Early math can’t be just ‘exposure’

Math doesn’t have to be boring, opines the New York Times.  The editorial recommends “very early exposure to numbers,” better teacher prep, better integration of engineering and “real-world” connections, opines the New York Times.

The Times shows a striking naiveté, responds cognitive scientist Dan Willingham.  To start with, exposing kids to numbers in preschool won’t help.

Math is not learned like a language. Children can learn vocabulary and more complex syntax by mere exposure. They can’t learn math that way.

Early learning is important, he writes. American kids tend to be  “okay (not great) on math facts and okay (not great) on algorithms. On conceptual understanding, they are terrible.”

This conceptual understanding ought to start in preschool with ideas like cardinality and equality. “Very early exposure to numbers” is not going to do it. That doesn’t mean taking what we had been doing in first grade and asking kids in pre-K to do it. That means putting activities into pre-K (e.g., games and puzzles that emphasize the use of space) that will provide a foundation for conceptual understanding so that first-graders will be in a better position to understand what they are doing. (Though first grade math will also have to change for that happen.)

In calling for “better teacher preparation,” the Times focuses on high school.  Getting more physics majors to teach high school physics isn’t the main problem, Willingham writes.

Most American teachers—like most American adults, including me–don’t have a deep conceptual understanding of math. They are a product of the system we are trying to change. You cannot teach what you don’t know.

We need “to train teachers in the conceptual side of math” so they can help children understand how math works, Willingham writes.

Why am I blogging when I’m supposed to be in Iceland? Because I left my purse on a shuttle bus from the rental car center to the terminal at Logan Airport. Many people tried to help,but it took more than five hours to track down the purse at the MassPort bus dispatcher’s office. My passport, cash, credit cards,cell phone, etc. were all there. Conclusion: Bostonians are nice people. I am stupid.

We’re trying again this evening.

About Joanne


  1. Does Willingham really believe “Children can learn vocabulary and more complex syntax by mere exposure?” That’s a shockingly irresponsible statement, even from Willingham.

    • Mark Roulo says:

      Maybe we are talking at cross purposes … how much formal training in vocabulary and syntax do you think kids typically got in, say, 1800?

  2. Actually, children DO learn the vocabulary and syntax of their native languages by exposure. And also of second languages, if begun early enough. The proof is that no-one teaches these things explicitly to children under 3, and yet they learn them. And most of the vocabulary that they learn even when school-aged, they learn through exposure.

  3. What a nightmare about your purse! I’m glad you found it and wish you well on the remainder (that is, almost all) of your vacation!

  4. You know (and I’m sure people are sick of me saying this), we USED to know how to teach math. Along with many of my peers, I got math through calculus in high school back in the 1970s. I understand that the kids of today aren’t exactly the same as kids back then, but certainly their innate ability is exactly the same. Why can’t we go back to teaching math the way we used to, back when it actually worked?

    On the other hand, I think I know the answer. Yes, we probably could see some gains by going back to tried and true methods, but the big change is in our society, which no longer values learning, education or hard academic work of any sort. You can’t expect a kid to buckle down and work when everyone around them is giving them the opposite message.

    We had a good run for a couple of centuries, but -short of some sort of probably unpleasant revolution- I guess we’re done. It’s just sad having to watch it fade, knowing full well that there was no good reason for it.