables, these researchers noted that attentional athletes to help them maximize their athletic faculties exhibited a sustained association with performance. 15 International Journal of Science Annals, Vol. 6, No. 2, 2023 рrint ISSN: 2617-2682; online ISSN: 2707-3637; DOI:10.26697/ijsa Acknowledgments and Cognition, 33(4), 747-756. We are grateful to all study participants and https://doi.org/10.1037/0278-7393.33.4.747 collaborators. Carrascosa, J. (2003). Saber competir: Claves para soportar y superar la presion [Knowing how to Ethical Approval compete: Keys to withstand and overcome This study received approval from the scientific council pressure]. Gymnos. of the Higher Institute of Intercultural and https://sabercompetir.com/publicaciones/ Transdisciplinary Studies of Almada. Coe, D. P., Pivarnik, J. M., Womack, C. J., Reevees, M. J., & Malina, R. M. (2006). Effect of Funding Source physical education and activity levels on This research did not receive any outside funding or academic achievement in children. Medicine and support. Science in Sports and Exercise, 38(8), 1515-1519. https://doi.org/10.1249/01.mss.0000227537.13175.1b References Costa, A., & Pinho, M. S. (2010). Sugestionabilidade Anobile, G., Stievano, P., & Burr, D. (2013). Visual interrogativa em crianças de 8 e 9 anos de idade sustained attention and numerosity sensitivity [Interrogative suggestibility in 8 and 9 year old correlate with math achievement in children. children]. Análise Psicológica, 1(28), 193-208. Journal of Experimental Child Psychology, 16(2), https://doi.org/10.14417/ap.266 380-391. https://doi.org/10.1016/j.jecp.2013.06.006 Crollen, V., & Noël, M. P. (2015). The role of fingers in Aragón, E., Serrano, N., & Navarro, J. I. (2018). Do boys the development of counting and arithmetic skills. and girls learn the same way? A preliminary study Acta Psychologica (Amst), 156, 37-44. in primary education analyzing gender https://doi.org/10.1016/j.actpsy.2015.01.007 differences. Electronic Journal of Research in Deutsch, J. A., & Deutsch, D. (1963). Attention: Some Educational Psychology, 16(3), 537-553. theoretical considerations. Psychological Review, https://doi.org/10.25115/ejrep.v16i46.2234 70(1), 80-90. https://doi.org/10.1037/h0039515 Barrocas, R., Roesch, S., Dresen, V., Moeller, K., & Dias, P., & Gonçalves, M. (1999). Avaliação da Pixner, S. (2020). Embodied numerical ansiedade e da depressão em crianças e representations and their association with multi- adolescentes (STAIC-C2, CMAS-R, FSSC-R e digit arithmetic performance. Cognitive CDI): Estudo normativo para a população Processing, 21(1), 95-103. portuguesa [Assessment of anxiety and https://doi.org/10.1007/s10339-019-00940-z depression in children and adolescents (STAIC- Becker, D. R., McClelland, M. M., Geldhof, G. J., C2, CMAS-R, FSSC-R and CDI): Normative Gunter, K. B., & MacDonald, M. (2018). Open- study for the Portuguese population]. In A. P. skilled sport, sport intensity, executive function, Soares, S. Araújo, & S. Caires (Eds.), Avaliação and academic achievement in grade school Psicológica: Formas e Contextos / VII children. Early Education and Development, Conferência Internacional (pp. 553-564). 29(7), 939-955. APPORT. https://doi.org/10.1080/10409289.2018.1479079 https://sigarra.up.pt/flup/pt/pub_geral.pub_view? Bransford, J. D., & Stein, B. S. (1993). The ideal problem pi_pub_base_id=12274 solver: A guide for improving thinking, learning, Ding, X. P., Heyman, G. D., Sai, L., Yuan, F., and creativity (2nd ed.). W. H. Freeman and Winkielman, P., Fu, G., & Lee, K. (2018). Company. Learning to deceive has cognitive benefits. https://www.tntech.edu/cat/pdf/useful_links/ideal Journal of Experimental Child Psychology, problemsolver.pdf 76(2018), 26-38. Brickenkamp, R., & Zillmer, E. (2010). The d2 test of https://doi.org/10.1016/j.jecp.2018.07.008 attention [manual]. Hogrefe. Evans, A. D., & Lee, K. (2011). Verbal deception from https://www.worldcat.org/title/935291577 late childhood to middle adolescence and its Broadbent, D. E. (1958). Perception and communication. relation to executive functioning skills. Pergamon Press. Developmental Psychology, 47(4), 1108-11166. http://www.communicationcache.com/uploads/1/ https://dx.doi.org/10.1037%2Fa0023425 0/8/8/10887248/d_e._broadbent_- Gashaj, V., Oberer, N., Mast, F. W., & Roebers, C. M. _perception_and_communication_1958.pdf (2019a). Individual differences in basic numerical Butterworth, B. (2005). The development of arithmetical skills: The role of executive functions and motor abilities. Journal of Child Psychology and skills. Journal of Experimental Child Psychology, Psychiatry, 46(1), 3-18. 182(June), 187-195. https://doi.org/10.1111/j.1469-7610.2004.00374.x https://doi.org/10.1016/j.jecp.2019.01.021 Carlson, R. A., Avraamides, M. N., Cary, M., & Gashaj, V., Oberer, N., Mast, F. W., & Roebers, C. M. Strasberg, S. (2007). What do the hands (2019b). The relation between executive externalize in simple arithmetic? Journal of functions, fine motor skills, and basic numerical Experimental Psychology: Learning, Memory, skills and their relevance for later mathematics achievement. Early Education and Development, 16 International Journal of Science Annals, Vol. 6, No. 2, 2023 рrint ISSN: 2617-2682; online ISSN: 2707-3637; DOI:10.26697/ijsa 30(7), 913-926. performance in children: The role of core https://doi.org/10.1080/10409289.2018.1539556 executive functions. Cognition, 200, Article Hill, F., Mammarella, C., Devine, A., Caviola, S., 104271. Passolunghi, M. C., & Szücs, D. (2016). Maths https://doi.org/10.1016/j.cognition.2020.104271 anxiety in primary and secondary school students: Pizzie, R., McDermott, C., Salem, T., & Kraemer, D. Gender differences, developmental changes and (2020). Neural evidence for cognitive reappraisal anxiety specificity. Learning and Individual as a strategy to alleviate the effects of math Differences, 48(May), 45-53. anxiety. Social Cognitive and Affective https://doi.org/10.1016/j.lindif.2016.02.006 Neuroscience, 15(12), 1271-1287. Hopko, D. R., McNeil, D. W., Gleason, P. J., & https://doi.org/10.1093/scan/nsaa161 Rabalais, A. E. (2002). The emotional Stroop Rapin, I. (2016). Dyscalculia and the calculating brain. paradigm: Performance as a function of stimulus Pediatric Neurology, 61, 11-20. properties and self-reported mathematics anxiety. https://doi.org/10.1016/j.pediatrneurol.2016.02.007 Cognitive Therapy and Research, 26, 157-166. Reeve, R., Reynolds, F., Humberstone, J., & https://doi.org/10.1023/A:1014578218041 Butterworth, B. (2012). Stability and change in Hosker, D. K., Elkins, R. M., & Potter, M. P. (2019). markers of core numerical competencies. Journal Promoting mental health and wellness in youth of Experimental Psychology: General, 141(4), through physical activity, nutrition, and sleep. 649-666. https://doi.org/10.1037/a0027520 Child and Adolescent Psychiatric Clinics of North Sailors, P. R., Teetzel, S., & Weaving, C. (2017). America, 28(2), 171-193. Cheating, lying, and trying in recreational sports https://doi.org/10.1016/j.chc.2018.11.010 and leisure practices. Annals of Leisure Research, Landerl, K. (2013). Development of numerical 20(5), 563-577. processing in children with typical and https://doi.org/10.1080/11745398.2017.1284009 dyscalculic arithmetic skills – A longitudinal Salminen, J., Koponen, T., & Tolvanen, A. (2018). study. Frontiers in Psychology, 4, Article 459. Individuality in the early number skill https://doi.org/10.3389/fpsyg.2013.00459 components underlying basic arithmetic skills. Maggioni, M. A., & Rossignoli, D. (2020). Clever little Frontiers in Psychology, 9, Article 1056. lies: Math performance and cheating in primary https://doi.org/10.3389/fpsyg.2018.01056 schools in Congo. Journal of Economic Behavior Simões, M. R. (2002). Utilizações da WISC-III na & Organization, 172(C), 380-400. avaliação neuropsicológica de crianças e https://doi.org/10.1016/j.jebo.2019.12.021 adolescents [Uses of the WISC-III in the Matias, D., Leime, J., Amorim, C., Bezerra, G., & Torro- assessment neuropsychological of children it is Alves, N. (2015). Lying: Social and adolescent]. Paidéia (ribeirão Preto), 12(23), neurobiological aspects. Psicologia: Teoria e 113-132. https://doi.org/10.1590/S0103- Pesquisa, 31(3), 397-401. 863X2002000200009 https://doi.org/10.1590/0102-37722015032213397401 Steele, A., Karmiloff-Smith, A., Cornish, K., & Michel, E., Molitor, S., & Schneider, W. (2020). Scerif, G. (2012). The multiple subfunctions of Executive functions and fine motor skills in attention: Differential developmental gateways to kindergarten as predictors of arithmetic skills in literacy and numeracy. Child Development, 83(6), elementary school. Developmental 2028-2041. https://doi.org/10.1111/j.1467- Neuropsychology, 45(6), 367-379. 8624.2012.01809.x https://doi.org/10.1080/87565641.2020.1821033 Storbeck, J., & Clore, G. L. (2007). On the Nogues, C. P., & Duro, M. L. (2016, July 13-16). interdependence of cognition and emotion. Desenvolvimento da estimativa numérica e Cognition and Emotion, 21(6), 1212-1237. desempenho em aritmética em crianças: Um https://doi.org/10.1080/02699930701438020 estudo comparativo entre tarefas [Development Syväoja, H., Kankaanpää, A., Hakonen, H., Inkinen, V., of numerical estimation and arithmetic Kulmala, J., Joensuu, L., Räsänen, P., performance in children: A comparative study Hillman, C., & Tammelin, T. (2021). How between tasks]. XII Encontro Nacional de physical activity, fitness, and motor skills Educação Matemática, São Paulo, Brasil. contribute to math performance: Working http://www.sbem.com.br/enem2016/anais/pdf/71 memory as a mediating factor. Scandinavian 05_3110_ID.pdf Journal of Medicine & Science in Sports, 31(12), Ommundsen, Y., Roberts, G. C., Lemyre, P. N., & 2310-2321. https://doi.org/10.1111/sms.14049 Treasure, D. (2003). Perceived motivational Swanson, H. L., & Beebe-Frankenberger, M. (2004). The climate in male youth soccer: Relations to social- relationship between working memory and moral functioning, sportspersonship and team mathematical problem solving in children at risk norm perceptions. Psychology of Sport and and not at risk for serious math difficulties. Exercise, 4(4), 397-413. Journal of Educational Psychology, 96(3), 471- https://doi.org/10.1016/S1469-0292(02)00038-9 491. https://doi.org/10.1037/0022-0663.96.3.471 Orbach, L., Herzog, M., & Fritz, A. (2020). State- and Tamorri, S. (2004). Neurociencias y deporte: Psicología trait-math anxiety and their relation to math deportiva. Procesos mentales del atleta 17 International Journal of Science Annals, Vol. 6, No. 2, 2023 рrint ISSN: 2617-2682; online ISSN: 2707-3637; DOI:10.26697/ijsa [Neurosciences and sports: Sports psychology. M. J. Seabra-Santos, C. P. Albuquerque, Athlete’s mental processes]. Paidotribo. M. Pereira, A. M. Rocha, C. Ferreira, Trans.). https://dialnet.unirioja.es/servlet/libro?codigo=390056 Cegoc. (Original work published 1991). Vallée-Tourangeau, F. (2013). Interactivity, efficiency, https://cineicc.uc.pt/wisc-iii-wisc-iii-info/ and individual differences in mental arithmetic. Wong, T., & Liu, D. (2020). The association between Experimental Psychology, 60(4), 302-311. visual attention and arithmetic competence: The https://doi.org/10.1027/1618-3169/a000200 mediating role of enumeration. Journal of Vukovic, R., Kieffer, M., Bailey, S., & Harari, R. (2013). Experimental Child Psychology, 196, Article Mathematics anxiety in young children: 104864. https://doi.org/10.1016/j.jecp.2020.104864 Concurrent and longitudinal associations with Wu, S., Chen, L., Battista, C., Watts, A., Willcutt, E., & mathematical performance. Contemporary Menon, V. (2017). Distinct influences of affective Educational Psychology, 38(1), 1-10. and cognitive factors on children’s non-verbal and https://doi.org/10.1016/j.cedpsych.2012.09.001 verbal mathematical abilities. Cognition, 166, Wechsler, D. (2003). Escala de inteligência de Wechsler 118-129. para crianças (WISC-III) [Wechsler intelligence https://doi.org/10.1016/j.cognition.2017.05.016 scale for children (WISC-III)] (M. R. Simões, Cite this article as: Serra, L., Guerreiro, C., & Silva, L. (2023). Prediction of arithmetic abilities of children who practice sports: The use of the gamma model. International Journal of Science Annals, 6(2), 10–18. https://doi.org/10.26697/ijsa.2023.2.1 The electronic version of this article is complete. It can be found online in the IJSA Archive https://ijsa.culturehealth.org/en/arhiv This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/deed.en). 18