The moment toddlers come home and recite “One plus one equals two,” we shout it from the highest mountaintops (or family WhatsApp groups). Our child is a maths genius, we proclaim.

But here’s the thing: Our little maths prodigies don’t actually have these math skills either. They may be able to memorize the phrase, just like they memorize the names of their friends, but their little brains haven’t developed enough to actually do the computation. The words – and amounts – mean nothing to them.

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Over the past century, our understanding of very young children’s maths skills has fluctuated wildly between the view that children are incapable of mathematical thought and the argument that they are innately endowed with the ability to count. More recent research reveals a middle ground now accepted by most experts: The vast majority of preschool-aged children are not capable of even basic arithmetic. However, they do have a nonverbal numerical ability that needs to be nurtured in order for them to be capable of arithmetic and more in the future.

Nonverbal numerical ability sounds complicated, but it’s actually the simplest form of computational thought and the easiest ability for parents and caregivers to nurture. Babies are born with an abstract sense of numbers and can differentiate a larger quantity from a smaller quantity even if they don’t have the words to describe it. This sense continues to develop as they grow – as any parent who has ever accidentally given a slightly larger piece of cake to one of two children knows.

So, what are the toddler-level nonverbal math skills you should actually celebrate?

• Number sense: Math for toddlers is basically counting, even only up to X, without skipping. This is a critical, age-appropriate math skill to throw a parade for.
• Representation: If your preschooler understands the word ‘four’ means four items (not simply the word that comes after three), that is a foundational maths skill to celebrate. Don’t scoff at the simplicity of math for preschoolers – if a child never understands what our words for numbers mean, she’ll never be able to ‘do maths.’
• Spatial sense: If your preschooler can identify different shapes and sizes, as well as understand that these can appear in different positions, point in different directions, and move, that’s a milestone.
• Measurement: If your toddler understands that things can be measured, and that units of measurement correspond to the object’s size, quantity, amount, weight, he is on solid academic ground.
• Relative comparison: If your toddler can approximate the size of objects with words like bigger, smaller, fewer, more, that is a big step toward big-kid maths skills like addition and subtraction.
• Patterns: If your child understands how patterns work – whether with images, shapes or numbers – and can start to identify ‘what’s next,’ pop the champagne and juice boxes.
• Problem solving: If your toddler has started using his or her experiences to perform an activity – like putting a triangular block into a triangular box without trial-and-error – that is the seed of the problem-solving ability upon which maths are based. Start filling out her biodata with ‘engineer’ now.

Primary school-level mathematics is actually quite advanced and can only be understood once toddlers have mastered these foundational numerical abilities.

Still, you may ask, what’s the harm in showing off a young kid’s ability to say “One plus one equals two. Two plus two equals four”? Surely, he’ll just fill in the understanding later on, once his nonverbal math skills have developed.

Not necessarily.

Research has shown that overlooking informal, nonverbal numeracy development in favor of the formal maths instruction necessary for kids to parrot “One plus one equals two” can actually lead to learning difficulties and maths anxiety later on.

And celebrating recitation where there’s no understanding teaches children memorization is the priority, not understanding. This, too, can have the opposite result that parents hope for; a 2012 PISA report found that students who used memorization as a study technique were the lowest achievers.

So, how do you encourage your kid to develop informal, foundational math skills? Well, there are no flashcards for it. But a simpler method exists: Talk to your kid, particularly while she plays. You can try playing age-appropriate math activities for kids that nurture these skills. Or you can fill your everyday conversation with math for toddlers:

• “How many shoes are in a pair?” “Which of the four apples do you want to eat?”
• “Is my bed bigger than yours?” “When you eat five grapes, are there fewer grapes on your plate?”
• “Will the triangle fit in the square-shaped hole?”
• “What comes next in this pattern?”
• “How did you finish this puzzle last time?”

The transition from an abstract sense of numbers to concrete mathematical knowledge is a slow progression and cannot be rushed by formal teaching methods – but it can be nurtured by how we interact with our children. We all like to believe our kids are prodigies, but the chances of any toddler understanding what 1 + 1 = 2 means is slim. Which is something they’ll learn when they cover probability around 8^th standard, assuming they’ve built these basic math skills first.