Remote Learning — Week 6

Assessment of learning is one of the great challenges of teaching. It’s a complex endeavor under normal circumstances, made even more difficult in emergency Remote Learning. To math teachers, assessment often means testing, and some teachers are trying hard to replicate the experience of classroom tests. They’re experimenting with different delivery platforms, administering tests synchronously under time constraints, and even having students test in front of their webcams.

Other teachers have entirely abandoned tests in the traditional sense. I’m firmly in this group, but I do empathize with the former. I enjoy writing and giving a good test, and a steady stream of supervised student work is fuel for my instruction. But I just don’t see how I can give a traditional timed test in a fair and reasonable way in the current situation.

One approach I’ve taken is inspired by the principles of Mastery Grading. I’m assigning assessment items similar to what students would see on a test, but giving them several days to complete the work and allowing them multiple resubmissions after feedback. In this model, students can revise and resubmit their work until it is as complete and correct as they wish. It’s not an approach I’ve used much in the past, but it’s working for us: I like the interactions around mathematics I’m having with students as I provide them feedback, and I’m getting that stream of work I need to tune my teaching.

Some teachers are very concerned about cheating. I’m not one of those teachers. I’ve been teaching long enough to know that the vast majority of students will do the right thing when they, themselves, are treated right. There may be a few students looking for a shortcut, but those cases are isolated incidents to be handled individually.

While the system in place may be vulnerable to some abuse, I feel it treats students right. Everyone has a chance to master the assignment to their satisfaction, and the weekly assessments are frequent enough to dilute the stakes of any individual task. No student will feel penalized for doing the right thing, and the incentives to do the wrong thing have mostly been removed.

And all the evidence points to students doing the right thing. I grade the assignments on a rolling basis, and the work that comes in late shows the same kinds of correctable errors as the work that comes in early. Often students will submit something that’s mostly complete and say “I’m not sure what to do from here”. Usually a single hint or a suggestion is enough for them to finish up. The personal exchanges, in comments and resubmissions, serve as an audit of the student’s process.

I always assess in many different ways, some of which are less impacted by the circumstances of Remote Learning: individualized assignments, technology projects, and oral exams all work mostly as well now as before. But this new approach is working for us, and seems particularly well-suited to the circumstances. It requires trust, but then, all good teaching does.

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Remote Learning — Week 5

I established a simple and productive work cycle for my classes during the first two weeks of Remote Learning. With a foundation in place, I’m now trying to find ways to reproduce what we’re missing from our typical in-person classes.

One thing I tried was starting the week’s unit with a single question.

After answers came in I shared some representative responses with the class:

The shape on the left is easier to compute the area of because it can be divided into recognizable polygons (such as a triangle)

It is easier to compute the area of the region on the left because it is made out of lines.

The region on the left’s area is easier to compute since it can be triangulated.

Then I posted follow-up questions for students to think about as homework:

  • Why do straight lines make finding area easier?
  • Why does breaking something up into triangles and rectangles make its area easier to compute?
  • An answer to the previous question might be “Because we have formulas for those shapes”. Why, then, do we have formulas for the areas of those particular shapes?

This work motivated the next day’s video, which was designed to leverage this specific conversation (as discussed in last week’s post), which launched our standard cycle of

Video Intro➜ Text + HW ➜ Formative Assessment Quiz ➜

Written Work Submission ➜ Feedback and Revision

I often design lessons around simple but provocative questions like this, stirring up conversation and debate and then moderating a whole-class discussion that leads us in the right direction. In the first few weeks of Remote Learning I’ve been missing that. This small change brought back a little of what’s been missing.

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Remote Learning — Week 4

Like many teachers thrust into emergency remote learning I’ve been making videos for my classes. Having observed the flipped classroom bubble from a safe distance, I definitely had opinions about instructional videos, even if I didn’t have much experience making them myself.

I got some good advice from a colleague early on: Don’t waste time replicating what’s already out there. It’s the kind of obvious advice someone used to doing everything from scratch needs to hear. Using Khan Academy videos wouldn’t be my first instinct, but they’ve been a useful resource for teaching AP calculus: They’re aligned to the curriculum, they cover the key procedures, and they already exist.

The existence of a core set of instructional videos for calculus has allowed me to use my limited time to target what my students want and need: They’ve asked for videos that explain concepts, cover more challenging examples, and review our assessment items. I can invest my time in those, as well as videos for my geometry classes, for which there aren’t as many suitable resources available.

I’d say the most useful videos I make are those that are responsive to my students. They are videos driven by student need or informed by student work. Making a video review of a math task for a class is much more meaningful having looked at all of the students’ work. The video isn’t just about what I would do; it’s about what we all have done.

There’s this ideal of “putting your course out there”, publishing your full set of instructional videos once they’re set and done. But at the moment the value in video for me is in capturing and narrating our shared mathematical experience. Those videos have value for us right now, but maybe not the next time around, when a different group is experiencing a different story.

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Remote Learning — Week 3

The end of week 3 of remote learning in NYC brought news that schools will not reopen during the 2019-20 school year. This is by no means shocking — perhaps only the timing is a surprise — but it’s still a remarkable decision.

This announcement probably marks the end of the honeymoon period of remote learning for students and teachers. If the novelty of zoom meetings and recorded lectures hasn’t warn off yet, looking ahead to 10 more weeks of classes-at-a-distance could be a potent dose of reality.

The cancellation of the Regents exams offer another set of challenges. While an understandable decision, the tests serve as summative assessments in many high school courses. How will students respond knowing there’s no longer a Regents exam to pass to earn credit for a course? How will teachers and schools adjust to the loss of their courses’ final exams? Every week of emergency remote learning brings much to think about.

I’m hoping the structures I’ve put in place and the relationships I’ve built with my students can carry us to the end of the year. I’ll make sure students get what they need out of my courses and are prepared for next year, but I’ll also use our time together to get creative and do some fun extra-curricular work. The end of the year is a good time to try new things, even if the entire enterprise is an experiment!

We have a long way to go. And even doing our best, we’ll still have the fallout of a million disrupted educations to reckon with in September. One crisis at a time.

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7 Ways to Explore the Math of the Coronavirus Using the New York Times

My latest piece for the New York Times Learning Network is “7 Ways to Explore the Math of the Coronavirus Using the New York Times”, a collection of ideas for using NYT articles, infographics, and interactives to explore the mathematics underlying the current coronavirus epidemic.

The opportunities range from statistical literacy to network theory. Here’s an example of some data analysis you can engage in using a wonderful NYT interactive:

By using sliders to change, for example, the level of intervention (e.g., moderate or aggressive) or the length of intervention (e.g., 14 days or 60 days), students can see how outcomes change. And, by playing with the model, they will be able to answer questions like: “What is the impact of shortening our social distancing period?” or “What happens when we delay the start of our interventions?”

The full article is freely available on the New York Times Learning Network.

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