A School for Complete Mathematical Understanding (2 of 2)

(Also entirely true!)

Complete Math Understanding and Social Justice

In my last post, I identified a huge problem with traditional schools: they don't reliably bring all students up to a complete understanding of math.

This was a problem in the middle of the 20th century. This is a disaster at the beginning of the 21st. 

If I can interject a bit of social justice: the inequalities in contemporary American society as numerous as they are complicated — but there is a strong correlation between economic success and mathematical understanding. This holds through many inequalities.

There's a gap between the outcomes of males and females, but when you filter out differential math abilities, the gap gets smaller. There's a gap between the outcomes of white students and students of color, but when you filter out differential math abilities, the gap gets smaller.

Obviously — obviously! — these disparities are not reducible to math performance. There is sexism, and it matters. There is racism, and it matters.

But there's good evidence to say that if we provide a way for all students to excel at math, we will make a significant stride toward reducing inequality in American society. This is something worth fighting for.

All right. So: how can we accomplish this?


Step #1:  JUMP Math

We'll start by using the gold standard for curricula that achieve full comprehension: JUMP Math.

JUMP is published by a non-profit organization from Canada, the brainchild of John Mighton: an actor-turned-playwright-turned-math-tutor-turned-Math-Ph.D.-turned revolutionary-curriculum-designer. (Y'know, one of those people).

(Not that it particularly matters, but you might have seen Mighton before — he played the inspirational teacher in Good Will Hunting.)

The heart of JUMP Math is the insight that each math concept — even the very most complex ones — can be broken down into smaller and smaller chunks, until they're small enough for students to understand in mere seconds. Students come to understand (not merely perform) each chunk quickly, and then jump onto the next micro-concept.

Emphasis on quickly. In JUMP, students move from insight to insight, with only a small bit of struggle in between. There's little of the floundering that makes many (many) students feel that they're just spinning their wheels, that they'll never understand math.

People don't like floundering. People don't like struggle without hope. People love to struggle and achieve.

Video game makers understand this. In the last few decades, they've mastered the psychology of struggle and reward, and have made video games into feedback systems so well-suited for human brains that they are nearly addictive.

JUMP stokes the ego. JUMP (metaphorically) turns math into video games.

Learning anything — feeling the change from not-knowing to knowing well — feels fulfilling. Learning quickly feels especially fulfilling.


a (Crucial) Side Note

Crucial side note: small struggles are not enough. To be psychologically healthy, humans also need big struggles — we need to take on enormous projects that we're not confident we'll be able to solve.

In our school, our math curriculum will also have another component — baffling puzzles that students will need hours and weeks to unravel; puzzles that will allow for creativity and individualized solutions.

Our school's math curriculum will be both/and: students will fully learn the core K-12 math curriculum through a micro-scaffolded JUMP Math curriculum, and they will cultivate their creative brilliance through non-scaffolded puzzles.

I'll be blogging later on the second half of this.

End of side note.


What about Struggling Students?

Some students, of course, have more difficulty learning math. (Again: people are not blank slates.) That doesn't mean their mathematical understanding has a ceiling. 

JUMP Math works wonderfully for them, too. Teachers simply break the micro-concepts down into still-smaller chunks — however small the student needs to quickly and fully understand the concept.

Every student can learn one more concept. Every student can learn another concept after that. There are no ceilings in math.

This psychological insight is perhaps the most revolutionary piece of JUMP. My students who use JUMP report having new faith in their abilities to learn. JUMP teaches that anything is possible in learning.

Learning to teach the JUMP Math way is an art: one of the most joy-inducing skills I've honed as a teacher.


How is This Different?

Traditional math books have two phases: they introduce the concept (the first couple pages of each chapter, replete with 2-3 sample problems), and then they ask students to apply the concept (the next few pages, featuring about 20-30 problems).

JUMP Math doesn't do that — it teaches new concepts through the very problems it presents.

Every question enlightens. Students learn constantly. No problem is wasted.

I recall, when I was in high school, staring blankly at my math book, reading the sample problems a third, fourth, and fifth time, wondering what I wasn't getting.

(I also remember stabbing my book in frustration. Lost a good pen that way!)

JUMP, again, makes learning math easy. It makes achieving a fundamental skill of the 21st century simple, something everyone can do.

This seems, to me, a fundamental human right.


But Wait, There's More!

Any curriculum that did all the above would be excellent, but JUMP Math goes an extra step.

Instead of asking students to merely perform math, JUMP leads them into the messy guts of understanding.

JUMP helps all students clearly understand somewhat-obtuse concepts that I recall merely memorizing.

Students understand why order matters in subtraction and division. Students understand why order doesn't matter in addition and multiplication. Students understand why you can't divide by zero. (Hint: it has nothing to do with blowing up the universe.) And so on.

Again, I'm pretty "good" at math: I got a perfect score on my GRE Quantitative, for example. But I regularly learn new things when I teach with JUMP. Big things. Things I never thought to ask about. Things that make me aghast I didn't know them before.

JUMP Math makes it simple for every student to develop full mathematical understanding. We'll ground our curriculum in it — and move beyond it, too.


I listed, in the last post, four things we should be able to promise students vis-à-vis math. By explaining JUMP, I think I've handled the first two of them — complete (2) understanding and (3) solving of the K-12 curriculum.

I haven't touched on (4) remembering everything that students learn, and (4) allowing students to be active learners, rather than passive receivers.

But I suspect I'm pushing the upper bounds of how long a blog post ought be already. I'll look forward to addressing those in future posts!


 

In Brief:

Understanding math is (and will continue to be) crucial in the 21st century. Yet our brains aren't built for it. What's needed — and what our school will set itself to delivering — is a math curriculum that takes seriously how difficult and unnatural math learning is, and then helps students master it entirely. To do this, we will start with the JUMP Math curriculum, and build from there.


 

For Further Reading:

John Mighton has written two books — The Myth of Ability and The End of Ignorance. Both are excellent, though start with the first. For a quicker overview of JUMP, however, take a peek at these two excellent posts in the New York Times Opinionator column — "A Better Way to Teach Math," and "A Better Way to Teach Math, Part 2."

Brandon Hendrickson

Seattle, WA