“Her is a bad guy!” This is a nerve-racking moment, not the first and not to be the last. My son Henry is describing the squid-witch Ursula, from Disney’s “Little Mermaid”, to his brother Jack. “She” is one of the most common words in the English language, but Henry has botched it and come up with “her”. He has just turned four. He should be able to use “she” properly at his age. Is his bilingual upbringing holding him back?

My wife is Danish; we met and married in New York. I sweated to learn Danish partly because she emigrated to be with me; I wanted to make the deal fair and be part of her world too. If you don’t speak a person’s native language, there’s always a corner of their mind you can’t quite reach. But everyone who has learned a language in adulthood knows how hard it is, with the grammar books and the flash cards, the pronunciation problems and the awkward rhythm, never quite getting to fluency. How much better to raise a genuine bilingual.

Plenty of parents have come to that conclusion. The new German-English state school near us in London is full to capa­city. The French-English bilingual programme in our old neighbourhood in Brooklyn is crammed to the rafters.

Parents normally use one of two strategies to make sure the minority language sticks: either “one parent, one language”, or “one language at home, the other outside”. Neither would work for us, as Jack is the offspring of a previous relationship, and speaks only English. But while my wife speaks English to Jack, she has stuck to speaking only Danish to Henry.

“Daddy, come heredown!” Like all bilingual kids, Henry sometimes uses the words or grammar of one language in the other. Kom herned is perfect Danish, but “come heredown” is goofy (if cute) in English. Bilinguals hit developmental milestones at the same rate as their monolingual peers. But they are prone to errors, and their total vocabulary is divided between two languages. So they usually lag behind slightly in the vocabulary of the schooling language. When these kids get to school, many teachers, with the support of doctors unfamiliar with the research, begin telling parents to speak only the majority language with the child – and many parents give in and do so.

A century ago, bilingualism was blamed for lower IQ scores among the children of non-English-speaking parents. The culprit was poverty, not bilingualism. But researchers may also have been influenced by the fear that language diversity would interfere with nation-building. A good American speaks English. By faulty syllogism, this meant that a second language made a bad American, so educational policy set about creating a nation of monoglots.

Today, the prevailing wisdom has been flipped on its head: researchers now propose a “bilingual advantage”. The godmother of the field is Ellen Bialystok, a researcher at York University in Canada. She has found that native bilinguals (that is, not someone who has picked up passable French later in life) show cognitive strengths relative to monolinguals. Such benefits are thought to be a result of the constant mental exercise of switching languages regularly and always having to inhibit one. She has found that bilinguals develop dementia, on average, four years later than monolinguals. Other researchers have found that bilinguals seem to recover brain function better after strokes. But for parents, who after all worry more about the start than the end of a child’s life, there is another purported benefit. Bialystok has found that bilinguals seem to have better executive function – the ability to plan and carry out complicated tasks.

For example, researchers assign a “Simon task” where subjects are to press a button on their left if the word “left” appears on the screen, and the button on the right when “right” appears. This is simple – except when the word “left” appears on the right side of the screen, and vice versa. Bilinguals are better at it than monolinguals. Roberto Filippi of Anglia Ruskin University has also found that bilingual children are better at tuning out distracting spoken language in the background.

The research is contested. Some studies have proved hard to replicate and Filippi (who, besides having found several advantages in his research, is raising his children bilingually) has, in one study, found bilinguals actually performing worse on a single task. But in today’s distracted world, parents are inclined to latch onto anything that might keep the child focused on that calculus problem and ignoring the nearby smartphone.

It’s an OCT-topus! Henry now has an English accent at nursery, showing off his stuffed octopus to his friends with a lilt that would please the Queen. At home, he speaks in the same American tones as my other son and I do. Many bilinguals say that they feel like different people in their different languages; we already see signs of Henry instinctively modulating his intonation according to his context.

Some people even report that the languages themselves impose different personalities on them, and that each language has its own spirit. Many people think German is logical, Italian is romantic and English is practical. Two early-20th-century linguists, Edward Sapir and Benjamin Lee Whorf, hypothesised that a person’s language strongly influences how they see the world (Whorf had studied Amerindian languages with very different structures). It is a romantic notion.

But in the second half of the 20th century, the intellectual pendulum went the other way. Noam Chomsky theorised that human language is a single phenomenon, with relatively trivial surface differences between languages. Researchers today have begun rehabilitating Sapir’s and Whorf’s ideas, but the results they find fall short of the notion that Russian, say, encapsulates an entirely different worldview from that of English. They find, rather, that different languages may force people to pay attention to things they otherwise wouldn’t – such as different levels of formality, in languages that have both a formal and an informal word for “you”. Russians are faster to distinguish two shades of blue – by a tenth of a second – if those two shades correspond to two different words for blue in Russian. Interesting, but hardly a “worldview”.

There is a simpler reason why languages may feel different to people. A language spoken only by family in the home may evoke the culture of home and feelings of warmth, and a language spoken at work may prime serious thinking and businesslike attitudes. In other words, it may have less to do with the structure of the language itself (say, that Spanish is “warm” and English is “serious”) but with associations (American Latinos think of friends and family and relax when speaking Spanish; they mentally “button up” when speaking English).

Hvad tænker du på? Henry has fallen in love with asking (usually in Danish) “What are you thinking about?” It’s possible that his bilingualism makes him more curious about others’ thoughts. In one study, bilingual children did better on a task testing “theory of mind”. This is the knowledge, still developing in small children, that others have minds with different contents. Researchers placed three different-sized cars in the child’s view; the smallest car was hidden from the researcher’s view by a screen but could be seen by the child. When the researchers asked “can you hand me the small car?”, the bilingual children were better at realising the researcher could not see the smallest car, and so handed over the second-smallest. The theory is that bilinguals are constantly working out who speaks what to whom around them, and that this strengthens the habit of paying attention to other minds generally.

Languages learned imperfectly in adulthood – like my Danish – have not shown this effect in the lab. But they may still open the mind to other perspectives. Learning a second language as an adult is usefully humbling: there is nothing quite like being corrected by a three-year-old native speaker. A second language acts as a constant reminder that other people have different knowledge, different points of view from one’s own.

Some writers have purposely adopted another language to expand their own minds. Conrad, Nabokov and Beckett are best known for their work in non-native languages. Conrad held the romantic view of Sapir and Whorf, saying he had been “adopted by the genius” of English. But Beckett had another motivation: his career had not taken off. English was a “veil that must be torn apart”; he wanted to “sin against” it. Switching to French forced him to write in a radically new way. Jhumpa Lahiri, unlike Beckett an award-winning writer in her native English, has nonetheless also forced herself to begin writing solely in Italian.

Intriguingly, people do indeed seem to think differently in a language they have learned after the infant years. They may think more consciously about the language itself. Many people report their first real understanding of grammar upon learning a second language. And they may think differently when working in those second languages. Psychologists have found that they answer test questions more deliberately. In one study, they had more success in avoiding cognitive traps: when asked a question with an obvious answer that happens to be wrong, they were better at thinking twice and reaching the non-obvious but correct answer.

“Snoofy speaks Danish and Eng…Engl…English!” Having struggled through the tricky consonant cluster in the middle of “English”, Henry holds his stuffed toy dog up for me to say goodnight. He’s going to be fine. Just before his fourth birthday he began talking explicitly about his two languages. He knows which books are in which languages. He knows Danish is mommy’s language and English is mine and his brother’s.

More importantly, he has reached another milestone. Snoofy is a cipher for his emotions: Snoofy is tired when a certain little boy is tired; sometimes Snoofy doesn’t want any more vegetables; and now Snoofy is an out-and-proud bilingual. “Good night, Snoofy. God nat, Snoofy,” I say dutifully, and kiss him on the head. Henry beams.

I’ve never managed to brave the difficult early-19th-century Danish of Hans Christian Andersen’s original “Little Mermaid”. But Henry will graduate to it one day. In the Disney version (spoiler alert!), Ariel happily marries her prince. In Andersen’s, the prince falls in love with another woman, and the heroine is promised that she will return to mermaid form if she kills him. She refuses, instead nobly dooming herself to become a “spirit of the air”.

A little can-do American optimism, a little Danish grit in the face of life’s harsh realities. If Henry acquires both of these, we will have done our job.