# Orchestrate More Productive Mathematics Discussions with Desmos Snapshots

Let me describe a powerful teaching tool we just released and the company values that compelled us to build it.

First, let’s acknowledge that statements of values are often useless. Values are only useful if they help people make hard decisions. Our company values should (a) help educators decide how we’re different from other math edtech companies, (b) help us decide how to spend our limited time in the world. So here is one of our values:

We believe that math class should be social and creative – that students should create mathematics in every form and then share those creations with each other and their teachers.

Many other companies disagree with those values, or at least they spend their limited time in the world acting on different ones. For example, many other companies think it’s sufficient for students to create multiple choice and numerical responses to express their mathematical thinking and to share those responses with a grading algorithm alone.

Our values conflict, and the result is that other companies spend their time optimizing adaptive grading algorithms while we spend our time thinking about ways to provoke mathematical creativity that algorithms can’t grade at all. We may both work in “math edtech” but we are on very different paths, and our path recently led us to a very thorny question:

What should teachers do with all these expressions of mathematical creativity that algorithms can’t grade?

Let’s say we ask students an interesting question about mathematics or we ask them to define a relationship and sketch its graph. That’s good math, but the teacher now has dozens of written answers and sketches that their computers can’t grade.

Other math edtech software offers teachers scarce insight into the ways students think mathematically. We offer teachers abundant insight which is a different kind of problem, and just as serious. We’ve spent months building a solution to this problem of abundance and we likely would have spent years if not for one book:

Mary Kay Stein and Margaret Smith’s Five Practices for Orchestrating Productive Mathematical Discussions.

Smith and Stein describe five teaching practices that promote student learning through summary discussions. Teachers should (1) anticipate ideas students will produce during a task or activity and then (2) monitor student work during class for those ideas and others that weren’t anticipated. Then the teacher should (3) select a subset of those interesting student ideas, (4) sequence the order of their presentation, and then help students (5) connect them.

In our classroom observations of our activities, we noticed teachers struggling to select student ideas because there were so many of them streaming from the students’ heads into the teacher’s dashboard. Sometimes teachers would make a note about an idea they wanted to select later, but when “later” came around, the student had already developed the idea further. So then we saw teachers take screenshots of that idea and paste them into slide software for sequencing. Smith and Stein’s recommendations are already ambitious and our software was not making it easier for teachers to enact them.

So we built “Snapshots.”

If you see interesting ideas at any time during an activity, press the camera icon next to it.

Then go to the “Snapshots” tab.

Sequence the ideas by dragging them into a collection.

Add a comment or a question to help students connect their classmates’ ideas to the main ideas of the lesson.

Then press “Present.”

We tested the tool ourselves during a summer school session in Berkeley, CA, and also with teachers around the country. What we’ve noticed is that students pay much more attention to discussions when the discussion isn’t about a page from the textbook or a worked example from the teacher but about ideas from the students themselves.

It’s the difference between “Let me tell you about a really useful strategy for multiplying two-digit number” and “Let me show you some useful strategies from around the class for multiplying two-digit numbers. They’re all correct. Decide which seems like less work to you.”

Here are some of our other favorite uses from the last month of testing.

Values help us all decide how to spend our limited time in the world, and nobody feels those limits quite like classroom teachers. Teachers frequently, and with good cause, evaluate new ideas and innovations by asking, “Does my class have time for this? What will we have to skip if we do this?”