Desmos Is Also a Curriculum Company Now

If you knew me as a classroom teacher, you knew I was very, very cranky about the ways many math textbooks treated students and mathematics, how they failed to celebrate and build on student intuition about mathematical ideas, how their problems were posed in ways that hid their most interesting elements, how they were way too helpful.

So it’s been a joy to get to do something more active about that problem than write cranky blog posts, to get to team up with some fantastic teachers, designers, engineers, and funders all continuously interrogating their assumptions about education, design, technology, math, and society, all to create what I think is …

the very best middle school math curriculum.

This is it.

Call off the search.

You found it.

Read more about the curriculum at the Des-blog, including details about our upcoming pilot.

[extremely Oprah voice] You get a debt of gratitude! You get a debt of gratitude! You get a debt of gratitude!

Aside from my enormous gratitude to the fantastic team I work with daily, I’m especially grateful to two groups:

  • The authoring / publishing team at Illustrative Mathematics / Open Up Resources who created and openly licensed a fantastic math curriculum, one which is the foundation of our own work. They dropped a massive gift on the math education community (or a hydrogen bomb from the perspective of the K-12 math publishing industry) and we were extremely happy to pick it up and build on it.
  • You. I’m talking about the folks who have been reading this blog, commenting on my posts, critiquing my ideas from day one. Your thoughts and mine are all tied together and run all the way through this curriculum.

This blog has been quieter over the last few years for reasons that are predictable – family, Twitter, the death of blogs, etc. – but also because, for the only time in my career, I haven’t been able to write about my work.

That changes today and I’m very excited to collaborate with you folks once again on the work that matters to me most. It won’t be at its best without you.

2020 Resolutions

Meanwhile, Nepantla Teachers, a group of math educators focused on social justice in their work, asked several educators to contribute a resolution for the new year. Here’s mine:

I'm resolving to spend as much time next year thinking about student lives outside of school as I do their lives inside of school. Teaching and curriculum have enormous influence on student learning but the influence of those in-school factors is dwarfed by out-of-school factors like housing and food security. So I'm resolving to practice humanizing pedagogies and to protest school closures in my city, to create interesting mathematical activities and to urge my representatives to protect and expand social programs. I'm resolving to ignore the distinction between educator and citizen. 

Click through to read resolutions from thoughtful people like Carl Oliver, Hema Khodai, Idil Abdulkadir, Marian Dingle, Makeda Brome, and Tyrone Martinez-Black.

The 2010s of Math Edtech in Review

EdSurge invited me to review the last decade in math edtech.

Entrepreneurs had a mixed decade in K-16 math education. They accurately read the landscape in at least two ways: a) learning math is enormously challenging for most students, and b) computers are great at a lot of tasks. But they misunderstood why math is challenging to learn and put computers to work on the wrong task.

In a similar retrospective essay, Sal Khan wrote about the three assumptions he and his team got right at Khan Academy in the last decade. The first one was extremely surprising to me.

Teachers are the unwavering center of schooling and we should continue to learn from them every day.

Someone needs to hold my hand and help me understand how teachers are anywhere near the center of Khan Academy, a website that seems especially useful for people who do not have teachers.

Khan Academy tries to take from teachers the jobs of instruction (watch our videos) and assessment (complete our autograded items). It presumably leaves for teachers the job of monitoring and responding to assessment results but their dashboards run on a ten-minute delay, making that task really hard!

Teachers are very obviously peripheral, not central, to the work of Khan Academy and the same is true for much of math education technology in the 2010s. If entrepreneurs and founders are now alert to the unique value of teachers in a student’s math education, let’s hear them articulate that value and let’s see them re-design their tools to support it.

Fave Five

Five of my favorite articles from the last month.

Estimation Isn’t Just Calculating Badly On Purpose

Here is a tweet I haven’t stopped thinking about for a couple of months.

I think it’s possible we should cut the student some slack here.

If the student has all the tools, information, and resources necessary to calculate an answer, we should be excited to see the student calculate it. Asking students to do anything less than calculate in that situation is to ask them to switch off parts of their brain, to use less than their full capacity as a thinker.

If we treated skills in other disciplines the way we often treat estimation in math …

… we’d ask students to spell words incorrectly before spelling them correctly.

… we’d ask students to recall historical facts incorrectly before recalling them correctly.

Estimation shouldn’t ask students to switch off parts of their brains or use less than their full capacity as thinkers. It should ask them to switch on new parts of their brains and expand their capacities as thinkers. Estimation tasks should broaden a student’s sense of what counts as math and who counts as a mathematician.

Estimation and calculation should also be mutually supportive in the same way that …

… knowing roughly the balance of yeast and sugar in bread supports you when you pour those ingredients exactly.

… knowing the general direction of your destination supports you when you drive with turn-by-turn directions.

… knowing the general order of your weekend schedule supports you when you carry out your precise itinerary.

Engaging in one aspect of mathematics makes the other easier and more interesting. That’s what Kasmer & Kim (2012) found was true about estimation. When students had a chance to first predict the relationship between two quantities it made their later precise operation on that relationship easier.

If we want students to develop their ability to estimate, we need to design experiences that don’t just ask them to calculate badly on purpose.

Create tasks where estimation is the most efficient possible method.

Take that worksheet above. Give students the same sums but ask them to order the sums from least to greatest.

Students may still calculate precisely but there is now a reward for students who estimate using place value as a guide.

Create tasks where estimation is the only possible method.

This is the foundation of my 3-Act Task design, where students experience the world in concrete form, without the information that word problems typically provide, without sufficient resources to calculate.

“Estimate the number of coins.” Estimation feels natural here because there isn’t enough information for calculation. Indeed, estimation is the only tool a student can use in this presentation of the context.

Meanwhile, in this presentation of the same task, there is enough information to calculate, which makes estimation feel like calculating badly on purpose.

Estimation isn’t a second-class intellectual citizen. It doesn’t need charity from calculation. It needs teachers who appreciate its value, who can create tasks that help students experience its benefits.

BTW

Featured Comment

William Carey:

One thing I love about calculus is is proceeds from estimation to exact calculation, and there’s no way to justify the exact calculations without working through the estimation first. We often think of mathematics as a discipline that proceeds deductively from perfect truth to perfect truth, but there are whole swaths of mathematics where the best way forward is to work from an answer whose incorrectness we understand towards an answer whose correctness we don’t yet understand.

Mark Betnel:

I agree with you, but I think it’s interesting to turn your non-math examples into better activities that reflect what we’re trying to do with “good” math estimation tasks.

Mr. K references Fermi problems, which fall really nicely in the category of “tasks where estimation is the only possible method.”

Theresa Clifford:

At the beginning of the year, I fill four jars around the room. One with M&M’s, one with eraser caps, one with cotton balls, and one with paper clips. They are all allowed a guess for how many in each jar. They enter their answer and their name on a slip of paper and place it in a collection jar. Whenever we come to a question where I want them to estimate first, I remind them of what they did when they first looked at the jar. I don’t tell them how many in each until the winter break – the suspense is awesome. Then in January I start with four new jars.

Joel offers an example of this kind of estimation exercise.