Teaching the Red Dot Right

or: An Open Invitation For School 2.0 To Pimp My Plans

I’m positive I could give that fable of greed, conspiracy, technology, and poker to a student teacher, ink still wet off her baccalaureate, and watch a pretty good show.

Every student has a natural preference for what is orderly, for what makes sense, whether they enjoy math or not. That red dot represents catharsis — the sense that mathematics has explained something very complex in very simple terms. This is an easy win.

Thing is, I’m unsatisfied by an instructional win here. I want to run up the score. So how do I maximize the value of this anecdote? I’m extremely interested in how othersSchool 2.0 to the white courtesy phone. would handle the same material.

The Ground Rules of Poker

You can’t assume too little here. All of my kids knew less about poker than I did. So I showed ’em hole cards (the properties of which kinda pin down this whole fiasco).

I asked them to rank the hands from worst to best. They missed a bunch. I asked why one hand beat another, drawing them towards this idea of probability — low and high.

Fake Hands

I took them through a hand, showing them their hole cards and asking them to raise a hand up if they wanted to fold their cards. If they wanted to see the next cards they’d have to wager $10. Imaginary math money. An extremely simplified version of poker.

Every step of the way, from pre-flop to the river, I asked them, what’s the best hand you could have here? What are you worried your opponent has?

The Problem With Absolute Poker

I asked them how online poker differed from table poker. I asked them how much money they’d feel comfortable pushing onto an electronic table, the only physical manifestation of which was a server farm in Costa Rica.

I pointed to the dollar figure in the screenshot — $62,250 — and told them that at the end of this particular tournament, the stakes were well into six figures.

Potripper’s Last Stand

Then I took massive creative liberties. I fabricated the final hand between Potripper and Crazymarco. It was only important to me that the students experience a hand which they absolutely should fold, a hand which a sane person would only hold onto if he could see his opponent’s cards.

I put four hearts on the board and gave my students two pair, a hand which, given the stakes, no one should play. If their opponent carried even one heart — not unlikely — they were totally hosed.

But I told them Potripper stuck it out and won the tournament on a weak hand.

I asked them, if you were Crazymarco, what would you think about all this? They suspected cheating, just as Crazymarco did.

I told them, well, either Potripper cheated or he was really really lucky. I told them Crazymarco asked Absolute Poker for a hand history. Hundreds of pages …

… which he and a pack of poker geniuses analyzed and organized into a spreadsheet.

Classwork

I gave them the two damning data sets (and retermed them so I wouldn’t have to explain concepts like “big blinds”): hands won and percent of hands played.

We talked a bit about what a negative number meant for hands won and what you do when someone with a low percent of hands played suddenly decided to raise the table. (A: fold pronto.)

I asked them for two histograms of each data set. We’ve done histograms. They’re powerful but good for nothing more than one data set at a time.

I asked them which stack held Potripper. They saw him but it wasn’t obvious yet if he was a lucky outlier or a guilty outlier.

So we made the move to two data sets. Graphing the two sets against each other was very revealing.

Lock Him Up

I showed ’em Michael Josem‘s sick plot. I asked them to point to the biggest loser on the board. And then I asked them if they saw Potripper.

They saw the red dot and I asked them if they thought that dot could hang so far out there propped up on luck alone. We agreed it was unlikely.

I quoted Josem’s back of the envelope calculation that this was like winning a million-to-one lottery …

… six times in a row.

Dude cheated. We felt it. We worked for it. That catharsis was earned. This was such an easy slide into two-variable scatter plots. The histograms didn’t yield anything valuable while the scatter plot all but put the cuffs on.

Pimp My Plans

I didn’t get much sleep the night before this lesson. Setting up slides like these, stocked with subtle, illustrative animationsSimple stuff like cards flipping over. Material this good doesn’t need much digital flash., takes timeNot next year it won’t. *pumps fist*. I coulda worked at it all night and, in truth, I made a lot changes — slight modifications to slide order, heavy modifications to handouts — between periods.

I got my money’s worth in the end, though. The students reviewed histograms, dug into a new concept successfully, and engagement was high.

But I was nagged often by the suspicion that a large group of educators I read regularly would cluck their tongues at the teacher’s prominence throughout the lesson. I mean, the teacher was talking a lot there. The desks were in rows. Where were the wikis, podcasts, digital cameras, etc?

So I’m curious, given a free hour, the objective that students need to review histograms and introduce themselves to scatter plots, how would School 2.0 rock this one? Feel free to use the Absolute Poker anecdote or not.

Tagging Darren and … uh … well, are there any other math teachers flying the School 2.0 flagAnd if there aren’t, um, shouldn’t the propaganda reflect that fact a bit more??

Enclosures:

  1. Keynote
  2. PowerPoint
  3. PDF
  4. Quicktime Movie
  5. Handout
About 

I’m Dan and this is my blog. I’m a former high school math teacher and current head of teaching at Desmos. More here.

11 Comments

  1. Why does your lesson need to be ‘pimped’ by the 2.0 crowd or otherwise?

    I always like to remember that the 2.0 crowd that ACTUALLY OCCUPIES CLASSROOMS, learned (hopefully) how to teach before they learned how technology might enhance a lesson / project / down time.

    If you’re satisfied with the level of student engagement, questioning, investigating, predicting, blah blah and so on down Bloom’s Taxonomy, then what are you really hoping to hear?

    Me, I’d just celebrate this lesson.

    The 2.0 crowd (and as a Tech Integrator / Instructional Specialist I must be included) surely doesn’t believe that everything needs a zap through the 2.0microwave.

    Conflict for conflict’s sake is a tiring endeavor.

    Just say you’re proud of yourself and what your students were able to accomplish/learn/so on and so forth.

    Those kids matter a lot more than any computer. Anyone who says differently, should, at least to me, grab an application for BestBuy. The holiday rush is a comin’!

  2. I’m more sincere than that. This was a great lesson, somewhere among my year’s best both in terms of measurable outcomes and that fuzzy/warm lightbulb-clicking-on feeling I experienced while leading it.

    But I’m discontent with something “great.” I’m interested in making this better.

  3. I’m serious on this one: what do you mean by ‘making this better’?

    When I work with teachers, the conversation usually goes this way:

    Teacher: I want to do this lesson differently; you know, better.
    Ken: Okay, what do you want the students to know?
    Teacher: Content
    Ken: Wait, I mean what skills do you want your students to improve?
    Teacher: Um…um..content, right?
    Ken: You’re not in a hurry to leave right now, are you???

    For this lesson, is ‘better’ less Dan and more student? What skills do you want them to refine/enhance/master (oh, the horror!)?

  4. I’m with Ken…

    Sure, you could have worked in presentation skills such that, after the kids were done, they created some kind of public presentation of their findings… in fact, why not still do that? See if one of the kids can get a Gaming Commission rep to do a conference call with the class (use Skype — it’s got 2.0 street cred.)

    Have the kids make a Google Preso of their findings or something so that the Gaming Commissioner can follow along, and then have the kids present it to that official for review and commentary.

    That’ll give their hard work context and meaning by placing it back into the larger world.

    But other than that, dude… great job.

  5. Yeah, that’s what I’m looking for. And, not to quibble, but pretty much any inquiry-based project (not just the School 2.0 variety) is gonna push past the hour I’ve budgeted for this unit.

    Do you find that you can hit all the state standards and still maintain your project-based stance at SLA?

  6. It’s a challenge, sure. Fortunately, in PA, they’ve distilled the state standards down to the state anchors… basically, they’ve showed their hands and told the schools what will and won’t be on the test.

    It makes it easier.

    (But, again in full disclosure, we do a lot more than the state anchors… but probably a little less than all the state standards in math.)

    I’m really lucky, I’ve got amazing math teachers who are able to really combine concepts into some amazing projects so that the when kids do apply what they’ve learned, they are doing it in powerful ways.

    Also remember, project-based learning doesn’t mean we never give quizzes… it means that the major assessments are projects, not just the minor ones. (Which is what I’ve seen in other non-PBL schools.)

  7. you’re doing amazing work here;
    i hope it’ll bring you a lot of attention.

    but i’m sure troubled by comments like
    “It’s called Information Design and I’m pretty sure it is the mathematical skill most lacking in our high school graduates.”
    .

    your graphic design skills are very impressive
    and your dedication to using ’em in creating
    effective lessons even *more* impressive …
    *but* i — and many another math-head —
    would very quickly have lost interest and chosen
    another playground if our teachers had
    openly *confused* math with graphic design!

    plenty o’ good math teachers can’t work a computer
    (or draw) very well at all and it’s gonna stay that way.
    obviously, at some level you understand this
    very well–witness your gentle rebukes of the 2.0 crowd.

    i promised here
    http://blog.mrmeyer.com/?p=339
    to leave you alone for a while;
    here’s hoping it’s been a long enough while
    that you won’t feel i’m abusing your hospitality.
    i just wish you’d reconsider (what appears to be)
    your conviction that *creating good looking documents*
    is somehow a vital component of good teaching.

    never mind being a good math *student*.
    if i start grading math students on presentation,
    may my right hand forget its cunning.

    pretty soon now you’ll probably quit this gig
    and get far better paid than you are now
    to *do* graphic design. this will of course be
    a loss for the math fraternity. meanwhile,
    i’ll still be at it, barely legible handwriting and all.
    & with any luck, some of my students will be glad i did.

    the “burnout” issue has come up from time to time
    on this blog and you’ve copped to the risk;
    this isn’t at all meant to accuse you
    of insufficient dedication. just, doggone it,
    admit you’re serving two masters or something.

    yours in the struggle; yours in the faith.

  8. Shoot, man, you want me to admit my conflicted interests, you got it. But I don’t want to confuse graphic design with tech know-how.

    I recently scanned a handout I found lying around — a gorgeous handout, clear, designed with intention, designed for understanding — which was handwritten.

    It was far better than what the teachers make who don’t know how to use a computer to keep their indents justified and whatnot.

    All that to say, my enthusiasm with graphic design predates computers. My assertion that, more than any other skill, high school graduates have no idea how to turn vast spreads of data (and nowadays you can’t get data in smaller quantities) into an understandable picture, also stands apart from technology.

    Always welcome ’round here, Vlorbik. Always glad for the opportunity to clarify my stance.

  9. This is a sweet lesson, for sure. Great hook. My question is, were you able to track how many kids fell off the clue train around the point where it pulled out of the poker hand station? My worry mirrors yours: With so much teacher-lead direction toward a goal, it’s inevitable that someone is getting dragged along a little faster than they can handle. And if I’m talking, it’s harder to listen for the screams.

    Now I’m assuming you do a lot of “checking for understanding” in here, but I’d be curious to know if you validate that externally. Maybe that’s a place the 2.0 crew would say you could keep your high-energy presentation but also collect more data (through clickers or whatever). I don’t think you need fancy toys to do it, but on my first reading of your lesson here, my questions are about how you did formative assessment.

  10. Yeah, good point.

    First, all that talking time was strictly storytelling time. No way any class outside of a college lecture hall would let me get away with teaching that long.

    The only objective here was that “students will understand why graphing data on one dimension is sometimes insufficient, why sometimes two dimensions are necessary.”

    To that extent, the razzle-dazzle was essential. They had to be clonked over the head with how easily that red dot hides amidst one-variable data but pops in two. That’s all.

    The real check for understanding (can you graph? can you draw conclusions from your graphs?) happened with How I Met Your Mother.

    Any improvements to propose on that one, by all means, let ’em fly.