‘Discovery Math’ is Weird but a Good Idea Nonetheless

This was brought to my attention by Jerry Becker
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From thestar.com, Saturday, September 3, 2016. SEE
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No, teaching math the “old-fashioned way” won’t work: Paul Wells
In response to the latest EQAO report, many parents insist that “discovery math” is the cause of low test scores in Ontario.
By Paul Wells  (National Affairs)
According to the latest EQAO report, half of Ontario Grade 6 students don’t meet the curriculum standard in math. That’s a problem. But it’s not the only one.

What worries me is that only 13 per cent of students who didn’t meet the provincial standard when they were in Grade 3 manage to catch up so they meet the standard for Grade 6. That’s the lowest number on that indicator in five years.

If you fall behind in math you stay behind. That’s why it’s important to get it right, not just at some vague moment in the future, but for kids who are in Ontario schools right now.

Fortunately, every parent in Ontario is sure they know how to teach math. Many parents want to get rid of “discovery math,” broadly defined as “doing it weird.” If only that loopy Liberal government would teach math the way we learned it when we were kids, the theory goes, there’d be no problem.

Sure, great, except for one thing. Very few parents I’ve met can perform more than the most rudimentary arithmetic for themselves. If you all learned math so well, why do you inch toward Junior’s algebra homework with a cross and a bulb of garlic?

Discovery math, to the extent it means anything, is an attempt to apply in a formal setting the insights about numbers that good mathematicians use routinely. People who are comfortable with numbers use all sorts of strategies to work with them. Confidently, through a kind of learned intuition.

So subtracting 272 from 836 is an altogether different proposition from subtracting 998 from

1,002. In the first case, you’re likelier to write it all out, solve the ones column first, carry 100 to the 10s column so you’re subtracting seven from 13, and so on. In the second case, I’d count up four from the lower number to the higher. It’s a really big drag on a kid to make her do the second problems the same way as the first. And parents who read “add to subtract” on a homework sheet, chuckle and roll their eyes, are committing malpractice.

This summer I made my stepson spend some time on Khan Academy, an educational website, to brush up his math before he enters Grade 8. He was briefly baffled by questions that asked, say,

6 1/4 – 3 3/4. One way to do it is to convert both sides to improper fractions. But it’s easier if you simply recognize that 6 1/4 is the same as 5 5/4. You can do the differences in your head in about two seconds.

The question is, how do you produce the kind of students who will make that insightful leap? All I know for sure is that you don’t do it by teaching a bunch of rules students will learn by rote – the beloved “old-fashioned way.” That may work for basic math facts. I did make our son practice his basic addition, subtraction and times tables one summer until he knew them from memory. I wish schools would take more time to nail those basic facts down. Since our school wouldn’t take the time, I did.

But very quickly, math becomes so complex you can’t have a rule for everything. Khan Academy teaches and tests 111 different skills at the fifth-grade level alone. You’d go crazy learning a rule for each skill. You must be able to intuit a useful method for each situation.

Modern curricula recognize, and try to teach, that flexibility. I refuse to say that’s a mistake. There is even empirical evidence it’s not. A March report from PISA, the international testing organization, found that in countries where students say they rely heavily on memorization, they scored starkly lower on complex advanced math questions than students who memorize less. “To perform at the very top,” the report concludes, students must learn to do math “in a more reflective, ambitious and creative way.”

What’s to be done about those declining EQAO scores? First, Ontario should support teachers by sharing best teaching practices more widely. In some countries, like Japan, teachers spend far more time mentoring younger newcomers to the profession, and sharing techniques among colleagues. Ontario schools should follow suit.

Second, support students by giving them more practice time. The only way to learn how numbers work together is by tackling incrementally more difficult questions, lots of them, over time. Kids need to practice insight just as their parents practiced times tables. If they do, they may just grow up knowing how to do math, not just how to complain about math teachers.

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Paul Wells is a national affairs writer. His column appears Wednesday, Friday and Saturday.
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ALSO THIS RESPONSE TO THE EARLIER POSTING, FROM Michael Paul Goldenberg:
It never appears to occur to either journalists or educational conservatives (or political ones) or to those deeply invested in undermining public education in the interest of turning it into a for-profit investment that curricula come and go due to fluctuations in standardized test scores, but the one sacred cow that is NEVER seriously interrogated is the testing process or its concomitant methods. Give me control of the tests and how they are scored and I ABSOLUTELY GUARANTEE that I can make results fluctuate to suit any political agenda and outcomes one might wish to see.
Mathematics itself has changed almost not at all when it comes to the content of K-12 curricula in most countries (and certainly in the US and Canada). Blaming decreasing test scores entirely on a teaching approach to math that is politically unpopular misses almost entirely that if assessments are skewed away from the kinds of thinking that teachers are trying to help students develop, it’s a slam dunk that scores wlll go down. And when assessments are developed to reflect more conceptual understanding (and scores go up), the conservatives and nay-sayers scream that the tests are “fuzzy.”
Once this sort of politicization of education is allowed to dominate the conversation, as it clearly is doing in this article and in many of the accompanying comments, there’s no chance for thoughtfu educators to pursue anything but lock-step, computation-dominated “math” teaching. Only that’s not math, and my Smart Phone does all of that vastly quicker, more accurately and more easily than nearly every human who has ever lived or ever will. If you want
 kids to be adept at replicating donkey arithmetic, so be it, but no one I teach will be encouraged to limit herself in that way.
Published in: on September 15, 2016 at 10:20 pm  Comments (1)  
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  1. […] I recommend looking at different ways to teach mathematics. Here is one take on the topic, from our friends up north. I reprinted this on my mostly-education blog, here. […]

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