Left to their own
devices, kids discover strategies that make math meaningful.
Unfortunately, however, kids are often taught that these strategies are
At least, that's what happens in Western countries like the United States and France--countries where students spend a lot of time being drilled on the mechanics of calculation. Kids are chastised for counting on their fingers because this is somehow viewed as cheating. So are kids who use shortcut strategies to solve problems.
For example, Dehaene says, a child might solve the problem
By recalling that 6+6 =12 and that 7 is one more than 6. Ergo, 6+7 = 13.
Or, Dehaene says, consider this example from an experiment conducted by Jeffrey Bisanz.
Bisanz presented American 6 year olds and 9 year olds with this problem:
5 + 3 – 3 = ?
The 6-year olds tended to solve this without doing any calculations. They just observed that the positive 3 and the negative 3 cancel each other out.
But the 9-year olds (who had learned from their teachers what the "right" approach was) were more likely to take the long route to the answer:
5 + 3 = 8
8 - 3 = 5
In other words, 9 year olds had learned that they should follow the teacher’s procedure first, and think later.
This reminds me of my own childhood, when I was learning multiplication. What is 7 x 8? If I couldn’t remember, I’d add together a string of seven 8s. Since I hated memorizing my timetables, I ended up doing a lot of sums.
Hardly a clever shortcut, and it was prone to error because I’d sometimes lose track. But I’ll say this for my slow-poke approach: It helped me understand the meaning of multiplication. It made things very concrete and intuitive.
According to Dehaene, one of the most common errors that kids make when presented with simple multiplication problem like
7 x 8 = ?
is to add the two numbers together:
7 x 8 = 15
So what’s worse? Using the clumsy-but-meaningful strategy of adding up a string of 8s, only to miscount and come up with 7 x 8 = 48?
Or misunderstanding the whole point and adding together 7 and 8?
Dehaene favors meaning. When kids are trained to emphasize procedures over meaning, they fail to develop an intuitive sense of number.
And that leads to all kinds of trouble...confusion, boredom, a poorly developed number sense, and (perhaps) a lifelong dislike of math.
Dehaene’s tips for making math intuitive
Dehaene argues that we can foster our children’s sense of quantity by grounding mathematics knowledge in concrete, familiar situations. For instance, when we teach our kids subtraction, we can present kids with the concrete operation of removing apples from a basket.
And here are more recommendations from Dehaene:
• Let kids count on their fingers
• Teach kids about fractions by having them envision the division of a pie
• Teach kids about negative numbers by having kids think of temperatures.
Negative 5 may not mean much in the abstract...but how about 5 degrees below zero...?
Humans aren't the only ones with a bit of number sense, and even
human babies can perform certain mental calculations. For more
information, see my evidence-based guide to the
development of number sense.
In addition to highlights of the latest research, it includes more research-based for encouraging math skills in young children.
Dehaene S. 1997. The number sense: How the mind creates mathematics. New York: Oxford University Press.