A little understanding of how a child’s brain works at different ages can go a long way in helping a parent cope.

It’s back-to-school season. Parents mark their youngsters’ height on the wall and marvel at how much they’ve grown – but what’s going on just below the pencil line in that child’s brain?

We know brain development continues from infancy to adulthood, but many parents underestimate how much a child’s brain changes from year to year, and how those changes can influence behaviour.

Decades of scientific studies have shown even an immature brain is capable of extraordinary feats. Yet a fully developed brain is necessary for actions that adults take for granted, such as risk assessment and self-control.

According to developmental psychologists, parents who better understand the stages along the way can help guide their child over the hurdles.

Babies, for example, are surprisingly good at communicating.

They are looking, listening and imitating from the time they are born. Stick your tongue out at a baby, even an infant just hours old, and he or she may do the same back at you, said Sarah Lytle of the Institute for Learning and Brain Sciences at the University of Washington.

Yet many parents don’t realise how quickly infants begin to develop social and emotional awareness, said Ross Thompson, who is president of the child development organisation Zero to Three, and a cognitive psychologist at the University of California at Davis.

“Parents underestimate how sensitive a child is to their emotions,” he said. As early as six months old, a child can be affected by a parent’s depression or anxiety, and by marital squabbles.

Babies also look to their parents for guidance in uncertain situations. If you’re on a subway and start interacting with the little one next to you, the baby may turn to the parent to see how to respond to you.

This process is called “social cognition” or “social referencing”, and it’s not so different from when adults at a party wait to respond to a joke when they’re unsure whether others will find it funny or offensive.

To help infants learn, Lytle suggests that parents should frequently look at what they’re talking about, and change their gaze slowly. This important social cue helps with language development, she said – with babies who follow gazes closely having a more diverse vocabulary by the time they’re two.

All languages sound the same initially to a newborn, and then a tuning process begins. By about 10 months, babies start to specialise in the language they’re used to hearing.

It’s important to talk to your child during the first year, especially using “parentese”, Lytle said. This infant-directed speech is not “baby-talking”, despite its typical singsong tone and repetition, but uses real words in grammatically complete sentences.

While we typically underestimate babies’ ability to understand and communicate before they begin speaking, we tend to overestimate the brain power of walking, talking toddlers.

Toddlers are seemingly mentally incapable of sharing and self-control.  In a survey conducted by Zero to Three in 2015, nearly half of parents believed their children could learn to share by the time they are two.

But according to the cognitive psychologists at Zero to Three, this skill does not typically develop until a child is three or four. That may be because they haven’t yet developed what’s known as “theory of mind”.

Theory of mind is the ability to differentiate one’s own perspective and preferences from someone else. A classic experiment in theory of mind is known as the “Sally-Anne test”. A child is told Sally has a basket and Anne has a box. Sally puts an object in her basket, then leaves. While Sally is gone, Anne moves the object to the box.

The child is then asked where Sally will look for the object when she returns. Correctly answering that Sally will look in her basket signals the child understands they have a perspective that is different from Sally’s.

Theory of mind is important for developing empathy, making friends and even doing well academically, Lytle says. Parents can help their children develop perspective by talking them through scenarios like the Sally-Anne test, or reading books that help them to build cognitive parallels. For example, in a book where a character goes to a doctor, they can compare the situation to when the child went to the doctor and discuss how the experiences were similar or different.