This has made the rounds on the Internet, and it has angered lots of folks in education. And rightly so. Because there is no learning going on in that video.

But those teachers are being trained to deliver that sort of instruction to students in classrooms. Go ahead and search EDI or whole-brain teaching. You’ll see these very techniques being promoted as good practice.

So, is it how people learn, or is it not?

Tip of the cap to David Wees for reminding me that the parallels are not necessarily obvious.

Here are two conversations for which I have no patience at all…

“They should know X”

“You should teach X in manner Y.”

Conversation number 1 is the reason they are students, and the reason you are a teacher. What they should know is not relevant here; only what they do know is. So let’s factor that into our instruction.

Of course, the problem is deeper than a handful of students who accidentally say ironically stupid things. The problem is that American high school students are taught something named “math” for four years which is not even close to math.

Pretty sweeping generalization here. But I don’t disagree with the basic premise, which is that we aren’t doing the job of bringing mathematics to students (and students to mathematics) that we should be doing. I do disagree that the K-12 system is the only place this problem exists, but let’s get back to the matter at hand.

I fear my rant may disguise my true intentions: the problem is not the content. Geometry and calculus and algebra are very fine subjects of mathematics. The problem is that they’re taught in a way that strips out all the math and leaves a vapid husk of an education.

Now things are starting to spin a little bit out of control. Vapid husk of an education? Wow.

And the solution?

[I]f you give me an hour with a group of disillusioned but otherwise motivated high school students, I can teach them more mathematics than they have ever done in their entire lives. I can give them a dose of critical thinking and problem solving like no algebra problem can.

Child, please.

I teach at the college level these days, so I am accustomed to this sort of bravado. I try (perhaps unsuccessfully) to avoid it in my own writing because it is (a) unproductive, and (b) false.

But my beef isn’t so much with the author (although…) No, my beef is with EdSurge.

Why not feature the vibrant work that is going on in K—12 math education?

Why not post Andy Schwen’s video of a kid talking about the relationship between slope and rate of change while working on Function Carnival?

Why not feature the work of people trying to bring real mathematics to young children? Moebius Noodles, Math in Your Feet, Talking Math with Your Kids, Math Munch—these are projects where people are working on a daily basis to help parents, teachers and caregivers to support meaningful mathematical thinking for children. No bravado. No blame. Just hard working, thoughtful people working to solve a problem.

Because there is a problem. For sure there is a problem.

But an hour with Professor Awesome isn’t going to solve it.

Interesting conversation on Twitter today with Bryan Meyer, Denise Gaskins and Justin Lanier. It began with these tweets on my part, the result of grading some student work.

Oh dear. Class inclusion is giving some of my elementary kiddos fits. Do we have any post-Piagetian research on this?

An example of something my students struggle with is answering a question such as, Is a square a rectangle?

This type of question asks about class inclusion. Is an element of a subset also an element of the larger set?

Many useful and interesting questions in geometry have to do with whether one class is a subset of another class. Do all isosceles triangles have a pair of congruent angles? Are all quadrilaterals formed by connecting midpoints of other quadrilaterals parallelograms? Are all Stacys concave?

I am trying to sort out the extent to which my students’ struggles with questions of this sort are linguistic, and the extent to which they are about struggles with the idea of class inclusion.

Justin suggested this wording, which I will investigate:

Is a square an example of a rectangle?

Or, more generally:

Is an X an example of a Y?

My suspicion is that this will be helpful for some students when asked in this direction. But I also suspect that asking it in the other direction will be problematic.

Is a rectangle an example of a square?

See, part of what I wonder about is whether class inclusion—and the fact that it doesn’t have to be symmetric—is at the heart of a particular kind of struggle in geometry, and whether this is also related to the ways students think about and use language.

I want to use this space to make a pitch for a conference session.

See, there is this thing called Twitter Math Camp. It is professional development by teachers, for teachers—nearly all of us connected through Twitter. It takes place this summer near Tulsa, OK.

I am presenting with Malke Rosenfeld. Our official description is copied below.

We are planning a session that will force our groups (including ourselves) to wonder about the origins of mathematical knowledge. We will question our assumptions about terms such as concrete, hands-on and kinesthetic.

We will participate in mathematical activity both familiar and strange—all in the service of better understanding the relationship between the physical world and our mathematical minds.

We will dance.

We will make math.

We will laugh and possibly cry.

Below is an example of Malke’s work. When I participated in a workshop last summer, my head was spinning with math questions as a result. It’s great stuff and we will use it as a launching point for inquiry into our own classroom teaching.

So if you’re coming to Tulsa, please consider joining us for our three 2-hour morning sessions.

Of course you’ll miss out on other great people doing other great sessions. But you won’t regret it. I promise.

And if you choose a different session (perhaps because you’re leading one of them!), I have a hunch there will be after hours percussive dancing in public spaces. Come join in!

—

Our session description

This workshop is for anyone who uses, or is considering using, physical objects in math instruction at any grade level. This three-part session asks participants to actively engage with the following questions:

What role(s) do manipulatives play in learning mathematics?

What role does the body play in learning mathematics?

What does it mean to use manipulatives in a meaningful way? and

“How can we tell whether we are doing so?”

In the first session, we will pose these questions and brainstorm some initial answers as a way to frame the work ahead. Participants will then experience a ‘disruption of scale’ moving away from the more familiar activity of small hand-based tasks and toward the use of the whole body in math learning. At the base of this inquiry are the core lessons of the Math in Your Feet program.

In the second and third sessions, participants will engage with more familiar tasks using traditional math manipulatives. Each task will be chosen to highlight useful similarities and contrasts with the Math in Your Feet work, and to raise important questions about the assumptions we hold when we do “hands on” work in math classes.

The products of these sessions will be a more mindful approach to selecting manipulatives, a new appreciation for the body’s role in math learning, clearer shared language regarding “hands-on” inquiry for use in our professional relationships and activities, and public displays to engage other TMC attendees in the conversation.

Last summer, the super-smart, super-creative team at Desmos (in partnership with Dan Meyer, who may or may not be one of the Desmos elves) released a lovely lesson titled “Penny Circle“. It’s great stuff and you should play around with it if you haven’t already.

It was a ton of fun to make. I was delighted to have the opportunity to offer my sharp eye for pedagogy and task design, and to argue over the finer details of these with creative and talented folks.

Nature v. nurture. Age-old debate on relative importance. Not gonna settle it here. Not even in the limited context of factors influencing mathematics success.

There is lots of interesting research going on, of course. I want to tell you a quick story about a very small subset of that research.

A few years back, a group of educational psychology researchers published a study that phys.org headlined, “Math ability is inborn“.

The study investigated the ability of 4-year olds to choose the larger of two sets of dots when these sets were viewed briefly (too briefly to allow for counting).

They found that children who were better at this task also knew more about numeration and counting.

A quote from one of the researchers, Melissa Libertus:

“Previous studies testing older children left open the possibility that differences in instructional experience is what caused the difference in their number sense; in other words, that some children tested in middle or high school looked like they had better number sense simply because they had had better math instruction. Unlike those studies, this one shows that the link between ‘number sense’ and math ability is already present before the beginning of formal math instruction.”

If a child has not had formal instruction in mathematics, is the only remaining possibility that her mathematical performance is due to innate skill?

Of course it isn’t.

There is also the possibility that the child has absorbed some mathematical knowledge from her environment, and that different environments might provide differential input.

Maybe the child who is better at discerning the larger set has more practice doing just that. Maybe that child’s parents have been asking her how many? how much? and which is more? for the last two or three years.