I've spent the last four years teaching my daughter to be human. There's a lot to learn, from walking, talking and the (strangely challenging) task of not soiling yourself, to how to make choux pastry, Chinese history and the basics of quadratic equations.

Although we still have some way to go, it already feels like a hefty parental investment, especially when compared with species like the blue wildebeest, whose newborns can stand, walk, and even outrun predators just a few hours after leaving the womb. But humans aren't the only species genetically predisposed to spend years rearing their offspring. Our closest relatives, chimpanzees, also enjoy a prolonged childhood. As a socially complex species, their infants stick close to their mothers for the first five years of life, picking up a laundry list of essential skills by observing and imitating their elders.

Telling a Picasso from a Monet, for example, should be easy for a chimpanzee

Many skills that we consider complex are in fact the result of relatively simple - and often universal - cognitive abilities shared by a great many species

Of course, the life skills a chimpanzee eventually acquires are nowhere near as complex as those I'm teaching my daughter. Don't get me wrong – learning how to make a termite-fishing stick is cognitively complex, but it's hardly up there with learning to read, or being able to differentiate between a Picasso and a Monet. After four years of dedicated training from her parents, my daughter should be able to beat a chimpanzee in a battle of wits, right?

Wrong. Or at least, it depends on the battle. In fact telling a Picasso from a Monet, for example, should be easy for a chimpanzee – both honeybees and pigeons have been trained to do it. Scientists taught these small-brained species that chambers next to pictures by one or other of these artists contained food. When later presented with new Picassos and Monets, they were more likely to opt for the artist whose work had previously led them to a reward - meaning they had picked up on underlying stylistic differences. Many skills that we consider complex are in fact the result of relatively simple - and often universal - cognitive abilities shared by a great many species.

In reality, when it comes to cognitive development, the divide between infant chimpanzees and infant humans is often startlingly small. So small in fact that psychologists once wondered if the key difference between the two species was not our underlying mental machinery, but the cultural traditions and recorded knowledge that humans had accumulated through the ages. Perhaps if an infant chimpanzee was raised in an exclusively human environment, it would acquire human abilities, complete with language competency and table manners.

Previous experiments showed chimpanzees lacked the vocal structures to produce the sounds of human language

In order to test this hypothesis, Allen and Beatrix Gardner, psychologists at the University of Nevada, Reno, acquired a 10-month-old chimpanzee named Washoe. She had been born in the wild in West Africa in 1965, where she was "recruited" by the US Air Force for use in biomedical testing as part of the space programme. The Gardeners brought Washoe into their home in 1966. She was dressed in human clothes, and joined the Gardeners at the dinner table each evening. Every effort was made to replicate the childhood of a typical human infant with the hope that she would not just learn human language, but learn to be human.

Aware from previous experiments that showed chimpanzees lacked the vocal structures to produce the sounds of human language, Washoe was taught to communicate using a form of American Sign Language. By the time she left the Gardeners in 1970, she could communicate using a few hundred signed symbols. For some, the fact that she could combine symbols to form new words such as "water bird" when shown a swan for the first time was evidence of at least rudimentary language capacity. Many scientists, however, remained skeptical, suggesting Washoe and other apes were simply responding to unintentional cues from the researchers working with them.

It was obvious from the Gardeners' experiment that being raised in a human environment could not give a chimpanzee a human mind. Although she was one of the first non-human apes to communicate with humans in the form of signed symbols, she did not ever truly acquire language. The question scientists still wrestle with today is what exactly is going on in the minds of toddlers that allows them to acquire and use language where chimpanzees fail? And how does this relate to the skills that define human intelligence, allowing us to create moon landers and chai lattes?

The human need for deeply cooperative group living brought with it the ability to get into each other's heads

Michael Tomasello, a psychologist and co-director of the Max Planck Institute for Evolutionary Anthropology in Leipzig, Germany, has spent the last 30 years studying primate cognition in an effort to answer questions like these. In his recently published book A Natural History of Human Thinking, he develops the "shared intentionality" hypothesis to explain the basic difference between human and chimpanzee cognition. He defines this as the ability "to participate with others in collaborative activities with shared goals and intentions".

"Although humans' great ape ancestors were social beings, they lived mostly individualistic and competitive lives," suggests Tomasello, "but early humans were at some point forced by ecological circumstances into more cooperative lifeways, and so their thinking became more directed toward figuring out ways to coordinate with others to achieve joint goals or even collective goals. And this changed everything."

This human need for deeply cooperative group living brought with it the ability to get into each other's heads. Being able to share intentions and goals in this way is extremely rare in the animal kingdom, and many experiments suggest that it's a skill that my daughter has, but that chimpanzees - like Washoe - lack.

Consider the enigma of human pointing – a strangely difficult signal for chimpanzees to wrap their heads around. They do not typically point in the wild, although individuals working with humans in the lab will often gesture towards food or objects they want, and sometimes they do so with a pointed finger. What scientists want to know however is whether or not a pointing chimpanzee is trying to connect with the person watching them by establishing collaborative, two-way communication. It is obviously a communicative act, but the question is whether it is the result of the chimpanzee trying to get inside the head of the observer to convey the message: "Excuse me, I would really like you to fetch that banana for me."

Whereas the babies sat politely and pointed toward the object in an attempt to get their caregiver's attention, the chimpanzees moved towards the object while making pointing and reaching gestures

For humans, these collaborative messages are commonplace, even without the use of language. Imagine for a moment that I had lost my voice. I could ask my wife to pass the salt simply by pointing to the salt shaker sitting on the table. Via this signal, I could share with my wife the knowledge that I want the salt, and she would immediately realize that I am asking for her help in achieving what I hope is now a shared goal. I don't need to fling myself across the table while making exaggerated grabbing motions.

Chimpanzees, on the other hand, do. In a recent experiment, chimpanzees were pitted against one-year-old children to see how their behaviour differed when something they wanted was just out of reach. Whereas the babies sat politely and pointed toward the object in an attempt to get their caregiver's attention, the chimpanzees moved towards the object while making pointing and reaching gestures. The key difference, the researchers concluded, was that the human infants realized the pointing gesture alone was enough to tell their caregiver what they wanted.

Humans, it seems, are born ready to share their thoughts with others.

Once we set aside the cognitive traits that encompass Tomasello's idea of shared intentionality, however, the list of skills that my daughter possesses that surpass those of chimpanzees is nearly exhausted. In fact, there are cognitive skills at which chimpanzees can easily outshine my daughter. Or you and me for that matter.

In another recent study, chimps went head-to-head with humans in a test of their strategic thinking. Participants played a simple two player computer game in which they had to choose one of two squares displayed on a screen. Player one won if both players chose the same square, and player two won if both of them chose the opposite squares. After each game, the two players could see which one their opponent had chosen, allowing them to learn about their opponent's behaviour and make educated guesses about their future choices. Players were pitted against others of their own species, and human winners were rewarded with cash prizes while chimps that came out on top got pieces of apple.

If the players make the best possible moves, the game should develop a specific pattern predicted by game theory. It turned out that after playing the game for a while, chimpanzees made moves that closely resembled the optimal strategy predicted by mathematical models. Humans, on the other hand, didn't.

Perhaps humans just don't have the level of fighting spirit (or desire for infidelity) that gives chimpanzees the edge in some battles of wits

With our infamous critical thinking skills, how could humans wind up being soundly beaten by chimpanzees? We know from previous research that chimpanzees can have stunning visual memory, and this might be the key to their success. Ayumu, a young chimpanzee involved in cognitive research at the Primate Institute of Kyoto University, in Japan, is famously able to memorize the position of the numbers one to nine in random positions on a screen in as little as 0.67 seconds. No human even came close to Ayumu's performance. The scientists studying Ayumu suggest that chimpanzees simply have a better working memory for visual information than humans - which might explain why they can beat us in strategy games involving visual tasks.

The researchers who ran the computer game experiment suggest that it might also be the ultra-competitive mindset of the chimpanzee that makes them better at developing strategies. Chimpanzees live in a social world where they are often trying to outwit other members of their inner circle. Lower ranking males, for example, try to outwit the alpha males by having secret trysts with females behind their backs. Plotting and scheming might be second nature to chimpanzees.

Perhaps humans just don't have the level of fighting spirit (or desire for infidelity) that gives chimpanzees the edge in some battles of wits. Maybe in some cognitive realms our bias towards co-operating lets us down.

All of which leaves me wondering whether it's really fair to consider my young daughter to be any smarter than a chimpanzee. Chimpanzees lead lives that are not all that dissimilar from our own recent ancestors in the days before we invented, and were able to share our knowledge of, medicine, mathematics and physics. And much of the social behaviour, problem solving, and reasoning displayed by chimpanzees frolicking in the bush is still indistinguishable from children playing in the schoolyard. And, as we've seen, they even outperform humans at some skills.

In the end, though, it's not about who’s smarter. Both chimpanzees and humans have cognitive skills that help them survive in their own worlds. Over the next few years, my daughter's mind will blossom in uniquely human ways. She'll tap into her shared intentionality skillset, and join the ranks of schoolchildren learning their ABCs and capital cities. Thanks to her human mind, this knowledge will be transferred straight from her teacher's mind to hers through the medium of language. These skills don't make my daughter any smarter than a chimpanzee because smartness is a concept that is in the eye of the beholder.

From my very human perspective, experiencing my daughter wanting to share her thoughts with me is about the best thing in the whole wide world. I suspect chimpanzee mothers love their young just as deeply though, even if they can't – or don't want to – tell anyone about it.