Teachers Decide What’s Money

“Feel free to answer like a seventh grader,” I told teachers as I led them through one of the lessons from our Middle School Math Curriculum.

A printer prints out a scaled copy of a shape on an iPad.

The question about those images was, “What stays the same? What changes?” And people did not answer like seventh graders.

A response that has a lot of formal mathematical language.

Instead, there was lots of discussion around proportionality, congruency, ratios, and other attributes of the shapes that are going to be one million miles from the minds of seventh graders in school right now.

But several teachers took me up on my offer and answered a little bit like children. I snapshotted them, paused the class, and presented them.

A response that cites the color of the scaled shape.

Things they told me that stay the same:

  • The shape, the angles, the color, the orientation
  • The color and the angle of the vertices
  • The color and the paper size are the same
  • The shape and the color
  • Shape, color, orientation, centered on paper

“I love that you folks are finding patterns, noticing similarities, deciding what varies and doesn’t vary—including color!—using your eyes, your vision, your senses. That’s math!”

I read them an excerpt from Rochelle Gutierrez which is on my mind a lot these days.

A more rehumanized mathematics would depart from a purely logical perspective and invite students to draw upon other parts of themselves (e.g., voice, vision, touch, intuition).

By naming those responses “mathematics,” I turned them into money.

As a society, we decided long ago that certain pieces of paper had value—that they’re money. In much the same way, you are the central bank of your own classroom and you decide which student ideas are money. You decide which of them have value and, by extension, you influence a student’s sense of their own value.

I’m not hypothesizing here! Watch what happened with the teachers. On the very next screen in our lesson, we ask students to describe how this printer is broken.

A printer prints out an unscaled scaled copy of a shape on an iPad.

Teachers clearly received my signal about what kind of mathematics was valuable.

A response: "My shape is drunk."

They brought metaphors, imagery, and analogies that I don’t think they would have brought if I only praised deductive, formal, and precise definitions.

  • My shape is drunk
  • The lines do not stay straight…they are wobbly
  • My pacman lines are no longer straight. The new figure looks droopy and sad.
  • It got curvy, kind of sexy looking

The ability to decide what’s money is a lot of power! In this time of distance teaching, you have fewer ways to broadcast value to students than you would if you were in the same room together. But I’m so encouraged to see teachers using chat rooms, breakout groups, video responses, written feedback, snapshot summaries, whatever they can, to enrich as many students in their classes as possible.

About 
I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.

12 Comments

  1. Reply

    For the record I cannot taste all the underlying flavors of the wine. When someone tells me it’s plum or oaky – I have no clue because I cannot taste it because I have a poor sense of smell. The only time I understood was when the sommelier said a white wine tasted like wet rocks. It did – although I have no memory of every tasting wet rocks. But I am successful at choosing wines that are considered good – holistically. “I knows it when I tastes it.”
    This is – my shape is drunk. We all start life thinking mathematically but school jumps much to quickly to the formal refined level when we can tell the oaky from the plum but kill the holistic by doing so. We are taught not use our holistic/intuitive processing. We need both in life and math. When a mathematician works on a new theorm they make an intuitive leap (conjecture) and then refine it to prove it. If we want students to move towards proof they must first learn to conjecture – make leaps. We need to keep math “sexy”.

  2. Michael P Goldenberg

    October 8, 2020 - 8:12 am -
    Reply

    Have you written about this “What’s money?” idea before? If so, I’ve missed it. If not, perhaps you could flesh that idea out further, possibly with other examples of what you mean.

    Can we perhaps discuss how our classrooms might change (for the better or worse or simply for variety) if someone else – e.g., the students – determined what money is in that classroom? How do we imagine that would go?

    • There are some parallels here but this is mostly a new metaphor I’m playing with.

      Students do and should also determine what the class values. That’s a super important point and I’m glad you raised it. By virtue of their status / role / expertise (perceived or real) I think teachers will always have a role to play in assigning competence / status to students.

  3. Mireille Geha

    October 8, 2020 - 2:01 pm -
    Reply

    That’s interesting! I catch myself not saying (with words or body language) a discouraging thing when a student says something completely off the track to the discussion. What did you tell “your students” when they answered with discussions around proportionality ie not as year 7 students? Did you completely ignore their answer and turned to hear others? Did you write/type all the answers? How can I show students that I heard their answer without allowing the discussion to veer in that direction? Or is “hearing” it not enough? How can I not discourage them?

    • All great questions! I have actually lost classes more quickly when I have left comments like “drunk shape” unacknowledged rather than when acknowledge them. When I acknowledge them, I can turn them into money (as it were) and then move with the same enthusiasm to another response.

  4. Reply

    I don’t teach. I am trying to figure out why mathematics, as taught, results in so much alienation and failure. I have experienced both, so there is a possibility I can approach the problem humanly. To keep this short, let pretend to be a wise one.

    Mathematics would not exist without the human mind. It is a matter of what a human mind can understand. On the other hand it is taught as problems for tangibly processing what senses provide: more or less the numerical and symbolic processing a computer can do better.
    Do young children have a mind for a mental life. I maintain is’s a no-trainer. Can they construct a mental picture of what multiplication does in order to formulate their own problem?
    Do they realize that Dan’s animation is the result of a human artifact made by someone just like them, just a little older. It is likely just a short list of instructions to a computer that is executing them over and over, In n a sense nothing is changing,.
    The programmer who made it understands the abstraction of a simple language. I could not find out if this Desmos code is open sourced, if it the students can see the result

  5. Reply

    It’s interesting that you chose money for your analogy.

    What I have learned from teaching is that all good teaching is socialist. Valuing everyone’s contribution in the classroom equally is no different from paying Jeff Bezos and an Amazon warehouse worker the same salary.

    So how do you convince capitalists to teach this way? When the system is clearly set up to value certain students/ideas more than others with magnet schools, college admissions, even just the existence of grades. Maybe you can convince middle schoolers, but by high school they are pretty jaded and understand the pre-existing hierarchy. A number on a report card means a lot more to them (and especially the adults at home) than a classroom discussion.

    This is not to say that it’s not a great idea–clearly it is. But for some reason spreading the money around to everyone equally has not caught on in either our schools or our society.

  6. Reply

    The concept of teachers deciding what is “money” in their classroom is a traditional approach to teaching based on the traditional structure of the curriculum that guides educators which tells educators what is “money” which in the past has largely been based on specific subject matter content.

    The great thing is that even though the content may be important, it doesn’t mean there aren’t multiple ways of meaningfully engaging students and different learning routes students can take to arrive at the same understanding. These approaches to teaching are more progressive but are often was is considered “good teaching” because it is often more engaging and personalized for students.

    One question that arises is, what can teachers do to empower students to determine what is considered valuable in the classroom while also maintaining roots in the curriculum?

    This is an approach I have been hoping to dabble with more in my own classroom and I would love to hear others’ ideas/opinions.

  7. Reply

    I have just returned to teaching after many years away and I am currently taking an additional qualifications course. I had never heard of Dan Meyer until a couple of weeks ago. I watched a couple of his videos from a few years ago – and what he was preaching then is still true today. Unfortunately – for various reasons – it is difficult to get these “new” ideas into the classroom learning environment.

    Thanks.

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