Math skills improved when parents play number games with 3-year-olds

Photo: Yoshiyasu NISHIKAWA. Creative Commons.

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Researchers have found a link between parents’ naming (or “labelling”) the number of small sets of objects with their three-year olds and the children’s cognitive development in math.

Early math skills go through six stages:

  1. Rote counting: being able recite numbers in the right order. (This happens around two years.)
  2. Understanding what numbers mean (two to three years).
  3. Identifying written numbers (two to three years).
  4. One-to-one counting: the ability to count a series of objects from one to ten (two to three years).
  5. Attaching number word “labels” to small sets of objects: the ability to understand quantity, for example, to see three apples and be able to say “there are three apples here” (three years).
  6. The cardinal principle: the idea that the last number reached when counting any set of objects represents the quantity of the whole set (3.5 years and beyond).

Researchers consider the sixth step, the cardinal principle, to be the “big idea” in the development of early numerical skills. It is the fundamental basis of future math learning.

Research has shown that early parental support with the first five stages improves the child’s grasp of the sixth stage, the cardinal principle. The theory is that, as the child grows in understanding, the parent is constantly tapping into the area just beyond the child’s grasp without some help. This is known as the “zone of proximal development”.  Through this relationship with the caregiver, the child’s cognitive development progresses.

When parents support three-year-olds with stage 5 – “labelling” – the children do better in math later

The researchers looked at how 140 mothers of three-year-olds in Boston, Massachusetts, USA supported children in the third, fourth and fifth stages above: identifying written numbers, one-to-one counting and labelling set sizes. Then they looked at the math abilities of the same children later at four and a half years old and six to seven years old. (The study also looked at reading skills at these two ages, but found no correlations with earlier numerical support.)

The mothers were filmed for 10 minutes during a series of play exercises with toys with their three-year-olds. One toy was a cash register with numbers on the keyboard. Another toy was a Duplo set with pieces of different sizes and colours. The mothers were given no instructions at all. Their activity was then scored for how many times they engaged the child in identifying numbers, one-to-one counting and labelling set sizes.

The researchers found a correlation between labelling set sizes (stage 5) and the child’s math ability at both four and a half and six to seven years. This relationship still held after controlling for various other family factors known to influence children’s math ability, such as race and gender, family income, the child’s intelligence and the mother’s education, language ability and level of parenting stress.

Implications for teaching children math: encourage parents to play number games with their toddlers

Research shows that parents have little idea about how to teach their preschool-aged children math. Yet early math support is important because what happens at home before school influences numerical skills, which in turn strongly predict later cognitive development outcomes, including the odds of completing school and earnings in adulthood. The teaching process is not burdensome: it involves singing number songs, playing board games, and talking about numbers in everyday conversations.


Casey BM, Lombardi CM, Thomson D, Nguyen HN, Paz M, Theriault CA & Dearing E (2018), Maternal support of children’s early numerical concept learning predicts preschool ad first-grade math achievement, Child Development 89.1