Self-graded quizzes and learning how to ask questions

This whole remote learning thing has given me a lot of time to think. Well, maybe not a lot of time, given that I’m trying to plan, teach, and call parents with two toddlers dragging me into a never-ending game of hide-and-seek. But despite this, and the fact that I’m in essence a first-year teacher again, I have been trying my best to lean into this moment and try out some new things.

One of these things has been self-graded quizzes using Google Forms. Amy Hogan uses them a lot and was kind enough to share one of hers with me to get me started. After using hers as an example, I’ve created two in the past two weeks and really like them. I have attached a small grade to the quizzes to encourage kids to do them and take them seriously, but in the future I want them to be gradeless. Because of their self-graded nature, they do take a bit of time and energy to set up, but the flexibility and convenience they offer is pretty sweet. Trying to come up with interesting questions has been fun.

Since I try to leverage student work a lot, I’ve tried to come up with questions that ask students to analyze a piece of student work. Here are two that I conjured up:

As a formative assessment, seeing if my students can find errors in a coherent piece of work is a valuable task, but having the assessment data immediately available is actually what makes these types of questions worth asking. If these were free response questions, it would be a nightmare. I’d have to wade through the mire that is their responses and still wouldn’t have the clean, informative data that the self-graded quizzes give me.

Though I have included a couple free response questions, I’ve been trying to avoid them. Combing through all of their answers to check for equivalent solutions is something I’d rather not do. It defeats the purpose. When I do give a free response question, though, I’m learning how to include in the question what the format of the answer should be. For example:

That worked. Here’s one that didn’t:

The kids submitted all sorts of craziness from “105” to “the answer is 105” to “the remainder will be 105” to “105/x-5.” This turned into me checking through their answers one-by-one, like I would have normally without the use of a self-graded quiz. No fun.

On the other hand, here’s a question I created as a workaround to simply asking students to find the value of csc(π/2):

It’s not a great question by any means (neither are the other two), but at least it’s not free response and it’s a little less Googleable than it otherwise would be. Plus, when combined with the work they submit through Classroom for other problems we do, the question helped give me a loose understanding of what the kids know about radians. Then again, who knows. This is remote learning. Their big sister could be doing these quizzes.

I’m left thinking about how else I can spin my questions. How might the format of the question depend on the math that it’s asking about — and vice versa? What about using response validation? This would take even more work to design, but it is interesting to see where it could go (pun intended). I’m also thinking about using checkboxes in a question with multiple correct solutions and requiring students identify one or all of them. I could also give a multiple choice question, not including the correct answer as one of the choices, but having an “other: ______ ” option where they would enter their answer. This could be a nice alternative to the remainder question I gave above because it would let kids know how to format their answer and could then be easily self-graded by the form.

There’s so much room for creativity in these quizzes that I wish I had more time to explore them. They’re so useful that I’m looking forward to having them follow me back into the classroom, whenever that happens. As for now, it’s back to figuring out where I’m going to hide next. The closet!


On writing thank you’s to fellow teachers

As part of Math for America’s #MfAThankATeacher campaign, I spent a good chunk of time last weekend writing Thank You notes to MfA teachers. Having been buried in remote learning, I started writing them on a limb right after breakfast. I realized soon after I started that I couldn’t stop. By the time I finished the first one, I was reminded of someone else and that triggered a feeling of gratitude that I had to honor. And then the second note did the same. And on and on it went for an hour and a half. At that point, I had unexpectedly written a dozen or so paragraph-length notes to teachers that have touched my career in major ways that they probably never knew about.

Besides having warm, fuzzy feelings hold me down for the rest of the weekend, writing those notes brought to mind the staggering number of teachers that I’ve met through Math for America and the spiderweb-like threads that connect us. I thought of how ideas and projects move so fluidly between people in MfA and how those people bond and grow as a result. I am happily in debt to so many people in the community and it felt great to finally pay up.

I’m excited that MfA created and is promoting this teacher-thank-teacher campaign because, during these extraordinary times, it’s especially important that we teachers take time to appreciate one another. While I’m flattered anytime anyone gives me love because I’m a teacher, receiving the respect and appreciation from a fellow teacher — especially one that I admire — lands differently with me. It’s a no-strings-attached, we’re-literally-in-this-together compliment. Coming from another teacher, it’s totally unexpected and unsolicited. That may be the best part. Most of us feel that our teaching is horrible right now and that nothing is working. A personalized note of appreciation from a colleague is a pleasant surprise that can cut through our many layers of angst. And, these days, we teachers need as many pleasant surprises as we can get.



Weekly Math Themes for Remote Learning

To cope with my own angst during these extraordinary times, but also to help breathe life into remote learning, I’ve begun exploring using weekly “themes” for Algebra 2. For the sake of my own sanity, I’m haven’t been looking to tie the themes directly to my Algebra 2 curriculum. I’m not fighting that battle right now. Instead, the themes will be filled with lots of tangential math that is generally interesting and useful. I’m also aiming to give my kids more exposure to the cultural and social underpinnings of math. These interactions will be surface-level by design; casual glances that may or may not stir something deeper within my students. I’m OK with this. With no state-testing breathing down our necks, my only hope is to escape the vice grips of the Common Core a little bit. I simply want to add dimension to our class. Alternatives. And, who knows, maybe this work will spark something that lingers when we resume the regularly scheduled program.

So, each week, in addition to the scaled-back algebra 2 content, I plan on offering up videos and readings that elicit the theme for that week and then ask my kids to produce something. This past week, for example, the theme was mathematical genius. I had the students watch a clips about Terry Tao, Jaxon Cota, and Magnus Carlsen, while also read this blog post. I then had them write a short reflection on their noticings, wonderings, and any themes they saw. (I got this whole theme idea passively from Benjamin Dickman, who posted his weekly plans for his Problem Posing class. Of course, I stole his first theme and resources.)

There is around two months of school left and I’m going to figure out the themes as I go. I have been brainstorming, though, and I want to dump my early deas into this post. I’ve been reading Mathematics for Human Flourishing by Francis Su — which is stocked with inviting ideas. I may pull from these as time passes.

Here’s what I have so far for possible themes, some related resources, and possible student outputs. It’s messy and incomplete, so bear with me.



Student work + Remote Learning

When it comes to actual teaching during these trying times, one of the biggest obstacles is getting into frequent contact with authentic student work. I don’t how authentic it is, but I have been able to examine student work just about everyday in a way that isn’t totally horrible. Plus, with a little prep beforehand, I’m experimenting with how to seamlessly bring their work into our Zoom sessions to start conversations. Here’s what I’ve been doing. (My pal Michael Pershan wrote a great post on this topic, too.)

1. Before class, students do some math by hand on a given problem I’ve assigned.

2. They scan their work using Genius Scan. Scanned work has some serious advantages over regular photos. It’s clearer and glare and other lighting issues are usually minimized. Genius App is free — and I’m sure there are others like it.

3. They upload their scanned work to Google Classroom. I create a new Assignment for each problem in Classroom so that I’m only looking at work from one problem at a time. I make it clear to the kids that their “grade” for the assignment is based purely on completion, not correctness. That’s the bait I use to encourage them to submit work that is genuine. I think it’s working, but who knows. What else do I have?

4. After they submit their work on Classroom, here’s how it appears on my end:

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In doing this almost every day, looking over their work and providing feedback has worked out far better than I thought it would originally. The whole process feels like it did when I collected work from them in person (minus handwritten feedback). The arrows near the top allow me to toggle between students with ease and leaving a “private comment” becomes a space for direct feedback that is emailed to each student on the spot. Copy and paste is my friend for common errors, which is a nice bonus that comes from typed feedback. In the comments, I have even been including links to other students’ work (anonymously) and YouTube videos that I know would help them. Some kids have told me that the feedback is helpful, but I know there are others that never use it…but this is not unlike the oft-ignored handwritten feedback I used to give them, right?

5. After looking at all of their work, I choose 3-4 interesting ones and paste those into a Google Doc. During our Zoom sessions, which are twice a week, I am developing a routine where I give the link to the doc and then put students in breakout rooms to discuss the work.

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What’s nice about this is that not only are they assessing other kids’ work, which I find to be a worthwhile and engaging task for them, but even if they didn’t do the problem or submit it on Classroom (which is A LOT of them), they still have access to it and can think about math. It keeps all kids in the loop. Well, at least in theory. Most of my breakout rooms are jarringly silent.