How Cognitive and Mathematical Skills Develop from Infancy to Early Childhood — And What Parents Can Do at Home

The early years of a child’s life are not only emotionally meaningful but neurologically critical. During this period, the brain develops at a speed that will never be repeated later in life. Research in developmental neuroscience shows that the foundations of thinking, attention, language, and early mathematics are shaped primarily during infancy and early childhood (Tierney & Nelson)

For parents, this raises an important question: How do cognitive and mathematical skills develop, and what can families realistically do at home to support them?

This article integrates evidence from longitudinal studies, developmental psychology, and neuroscience to explain how cognition and early math skills grow — and how everyday parenting practices can make a lasting difference.

What Is Cognitive Development and Why Does It Matter?

Cognitive development refers to the growth of mental abilities such as memory, attention, language, reasoning, and problem-solving. These skills do not emerge independently. Instead, they develop as interconnected systems that evolve over time.

A large longitudinal study following more than 6,000 children in New Zealand demonstrated that early cognitive functioning can be measured reliably in infancy and preschool years and that these early abilities predict later learning outcomes (Neumann et al). Children who showed stronger early cognitive profiles at age 4.5 were more likely to demonstrate better academic-related performance later in childhood.

This suggests that cognitive development is not random — early patterns often set long-term learning trajectories.

Brain Development: Why Early Experience Is So Powerful

Modern neuroscience has clearly rejected the idea that infants are born with a “blank slate” brain. Instead, the infant brain is highly plastic, meaning it is exceptionally sensitive to environmental input.

During the first years of life:

- Neural connections form rapidly

- Sensory and language systems become specialized

- Experience directly shapes brain organization

Research using EEG and neurodevelopmental tools shows that exposure to language, faces, and responsive caregiving influences how neural networks develop. Importantly, brain development is hierarchical — early neural systems support later learning capacities. When foundational systems such as attention and perception develop well, children are better prepared for academic challenges later on.

How Children’s Thinking Changes with Age

Jean Piaget’s theory of cognitive development remains influential because it highlights that children’s thinking changes qualitatively, not just quantitatively (Malik & Marwaha; Piaget Review).

Although modern research shows that development is more flexible than strict “stages,” Piaget’s framework still provides useful insight:

Infancy (0–2 years): Learning occurs through sensory exploration and physical interaction. Object permanence and cause-and-effect understanding emerge.

Preschool years (2–7 years): Language and symbolic thinking expand, but reasoning remains concrete.

Early school years (7–11 years): Logical thinking about real-world situations improves.

Adolescence (12+ years): Abstract and hypothetical reasoning develops.

A central message from this research is that children learn best through active engagement, not passive instruction. Talking, playing, experimenting, and problem-solving are far more effective than rote memorization.

Mathematical Development Starts Earlier Than Most Parents Expect

Many parents associate mathematics with school textbooks and formal instruction. However, research shows that early math development begins long before formal schooling.

Early mathematical skills include:

- Recognizing quantity differences

- Counting small sets

- Comparing size and magnitude

- Understanding simple patterns

- Identifying shapes

Longitudinal studies demonstrate a strong association between early math proficiency and later academic success, not only in mathematics but also in reading (Why Do Early Mathematics Skills Predict Later…).

Children who develop early number sense and problem-solving strategies are more likely to perform well across multiple academic domains.

Executive Function: The Hidden Driver of Learning

One of the most important mechanisms connecting cognitive and mathematical development is executive function. Executive function includes:

- Working memory

- Inhibitory control (self-regulation)

- Cognitive flexibility

These skills allow children to focus attention, follow instructions, manage impulses, and adapt strategies during problem-solving.

Research shows that executive function begins developing in early childhood and continues to mature through adolescence (Best & Miller). Furthermore, executive function mediates the relationship between early math skills and later academic achievement.

In practical terms, this means that learning mathematics is not only about numbers. It also depends on a child’s ability to concentrate, remember steps, control impulses, and switch strategies when needed.

The Role of Parents and the Home Environment

Parents are children’s first and most influential learning partners. Everyday interactions — conversations, play, routines — all contribute to cognitive growth.

A large international meta-analysis examining home mathematical activities found a small but significant positive relationship between parent-led math-related interactions and children’s early math skills. Importantly, researchers emphasize that quality matters more than quantity. Natural, playful engagement is more effective than forced academic drills.

Neuroscience research further highlights the importance of responsive caregiving, emotional warmth, and rich language exposure for healthy brain development (Tierney & Nelson).

Practical Activities Parents Can Use at Home

Research consistently shows that learning is most effective when embedded in everyday experiences.

Ages 0–2: Building Foundations

- Talk to your child during daily routines

- Count visible objects casually

- Play simple cause-and-effect games

- Read picture books and name objects and shapes

These activities support attention, language development, and early number awareness.

Ages 3–5: Strengthening Thinking and Number Sense

- Count toys, snacks, or steps

- Sort objects by color, size, or shape

- Use puzzles and matching games

- Encourage pretend play involving planning and roles

These activities promote symbolic thinking, working memory, and early logical reasoning.

Ages 6–8: Applying Skills in Real Life

- Involve children in cooking and measuring

- Play board games that require counting and rule-following

- Talk about money and basic budgeting through play

- Encourage children to explain their problem-solving strategies

These experiences strengthen executive function while reinforcing mathematical reasoning.

Three Things Parents Can Start Doing Today

If you take nothing else from this article, start here:

1. Talk More Than You Think You Need To

Language exposure strengthens cognitive development and supports early math understanding through labeling, counting, and describing patterns.

2. Turn Daily Routines Into Learning Moments

Meals, grocery shopping, and playtime offer natural opportunities for counting, comparing, and problem-solving.

3. Focus on Attention and Self-Regulation, Not Just Numbers

Games that require turn-taking, memory, and rule-following strengthen executive function — a key driver of long-term academic success.

Final Thoughts

Parents do not need expensive educational tools or formal programs to support cognitive and mathematical development. Research consistently shows that consistent interaction, playful learning, and emotionally supportive relationships are the most powerful drivers of early learning.

Early childhood is not simply preparation for school. It is the foundation for lifelong learning.

By being present, responsive, and engaged, parents actively shape how their children think, learn, and grow.

Authored by:

Dr. Alireza Sarmadi
Family Physician

References

- Neumann, D., Peterson, E. R., Underwood, L., Morton, S. M. B., & Waldie, K. E. (2021). The development of cognitive functioning indices in early childhood. Cognitive Development, 60, 101098.

- Malik, F., & Marwaha, R. (2023). Cognitive development. Case Western Reserve University / MetroHealth Medical Center.

- Tierney, A. L., & Nelson, C. A. (2010). Brain development and the role of experience in the early years. Harvard Graduate School of Education / Harvard Medical School.

- Best, J. R., & Miller, P. H. (2010). A developmental perspective on executive function. University of Georgia.

- Andersson, U. et al. (2021). Why do early mathematics skills predict later academic achievement? Elsevier.

- Meta-analysis Consortium (2021). Do home mathematical activities relate to early mathematical skills? International systematic review.