But what you said about the students- It’s not really true, is it?

It’s true. Not of every student in the entire world, of course, but certainly true of the majority of my (as I noted in that presentation) remedial Algebra students.

I would even go so far as to label them ‘desperate for a really good product but doubtful any teacher can provide it.’

Why are they “desperate?” Do your two different approaches and spiraled homework make them desperate to know more about mathematics?

I don’t want student gains best expressed through poetry. I want my students to know the difference between quadratic, exponential, and linear functions.

My students out-performed and out-paced my department. Not the departmental average. The entire department.

I would like you to meet us in the middle, man.

It’s this revolutionary: if a problem claims to be an application of math to the real world, let’s make sure both the real world and the problem solving process of real people are accurately portrayed.

No one’s winning any comparisons to John Dewey with that kind of pedagogy.

If I don’t blog about assigning twenty problems of classwork or teaching trinomials with the box method, it’s because that stuff is easy. Making them desperate for math, though, that’s the real trick, innit?

Your crowd is with you. You slay them with patient problem solving and minimalist digital design.

I know it was for comedy. But I’d like to deeper look at that statement, knowing full well that devil’s advocate is just…ungrateful. I have literally pillaged your site for material and deeply admire your thoughtfulness.

But what you said about the students- It’s not really true, is it? And neither is this propagated misconception that weepy films like ‘Waiting for Superman’ try to sell. It’s either a) students are disengaged and hate math or b) students are heros tragically let down by unwise, avaricious adults.

Taught math for five years in NYC and Chicago. Never once would I describe my occasionally challenging populations as a market ‘not wanting’ the product I was selling but ‘forced to buy it.’

I would even go so far as to label them ‘desperate for a really good product but doubtful any teacher can provide it.’

It’s these ideas that make people tilt their head and look at you teary-eyed when you tell them you teach math in the city. ‘That’s just so nice of you’ or ‘How do you do it? Isn’t it dangerous?’

WCYDWT is creative and engaging. It is unlike anything I’ve taught. It is- and I love this- fascinating.

Your Feltron project write-up, though, troubled me. How much time was wasted while doing that if just over half even completed the assignment? How much time is wasted in WCYDWT in general? And don’t come back with something like,’ Ah, but the gains were ineffable. My precious students learned how to think…’

I don’t want student gains best expressed through poetry. I want my students to know the difference between quadratic, exponential, and linear functions.

How do we do this? Simple strategies. Show them two different approaches to the same problem simultaneously. Spiral homework every night. Do not rely on discredited research like ‘learning styles.’

I would like you to meet us in the middle, man.

Problems are the fundamental unit of measurement from which all organization flows for math instruction. If you research top scoring countries, its not their method of instruction that has commonalities, its their problem design.

Sean: First, why is this data meaningful? The short answer: it is not. But to assume that the student is not engaged in or cannot learn something algebraically meaningful is not true.

Sure. But whatever algebra the student learns must be balanced against the cost of using unreality to try to prove to students that math is used in reality. The cognitive dissonance is so dangerous I’d so much rather tell my students, “I have two numbers sealed in this envelope. They add up to 400. And when you double one number and add it to seven times the second, you get 1700.”

If we really can’t find a natural context for systems of equations, it does us no good to force an unnatural context.

I do not like this problem. There is not a sillier, more contrived context. But, in fairness to you, how different is that from seconds gained or lost taking the stairs?

I’m trying to figure out if you’re talking about my escalator problem. I’m happy to explain the difference but only if I’m not misreading you here.

Many textbooks present artificial (often comically bizarre) situations for systems . From your writings, I know this drives you mad. It does me, as well. Something like:

‘You sell 400 tickets to the school production of ‘My So Called Life.’ You made $1700. Student tickets cost $2 and adult tickets cost $5. How many adult tickets did you sell? How many student tickets did you sell?’

First, why is this data meaningful? The short answer: it is not. But to assume that the student is not engaged in or cannot learn something algebraically meaningful is not true.

Second, there are dozens more creative ways of figuring this out than setting up a system of linear equations.

Let the students explore them! Provide them with a highly structured problem like this. Have them solve it in three ways. In six ways. Have them solve it in a way that their little sister would understand. Have them solve it in a way that would impress a math teacher. Have them solve it as if they were trying to explain it to their past selves.

And if you much teach systems, and you must use this problem, dig deeper into it. Do not make your students robots so that they recognize a problem-type, rather than a context. Persistently- annoyingly even- make them think about what each component of the problem represents. Engage the process and not the answer.

I do not like this problem. There is not a sillier, more contrived context. But, in fairness to you, how different is that from seconds gained or lost taking the stairs?

Sean: I am interested in your vitriol towards textbooks. Textbooks are created by experts in the field- a panel comprised of dozens and dozens of committed, educated professionals- many at the forefront of math education. While their design and layout is troubling (see dog, handkerchief) there are often excellent activities that provide structure around important concepts.

Sometimes textbooks present interesting problems in helpful ways. Too often, though, textbooks ask students to pseudo-solve pseudo-contexts. Which is to say, they present real-world problems where math only applies if you suspend your understanding of the real world and and students are supposed to solve them in this weird structured way that in no way resembles how real people (or real mathematicians) solve real problems.

If we were talking about one small-cap company, I’d probably lay off a little. But this a multi-billion dollar industry that defines pedagogy in the U.S. I don’t think there’s such a thing as too much scrutiny here.

You’re an enormous influence. Thank you. Used the ‘How I met Your Mother’ bit in my summer school section. It uplifted an otherwise dry five hours. Curiously, they didn’t need clarification that the data was made-up. Of course it is, one girl said, no way you had ten girlfriends.

I am interested in your vitriol towards textbooks. Textbooks are created by experts in the field- a panel comprised of dozens and dozens of committed, educated professionals- many at the forefront of math education. While their design and layout is troubling (see dog, handkerchief) there are often excellent activities that provide structure around important concepts.

In other words, it’s not all 3x + 12 = 9.