It Is Fun to Pretend That Hard Things Are Easy!

A new online math platform promises to teach math 4x faster. Here is how!

Whenever I see someone trying to convince the world that they have discovered the secret to schooling, it generally takes no more than seven seconds to spot the selection effects. Invariably, they have found a way to curate their student body so the students have fewer disabilities, fewer special education and language needs, so their families have more wealth and time. That’s generally the One Weird Trick. I’m not a nihilist. There are some states and districts doing very focused, very well-resourced work in curriculum, pedagogy, and professional learning. But on some level everyone knows you get the big results through selection effects. The only question is whether you are paid to not know this.

Similarly, whenever I see someone trying to convince the world they have found a way to dramatically accelerate math learning, it takes only a quick tour of their webpage to understand that they have redefined “math learning” to mean something other than what it means to the vast majority of math teachers, mathematicians, math professionals, schools, universities, assessment agencies, and accreditation bodies. They invariably redefine math to mean “becoming an absolute demon at math exercises.”

“My second grader learned calculus on his own. Why aren’t schools like this??!”

My kids are in first and second grade. They are fine math students, working hard at working hard and also at operating with two-digit numbers.

Yesterday, they were learning elementary math skills, but today, on a sick day, I took no more than fifteen minutes to teach them how to take a derivative. Like calculus derivatives! I got them to successfully find the derivative of y = x^9. Then they completed the Khan Academy power rule practice set, getting four questions correct in a row.

What is my secret? How did I manage to teach a couple of little kids a skill that eludes many older students? Easy! All I did was tell them to take the number above the x and write it next to the x, then to subtract one from the number above the x. That’s it. How is this so hard for so many people? What are math teachers doing with all that time between first grade and high school? Have I discovered a previously unknown way to hack math education?

For increasing numbers of increasingly confident people, the answer is “yes.” My answer is “that isn’t math.”

After my kids completed their derivative exercises I asked them, “So what is a derivative?” The second grader said, “it’s an x and with whatever number it is it has to be the lower number,” and the first grader said, “what he said.”

All of this is just introduction to an excellent essay from Michael Pershan about the month he spent learning in a new math platform called Math Academy, a platform which claims to help students learn at “four times the speed of a traditional math class.” If you’d like a clearer sense of the liabilities of software-as-a-teacher and the ways software can distort mathematics itself, please click in. 👇

Math Academy Wants To Supercharge Your Learning

It includes good writing on good teaching:

Good teachers don’t sit around and watch kids read. They ask probing questions. They ask for explanations. They build understanding. Given the choice, most people will skim over technical explanations. During my month on MA, enrolled in Probability & Statistics, I was no different, especially since the worked examples were briefer, clearer, and always sufficient for passing the lesson.

… and one reason why learning with a good teacher takes longer than learning on your own:

In classrooms, we don’t let kids hit fast-forward. We prompt with questions. We command attention in real-time. Admittedly, that slows things down. I know a lot of kids would skip it if they could—that’s why you hand out the worksheet after the discussion, you know?

… and this observation about the conceptual learning missing in many of these platforms:

It made me feel sad and stupid to know how to answer questions but only in this shallow way. It also meant that, for all the criticism in “Math Academy Way” of unguided instruction, I was essentially left on my own to flesh out my understanding. Math Academy offers direct instruction for procedures, discovery learning for concepts.

A senior Math Academy employee engaged Michael in his comments and claims their written explanations are, in fact, conceptually rich. This, in my view, is a tragedy, like posting your aching manifesto on a freeway median. You don’t get Math Academy “experience points” for reading conceptually rich explanations. You get them for completing exercises. If the exercises don’t require the concepts, then the concepts only inhibit your progress and kids will drive past them at 75 mph.

This is one reason we need teachers—to make sure the necessary slow learning happens at all.

Featured Comment

Usha Kotelawala:

I have been a proponent of the social aspect that is critical to learning math. When you have those discoveries in math, you need people to celebrate them with. You need peers and facilitators to challenge whether it really works and ask why.

As my career took me to cities and regions where shortages of math teachers dominate hiring, I waver at times. When a school can't find the teacher, is turning to a digital option a more likely success than the long term aim to fix the supply and demand of math teachers? What is going to help the hundreds of students in your community today? Because if it takes a year or two or more, what will happen to those kids?

I think this is a very haunting and sad question and not one I have been excited to take up. But the existing answers, including the one I’m describing in this post, seem so uninterested in people it’s almost enough to get my attention.