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.

Upcoming Conferences

Come hang out with me at California Math Council’s North and South conferences in November and December.

CMC-South. Palm Springs, CA. November 15-16. I’m going to describe how “rich tasks” and “bland tasks” both fail our students. And I’m going to do it with 15 students on a stage in a live lesson demonstration. Let’s gooo! [register]

CMC-North. Pacific Grove, CA. December 6-8. I’ll share some of the ways my colleagues and I at Desmos are designing for belonging in math class, specifically how we try to expand the list of who counts as a mathematician and what counts as mathematics. [register]

Fave Five

Five of my favorite articles from the last month.