This article from The Toronto Star exemplifies the ever-pervasive group-think about why the traditional method of teaching math won’t work.
From the article:
“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?”
First of all, not all parents are like that. Second of all, there are some aspects of math that parents haven’t done in a while, so they are rusty. Unless you use something often, you forget how things are done. I myself have to brush up on percentages if I haven’t worked with them for a while. Same with calculus, linear algebra and other topics. It doesn’t stand as proof that the traditional method failed. Also what does he mean by “very few parents I’ve met”?
He goes on:
“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?”
Khan Academy is very traditional–a detail this author conveniently ignores. And recognizing that 6 1/4 is the same as 5 5/4 comes after being instructed in the procedure (which Khan provides) and practicing with it. It doesn’t come intuitively for most people. So that “insightful leap” as he puts it, is more like procedural fluency giving way to doing it in your head–as he likely learned it years ago.
He goes on:
“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….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.”
And many of these skills grow from basic traditional instruction in procedures which give way to transfer. He ends on this note:
“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 what he means by practicing insight is practicing procedure which in many cases leads to understanding, well then: I guess he and I are saying the same thing: Traditionally taught math works well.
traditional math 
This journalist’s opinions are certainly interesting. However, Canada’s experiment in moving away from more traditional forms of maths instruction is perhaps more interesting. I am cautious about drawing between-country comparisons on PISA but looking at the same country over time can be instructive. Many Canadian provinces seem to be significantly declining on PISA maths and this seems to correlate to a shift towards the kinds of teaching that feel right to this journalist. And this is on a test designed by maths reformers that favours real-world examples over abstract calculations.
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Paul Wells is a walking talking contradiction on this one. He eschews the virtues of traditional math instruction by insisting his own kids master the basics AT HOME, yet supports the Ontario math curriculum which devalues these same methods. Must be nice to be a national columnist to sound off on your own “opinion” and at the same time practically namecal.l those who want decent math instruction for their own kids to be taught in the classroom. No evidence to support what he’s saying is even factual. And even if it’s fiction, he’s harming kids by making these false assumptions.
Shameful, in my opinion. And yes, I have let him know that.
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It’s very telling that, first the Star does not allow comments on this piece. Then he’s complaining on Twitter that he’s getting more email on this piece than most he writes, and he tweets gloatingly about his article. So I “engage” him with a series of responses to his tweets. He does not respond to me — but tweets a snide remark about one of my tweets, being sure not to tag me, apparently hoping I don’t see the response.
What has happened to the profession of journalism? Do they really think their own voice is so important it’s unnecessary to engage with the proles — even those with PhD’s in the very subject under question?
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Yes, this is a reflection of modern journalism and is another example of Crighton’s “Gell-Man Amnesia Effect.” In our big regional newspaper, their main educational journalist does not have a degree in education, math, or science. When I once critiqued one of her articles (opinions? Journalists can’t seem to keep them separate anymore.) from a STEM perspective and raising very specific questions, she told me that she respects the views of many teachers she knows very well. This is what journalism is now all about. They can’t properly pick experts from two sides of an issue – or they just don’t care to do so. Too many journalists without content knowledge seem to think they have the expertise to become commentators on any subject. That seems to be their desired career path over a focus on “mere facts.” Journalism is now all about celebrity, pushing hot buttons, and ratings.
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I was going to go into a more detailed analysis of the article, but there are too many problems just from an analysis (STEM, math, critical thinking?) point of view, no matter which side I’m on. Note that the article is in the section called “News – Canada”, when it’s clearly filled with bias and opinion.
“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.”
Bwa Ha Ha! Did you ask any of us STEM experts? We are the ones ensuring mastery of basic skills at home (thereby increasing the academic gap) to make up for all of the silly hands-on “learned intuition” discovery done at school. We are the parents who create most of the students properly prepared for STEM careers. Ask us. It’s easy. Have schools send home questionaires. We don’t just turn off the TV and model a love of learning. We ensure basic math skills. In 7th grade and after, when my son (finally!) got into traditionally taught AP Calc track classes with proper textbooks, there was no problem at all. I didn’t have to do anything at home. The students I tutor in high school need help only to fix issues left over from K-6 – missing skills and the inability to properly do complete homework sets. They are too used to in-class group work and almost no individual homework problems.
“It’s a really big drag on a kid to make her do the second problems the same way as the first.”
I’m going to puke. He doesn’t have a clue, so what makes him think he does? Is that what journalism teaches (like ed school) – that content doesn’t matter – that only the process of teaching or the process of journalism matters? Is the goal of journalism just to find a good hot button hook? What about the process of finding proper experts on both sides of an issue?
“The question is, how do you produce the kind of students who will make that insightful leap?”
Wrong, wrong, wrong. Ask a content expert.
“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.””
Of course he knows “for sure” because he’s a journalist and all of those other parents he disagrees with (and stereotypes) do not. I thought that journalism taught students how to dig for facts and not opinion.
“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.”
Ding! Ding! Ding! Ding! Ding! Did any of your “discovery” bells go off? I used to get notes from my son’s school telling us parents to work on basic “math facts” at home. That is incompetence and is THE major problem in math education. Forget discovery. If schools fixed this mastery problem, then the standardized test scores would be so much higher that nobody would be talking about discovery. When my son was in pre-school I decided I wanted him to have more than what I had in math long ago. Then I found out that our school used MathLand. They got it completely wrong. I got to calculus without any help from my parents. That can’t happen anymore.
“But very quickly, math becomes so complex you can’t have a rule for everything.”
Like starting in Kindergarten. That’s because it’s always more than rote. Always. It may be partial understanding, but understanding comes in many levels and it’s always there in each grade. Many just don’t notice it anymore in the early grades. It’s there, and it comes from practice and mastery of basic skills. Skills are NEVER rote.
“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.”
Give them more practice time? It’s just an issue of time allocation? Let me see. Traditional math textbooks assign nightly (individual!) homework sets that have to be turned in. Tests are given for those skills (and understandings). The teacher directly teaches those skills and tries to keep everyone at the same level. In K-6, students usually have almost an hour each day for math, but most of the time – by definition of modern fuzzy math – it’s used up on hands-on group discovery projects. It’s the fuzzy discovery math that specifically denigrates individual skills and takes away that time. On purpose!
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Bravo, you have absolutely nailed the problem here in a clear and eloquent manner. Thank you for taking the time to respond. I hope you don’t mind if I quote part of your response in future discussions on this subject.
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Go ahead and quote. I’ve been dealing with this issue since 2000 when my son was 4 and I decided that I wanted more for him than what I got from my traditional math schooling in the 50’s and 60’s. Then I found that my son’s school was using MathLand. They got it completely backwards!!! Then they complain that we older parents just want what we had when we were growing up. Do they ever ask us? No. All I remember is an open house for MathLand where the first grade teacher directly (!) lectured us parents (many of whom were STEM graduates) on the benefits of having our children explain why 2 + 2 = 4 and write about their favorite number. Then they switched to Everyday Math which was not much better. I had to help my son at home with mastery and then in fifth grade the school couldn’t quite explain why many bright kids still didn’t know the times table and why some still used their fingers to add 7+8.
Go ahead and teach the fuzzy stuff and claim how much you love the balance of understanding and skills. Does it work? No. Either skills matter or they don’t. Apparently, their job is to spiral (circle with repeated partial learning) through the material with Everyday Math and then blame the kids, parents, peers, society, lack of engagement, or whatever when it doesn’t work. If you pass the kids along each year and wait long enough, the kids will even blame themselves. I’ve heard bright kids specifically tell me that they are stupid. Go ahead and focus on engagement, “critical thinking” and happiness in math. The students might like math until they can’t pass the traditional college algebra or trig course required to get the degree they want. It doesn’t matter because they will be long gone.
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