Have you read Dale Carnegie's How to Win Friends and Influence People? If you are a math prof, I'll wager that your answer is "No". Maybe that might explain the unpleasantness that occurred during a math conference in Alberta. (The conference was over a year ago. I was not there, so my comments here are second hand, but my information comes from a reliable source.)

In attendance were both mathematicians and school teachers. During the proceedings, a few mathematicians took to the stage and panned both the math curriculum and the teaching methods being used. In effect they dressed down the teachers and told them how they should be doing their jobs.

I guess this happened more out of arrogance than malice. Yes, I do know that arrogance does not invalidate the professors opinions, but it makes me think twice about any advice they might offer.

A lot of math profs agreed with the criticisms raised at the conference. I too have opinions about curriculum and teaching methods, but I would expect a school teacher to be very skeptical about my advice. And there would be a good reason to be skeptical: unlike school teachers, I have not been taught how to teach, and neither have most of my colleagues. This does not mean that our opinions are automatically wrong, but it sure casts a shadow over them.

Here's the problem. Some math profs have done a lot of teaching and have even become quite good at it. And like most people, they like to dispense the wisdom that they have garnered from their experience. Fair enough, but that experience is limited to university courses whose class members are not typical school students but are, in fact, the cream of the crop. Although the profs may have developed some very good teaching practices, those practices are geared towards university students and likely won't transfer well to a K-12 classroom.

(Is there not a little irony here? We mathematicians haven't even been trained how to teach at a university, and yet we are willing to issue directions about how to go about it in a vastly different setting.)

But there must be some value in what math profs say about math education: after all, they are experts at mathematics. This is a slippery argument, and you may have come across something like it before. It appears in different forms:

"I'm the CEO of BigOilCorp. Climate change is bunk."

"I'm a certified marriage counsellor, and I know what I'm talking about. Children should be spanked for bad behaviour."

"He says that the Edmonton Oilers stink. He has a degree in sports journalism, so he must be right."

OK, so you may on board with that last one, but the reasoning is faulty. It's called "argument from authority" and in its undisguised form it goes like this:

- So-and-so is an authority about topic X.
- So-and-so makes a statement about topic Y.
- Therefore the statement must be correct.

Being experts at mathematics in no way confirms that our opinions about how to teach it are valid. Appealing to our mathematical expertise is simply an argument from authority.

But why are math profs so ready to be critical? I have some thoughts about that.

Some say that their children have not learned the basics in elementary school. It's difficult to comment about this because it is so personal, but it is a concern held by a much larger group of people.

What I am about to say may be educational heresy. I think there will always be a substantial number of children who will have difficulties with math. It was true when I was a student, and it was true when my children were students, and it is true now that my children's children are students.

I don't think the problem is wholly dependent on either the curriculum or the way it is being taught. From talking to my grandchildren, and from what I have learned from school teachers, (and also from a brief examination of the K-6 curriculum), my own conclusion is that students today

*are*being taught the basics, just in a different way than we were.
On a less personal level, some professors are concerned that students entering university have not mastered the fundamentals. They perceive that students arriving at university from high school today are not as adept at mathematics as they themselves were in the past. As long as I can remember, math profs, including me, have held that view. (And in fact you can go back 100 years and read the same complaint.)

When I first started teaching, our department's concern led to an "advisory exam" that we gave to first year students to check that their background was sufficient. Sometimes it wasn't, and our conclusion then was pretty much the same as what math profs conclude now: there must be a problem with the way math is being taught in school. Sigh. Perfectly logical mathematicians affirming the consequent.

There is another thing that bothers some mathematicians. They are worried about Canada's falling rank in international math tests, you know, those PISA tests that have caused so much panic. Some trace the decline back to the introduction of our current elementary math curriculum along with the teaching methods that support it. I don't know if its true that a majority of math profs agree with that viewpoint, but a good many have signed a petition that promotes it, so I assume that plenty actually do believe it. Sigh. Post hoc, ergo propter hoc.

I don't personally think that there is a problem with our PISA rank, but that's a topic for a later discussion. However, in the meantime I would point you to an article by Joanne Jacobs. Take a look at this question:

Did this spark a WTF moment for you like it did for me? Well, what is happening here is that the children are being asked to compute 8 + 5 by splitting the 5 into 2 + 3 as follows:

8 + 5 = 8 + (2 + 3) = (8 + 2) + 3 = 10 + 3

There's no mystery here: As the teacher's feedback says, take 2 from the 5 and add it to the 8. That's what "making 10" out of 8 + 5 means. It's a method for addition that doesn't rely completely on rote memorization, and it is one of the strategies that some think confuses the children and contributed to our reduced PISA score.

The comments following the Joanne Jacobs post are worth a look. Although there is the expected outrage, at least one person pointed out that "making 10" is one of the strategies taught to the kids in Singapore. And if you have been following the articles about the PISA math test, you know that Singapore ranked much higher than Canada. I find that somewhat thought-provoking.

That's it. Now, if I could just remember where I put that Dale Carnegie book.

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