Working memory involves the ability to actively hold information in mind and manipulate it to guide thoughts and behavior. Baddeley’s influential model proposes working memory comprises a central executive system that controls two short-term storage systems retaining verbal and visual information.
Children with attention-deficit/hyperactivity disorder (ADHD) frequently demonstrate working memory deficits, which impairs their capacity to regulate attention, think through problems, and accomplish tasks requiring temporary information retention.
Gaye, F., Groves, N. B., Chan, E. S. M., Cole, A. M., Jaisle, E. M., Soto, E. F., & Kofler, M. J. (2024). Working memory and math skills in children with and without ADHD. Neuropsychology, 38(1), 1–16. https://doi.org/10.1037/neu0000920
Key Points
- Children with ADHD frequently have deficits in working memory and math skills. The study examined relations between specific working memory components (central executive, phonological short-term memory, visuospatial short-term memory), ADHD symptoms, and math achievement in 186 children ages 8-13 years.
- All three working memory components significantly and approximately equally predicted children’s math achievement, explaining 56% of variance.
- The central executive’s relation with math was partially conveyed via shared associations with ADHD inattentive symptoms. In contrast, phonological and visuospatial short-term memory were unrelated to ADHD symptoms.
- While enlightening, limitations include the cross-sectional design and potential reduced generalizability due to the majority White sample.
- Findings inform potential targets for math interventions among children with attention or working memory difficulties.
Rationale
Numerous studies have reported working memory deficits among children with ADHD (Kasper et al., 2012; Martinussen et al., 2005) as well as math difficulties in this population (DuPaul et al., 2013).
Baddeley’s (2007) influential model proposes working memory comprises a central executive system that manipulates information held briefly in phonological and visuospatial short-term memory subsystems.
Understanding relations between specific working memory components, ADHD symptoms, and math skills could inform academic interventions for children with ADHD.
Although studies generally link working memory with math skills in typical development (Peng et al., 2016; Swanson & Fung, 2016) and ADHD samples (Friedman et al., 2018; Rogers et al., 2011), questions remain regarding the unique contributions of the central executive, phonological short-term memory, and visuospatial short-term memory.
Prior studies differed in their measurement approaches (Snyder et al., 2015) or had small samples of only boys (Friedman et al., 2018).
The present study addressed these gaps by examining all three working memory components’ relations with a latent math variable using validated tests (KTEA-3), advanced statistical methods (bifactor modeling), and a large, carefully diagnosed sample of girls and boys with and without ADHD.
Determining the extent to which specific working memory components predict math achievement can elucidate neurocognitive mechanisms underlying math difficulties in ADHD and inform potential intervention targets.
Method
Materials/Instruments:
- Working memory: Rapport et al. (2008) computerized working memory tasks that involve recalling sequential numbers and cross-modal sequence positions.
- Math skills: Kaufman Test of Educational Achievement–Third Edition (KTEA-3), a nationally standardized assessment of math computation, applied problem-solving, and fluency skills across mathematical domains.
- ADHD symptoms: ADHD Rating Scale (ADHD-RS-4/5), a psychometrically valid measure of ADHD symptom frequency and severity as rated by parents and teachers.
Design/Procedure:
- Working memory and psychoeducational testing occurred across two separate 3-hour assessment sessions
- Bifactor modeling used to estimate central executive, phonological short-term memory, and visuospatial short-term memory
- Two-tier structural equation models tested (a) working memory components predicting math; (b) ADHD symptoms as intermediate effects
Analysis:
- Full information maximum likelihood estimation
- Sensitivity analyses were conducted to assess the robustness of the results
Sample:
- 186 children ages 8-13 years (M=10.40 years) recruited from a university-based research clinic
- 120 children met criteria for ADHD based on comprehensive evaluation (84 males/36 females); 66 non-ADHD controls (40 males/26 females).
- 69.9% White/non-Hispanic
- Groups comparable on SES and IQ
Statistical Measures:
- Structural equation modeling via R package lavaan
- Bifactor (S·I-1) model to estimate working memory components
- Model fit assessed using CFI, TLI, RMSEA, χ2 difference test
- Bias-corrected bootstrapping (5,000 resamples) for indirect effects
Results
The working memory bifactor (S·I-1) model showed excellent fit. All three working memory components significantly predicted the latent math outcome (R2=.56), with no significant difference between the strengths of their effects.
The central executive (β=.50), phonological short-term memory (β=.45), and visuospatial short-term memory (β=.29) were all significant predictors, suggesting approximately equal influence.
Follow-up analyses indicated 24% of the central executive’s effect on math was indirect via relations with inattentive ADHD symptoms. The central executive predicted lower inattentive (β=-.40) and hyperactive/impulsive symptoms (β=-.24).
In contrast, phonological and visuospatial short-term memory were unrelated to ADHD symptoms, precluding significant indirect effects on math.
In summary, all three working memory components emerged as important predictors, together explaining over half of variance in children’s math achievement.
The central executive’s role was partially shared with regulating attention as expected, but phonological and visuospatial short-term memory exhibited significant direct effects on math skills.
Insight
This study makes several valuable contributions regarding neurocognitive processes underlying math difficulties among children with ADHD.
First, findings bolster similar evidence in community samples that working memory broadly supports math achievement (Peng et al., 2016). However, the application of bifactor modeling clarified the approximately equal roles of the central executive and subsidiary short-term memory systems specified in Baddeley’s (2007) working memory model.
Rather than the central executive alone primarily limiting math performance, as some posit (Swanson & Fung, 2016), phonological and visuospatial short-term memory also contributed significantly.
Second, despite no association with ADHD symptoms, phonological and visuospatial short-term memory retained direct predictive effects on math skills. Difficulties holding math information briefly in mind, therefore, could hinder math performance in ADHD even with an intact central executive.
From an intervention perspective, this pattern suggests targeting short-term memory may augment benefits from central executive training protocols that effectively reduce ADHD symptoms (Rapport et al., 2013) but produce only small math gains for some children (Singh et al., 2022). Further experimental work is needed to test this possibility.
Finally, findings highlight ADHD inattention symptoms as a mechanism that partially mediates some but not all working memory-math relations. Specifically, inattentive symptoms overlapped somewhat with the central executive’s role in supporting math achievement.
Still, phonological and visuospatial short-term memory influenced math skills independent of overt attention difficulties.
Consideration of both neurocognitive and symptomatic factors, therefore, will likely maximize our understanding of heterogeneous math-related impairment among children with ADHD (see Friedman et al., 2017).
Strengths
- Large clinically evaluated sample of boys and girls with and without ADHD diagnoses
- Rigorous ADHD diagnostic procedures incorporating multiple informants
- Multicomponent assessment, including validated tests of working memory, academic achievement, and ADHD symptom severity
- Sophisticated bifactor modeling approach and structural equation models
- Sensitivity analyses evaluating the robustness of results to changes in modeling approach or subgroups examined
- Relatively high retention rates and low missing data
Limitations
- Primarily cross-sectional design limiting causal conclusions
- Teacher ADHD symptom ratings were not always consistent with parent reports in exploratory models
- Majority non-Hispanic White sample could restrict the generalizability
- Working memory training study is needed to test hypothesized augmentative intervention effects definitively
- ADHD presentations combined given instability over development
- Did not assess potential bidirectional relations between working memory and math skills
Implications
This rigorously designed study makes a valuable contribution by accounting for over half of variance in children’s math competence based on components of working memory.
Clinically, findings identify neurocognitive abilities for screening children with attention or learning difficulties and have implications for developing tailored math interventions.
All three working memory components seem worthy of assessment when evaluating children struggling in math. However, central executive training protocols may provide the most generalizable benefits by boosting controlled attention and directly bolstering math problem-solving skills (Rapport et al., 2013).
Still, directly training short-term memory could augment and expand intervention responders given retained relations with math achievement.
Broader implications pertain to relations between working memory, ADHD symptoms, and academic functioning.
In particular, both overlapping and distinct neurocognitive and symptomatic factors appear important for understanding heterogeneous learning-related impairments in ADHD (Friedman et al., 2017). Shared and independent predictive effects, therefore, warrant consideration when selecting treatment targets.
Finally, this study adds to substantial evidence linking working memory to mathematics in neurotypical and clinical child populations (Geary, 2011; Swanson & Fung, 2016).
Bifactor modeling provided unique leverage to disentangle the alternatively blurred (Friedman et al., 2018) versus distinct (Metcalfe et al., 2013) contributions of component working memory processes based on prior measurement models.
Findings thus further specify neurocognitive skills supporting the complex task of math problem solving in developing learners.
References
Primary reference
Gaye, F., Groves, N. B., Chan, E. S. M., Cole, A. M., Jaisle, E. M., Soto, E. F., & Kofler, M. J. (2024). Working memory and math skills in children with and without ADHD. Neuropsychology, 38(1), 1–16. https://doi.org/10.1037/neu0000920
Other references
Baddeley, A. (2007). Working memory, thought, and action. Oxford University Press. https://doi.org/10.1093/acprof:Oso/9780198528012.001.0001
DuPaul, G. J., Gormley, M. J., & Laracy, S. D. (2013). Comorbidity of LD and ADHD: Implications of DSM-5 for assessment and treatment. Journal of Learning Disabilities, 46(1), 43–51. https://doi.org/10.1177/0022219412464351
Friedman, L. M., Rapport, M. D., Orban, S. A., Eckrich, S. J., & Calub, C. A. (2018). Applied problem solving in children with ADHD: The mediating roles of working memory and mathematical calculation. Journal of
Abnormal Child Psychology, 46(3), 491–504. https://doi.org/10.1007/s10802-017-0312-7
Friedman, L. M., Rapport, M. D., Raiker, J. S., Orban, S. A., & Eckrich, S. J. (2017). Reading comprehension in boys with ADHD: The mediating roles of working memory and orthographic conversion. Journal of Abnormal Child Psychology, 45(2), 273–287. https://doi.org/10.1007/s10802-016-0171-7
Geary, D. C. (2011). Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study. Developmental Psychology, 47(6), 1539–1552. https://doi.org/10.1037/a0025510
Kasper, L. J., Alderson, R. M., & Hudec, K. L. (2012). Moderators of working memory deficits in children with attention-deficit/hyperactivity disorder (ADHD): A meta-analytic review. Clinical Psychology Review, 32(7), 605–617. https://doi.org/10.1016/j.cpr.2012.07.001
Martinussen, R., Hayden, J., Hogg-Johnson, S., & Tannock, R. (2005). A meta-analysis of working memory impairments in children with attention-deficit/hyperactivity disorder. Journal of the American Academy of Child& Adolescent Psychiatry, 44(4), 377–384. https://doi.org/10.1097/01.chi.0000153228.72591.73
Metcalfe, A. W., Ashkenazi, S., Rosenberg-Lee, M., & Menon, V. (2013). Fractionating the neural correlates of individual working memory components underlying arithmetic problem solving skills in children. Developmental Cognitive Neuroscience, 6, 162–175. https://doi.org/10.1016/j.dcn.2013.10.001
Peng, P., Namkung, J., Barnes, M., & Sun, C. (2016). A meta-analysis of mathematics and working memory: Moderating effects of working memory domain, type of mathematics skill, and sample characteristics. Journal of Educational Psychology, 108(4), 455–473. https://doi.org/10.1037/edu0000079
Rapport, M. D., Orban, S. A., Kofler, M. J., & Friedman, L. M. (2013). Do programs designed to train working memory, other executive functions, and attention benefit children with ADHD? A meta-analytic review of cognitive, academic, and behavioral outcomes. Clinical Psychology Review, 33(8), 1237–1252. https://doi.org/10.1016/j.cpr.2013.08.005
Rogers, M., Hwang, H., Toplak, M., Weiss, M., & Tannock, R. (2011). Inattention, working memory, and academic achievement in adolescents referred for attention deficit/hyperactivity disorder (ADHD). Child Neuropsychology, 17(5), 444–458. https://doi.org/10.1080/09297049.2010.544648
Singh, L., Gaye, F., Cole, A. M., Chan, E., & Kofler, M. (2022). Academic outcomes: Behavioral parent training vs. central executive training vs. inhibitory control training for ADHD. PsyArXiv. https://doi.org/10.31234/osf.io/jmwbx
Snyder, H. R., Miyake, A., & Hankin, B. L. (2015). Advancing understanding of executive function impairments and psychopathology: Bridging the gap between clinical and cognitive approaches. Frontiers in Psychology, 6, Article 328. https://doi.org/10.3389/fpsyg.2015.00328
Swanson, H. L., & Fung, W. (2016). Working memory components and problem-solving accuracy: Are there multiple pathways? Journal of Educational Psychology, 108(8), 1153–1177. https://doi.org/10.1037/edu0000116
Keep Learning
Here are some thought-provoking discussion questions about this research a college class could explore:
- What type of math skills or problem-solving abilities do you think depend most strongly on working memory? Why? Provide examples.
- How could this study’s working memory training suggestions be practically implemented by teachers in normal classrooms? What barriers might exist?
- What future studies could build on these findings to elucidate the potential causal relations between specific working memory subcomponents and math skill development?
- Why might improving working memory abilities fail to fully resolve math difficulties for some children with ADHD? What other factors could be involved?
- Given limitations of the study’s cross-sectional design, how might longitudinal tracking inform our understanding of working memory, ADHD, and mathematical development over childhood and beyond?
