Four studies of children and math
I am presenting studies of preschool, elementary, and teenage children, as well of one of parents’ attitudes. In the first study, Mou, Zhang & Hyde (2022) published “Directionality in the Interrelations Between Approximate Number, Verbal Number, and Mathematics in Preschool-Aged Children” in Child Development. Here’s the abstract:
A fundamental question in numerical development concerns the directional relation between an early-emerging non-verbal approximate number system (ANS) and culturally acquired verbal number and mathematics knowledge. Using path models on longitudinal data collected in preschool children (Mage = 3.86 years; N = 216; 99 males; 80.8% White; 10.8% Multiracial, 3.8% Latino; 1.9% Black; collected 2013–2017) over 1 year, this study showed that earlier verbal number knowledge was associated with later ANS precision (average β = .32), even after controlling for baseline differences in numerical, general cognitive, and language abilities. In contrast, earlier ANS precision was not associated with later verbal number knowledge (β = −.07) or mathematics abilities (average β = .10). These results suggest that learning about verbal numbers is associated with a sharpening of pre-existing non-verbal numerical abilities.
I like this study because it reinforces the value of preschoolers’ verbal number knowledge.
In the second study, Guillaume et al. (2022) published “Groupitizing Reflects Conceptual Developments in Math Cognition and Inequities in Math Achievement from Childhood Through Adolescence” in Child Development. Here is edited information from the article:
Understanding the cognitive processes central to mathematical development is crucial to addressing systemic inequities in math achievement. We investigate the “Groupitizing” ability in 1209 third to eighth graders (mean age at first timepoint = 10.48, 586 girls, 39.16% Asian, 28.88% Hispanic/Latino, 18.51% White), a process that captures the ability to use grouping cues to access the exact value of a set. Groupitizing improves each year from late childhood to early adolescence (d = 3.29), is a central predictor of math achievement (beta weight = .30), is linked to conceptual processes in mathematics (minimum d = 0.69), and helps explain the dynamic between the ongoing development of non-symbolic number concepts, systemic educational inequities in school associated with SES, and mathematics achievement (minimum beta weight = .11) in ways that explicit symbolic measures may miss.
Let me take a moment to define subitizing: to make an immediate and accurate reckoning of (the number of items in a group or sample) without needing to pause and actually count them: for an average adult, the maximum number of such items is generally observed to be six.
McCandliss et al. (2010) introduced a new construct to the lexicon of enumeration processes—groupitizing—to describe how exact enumeration speed is enhanced by grouping cues that segment a large set into subitizable subgroups of up to four items, which rests on the conceptual understanding of cardinal values as composed of subsets: for instance, the value “3” is composed of three units (i.e., 3 = 1 + 1 + 1) but “3” can also be composed of one subset of two units and another subset of one unit (i.e., 3 = 2 + 1).
Our study emphasizes that groupitizing is a cognitive ability that predicts math achievement over and above socioeconomic, domain-general and domain-specific factors. Groupitizing cannot be reduced to math fluency or more generally math ability, but it does involve mental arithmetic processes. This is likely the reason why it strongly correlates with math ability and uniquely predicts math achievement. Furthermore, we claim that groupitizing is an interesting proxy to assess non-symbolic arithmetic. As such, groupitizing seems to be an appropriate tool to evaluate and train mental arithmetic among some at-risk populations, such as low income children or dyscalculic patients. We believe in this context that groupitizing might be an interesting asset in the future to diagnose and remedy specific math disabilities. More generally, we advise future studies aiming at evaluating numerical abilities to measure groupitizing.
In the third study, Borriello, Grenell, Vest, Moore & Fife (2022) published “Links Between Repeating and Growing Pattern Knowledge and Math Outcomes in Children and Adults” in Child Development. Here’s the abstract:
This study examined repeating and growing pattern knowledge and their associations with procedural and conceptual arithmetic knowledge in a sample of U.S. children (N = 185; Mage = 79.5 months; 55% female; 88% White) and adults (N = 93; Mage = 19.5 years; 62% female; 66% White) from 2019 to 2020. Three key findings emerged: (1) repeating pattern tasks were easier than growing pattern tasks, (2) repeating pattern knowledge robustly predicted procedural calculation skills over and above growing pattern knowledge and covariates, and (3) growing pattern knowledge modestly predicted procedural and conceptual math outcomes over and above repeating pattern knowledge and covariates. We expand existing theoretical models to incorporate these specific links and discuss implications for supporting math knowledge.
As background, in a repeating pattern children need to focus on what remains the same (i.e., the unit of repeat), whereas in a growing pattern children need to focus on what changes (i.e., the rule). Since young children spend more time with patterns than changes, this makes sense to me as another possible intervention with growing pattern knowledge essential in development of later math skills.
So, now we know that number knowledge is important for preschoolers, then groupitizing in elementary school, then repeating pattern knowledge. Finally, we look at parental attitudes. Hildebrand, Posid, Moss-Racusin, Hymes, & Cordes (2022) published “Does My Daughter Like Math? Relations between parent and child math attitudes and beliefs” in Developmental Science.
As early as age six, girls report higher math anxiety than boys, and children of both genders begin to endorse the stereotype that males are better at math than females. However, very few studies have examined the emergence of math attitudes in childhood, or the role parents may play in their transmission. The present study is the first to investigate the concordance of multiple implicit and explicit math attitudes and beliefs between 6- and 10-year-old children and their parents. Data from implicit association tasks (IATs) reveal that both parents and their children have implicit associations between math and difficulty, but only parents significantly associated math with males. Notably, males (fathers and sons) were more likely than females (mothers and daughters) to identify as someone who likes math (instead of reading), suggesting gender differences in academic preferences emerge early and remain consistent throughout adulthood. Critically, we provide the first evidence that both mothers’ and fathers’ attitudes about math relate to a range of math attitudes and beliefs held by their children, particularly their daughters. Results suggest that girls may be especially sensitive to parental math attitudes and beliefs. Together, data indicate that children entering formal school already show some negative math attitudes and beliefs and that parents’ math attitudes may have a disproportionate impact on young girls.
Taken together, I like breaking down the skills to ask about and intervene with, especially those that are basic cognitive skills. The work on parents’ attitudes is especially troubling.