The Child’s Mathematical Mind

Supporting the Child’s Mathematical Mind

Take a look at children’s goods and the numbers one to ten are everywhere—from tea sets to books to baby toys! Numbers are important, and exposure to them is a key way that children eventually learn how to count.  However, numeracy, or mathematical literacy, is so much more than being able to count from one to ten.  Before a child can even grasp numbers as symbols for quantity, a child needs to understand quantity and order.  Before learning the names of circles and squares, a child learns objects have spatial relationships with each other.  Before undertaking more complex calculations, she learns about patterns, repetition, and change.

To parents feeling increasing pressure to teach math skills to their sons and daughters: take heart, not every concept is taught or learned.  In fact, humans are born with innate mathematical skills.  Newborns can tell differences in quantity, and their ability to discriminate only becomes more precise as they get to six and nine months of age (Izard et al., 2009).  Very young infants notice differences in not only quantities they see, but quantities they hear, like tones and syllables (Allman et al., 2011).  Much research has been done on what babies know about numbers, to include their ability to perform very basic calculations (McCrink and Wynn, 2005).

That said, these innate skills still require development.  Young children are cognitively immature, and as their brains grow so do their abilities to grasp increasingly complex concepts.  For example, young children think of numbers logarithmically vice linearly, and research by neuroscientist Stanislas Dehaene suggests that children would retain this thinking as adults if they were not taught otherwise (Radiolab, 2009).  Dehaene observed that adults of the Munduruku, an indigenous people in the Amazon with limited mathematical vocabulary and education, still mapped numbers logarithmically (Harvard, 2008).

How parents can develop mathematical literacy 

Here are three interrelated ways that parents can develop their child’s mathematical literacy that don’t require fancy toys or apps or videos, and which can be implemented long before children set foot in preschool or kindergarten.

Use a child’s current schemas to build math skills. As said by University of Sheffield Professor of Education Cathy Nutbrown, “When children are interested, they learn.”(Arnerich, 2019).  Her observation is supported by research.  One recent study by Thomas and Jones (2020) indicated that children were more involved with both literacy and numeracy activities when the activities supported their schemas.  Schemas are repeated behavior that children use to explore the world. Another way to think of them is as a theme to a child’s play.  For example, a child may be particularly interested in pouring sand in a bucket, placing toys in the trash can, and climbing inside the laundry basket. These actions all seem unrelated, but the theme is containment.  The child is exploring this concept across mediums and making observations. The observant caregiver could appeal to this schema by providing the child with different sizes and types of containers and various substances to go inside them.  The child will explore them and naturally draw lessons about capacity, volume, weight, speed, and more.  Another child might have a completely different schema, like a fascination with trajectory or positioning.  Parents just need to identify that interest and support it.

Provide the child with appropriate mathematical vocabulary.  While children are constantly making observations, they may not have the words to fully describe or understand what they experience as they play.  By providing mathematical words, parents make children aware that they are surrounded by mathematics, adding to the child’s mathematical literacy. Parents can provide vocabulary not only as the child plays, but throughout normal day-to-day life.  According to Nutbrown (2011),

“It is difficult to know whether children understand cause-and-effect relationships if they do not articulate their thinking.  It is a responsibility of teachers and other educators to include children in discussions that feature different terminology so that children can build on these modelled vocabularies and generate the words they need to talk about their own findings and ideas” (p. 91).  

The examples provided below are based on examples provided by Greenberg (2012) to highlight five components of math (p. 62-63):

- number and operations (counting, quantity, how numbers are represented)

This table has four chairs. This fourth one is yours. Let’s count the seats: 1, 2, 3, 4.

- shapes and spatial relationships (geometric appearance, physical relationship between self and objects)

Your pizza is round. The sauce is under the cheese. The toppings are on top.  

- measurement (qualities such as size, weight, quantity, volume, and time)

This box is the smallest but feels heavy.  That box is the biggest but feels light.  Let’s use a scale to see how much they weigh.  

- patterns, relationships and change;

Your new shoes have a pattern of pink, green, white, pink, green, white. Since your third birthday you have grown taller.

- collecting and organizing information

You placed the red napkins by the red plates and the blue napkins by the blue plates.  

Use physical movement to teach math concepts. A study from the University of Copenhagen showed that children improved at math when the instruction involved their entire bodies (gross motor activities). In the study, first grade children that had whole body movements like skipping, crawling, and throwing integrated into their mathematical lessons showed a greater improvement in math performance that those that just did fine motor activities or those that did not have any additional movement (Beck etal., 2016).

In this day and age when parents have many pressures and responsibilities on their plate, parents can take comfort that developing their child’s math skills does not have to be hard or require special purchases.  With observation, conversation, and movement, parents can strengthen their child’s innate interest in math and set the foundation for future academic growth.


Abumrad, J., Krulwich, R. (2009) Innate Numbers? [Audiopodcast]. Radiolab.


Allman, M., Pelphrey, K., Meck, W. (2011). Developmental neuroscience of time and number: implications for autism and other neurodevelopmental disabilities. Frontiers in Integrative Neuroscience, 6, 1-24. Retrieved 17 Jan 2021 from

Arnerich, M. (2019). How to identify schemas in play: Cathy Nutbrown Interview.  Retrieved 20 Jan 2021 from


Beck, M., Lind, R., Geertsen, S., Ritz, C., Lundbye-Jensen,J., Wienecke, J. (2016). Motor-enriched learning activities can improve mathematical performance in preadolescent children. Frontiers in Human Neuroscience, 10(645). Retrieved 25 Jan 2021 from


Greenberg, J. (2012, May). More, all gone, empty, full: math talk every day in every way. Young Children, 62-64. Retrieved 25 Jan 2021 from


Harvard University. (2008, May 30). Slide rule sense: Amazonian indigenous culture demonstrates universal mapping of number onto space. ScienceDaily. Retrieved January 25, 2021 from


Izard, V., Sann, C., Spelke, E., Streri, A. (2009). Newborn infants perceive abstract numbers. Proceedings of the National Academy of Sciences of the United States of America, 106(25), 10382-10385.  Retrieved 19 Jan 2021 from


McCrink, K., Wynn, K. (2007). Ratio abstraction by 6-month-old infants. Psychological Science, 18(8), 740-745. Retrieved 26 Jan 2021 from


Nutbrown, Cathy. (2011). Threads of thinking: Schemas and young children’s learning (4th edition). Sage Publications.


Thomas, A., Jones, C. (2020). Exploring young children’s levels of involvement with numeracy and literacy – do schemas make a difference? Education, 3(13). Retrieved 26 Jan 2021 from


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