Category: ontheroad

Total 9 Posts

Making It All Worthwhile

I was at urinal during a break in my Grand Forks session. “I’ll give you this,” the guy said next to me. “You walk your talk.”

Two things:

  1. The etiquette on urinal interaction must be a little more relaxed in North Dakota than in California.
  2. You get the subtext right? “I’m not buying any of this stuff, obviously, but you put on a good show.”

I knew exactly what he meant.

I’ve facilitated enough PD to not feel new at it. I’ve taken enough coursework in PD at Stanford to feel like I get some of the theory behind teaching adults about teaching children. Whenever I’m planning a session or a talk, though, I don’t lean on the theory or my experience half as hard as I do on the fear that I’ll be working with a teacher who’s exactly like me, and he’ll hate me. Which is to say, rather, that I’ll hate me.

My urinal buddy helped me understand that whenever I blog or facilitate PD or give a talk or drive in traffic or cook a meal or talk to my friends, subconsciously, I’m always wondering, “Would I hate me?” It’s a coin flip, really, whether that’s evidence of personal integrity or flagrant self-absorption.

Grand Forks, ND

I added an #anyqs component to the workshop I facilitated in Grand Forks, ND, last week. This was new for me. At the end of the first day, I assigned homework:

Give yourself one photo or one minute of video to tell a mathematical story so perplexing that all of your students will want to know the ending, without you saying a word or lifting a finger.

I received e-mails all the way through the night and into the morning before the second day’s session. I loaded each entry into a slidedeck and reeled them off to the group over 25 minutes.

At the same time, I had the participants working in a Google Form. For each entry, they’d write up a) the name of its designer, b) the question it provoked, c) the perplexity of that question (ie. how bad they wanted to know the answer).

The yield on that investment of 25 minutes was incredible. We spent the next hour mining and interpreting data and drawing conclusions about effective curriculum design with digital media. It was some of the productive professional development I’ve ever been a part of.

I posed several rounds of questions for table discussion. The first round began after they had just submitted all of their questions:

  1. Was the exercise fun? Was the exercise useful?
  2. What will be the most common question for your entry?
  3. How curious will people be about it?
  4. Which ones were you most curious about?

Then I sent out a link to the Google Form results and posed the second round:

  1. How effective was your entry at provoking a common question?
  2. How could you have made your entry more perplexing?
  3. Whose entry was the “best”?
  4. What do we mean by “best,” anyway?

While they batted those questions around, I dug into the spreadsheet and found the median response for each entry’s perplexity rating. Six of them tied for the highest median rating:

We reviewed those six, briefly, and then I posed a third round of questions:

  1. What’s special about these entries?
  2. If you had a favorite that didn’t make the cut, what isn’t captured by this measurement (the median perplexity rating)?
  3. Dan and Nancy both feature leaky faucets filling up a container. In what ways are those two entries different?

Selected Answers To Those Questions

  • The unanimous consensus was that the exercise was fun. Fun isn’t necessarily a prerequisite for an effective PD exercise, but man does it ever help.
  • One participant said the #anyqs exercise was useful, mainly, for “training my eyes.” She elaborated that after just one pass at #anyqs the day before, she was already more alert to the applications of math in her life outside the math classroom.
  • The issue of subjectivity has been one of the most fascinating conversations about #anyqs online, and so it was in Grand Forks also. Are the questions of math teachers about this image a useful proxy for the questions of students? Will a student from North Dakota have a different question about a video of a wheat thresher than a student from California? One participant noted that the high school and middle school teachers in the workshop asked questions that were linked closely to their content areas? (Strong data mining, right?) The sum of my thinking to date? Yes, the process is subjective. In spite of its subjectivity, field testing my curriculum with teachers has improved it immensely for students. Perplexity can transcend our demographic differences.
  • I forgot to mention this in Grand Forks but the easiest, best way to make your video-based problems more perplexing is to use a tripod. Or to simply put your camera down on something sturdy. The reason being is that it’s so much harder to gauge so many different measurements (speed, for instance, or height) when the camera is wobbling back and forth and up and down, throwing your subject around in the frame.

General Remarks

  • I have designed a lot of different constructs to explain to myself (and others) perplexing curriculum design. None has been as effective as mathematical storytelling. I’m particularly chagrined to think back on all the times I’ve broken a problem down into the four tasks of “verbalization, visualization, abstraction, and decomposition.” That construct resonates with my grad school peers, but it’s terrible vocabulary for teacher professional development. (ie. “Okay, so where do you find the decomposition of this task. How would you help the student abstract the problem space?” etc. Gross.) I’ve never heard table groups reference “decomposition” in one of my design activities. The language of storytelling, in contrast, was a constant feature of their conversations.
  • One participant: “We need a website for sharing these.” Yes.
  • Another participant: “Kids should bring in their own photos and videos.” Maybe.
  • This is the dy/dan drinking game: every time I put my readers to work to make me smarter or more effective in my studies or at my job, drink. I was legally unsafe to drive after receiving hundreds of pages of student work for my Michael Benson experiment. I was black-out drunk after using the work of @salmathguy, @reimerpaul, @eduz8, @techsavvyed, @fnoschese, and @wpeacock202, for fodder in my #anyqs workshop. Y’all should be so lucky to have readers like y’all.
  • There was a horrible moment in the early morning of the last day when I planned to hand each participant 28 strips of paper (one for each person’s #anyqs entry) on which she’d write her question and the name of the designer. Once we finished, I figured we’d trade the slips back to each other, a process that would probably take forty-five minutes on its own, right? So take a shot for Google Forms as long as you have the bottle out.

Your Homework

  • How are the two leaky faucet videos [Dan, Nancy] different? Which one is better? Define “better.”
  • One participant submitted this video of Carl Lewis’ 1984 Olympics long jump. He was perplexed by the parabolic motion of Lewis’ jump. Instead, nearly all of his colleagues (and yours truly) wondered how fast Lewis was running at lift-off. Given infinite resources, tools, the ability to travel anywhere in time and space, how would you capture Lewis’ long jump in a way that highlights the perplexity of his parabolic motion?

And Now A Word From Our Sponsor

If any of this seems interesting to you, let me recommend my Perplexity Session, which I’ll be hosting in Mountain View on 9/10/11.

Here’s John Scammell with a celebrity endorsement:

As someone who was fortunate enough to see one of the early incarnations of this workshop, I can tell you that it is incredibly valuable professional learning. Dan is a skilled facilitator, and more importantly a great teacher. I highly recommend it.

Colchester, VT: Standards-Based Grading

[BTW: I updated the SBG prompts below with some answers from the comments.]

In addition to the material I facilitated on instructional design, the staff at Colchester High School wanted to work on their implementation of standards-based grading. Happily, they had already agreed on the fundamentals:

  1. We should assess students on what they know now, as opposed to what they knew when we first assessed them.
  2. Assessment should be atomized to the point that it empowers teachers and students in their remediation.

This left me all the creative, interesting parts. We talked about reporting methods for keeping students apprised of their progress, both individually and as a class. We talked about the effect of SBG on retention. Then we picked a concept and had pairs come up with a score of 1, 2, and 3.

We debated productively about marginal scores – when a 2 turns into a 3, specifically – and concluded that, in a system this forgiving, we’d rather underestimate a student (who could return to improve her score whenever, wherever) than overestimate her.

We discussed, afterwards, how to construct valid, manageable assessments. I gave them four test questions, each of which, in its own way, invalidated what it claimed to measure or was unmanageable at scale. I’ll leave them here. Feel free to kick them around in the comments.


The trouble with the two-step equation problem is that it’s also an intimidating decimal arithmetic question. If a student fails it, you don’t know which skill needs work.


The issue with the Law of Sines / Cosines problem is that you do not have to use the Law of Sines / Cosines to solve it. A student can get those right WITHOUT using the Law of Sines / Cosines, especially the 30-60-90.

Also, the concept is too broad. If a student has a 2/4 on “Law of Sines / Cosines,” how do you know which one to remediate?

“Quadrilaterals” is also too broad a concept. If a student has a 3/4 on “Quadrilaterals,” do you know what the student knows about quadrilaterals? Which ones she understands and doesn’t?

We decided “Linear Pairs of Angles” is too small a concept. If every concept were this granular, we’d have several hundred concepts to manage by semester’s end.

Madison, IN

I take these speaking jobs for three reasons.

  1. To maintain the tuna-casserole lifestyle to which I have become accustomed, even though I’m only bringing in the part-time research assistant money these days.
  2. To compel me to find better structures, metaphors, visuals, and exercises for communicating good curriculum design.
  3. For the helpful feedback and criticism the attendees offer.

These groups of grownups are my classroom for the foreseeable future. It’d be a waste of a blog if I didn’t share what I learned last weekend.

  1. Mathematical notation isn’t a prerequisite for mathematical exploration. Mathematical notation can even deter mathematical exploration. When the textbook asks a student to “find the area of the annulus” in part (a) of the problem, there are at least two possible points of failure. One, the student doesn’t know what an “annulus” is. (Hand goes in the air.) Two, the student knows the term “annulus” but can’t connect it to its area formula. (Hand goes in the air.) ¶ That’s the outcome of teaching the formula, notation, and vocabulary first: the sense that math is something to be remembered or forgotten but not created. ¶ Meanwhile, let’s not kid ourselves. The area of an annulus isn’t difficult to derive. Let the student subtract the small circle from the big circle. Then mention, “by the way, this shape which you now feel like you own, mathematists call it an ‘annulus.’ Tuck that away.” ¶ Similarly, if I give you this pattern, I know you can draw the next three pictures in the sequence. That’ll get old so I’ll ask you to describe the pattern in words. You’ll write out, “you add two tiles to the last picture every time to get the next picture.” I’ll show you how much easier it is to write out the recursive formula An+1 = An + 2. ¶ I’ll ask you to tell me how many tiles I’ll find on the 100th picture. You’ll get tired of adding two every time, and we’ll develop the explicit formula A = 2n + 3, which makes that task so much easier. ¶ Terms like “explicit” and “recursive” and “annulus” can do one of two things to the exact same student: make the kid feel like a moron or make the kid feel like the master of the universe.
  2. “Talk to someone who actually makes ticket rolls. What kind of math does he have to do to make the thing,” said Russ Campbell, a community college adjunct instructor at least twice my age. Great idea, Russ. Speaking of which, pursuant to some harebrained WCYDWT idea, I spent twenty minutes on the phone with my local and state Departments of Transportation last week and it was almost too much fun to handle, peppering questions at engineers who were all too delighted that anyone gave a damn about how they calculated recommended speeds for curved roads. More of this.