Studies of mathematical skills

As we learn more about the decline in math skills, it seems worth it to examine recent research. First, Amland, Grande, Scherer, Lervåg & Melby-Lervåg (2024) published “Cognitive Factors Underlying Mathematical Skills: A systematic review and meta-analysis” in Psychological Bulletin. Here are the edited abstract and public significance statement:

In understanding the nature of mathematical skills, the most influential theories suggest that mathematical cognition draws on different systems: numerical, linguistic, spatial, and general cognitive skills. Studies show that skills in these areas are highly predictive of outcomes in mathematics. Nonetheless, the strength of these relations with mathematical achievement varies, and little is known about the moderators or relative importance of each predictor. Based on 269 concurrent and 174 longitudinal studies comprising 2,696 correlations, this meta-analysis summarizes the evidence on cognitive predictors of mathematical skills in children and adolescents. The results showed that nonsymbolic number skills (often labeled approximate number sense) correlate significantly less with mathematical achievement than symbolic number skills and that various aspects of language relate differently to mathematical outcomes. We observed differential predictive patterns for arithmetic and word problems, and these patterns only partly supported the theory of three pathways—quantitative, linguistic, and spatial—for mathematical skills. Concurrently, nonsymbolic number and phonological skills were weak but exclusive predictors of arithmetic skills, whereas nonverbal intelligence quotient (IQ) predicted word problems only. Only symbolic number skills predicted both arithmetic and word problems concurrently. Longitudinally, symbolic number skills, spatial ability, and nonverbal IQ predicted both arithmetic and word problems, whereas language comprehensionwas important for word problem solving only. As in the concurrent data, nonsymbolic number skill was a weak longitudinal predictor of arithmetic skills. We conclude that the candidates to target in intervention studies are symbolic number skills and language comprehension. It is uncertain whether the two other important predictors, nonverbal IQ and spatial skills, are actually malleable.

This systematic review and meta-analysis found that symbolic number skills, language comprehension, and nonverbal reasoning skills are the most important foundational skills of achievement in mathematics in childhood and early adolescence. Children’s understanding of digits and number words seems to be the most promising target to design content that can be tested in future intervention studies. Moreover, whether interventions targeting language comprehension could benefit children struggling with mathematical word problems should be further examined. Mathematical skills is a fundamental factor both for a productive society and for individual development and employment and finding ways that might increase mathematical abilities can potentially have great consequences.

I thought this was interesting in identifying where we should target interventions with young children. The next study also looks at intervention. Shanley, Clarke, Kosty, Turtura, Cook, Sutherland & Smolkowski (2025) published “Examining Mathematics Intervention Effects on Domain General Skills: Are mathematics gains associated with improved domain general skills?” in Journal of Educational Psychology. Here are the edited abstract and impact statement:

Early mathematics achievement sets the stage for a range of important academic and career outcomes. As efforts to improve elementary mathematics instruction have increased, efforts to better understand how students develop mathematics knowledge and why students respond to mathematics instruction have also emerged. Given known correlations between domain general skills and mathematics achievement, the current study explored the development of domain general skills and mathematics learning in the context of a mathematics intervention efficacy trial to better understand relations between academic gains and the development of domain general skills. This study examined the concurrent development of domain general skills and mathematics skills for 470 first-grade students at risk for mathematics difficulties in the context of a mathematics intervention study. The results indicated that although students demonstrated gains in domain general and mathematics skills, domain general skill gains were not statistically significantly associated with gains in mathematics achievement. In addition, students who received mathematics intervention did not demonstrate greater gains in domain general skills, despite the positive effect of mathematics intervention on mathematics skills. Implications for mathematics instruction, curriculum development, and future research are discussed. 

This study investigated whether young students receiving math intervention made gains in domain general skills in addition to math skills. Overall, math skills were positively related to domain general skills, but math intervention did not affect domain general skills. Because math intervention alone may not lead to improved domain general skills, additional research is needed to better understand how domain general skill development is related to math learning and whether targeted instructional programs can affect domain general skills and math achievement. 

Here we see that, just because there is a correlation doesn’t mean an intervention will impact both skills. The final study looks at spatial skills and math. Harris, Resnick, Logan & Lowrie (2024) published “Pathways from Spatial Skills to Mathematics: The roles of gender and fluid reasoning” in Developmental Science. Here’s the edited abstract:

There are contentious and persistent gender differences reported in some measures of spatial skills, particularly mental rotation and, to a lesser extent, perspective-taking, which may have an impact on mathematics success. Furthermore, pathways between spatial skills and mathematics may be mediated by other cognitive factors, such as fluid reasoning. Participants (N = 320, age range 8–12 years) completed measures of mental rotation, perspective-taking, fluid reasoning, and mathematics. Regression analyses were conducted to assess the mediation effect of fluid reasoning on the relations between mental rotation and perspective-taking, and mathematics. Moderated mediation was performed to assess the effects of gender and age on these relations. Mental rotation and perspective-taking both predicted performance in mathematics for the overall sample, and fluid reasoning was found to partially mediate these relations. For mental rotation, gender moderated the mediation model, with mental rotation directly predicting performance in mathematics for males but not females. The mediation model for perspective-taking and mathematics was not moderated by gender. Although a predictor of performance, age did not moderate any of the reported relations. These findings suggest that gender differences in some spatial skills, such as mental rotation, may extend to the pathways linking the skills to mathematics. Although mental rotation may be predictive of mathematics performance for boys, the same might not be so for girls. Extrinsic spatial skills, such as perspective-taking, offer new pathways to explore in the growing body of work examining the links between spatial reasoning and mathematics.

I found it fascinating that mental rotation predicts math in boys but not girls for whom perspective taking may be more important. Taken together, these studies illustrate the complexity of math skills and their relationships to other important skills.