A trio of studies published in Psychological Science, Scientific Reports, and the Journal of Experimental Child Psychology provides evidence regarding the development of early mathematical skills in preschool children. The findings suggest that the age at which a child grasps the concept of cardinality is a strong predictor of their first-grade readiness. The research also indicates that the complexity of parental speech and parental math anxiety significantly influence the development of these essential quantitative abilities.
Understanding the foundations of mathematics is a primary goal for developmental psychologists. While many children learn to recite numbers by rote memory, this does not necessarily mean they understand quantity. The conceptual leap occurs when a child understands cardinality. This is the principle that the last number word used when counting a set of objects represents the total quantity of that set.
Scientists sought to determine if the timing of this conceptual insight matters for future academic success. They investigated whether acquiring this knowledge early in preschool provides an advantage over acquiring it just prior to kindergarten. The researchers also aimed to identify specific home and parental factors that facilitate or hinder this learning process.
“This is part of a larger project funded by the National Institutes of Health that is focused on identifying the home (e.g., parent math anxiety) , school (e.g., classroom instruction), and child (e.g, working memory) factors that children’s early conceptual learning of the quantities represented by number word and numerals, as well as overall math achievement,” said study author David C. Geary, a Curators’ Distinguished Professor at the University of Missouri.
The first study, published in 2018, followed 141 children from the beginning of preschool through the first grade. The scientists assessed the children’s quantitative skills at multiple time points. To measure cardinality, the researchers utilized a “give-a-number” task.
In this procedure, a researcher asked the child to provide a specific number of objects, such as “give me three fish.” Children who do not understand cardinality might grab a random handful. Those who grasp the concept count out the exact number requested.
By the first grade, the researchers assessed the children’s number-system knowledge. This involves understanding how numbers relate to one another, such as knowing that the number seven is composed of a six and a one.
The data revealed that the age at which a child became a “cardinal-principle knower” was highly predictive of their later abilities. Children who understood this concept at the beginning of preschool showed significantly higher number-system knowledge in first grade. This advantage existed even after controlling for intelligence and executive function.
Executive function refers to a set of mental skills that include working memory, flexible thinking, and self-control. These cognitive processes allow children to focus attention and manage information.
The results suggest that simply understanding cardinality before kindergarten is not the only factor for success. The timing of this insight appears to be significant. Early mastery allows children to build a deeper understanding of number relationships before formal schooling begins.
Building on this, a second study published in 2025 examined what drives improvements in cardinal knowledge. The scientists focused on the home environment, specifically the nature of conversations between parents and children. They hypothesized that the quality of “number talk” would predict gains in a child’s understanding.
The researchers recruited 86 preschoolers and their primary caregivers. They assessed the children’s cardinal knowledge at the beginning of the school year and again five months later. To measure parental engagement, the scientists used a structured observation task.
Pairs of parents and children were asked to plan a pretend birthday party. They were given specific items like plates and goodie bags to encourage discussion about quantities. The researchers recorded these interactions and transcribed the conversations.
They coded the speech for complexity. Simple number talk involved basic counting or naming small quantities. Complex number talk involved comparing the size of two sets or labeling larger sets of objects.
The analysis indicated that the complexity of parental number talk predicted gains in the children’s cardinal knowledge. Children whose parents engaged in more complex quantitative discussions showed greater improvement over the five-month period. Simple counting activities did not show the same predictive power.
This study also highlighted the role of the child’s own cognitive abilities. Children with stronger executive functions tended to make larger gains in their understanding of number words. This suggests a bidirectional relationship where both the home environment and the child’s cognitive capacities contribute to learning.
The third study, published in 2026, investigated potential barriers to this early development. The researchers explored the impact of parental mathematics anxiety. They sought to understand if a parent’s fear or nervousness regarding math correlated with their child’s quantitative skills at the start of preschool.
This study involved 130 children and their parents. The parents reported their levels of math anxiety using a sliding scale. They also completed assessments of their own math and reading achievement.
The researchers assessed the children’s quantitative competencies using a battery of tasks. These included counting, recognizing numerals, and the give-a-number task. The scientists also measured the children’s executive functions.
The findings provided evidence that higher parental math anxiety is associated with lower complex quantitative knowledge in children. This relationship was particularly evident for cardinal knowledge. Children of highly anxious parents tended to perform worse on these conceptual tasks.
The data revealed an interaction between the child’s cognitive abilities and the parent’s anxiety. Children who possessed strong executive functions and had parents with low math anxiety demonstrated the highest competency levels. This suggests that a child’s ability to focus can amplify the benefits of a low-anxiety home environment.
“Children’s early home experiences with numbers, counting, and related topics contributes to their math development,” Geary told PsyPost. “Parents who avoid these activities place their children at risk of falling behind their peers.”
The study also clarified the nature of parental math anxiety. Parents who reported high anxiety also tended to have lower math achievement scores themselves. They reported lower confidence in their abilities and a tendency to avoid numerical information.
This implies that math anxiety is not an isolated emotional state. It appears to be part of a broader constellation of traits including lower subject proficiency and avoidance behaviors. These factors likely combine to create a home environment that is less conducive to early math learning.
Self-reported home numeracy activities, such as playing number games, did not strongly predict the children’s skills in this specific study. This suggests that general reports of activities may not capture the specific types of interactions that drive learning. The specific quality of engagement, as seen in the party-planning study, seems to be more significant than the frequency of general activities.
The studies — like all research — come with some caveats. The studies identify correlations but cannot definitively prove causation. While the longitudinal designs offer strong evidence, unmeasured genetic or environmental factors could play a role.
“We don’t fully understand the specific activities that promote early math development, but progress is being made,” Geary said.
The reliance on self-reports for some parental measures introduces potential bias. Parents may overestimate the frequency of educational activities.
“There was no relation between parents math anxiety and the math activities they reported engaging in, suggesting self-reports of these activities are not reliable,” Geary noted. “They stated they avoided math information and so they likely over-reported how much they engaged in these activities with their children.”
Future research should focus on experimental interventions. Scientists need to determine if coaching parents to use complex number talk can directly improve children’s outcomes. It would also be beneficial to explore if reducing parental anxiety leads to better math readiness in their children.
“We’re still collecting data,” Geary told PsyPost. “In the end, we’ll look at parent, classroom, and child factors that contribute to key aspects of math development over the two years of preschool.”
Despite these limitations, the implications for parents and educators are practical. The research suggests that early exposure to number concepts is beneficial. It indicates that the quality of interaction matters more than rote counting.
Parents might encourage their children by discussing the relationships between numbers. Conversations could involve comparing quantities, such as discussing which pile has more blocks. Labeling the total number of items in a set appears to be particularly helpful.
The findings also suggest that addressing parental attitudes is necessary. Parents who feel anxious about math may inadvertently limit their child’s exposure to complex concepts. Building parental confidence could be a key step in supporting the next generation of learners.
The study, “Early Conceptual Understanding of Cardinality Predicts Superior School-Entry Number-System Knowledge,” was authored by David C. Geary, Kristy vanMarle, Felicia W. Chu, Jeffrey Rouder, Mary K. Hoard, and Lara Nugent.
The study, “Complexity of parental number talk predicts preschoolers’ gains in cardinal knowledge,” was authored by David C. Geary, Emine Simsek, Sara Gable, Jordan A. Booker, Lara Nugent, and Mary K. Hoard.
The study, “Parental mathematics anxiety predicts children’s cardinal number word and numeral knowledge at preschool entry,” was authored by David C. Geary, Sara Gable, Mary K. Hoard, and Lara Nugent.
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