Mark Zuckerberg Got Lost in Terra Mathematica

Mark Zuckerberg misunderstood good teaching but he also misunderstood mathematics itself.

A month ago, the Chan Zuckerberg Initiative announced it was pivoting away from its $100 million investment into a personalized learning platform. I have wondered since then what kinds of knowledge about schools, teaching, math, and technology would have helped CZI avoid this kind of costly mistake. So I first described how I thought CZI misunderstood the work of good teaching.

Specifically, CZI seemed possessed of the idea that in a class of 35 students, a teacher can at most meet the needs of one student at a time, leaving at least 34 students to either get bored or struggle because that one student’s needs are either behind or ahead of their own. For example, here is CZI itself:

Rather than having every student sit in a classroom and listen to a teacher explain the same material at the same pace in the same way regardless of a student’s strengths, learning style and interests, research shows students will perform better if they can learn at their own pace, based on their own interests, and in a style that fits them.

Other technologist funders have thought similarly. For example, the Bill and Melinda Gates Foundation:

[Personalized learning] allows students to progress through content at their own pace without worrying about being too far behind (or ahead) of their classmates.

This perspective underestimates the ways skilled teachers make effective use of learner variability, how skilled teachers create better learning conditions for everyone because of, not in spite of, the fact that we are all thinking in different ways.

I illustrated this pedagogy with a class taught by Liz Clark-Garvey of NYCPS. Liz started the class by asking what students noticed about a shape and then used the different ideas to expand everyone’s knowledge.

But the other reason I believe that personalized learning is so appealing to many technologist funders, is that they underestimate mathematics itself. These are very bright people and I would not wish to compare our scores on the Putnam exam but they still underestimate the height and depth and breadth of mathematics.

Some comments on my post about Liz’s lesson effectively proxy the ways technologists think about mathematics.

The Contemplate then Calculate seems fun, but why are such simple concepts being taught to kids of that age?

… the verbal approach is not a mathematical approach.

“Noticing and describing,” according to these people, are not mathematical activities. What is then? Math, to hear many technologists describe it, is the basket of operations you can ask computers to perform, the formal operations that result in either a single correct answer or, if we absolutely must, multiple answers which computers can deterministically evaluate as correct or incorrect.

They see Terra Mathematica, the world of mathematics, as a series of mountain peaks, each one representing a single machine-gradable skill, each one inaccessible to every other one. 

Log into your account and we will place you on the correct mountain. There you will find food, water, a video explanation, perhaps a generative AI chatbot for company, and a multiple choice quiz to see if you are ready for the next mountain.

Given that perspective, it makes sense that these technologists don’t think students can benefit from one another’s experience. Their perspective is that students who are writing an algebraic pattern and finding the equation of a line (for example) are doing completely different math in completely different places.

With a broader understanding of math, however, you realize these students are actually doing similar mathematics in the same place, the same mountain range. You realize that those peaks and many others are connected by land bridges—elemental, concrete, and intuitive skills like noticing, naming, and using patterns.

These concrete skills make mathematics coherent and accessible to broad groups of learners. Dr. Rochelle Gutierrez has also claimed that these skills, including the use of “voice, vision, touch, and intuition,” make math accessible, in particular, to groups historically excluded from participation in mathematics, like Black, indigenous, and Latinx students. But many technologist funders do not seem to recognize these skills as mathematical.

When I say those technologists have a “narrow understanding of mathematics,” I mean they do not understand this important terrain that connects seemingly disparate mathematical peaks, but I also mean they do not understand how far they are from the summit!

Another representative commenter from my previous piece:

It’s inefficient and maybe even unjust that kids that already understand the algebra involved have to stay and twiddle their thumbs …

People will spend their whole life trying to get the highest score in Donkey Kong and you think you’re done solving equations in a single class period? People will spend years trying to perfect a roasted chicken and you think you have “mastered” proportionality? My friend, you are lost. You believe you are at the summit but it is many miles above you. Keep climbing!

For the border tiles problem, we could ask a student who believes herself to be done, and perhaps inhibited by those who are not yet done, to:

• extend the problem from an n x n square to an m x n rectangle

• add an arbitrary number of layers around the pool

• prove the equivalence between your expression and a different expression from a classmate

• etc.

We wouldn’t believe someone who claimed to have mastered a jump shot in an afternoon nor a casserole recipe in a day, yet many technologist funders find it plausible that students can master sophisticated areas of mathematics based on little more than a short multiple choice quiz!

These technologists do not understand the full terrain of Terra Mathematica, judging from their investments and public pronouncements. Their aperture is trained on the parts of that world that are formal and operational and produce answers that a computer can easily evaluate as correct or incorrect. 

Few students are interested in inhabiting this region of Terra Mathematica for any long period of time. Coincidentally, this region of the mathematical world is of decreasing value in the technological world these funders have, themselves, worked to create. Computers can grade this math and computers can do this math.

Occasionally, I have wished these funders would invest more of their resources into curriculum and pedagogy and technology that put learner variability to good use, that help students experience the full height, depth, and breadth of Terra Mathematica. Or perhaps that they would just buy a few football teams or anything else instead of tilting the edtech landscape towards technology that segregates students from each other and diminishes mathematics.

Happily, my entire experience in math education has convinced me there isn’t enough money in the world to convince students they’d rather learn without their friends, to convince them they’d prefer to live in the regions of Terra Mathematica filled with formulas and operations and exacting precision graded by machines. Instead, the regions where you find yourself noticing, naming, and using patterns with people you respect and like, are simply too interesting for students to content themselves with life in the arid regions of Terra Mathematica.

As much money and power as there is in the world, all of it is outweighed one thousand fold by a single child’s desire to know and be known by other people, to be seen as smart and full of value, in Terra Mathematica and everywhere else.