Parents have a lot on their plate when it comes to raising a child — that much is obvious. Past the bulk of daily tasks focused solely on keeping the child alive, parents must study their offspring with detective-like intensity: Is she crawling enough? Has he started grabbing yet? Why isn’t she talking?

Childhood cognitive development follows a fairly predictable path, science has found, which on the one hand may worry parents, whose child seems to be falling behind. But on the other, it can alert them to their child’s natural strengths and help them cultivate those talents. From an infant’s innate number sense to a pre-teen’s logical reasoning, here are several signs your child may be precocious.

## 1. Early Number Sense Predicts Future Math Skills

Children aren’t born with an innate understanding of numbers. Strictly speaking, the mathematical concepts are abstracts, instilled in kids through education of the Arabic symbols that represent them. Infants as young as 6 months old, however, can intuitively grasp the concept of value. A recent Duke University study has found the better a child can discern between differing values, the more likely he or she will excel on non-symbolic math tests later in life.

Scientists call children’s natural understanding of value their “primitive number sense.”

"When children are acquiring the symbolic system for representing numbers and learning about math in school, they're tapping into this primitive number sense," said study leader Dr. Elizabeth Brannon, a professor of psychology and neuroscience, in a statement. "It's the conceptual building block upon which mathematical ability is built."

Brannon had 48 6-month-olds look at two screens: one showed eight dots enlarging and changing position, while the other switched between eight and 16 dots, which also changed in size and position. Brannon and her colleagues concluded that babies that could tell the difference between the two numerical values looked at the numerically changing screen longer.

In follow-up studies three years later, non-symbolic number tests and preschool-calibrated IQ tests revealed that those infants who showed greater preference scores for the numerically changing screen performed better in later assessments.

"We can't measure a baby's number sense ability at 6 months and know how they'll do on their SATs," Brannon conceded. "In fact our infant task only explains a small percentage of the variance in young children’s math performance. But our findings suggest that there is cognitive overlap between primitive number sense and symbolic math. These are fundamental building blocks."

Early Detection Threshold: 6 months

## 2. Do They Hold False Beliefs?

Consider two friends, Sally and Anne. Sally has a marble, which she places in a box for safekeeping, before walking away. While she’s gone, Anne takes the marble from the box and puts it in her pocket. Sometime later, Sally comes back. Where will she look for the marble?

To the rational adult, the answer is obvious: she’ll look in her box, because that’s where she put it. But the developing child’s mind doesn’t think this way, at least not initially. Up until about kindergarten, a child’s brain isn’t formed enough to realize the people surrounding him have minds of their own — individual thoughts and fears unique to their personal experiences. The developing child can’t know that Sally doesn’t know. According to his brain, she has to know, for he has that knowledge himself.

So when he’s asked where Sally will look for her marble, the average child will reliably and confidently reply, “In Anne’s pocket.”

This phenomenon has been recreated countless times, with various backstories, and the conclusions have all upheld the original theory published 30 years ago by researchers Josef Perner and Heinz Wimmer in their model of the problem, which they dubbed the “False-Belief Test.” In their version, none of the 3- to 4-year-old children correctly indicated where the object was located, while 57 percent of 4- to 6-year-old children did so. What’s more, 86 percent of 6- to 9-year-olds indicated the location correctly. Their findings have since set a foundation for breakthrough research into childhood social disorders such as autism.

Early Detection Threshold: 4 years

## 3. What’s Inside The Box Of Crayons?

Researchers have tried to better understand the mechanisms of the False-Belief Test through other methods known as “appearance-reality tasks.” The skeleton of the study doesn’t change, but the implications of its results point in a slightly different direction.

Experimenters will present a child with a box of crayons. They ask the child, “What’s inside this box?” to which the child — and other trusting people — will reply, “Crayons.” But when the experimenter opens the box, out roll several pieces of chalk. The experimenter then re-closes the box and asks the child what she thinks another person, who hasn’t seen the chalk, would think is inside the box. If the child says “Chalk,” she fails the appearance-reality task, but if she says “Crayons,” she passes.

Psychologists Alison Gopnik and Janet Astington first devised this experiment in 1988. It, like the false belief test, has since spurred numerous offshoots investigating the role that cognitive deficiencies play in children with autism spectrum disorder.

Certain research has found adults with Asperger’s syndrome continue to exhibit the same behavior when confronted with eye-tracking tasks. Failure to gauge a person’s intent through eye movements has come to be known as “mindblindness,” and it’s another potential sign a child may be in the early stages of autism.

“We showed that, like infants, neurotypical adults’ eye movements anticipated an actor’s behavior on the basis of her false belief. This was not the case for individuals with Asperger syndrome,” states one report from a 2009 study. “Thus, these individuals do not attribute mental states spontaneously, but they may be able to do so in explicit tasks through compensatory learning.”

Early Detection Threshold: 4-5 years

## 4. Curious Kids Become Intuitive Learners

Several years down the road, children begin to grow curious, ask questions, and connect the dots of their environment, but only the more advanced individuals show particular traits. Developmental psychologist Jean Piaget called this the “Intuitive Thought Substage,” and at its most basic it’s the period in a child’s life where he realizes he has vast amounts of knowledge, without knowing how he acquired it. There are two basic measures for intuitive understanding: conservation and centration.

Conservation involves a child knowing that changing an object’s appearance doesn’t change its basic properties. Centration involves concentrating fully on one aspect of a situation and ignoring all others. Children in the Intuitive Thought Substage typically are unable to understand conservation, and instead display centration.

A simple example involves two beakers of varying shapes. Both are the same volume, yet one is short and squat while the other is tall and skinny. Due to their varying sizes, a quantity of liquid in the tall beaker will necessarily rise to a higher level than in the other. But if an experimenter pours the liquid into the short beaker, children in Intuitive Thought Stage will now say there is less liquid overall, because what they see is height, not volume.

The same experiment can be run using objects that are spread increasing distances apart:

Early Detection Threshold: 7 years

## 5. If A>B… And Other Logic

A milestone in cognitive development rests in a child’s acquisition of logic and reason. Limited inference skills once caused her to believe a phone ringing and a falling dish to be causally related because they happened close together, but now she understands time is not the only thing that ties actions together. Abstract problem-solving is still difficult, but concrete tasks pose less of a threat.

A child may know for instance, that certain objects are heavier because they weigh more, not because they happen to be different colors. But if she were told A>B and B>C, she would have trouble deducing that A>C.

Now, however, they are able to grapple with conservation. They can also create a fuller picture of a problem, sort items correctly, and pass the False-Belief Test and Appearance-Reality Task with flying colors.

From there, the only remaining cognitive abilities a child must sort out are symbolic formulations of concrete objects. They learn about ideas larger than themselves, about concepts and theories, and about diverse ideologies, all the while forming a conception of the world so that they, too, may one day become anxiety-stricken parents wondering if their child should be talking by now.

Early Detection Threshold: 7-11 years