I asked you, Teoh, please recall a time when you really love something a movie, an album, a song or a book, and you recommended it wholeheartedly to someone you also really liked.

And you anticipate that reaction.

You waited for it and it came back and the person hated it.

So by way of introduction, that is the exact same state in which I spent every working day of last six years.

I teach high school math.

I sell a product to a market that doesn't want it but is forced by law to buy it.

I mean, it's kind of it's just a losing proposition.

So there's a useful stereotype about students that I see Ah, useful stereotype about you all.

I could give you guys, uh, Algebra two final exam, and I would expect no higher than a 25% pass rate.

And both of these facts say, Say less about you or my students than they do about what we call math education in the US today.

To start with, I'd like to break math down into two categories.

One is computation.

This is the stuff you for gotten.

For example, factoring quadratic with leading coefficient greater than one.

Okay, this up is also really easy to relearn, provided you have a really strong grounding in reasoning, math, reasoning.

We'll call it the application of math processes to the world around us.

This is hard to teach.

There's what we would love students to retain, even if they don't go into mathematical fields.

This is also something in the way we teach it in the U.

S.

All but ensures they won't retain it.

So let's talk about why that is why that's such a calamity for society, what can do about it and to close with why this is an amazing time to be a math future.

Okay, so 1st 55 symptoms that you're doing math reasoning wrong in your classroom.

One is, ah, lack of initiative students don't self start.

You finish your lecture block and immediately of five hands going up, asking you to re explain entire thing at their desks.

Students lack perseverance.

They lack retention.

You find yourself re explaining concepts.

Three months later, wholesale there's an aversion to word problems, which describes 99% of my students and then the other 1% are eagerly looking for the formula to apply in that situation.

Okay, this is really destructive.

David Milt, a creator of Deadwood and other amazing TV shows, has a really good description for this.

He swore off creating contemporary drama shows set in the present day because he saw that when people fill their mind with four hours a day of, for example, 2.5 men, no disrespect.

It shapes the neural pathways, he said, in such a way that they expect simple problems.

He called it an impatience with irresolution.

You're impatient with things that don't resolve quickly.

You expect sitcom sized problems that wrap up in 22 minutes, three commercial breaks and a laugh track, and I'll put it to all of you.

What, you already know that no problem worth solving is that simple.

I am very concerned about this because I'm gonna retire in a world that my students will run.

I'm doing, I'm doing, I'm doing bad things to my own future and well being.

When I teach this way, I'm here to tell you that the way our textbooks, particularly mass adopted textbooks, teach math, reasoning and patient problem solving.

It's functionally equivalent to turning on 2.5 men and calling it a day in all seriousness.

Here's an example from a physics textbook.

It applies equally to math notice.

First of all, here that you have exactly three pieces of information there, each of which will figure into a formula somewhere eventually, which the student will then compute.

Okay, I believe in real life and ask yourselves, What problem have you solved ever?

That was worth solving, where you knew all of the given information advance where you didn't have a surplus of information and you had to filter it out.

Or you don't have insufficient information and had to go find some.

I'm sure we all agree that no problem where Sullivan is like that, and the textbook, I think knows how it's hamstringing students cause watch.

This is the practice problem set when it comes time to the actual problems that you have a problem like this right here, where we're just swapping out numbers and tweaking the context a little bit.

And the student still doesn't recognize the stamp this is molded from it helpfully explains to you, like what?

What sample problem you can return to to find the formula.

You could literally I mean this past, this particular unit, without knowing any physics, just knowing how to decode a textbook.

That's a shame.

So I can diagnose the problem a little more specifically in math.

Here's a really cool problem.

I like this.

It's about defining steepness and slope using a ski lift.

But when you have years actually four separate layers, I'm curious which of you can see the four separate layers, and particularly how when they're compressed together and presented a student all at once.

How that creates this impatient problem solving ill defined them.

Here you have the visual.

OK, you also have the mathematical structure talking about grids, measurements, labels, points, axes, that sort of thing.

You have sub steps, which all leads what we really want to talk about.

Which section is the steepest.

So I hope you can see.

I really hope you see how what we're doing here is taking a compelling question, a compelling answer.

But we're paving a smooth, straight path from one to the other and congratulate our students for how well they can step over the small cracks in the way.

That's all we're doing here so I want to put to you.

If we can separate these in a different way and build them up with students, we can have everything we're looking for in terms of patient problem solving right here.

I start with the visual, and I immediately asked the question, Which section is the steepest?

And this starts conversation because the visual is created in such a way where you can defend two answers.

So we get people arguing against each other, friend versus friend, uh, in pairs, journaling, whatever.

And then eventually we realize it's it's getting annoying to talk about the skier in the lower left hand side of the screen or the skier just above the mid line.

And we realize how great would it be if we just had some A B, C and D labels to talk about them more easily?

And then and then, as we start to define like what does steepness mean?

We realized, would be nice to have some measurements to really narrow it down specifically what that means.

And then and only then we throw down that mathematical structure.

The math serves the conversation.

The conversation doesn't serve the math.

And at that point, I'll put it to that.

Nine out of 10 classes are good to go on the whole slope steepness thing.

But if you need to, your students can then develop those sub steps together.

Do you guys see how this right here?

Compared to that which one creates that patient problem solving that math?

Reasoning?

It's been obvious in my practice to me, and I'll yield the floor here for a second to Einstein, who I believe has paid his dues.

You talked about the formulation of problem being so incredibly important.

And yet in my practice in the U.

S.

Here we just give problems a student.

We don't involve them in the formulation of the problem.

So 90% of what I do with my five hours of prep time per week is to take fairly compelling elements of problems like this from my textbook and rebuild them in a way that supports math, reasoning and patient problem solving.

And here's how it works.

I like this question.

It's about a water tank.

The question is, how long will it take you to fill it up?

Okay, first things first, we eliminate all the sub steps students have to develop those.

They have to formulate those and then noticed that all the information written on there is stuff you'll need none of.

It's a distracter.

So we lose that students need to decide.

All right, well, does the height matter?

Does the side like matter?

Does the color of the valve matter what matters here?

Such an underrepresented question.

Math curriculum.

So now we have a water tank.

How long will it take you to fill it up?

And that's it.

And because this is the 21st century and we would love to talk about the real world on its own terms, not in terms of line art or clip art that you so often see in textbooks.

We go out and take a picture of it.

Now we have the real deal.

How long will it take it to fill it up?

And then even better as we take a video, a video of someone filling it up and it's filling up slowly, agonizingly, slowly.

It's tedious.

Students are looking at their watches, rolling their eyes, and they're all wondering at some point or another man, how long is it gonna take to fill up.

That's how you know you baited the hook, right?

And that question off this right here is really fun for me because, like, I like the intro I teach.

I teach kids because of my inexperience.

I teach the kids that are the most remedial, all right, And I got kids who will not join a conversation about math because there's like someone else has the formula.

Someone else had to work the formula better than me, so I won't.

I won't talk about it.

But here, every student is on a level playing field of intuition.

Everyone's filled something up with water before, so I get kids answering the question.

How long will it take?

Kids who are mathematically and conversationally intimidated?

Joining the conversation we put, We put names on the board attaching the guesses and kids have bought in here.

And then we follow the process I've described, and the best part here, or one of the better parts is that we don't get our answer from the answer key in the back of a teacher's edition.

We instead just watch the end of the movie, and that's terrifying all right, because the theoretical models that always work out in the answer key.

The back of the teacher's edition like That's great, but it's scary to talk about sources of error when the theoretical does not match up with the practical.

But those conversations have been so valuable among the most valuable.

So I'm here to report some really fun games with students who come pre installed with these viruses.

Day one of the class.

Okay, these are kids who who now one semester in I can put something on the board totally new, totally foreign, and they'll have a conversation about it for three or four minutes more than they would have started the year.

Which is which is just so fun.

We're no longer averse toe word problems because we've redefined what a word problem is.

We're no longer intimidated by math because we're slowly redefining what math is.

This has been a lot of fun.

I encourage Matthews.

I talked to to use multimedia because it brings the real world into your classroom in high resolution, in full color.

To encourage student tuition for that level playing field toe, ask the shortest question you possibly can and let those more specific questions come out in conversation.

So let's do this.

Build the problem because Einstein said so And finally, in total, just be less helpful because the textbook is helping you in all the wrong ways.

It's helping you is buying you out of your obligation for patient problem solving and math reasoning to be less helpful and why This is an amazing time to be a math teacher right now, because we have the tools to create this high quality curriculum in our front pocket.

It's ubiquitous and fairly cheap, and the tools to distribute it freely under open licenses has also never been cheaper or more ubiquitous.

I put a video series of my blawg not so long ago.

I got 6000 views in two weeks.

I get emails still from teachers in countries I've never visited, saying Wow, Yeah, we had a good conversation about that.

Oh, and by the way, here's how I made your stuff better.

Which wow, I put this problem on my blog's recently in a grocery store.

Which, which line do you get into the one that has one cart in 19 items with lying with with four carts and 352 and one items linear modeling involved in that was some good stuff for my classroom.

But it eventually got me on Good Morning, America a few weeks later, which is just bizarre, right?

And from all of this I can only conclude that people not just students are really hungry for this.

Math makes sense of the world.

Math is the vocabulary for your own intuition.

So I really encourage you Whatever your stake is in education, whether you're a student, parent, teacher policy maker, whatever Insist on better math curriculum, we need more patient problem solvers.

## 影片討論