Does General Cognitive Capacity Training Improve Math Learning?

Proficiency in early math skills lays the groundwork for more advanced mathematical abilities, and socioeconomic disparities in these skills are apparent even before children begin formal schooling (e.g., James-Brabham et al., 2023). Given the importance of early mathematics proficiency, many educational initiatives have focused on ways to improve early math learning. This naturally leads to the question of which specific skills should be targeted through these efforts, and why.

Domain-Specific and Domain-General Skills

Cognitive theories (Kovacs & Conway, 2016) suggest two broad categories of skills that could be the focus of training and intervention. Domain-specific skills refer to abilities that are specific and unique to a particular domain, such as number skills in the field of mathematics. In contrast, domain-general skills encompass broader executive functions and cognitive capacities that are relevant across multiple domains, such as general intelligence.

Research has shown that domain-general skills, such as patterning skills, working memory, and spatial reasoning, can predict children's mathematics performance (Peng & Kievit, 2020). The rationale behind this is that these foundational cognitive capacities underpin the development of more advanced mathematical thinking and problem-solving. For example, the ability to recognize and extend patterns is thought to support the acquisition of numerical concepts and operations. Similarly, working memory allows children to hold and manipulate mathematical information, which is crucial for skills like mental calculation. Spatial reasoning, including the capacity to mentally visualize and transform shapes and objects, has also been linked to success in areas like geometry and problem-solving that involve spatial-temporal relationships. By tapping into these more general cognitive resources, training or supporting the development of abilities like patterning, working memory, and spatial skills may have the potential to boost children's mathematical learning and achievement.

However, the research on the transferability of these domain-general skills to specific mathematics outcomes has yielded mixed results (Fyfe & Borriello, 2024). For example, recent studies have failed to show that pattern training boosts young children's mathematical knowledge. Multiple investigations of both preschoolers (Wijns et al., 2021, 2022; Zippert et al., 2021) and kindergarteners (Kidd et al., 2019; McKnight et al., 2021; Mulligan et al., 2020; Pasnak et al., 2019; Shriver et al., 2017) have reported no benefits of pattern-focused instruction on measures of numeracy and broader math achievement.

For example, one study (Wijns et al., 2021) had preschoolers undergo 20 weeks of regular pattern training, which improved their patterning skills compared to controls. However, this targeted practice did not translate to any gains in the children's numerical understanding. Likewise, another study (Zippert et al., 2021) provided direct pattern training to pairs of preschoolers, but this did not give them an advantage over control groups in numeracy assessments. Collectively, this body of research suggests that while pattern training can develop those specific skills, it does not reliably enhance young children's overall mathematical knowledge and capabilities. Contrary to expectations, this type of focused instruction does not appear to meaningfully transfer to broader numerical and mathematical competencies.

Working Memory

The research literature on working memory is expansive, and while some aspects remain debated, the evidence clearly indicates that working memory training is unlikely to meaningfully improve children's mathematics knowledge (Melby-Lervåg et al., 2016; Sala & Gobet, 2020). Two comprehensive meta-analyses have shown that working memory training programs do lead to modest improvements in working memory-specific skills. However, these studies also reveal that scores on broader academic measures, including mathematics assessments, "were essentially unaffected by the training programs" (Sala & Gobet, 2020).

To illustrate, one study (Ramani et al., 2019) had 5-year-olds complete number games, working memory games, or control games on a tablet. While both the working memory and number game conditions enhanced children's working memory relative to controls, only the number games led to gains in numeracy knowledge. Thus, the available evidence suggests that despite enhancing targeted working memory capacities, standalone working memory training does not reliably translate to improvements in young children's broader mathematical understanding and performance.

The research on the impact of spatial training on mathematics outcomes also paints a somewhat mixed picture. A recent meta-analysis did report a small positive effect overall (Hawes et al., 2022). However, this effect was moderated by age, with the benefits appearing minimal for younger children. The studies included in this meta-analysis encompassed various types of spatial training, such as those involving gestures, spatial language, physical materials (e.g., tangrams, building blocks), and digital resources. Notably, only two of the 13 studies included demonstrated robust positive effects on children's mathematics knowledge (Judd & Klingberg, 2021; Mix et al., 2021). In contrast, five studies found no transfer to mathematics at all (Cornu et al., 2019; Hawes et al., 2015; Rodán et al., 2019; Sala et al., 2017; Xu & LeFevre, 2016), and six studies showed inconsistent and often non-robust transfer effects (Bower et al., 2020; Cheng & Mix, 2014; Cheung et al., 2020; Hawes et al., 2017; McDougal et al., 2023; Schmitt et al., 2018).

So, while the research does suggest some promise in using spatial training to potentially boost mathematics knowledge, the findings are decidedly mixed. The causal links between spatial skills and mathematics performance appear tenuous, especially for younger children. It remains an open question whether spatial training offers a more efficient pathway to improving mathematics abilities compared to more direct numeracy-focused interventions.

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Overall, although there are theoretical arguments for why training domain-general skills could potentially have a beneficial impact on children's mathematics knowledge, the evidence suggests that simply training domain-general skills in isolation, without explicitly connecting them to domain-specific mathematical content and instruction, does not appear to be an effective approach for enhancing children's mathematical knowledge.

However, the lack of a direct causal connection between a domain-general skill and mathematics knowledge does not mean that the correlational relation is irrelevant or unimportant. In fact, domain-general skills may serve valuable predictive roles in the context of mathematics development and performance. Even if the causal mechanisms are not fully clear, the correlational links between domain-general skills and mathematics knowledge can inform more effective assessment and identification of children at risk for mathematics difficulties.