A new study creates a mathematical model of teaching to show how the exaggerated sounds of “parentese” helps babies learn language.

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Baby talk — uttered in that singsong, high-pitched voice parents often use when speaking to infants — has long been seen as a way to boost language development.

Pioneering studies by Patricia Kuhl, co-director of the University of Washington’s Institute for Learning & Brain Sciences, found that baby talk exaggerates certain vowel sounds, making them easier to tell apart.

Babies whose parents often use “parentese” knew more than double the number of words by their second birthdays than babies whose parents did not.

That would suggest that baby talk is an effective form of teaching, but there also is a long history of research arguing the opposite. For example, some studies have shown that baby talk also squishes some vowel sounds closer together, which would seem to make them harder to tell apart.

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Now mathematicians at Rutgers University have weighed in on the debate in a new study that uses computer modeling to test whether baby talk is well designed for teaching.

That grabbed my attention because we’ve learned a great deal in the last few decades about how people learn, but we know very little about how they teach.

To help explain what the researchers were doing — their study involved something called a “Dirichlet process Gaussian Mixture Model” — I called the lead author, Patrick Shafto.

First, he helped me understand how a computer learns something new, like how to play chess.

If you feed a computer lots of examples of how past chess games have unfolded move-by-move, and then give it a procedure for detecting statistical patterns in that data, the computer will be able to make predictions about the moves that will most likely win a game.

The bigger the database of past games, the better.

But what if you wanted a procedure that would enable a computer to teach another computer how to play chess? In other words, how would you teach a computer to be a teacher?

In that case, the teaching computer would start with the same big database of games, but instead of just dumping the whole set on the learning computer, it would create a very small collection of games to get the learning computer to understand how to win as quickly and efficiently as possible.

Shafto’s team came up with such a procedure, not for teaching chess, but for predicting what baby talk would sound like if it were designed to teach language.

And instead of feeding chess games into the computer, they used part of an existing database of adult speech recordings that have been converted into numbers representing the sound frequencies that make up a dozen English vowels.

They found that the teaching computer chose samples from that speech data that were remarkably similar to the exaggerated vowels of baby talk.

And while that meant that others vowels got squished, it gave the learning computer a better chance of identifying the correct vowel sounds than if it had sampled the data without any guidance.

Do human parents use baby talk to do that, too? That seems to be the case, but how isn’t well understood.

“It’s not something you did consciously, but it automatically gets optimized for the learner to help them along,” Shafto said. “How we know this is a great mystery that I don’t have any answers to.”