The difficulties children with ADHD experience solving applied math problems are well documented; however, the independent and/or interactive contributions of cognitive processes underlying these difficulties are not fully understood and warrant scrutiny. The current study examines two primary cognitive processes integral to children’s ability to solve applied math problems: working memory (WM) and math calculation skills (i.e., the ability to utilize specific facts, skills, or processes related to basic math operations stored in long-term memory). Thirty-six boys with ADHD-combined presentation and 33 typically developing (TD) boys aged 8–12 years old were administered multiple counterbalanced tasks to assess upper (central executive [CE]) and lower level (phonological [PH STM] and visuospatial [VS STM] short-term memory) WM processes, and standardized measures of mathematical abilities. Bias-corrected, bootstrapped mediation analyses revealed that CE ability fully mediated between-group differences in applied problem solving whereas math calculation ability partially mediated the relation. Neither PH STM nor VS STM was a significant mediator. When modeled together via serial mediation analysis, CE in tandem with math calculation ability fully mediated the relation, explained 79% of the variance, and provided a more parsimonious explication of applied mathematical problem solving differences among children with ADHD. Results suggest that interventions designed to address applied math difficulties in children with ADHD will likely benefit from targeting basic knowledge of math facts and skills while simultaneously promoting the active interplay of these skills with CE processes.
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Studies by Rosen and Engle (1997) and others (e.g., Colom et al. 2005; Swanson and Kim 2007) provide compelling evidence that forward and backward simple digit span tasks load on a PH STM factor and are statistically separable from PH WM measures such as complex span tasks, the latter of which are more highly correlated with measures of children’s math competence.
Scores for one TD child exceeded 1.5 SDs on one of the two parents’ but not teachers’ rating scales. Parent interview revealed no significant ADHD symptoms or symptoms associated with other clinical disorders for the child. Six children with ADHD had subthreshold scores on teacher-rated hyperactivity/impulsivity. Follow-up clinical interviews, however, indicated the subthreshold symptoms were attributable to substantial psychostimulant effects while they were rated, and that all children demonstrated a history of significant, persistent levels of hyperactivity/impulsivity both at home and at school.
PH WM and VS WM performance data for a subset of the current sample were used in separate studies to evaluate conceptually unrelated hypotheses (Alderson et al. 2010, 2012; Friedman et al. 2017; Kofler et al. 2010, 2011, 2014; Raiker et al. 2012; Rapport et al. 2008, Rapport et al. 2009a, b; Sarver et al., 2015). We have not previously reported the Applied Problem Solving or Math Calculation data or their associations with our WM tasks for any children in the current sample.
SES and age were examined as potential covariates of the simple and serial mediation models presented below. Neither SES nor age were significant covariates of the model’s mediators or dependent variables, and inclusion of the covariates did not affect the pattern or interpretation of the results. Simple model results with no covariates are reported to allow B-weights to be interpreted as Cohen’s deffect sizes when predicting from a dichotomous grouping variable(Hayes 2009).
Alternative approaches were considered but not adopted because they share substantial variance with WM (e.g., the WISC-IV General Ability Index (GAI) is comprised of the Verbal Comprehension and Perceptual Reasoning Indices, and shares 25% to 40% of variance with WM).
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This study was conducted without external funding.
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The authors declare that they have no conflicts of interest.
All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.
Informed consent/assent was obtained from all participants included in the study.
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Friedman, L.M., Rapport, M.D., Orban, S.A. et al. Applied Problem Solving in Children with ADHD: The Mediating Roles of Working Memory and Mathematical Calculation. J Abnorm Child Psychol 46, 491–504 (2018). https://doi.org/10.1007/s10802-017-0312-7
- Attention/deficit-hyperactivity disorder (ADHD)
- Working memory
- Arithmetic calculation
- Applied math problems, executive functions