Month: November 2016

Total 8 Posts

What I’m Working on the Day After the Election

Every morning, the four members of the teaching team at Desmos post a note to their Slack channel listing all the tasks they’re working on that day. We use the hashtag #workingon for easy reference. This is what I posted this morning.

I don’t know how any of you voted and I won’t make assumptions. (It’s clear that a lot of people who represented themselves one way to pollsters voted another way, and that likely holds true for our company as well.) But you may have voted like I did yesterday, leaving you bereft today, and struggling to locate some kind of purpose for your work, struggling to participate in the solution to a problem that has many names. If that’s you, then this what I’m telling myself about our work this morning.

If the name of that problem is economic anxiety, if President-elect Trump was propelled to power by people whom globalization, open borders, and free trade have left behind, I encourage us to locate political and social solutions to their problems, definitely, but also to help those people (and their children, particularly) learn better math better. Capitalists continue to automate routine manual jobs, leaving behind more and more non-routine cognitive jobs. Non-routine math tasks are difficult to design, difficult to teach, difficult to learn, and increasingly essential to full economic participation. We can help design them and we can give teachers tools to make them easier to teach.


If the name of that problem is bigotry, then we should help teachers facilitate constructive arguments, cultivate empathy, and emphasize patience. One dimension of bigotry is impatience, a sense that “I know everything there is to know about a person based on his or her most easily observed characteristics.” The traditions of many math classes – completing short problems resulting in simple answers that are easily verified in the back of the textbook – only exacerbate this problem. Christopher Danielson’s “Which One Doesn’t Belong,” by contrast, invites students to realize that all of those objects don’t belong for one reason or another, that we can negotiate those reasons productively, and that we can understand the world through the eyes of another.


Obviously we have lots of work to do in our neighborhoods, our churches, our social networks, our local and state governments, and in ourselves, work that is probably larger than anything we’ll do at Desmos today. But if yesterday’s election left you wondering what work you can do at Desmos to help solve a problem with many names, this is what I’m #workingon.

BTW. I’m watching Twitter for examples of math teachers helping their students understand where they live today. I’ll continue to update this post throughout the day.

Matt Enlow:

When you learn mathematics, you also learn a lot of other things. Here are three of those things.

John Golden:

We did Elizabeth Statmore’s talking points for Math Mindsets Chapter 7 (tracking), then for the election, then we looked at Megan Schmidt’s Social Justice Math slides.

wwntd offers her classes some words of consolation.

Dianna Hazelton asks her class:

What does the word empathy mean? How do you show empathy?

[Pseudocontext Saturday] Photos

This Week’s Installment


What mathematical skill is the textbook trying to teach with this image?

Pseudocontext Saturday #4

  • Reasoning with proportions (63%, 523 Votes)
  • Calculating exponential growth (19%, 154 Votes)
  • Simplifying expressions (18%, 151 Votes)

Total Voters: 828

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(If you’re reading via email or RSS, you’ll need to click through to vote. Also, you’ll need to check that link tomorrow for the answer.)

Current Scoreboard

Team Me: 3
Team Commenters: 0

Pseudocontext Submissions

Michelle Pavlovsky


Paul Hartzer



Every Saturday, I post an image from a math textbook. It’s an image that implicitly or explicitly claims that “this is how we use math in the world!”

I post the image without its mathematical connection and offer three possibilities for that connection. One of them is the textbook’s. Two of them are decoys. You guess which connection is real.

After 24 hours, I update the post with the answer. If a plurality of the commenters picks the textbook’s connection, one point goes to Team Commenters. If a plurality picks one of my decoys, one point goes to Team Me. If you submit a mathematical question in the comments about the image that isn’t pseudocontext, collect a personal point.

(See the rationale for this exercise.)



The judges rule that this problem satisfies both criteria for pseudocontext:

Given a context, the assigned question isn’t a question most human beings would ask about it.

I invite any commenter to rationalize the constraint that exactly 15 photos must be purchased and we don’t know which of them will be small or large. More often (always?) people begin with the photos they want, or perhaps they work from a total budget. “I can only buy 15 photos and the number of large photos I purchase can vary from zero to fifteen,” said no one ever.

Given that question, the assigned method isn’t a method most human beings would use to find it.

If most human beings were going to find out the cost of five large photos and ten small photos, they’d multiply each kind of photo by its price. Variables aren’t a useful tool.

So the textbook has made the world serve the math when math should serve the world. If the world doesn’t need math’s service, then math should be gracious enough to step out of the way.

Featured Comments

Jonathan Claydon:

I guessed correctly. The first and third choices made too much sense. Always step up to the plate thinking curveball.


The problem here is that the customer has no use for a general equation, but the store owner might–she’s got to deal with people who call in with all kinds of crazy orders and questions. Still, it’s unlikely the store owner would write an equation for just small and large pictures. It’s much more likely that she’d come up with a pricing scenario for unusual picture sizes.

Great Classroom Action


Tricia Poulin makes some awesome moves in her #bottleflipping lesson, including this one:

Okay, so now the kicker: will this ratio be maintained no matter the size of the bottle?

Graham Fletcher offers us video of kindergarten students interacting in a 3-Act modeling task:

It’s always great to engage the youngins’ in 3-Act Tasks. I’ve heard colleagues say, “I don’t have time to do these types of lessons.” I hope this helps show that we don’t have time to not have the time.

Wendy Menard offers her own spin on the Money Duck, one of my favorite examples of expected value in the wild:

The students designed their own “Money Animals”, complete with a price, distribution, and an expected value. This was all done on one sheet; the design, price and distribution were visible to all, while the calculations were on the back. After everyone had finished, we had our Money Animal Bonanza.

Sarah Carter hosts the Mini-Metric Olympics, a series of data collection & analysis events with names like “Left-Handed Sponge Squeeze” and “Paper Plate Discus”:

After the measurements were all taken, we calculated our error for each event. One student insisted that she would do better if we calculated percent error instead, so we did that too to check and see if she was right. In the future, I think I would add a “percent error” column to the score tracking sheet.