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Archive for July, 2010

A black rectangle and the pause button will take you 70% of the way.

Where do you put the black rectangle? What question does that provoke?

BTW: I would put a black rectangle above Rich Eisen’s speed and ask the students to guess at his speed. Then they’re converting from yards per second to miles per hour and you have a nice conversation about good time intervals for that calculation. (If you time him over the entire forty-yard dash, your estimate will be well below his top speed.)

Where do you press pause? What question does that provoke?

BTW: I would press pause on the clip where Eisen gets a head start on Jacoby and ask them how long it will take Jacoby to catch up to Eisen. Which is a nice enough way to introduce systems of equations.

2011 Feb 16: Rich Eisen calls me out on Twitter.

Kathy Clark Couey:

Can we see the “sturdy rubric describing the beginning, middle, and end of great application problems?”

Sure. The following rubric arose (without much coercion!) as we tried to resolve the different instructional outcomes between these two variations on the same theme.

What did we miss? Where did we overreach?

Beginning:

  • engage the students with multimedia — pictures, videos, sound.
  • the students come up with the question.
  • the students make predictions — “give me a guess.”
  • the students establish a range around their answer — “give me a wrong answer. give me an answer that’s too high, that’s too low.”
  • there isn’t information on the first image.
  • “announce the problem’s constraints quickly and clearly.”
  • ask questions that lend themselves to guesses: “how long? how many? how heavy? how far? how fast?”
  • try to translate questions that are harder to guess into questions that don’t change the objective but which lend themselves to guesses: “what is the area? what is the circumference?”

Middle:

  • ask: “what information do you need to solve this?”
  • ask: “how do you know that?”
  • ask: “why?” “how?” — even on right answers.
  • encourage students to explain their reasoning to other students.
  • ask students to collaborate — “what do you think about jerold did?”
  • ask: “how would that help you?” after they tell you certain information is necessary.
  • ask: “what isn’t necessary to find the answer? what information don’t we care about?”

End:

  • ask students to summarize the process.
  • sequel technique #1: change a variable. eg. change the height of the water tank. change the number of sides of the base. make it a hexagon or a dodecagon. change the rate of flow.
  • sequel technique #2: turn the answer into a question. at first we asked, “how many tickets are on a roll with a particular diameter?” now: “what’s the diameter of a roll that has 1,000,000 tickets?”
  • ask: “does the answer make sense?” — have them compare their answer to their ranges.
  • show, don’t tell, the answer — ie. the label said 2000 tickets; the timer said 8:12.
  • discuss sources of error.

I just finished facilitating “WCYDWT: The Workshop” over four days in Kannapolis, North Carolina. Maybe this should’ve been easy. I had three years of posts and a handful of presentations to draw upon for material. I had to condense the former resource, though, and expand the latter while adapting both formats for a workshop. The preparation lasted the first half of 2010 and was — hands down — the hardest work of my professional year. The facilitation was the most fun.

I learned a pile, both about facilitating workshops and about a model for instructional design I thought I had pretty well figured out. This is my usual debrief, then: notes that are useful to me, posted on the offhand chance they’re useful to you.

How We Used Our Time

  • 1.5 days — towards better conceptual problems
  • .5 days — towards useful tools for creating better conceptual problems
  • 1.5 days — towards better skill development problems
  • .5 days — towards lab work, as you like it.

Sessions

I can clarify that schedule and save myself some bandwidth at the same time by directing you to the session sites, which include more detail.

The Opener

If we did nothing else right, we opened our time together well with some highly combustible mathematics. Per Brian Lawler’s suggestion, we began with the ticket roll and the water tank (which, for the record, I had never attempted to solve until last Tuesday with those teachers in Kannapolis).

I tried to lead them through those problems as the best version of myself, by:

  1. asking them what questions interested them about the multimedia,
  2. soliciting their intuitive guesses towards those questions and encouraging a competition around those guesses,
  3. asking them to describe an answer they’d reject as too low or too high (ie. “give me a wrong answer.”) in order to set their parameters for an upcoming error check,
  4. asking them to tell me the information they’d need to solve their question,
  5. checking in with groups as they worked, bringing student work beneath the document camera, asking them a lot of questions that began with “why,”
  6. asking them to check their obtained mathematical answer against their error parameters from [2],
  7. comparing our mathematical answers to our intuitive answers and then to the actual, no-joke real-life answer,
  8. discussing possible sources of error, since nobody’s answer was exactly correct,
  9. extending the problem and differentiating between learners by offering what we came to call “sequels,” (eg. “what would the ticket roll’s diameter measure if it had 1,000,000 tickets?” or “how long would it take to release all the water from the tank?”, a problem which every group missed by a margin well above 200% but corrected quickly, which was awesome to witness. (Thanks, Steve.)

The moment of combustion came when I asked them to create the comparable problems they might assign out of a textbook. It’s always been true for me that I grow most as a teacher when I try to reconcile the exhilaration I often experience, personally, as a learner, with the tedium I often inflict upon my students, professionally, as a teacher.

The product of the first day was a sturdy rubric describing the beginning, middle, and end of “great application problems,” a rubric that arose naturally from those opening activities, a rubric by which we navigated the rest of the workshop.

What I Learned About WCYDWT

  • In terms of technical skills relevant to this kind of instructional design, a black rectangle and the pause button will take you 70% of the way. Exemplar forthcoming.
  • Storytelling is the technique by which one problem can be made simultaneously more engaging and more challenging than another problem that assesses the exact same content standard. For instance, consider the difference between “What is the area of the circular lawn?” and “How long would it take you to mow this circular lawn?” The difference between the two is an instructional bonanza. You’re getting so much for so little. (Thanks, Kyle.)
  • Graphing Stories is really boring, again, except for storytelling. Consider a fixed shot of a math teacher walking down two flights of stairs over fifteen seconds. That’s boring. But attach to that boring video the framing device “graph height against time” and suddenly we’re throwing pencils at each other, arguing over the effect of the curb at the thirteen second mark, etc.

Do Better

  • Send along a list of required software in advance. Day two slowed down quite a bit when we couldn’t install Handbrake, QuickTime, or Geogebra due to access restrictions on the teacher laptops. I should have made that list known to my liaisons a lot sooner. (Any experienced facilitators have a tip for me here?)
  • Lecture less. I initially tried to lecture my way into the rubric for great application problems and into the connection between storytelling and teaching. Clearly, I should have packaged that material as fodder for table discussions and then share-outs.
  • Stick tighter to the rubric. We had a good list. By the last day, we were evaluating every product against it, even ones I brought to the workshop. That should have been our m.o. all the way through.
  • Develop a rubric for great skill development problems. Those techniques are more abstract. The rubric would have been much shorter. It would have been a useful exercise, though.
  • Do more math. Do more teaching. During our lab time, I should have insisted that we actually teach each other and actually solve the math because a) that’s the fuel, teachers exhilarated by learning in a way that their students should be also, and b) merely describing a lesson or describing a solution allows you all kinds of fictions that only become obvious once you try them out.
  • Clarify misconceptions about my own WCYDWT workflow sooner. Unless you correct them explicitly, your workshop participants will assume you do all the awesome stuff you’re describing every period of every day. One participant called that effect “demoralizing.” I need to put it out there as soon as possible that this is a model for instructional design that I only aspire to every day.
  • Find an opening for Google Reader and Delicious. That’s the Swiss Army Knife right there. I couldn’t find the right moment, though.
  • What do you do about error? I reckon this question is worth half a day on its own, and I’m nowhere near qualified to answer it. What do you do when you see a student in the middle of an error in reasoning or computation? The answer to that question is somewhere central to this WCYDWT thing, but we didn’t address that one directly at all.

Meaningful Quotations

Paula, a workshop participant:

I don’t know if I’m creative enough for this. I think it probably just takes practice, though.

Dr. Tom Sallee, not in attendance:

A good problem announces its constraints quickly and clearly.

Statement of the Librarian of Congress Relating to Section 1201 Rulemaking:

Motion pictures on DVDs that are lawfully made and acquired and that are protected by the Content Scrambling System when circumvention is accomplished solely in order to accomplish the incorporation of short portions of motion pictures into new works for the purpose of criticism or comment.

It was getting to be a huge pain propping my Hi-8 camcorder up on a tripod in front of my TV just to grab clips from NBC comedies. [via]

Naples Daily News:

According to county guidelines, yellow lights should be on one second for every 10 miles per hour of the speed limit. With a 45-mph limit on Collier Boulevard, the yellow light should have been on for 4.5 seconds. Instead, it was only about 3.8 seconds, Mogil said.

Yellow Lights — Kannapolis, North Carolina from Dan Meyer on Vimeo.

So I’m thinking about an ongoing classroom project, something that includes a wall map of the county, push-pins marking off claimed intersections, students collecting data with stopwatches or cameras, developing (what seems to them) a fair algorithm for the duration of yellow lights, then researching the county code to determine the actual algorithm, finally marching down to city hall to call the mayor on the carpet (if need be) for his reckless disregard for public safety in pursuit of a little extra revenue.

The math isn’t terribly difficult here — algorithm development, some discussion of domain, data visualization — but it’s the sort of project a) that takes place largely outside of class, and b) that stitches a class together, united against The Man, in a way that’s hard to reconcile with the usual instructional value calculus. (ie. how many hours of class time would you spend to create this kind of community out of your classroom? At their twenty-year reunion, will your students remember their investigation of cylinder surface area or the time they brought down city hall?)

Also, I should point out that the first thing I did when I rolled into Kannapolis, North Carolina, last Monday was shoot video of twenty traffic lights. Because I am often little more than a breathing apparatus and a set of limbs for whatever muse puts these ideas in front of me and I have to keep her happy.

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