Month: March 2010

Total 13 Posts

What Can You Do With This: The Italian Job


If you’re the sort who likes to figure this WCYDWT thing out for yourself, here’s the clip I’ll be discussing after the jump. Also: my readers outside of Burma, Liberia, and the United States can safely skip this one.

Click through to view embedded content.


Whenever a student asks me how tall I am, I always answer “79 inches.” (It’s a math teacher thing.) The student’s first reaction is, inevitably, “Seven foot nine?!” The student’s second reaction, after dividing 79 by 12 and seeing “6.6” on her calculator is, “Oh. Six foot six.”

This drives me nuts. Once a student has the idea that decimals are inches, it’s nearly impossible to convince her otherwise.

Apparently, high school freshmen wrote the 2003 remake of The Italian Job. Halfway through the opening heist, Seth Green tells Edward Norton to mark “14 feet 8 inches from that west wall” but Norton measures out 14.8 feet on his distance sensor. Decimals aren’t inches, Ed! You’ve gone 1.6 inches too far!

I don’t know the extent to which that error should scuttle the entire plan but Mos Def makes the same mistake on the floor below so the whole thing looks pretty grim.

This is a clear application of entries #7 and #43 from the WCYDWT taxonomy.

#7: Put the student in the same mental frame as a character from a TV show or movie. Have the student solve the character’s problem.

#43: Allow overconfident learners to pursue incorrect answers.

So you put them in the same room as Edward Norton by giving them a piece of grid paper. You tell them every minor line represents an inch. You’ve really stacked the deck with this one, having drawn major grid marks every 10 lines, instead of every 12. You’re inviting the likely error.

You play the clip as many times as they want. Encourage solo work on this one. (Edward Norton was alone in the room, after all.) After a given time, you invite a confident student up to the board to draw a safe you know in advance to be incorrectly placed. At that point, most students have decided this activity is really easy and way beneath them. This overconfidence is gasoline. As students discover differing answers to the same totally easy problem, they’ll argue and debate. These frissons around the room are the little sparks in the combustion engine of learning.

If a student miscalculates my height by an inch, it’s no big deal to her. The stakes are too low and the percent error too insignificant. But if a student blows up the wrong part of a floor and loses millions of dollars in gold bricks she thought was a sure thing, that’s productive frustration, even though the stakes are imaginary. We can work with that.

BTW: Delise Andrews offers a handout that is much better than mine. Thanks, Delise.

Guess The Eggs

So you have here a fairly straightforward carnival estimation game, which I decided to complicate by filling up a smaller container with the same kind of (horrid) malted eggs and making that quantity known.

I surveyed my students, my math-department colleagues, some of their students, my principal, and the central office staff. A little over 100 guesses all told. I tagged each guess with the following metadata:

  • name,
  • guess type (gut check, visual estimate, math computation),
  • job description (student, math teacher, staff member, principal),
  • current math class (eg. Algebra 1, Geometry, AP Calculus, etc.),
  • grade level (freshman, sophomore, junior, senior),

I showed my students the raw data and asked them what they wanted to know. I wrote their questions on the board.

  1. who won?
  2. who guessed worst?
  3. what was the ranking of everyone in between?
  4. what type of people used math computation for their guesses?
  5. were there any tied guesses?
  6. what was the highest/lowest guess?
  7. which grade level guessed the most?
  8. which grade level guessed the best?

Define “Bounty”

I said I was offering a “bounty” for answers to those questions and asked them to define the term. Some kids had seen Dog the Bounty Hunter and explained it from that angle. I assigned each question a point value that corresponded roughly to a) the difficulty of the question and b) its relevance to my objective — how are absolute value and percent error useful for calculating accuracy? I offered 20 points for a picture of an interesting fact. (See “Interesting Pictures” below.)

They had to scrape together 100 points for the day and I offered extra credit for initiative, divergent thinking, etc.

What Happened

Students worked in pairs on laptops. They downloaded an Excel sheet with all this data, including the real name of every guesser. Naturally, they were into that.

The great part about a sample size of one hundred guesses is how easy it was to determine which groups were taking a tedious, manual approach to these questions and which were using Excel’s built-in capability for sorting and calculating. I circulated the classroom and could tell that a group was ready to learn more about Excel because they were using hash marks to count up every freshman, sophomore, junior, and senior. Those students were wandering the desert on foot, ready for the water, compass, and camels I could offer them.

Likewise, I saw another group of students subtracting all one hundred guesses from the actual answer (1831) one at a time on cell phones. It didn’t take much to convince them to experiment with another approach.

The Constructivism Multiplier

My favorite conversations with students centered around a definition of “accuracy,” as in, “who were the top ten most accurate guessers?” Our earlier trick of just subtracting the guesses from the answer messed with Excel’s sort mechanism, unhelpfully stacking positives on top of negatives, when, really, we didn’t care if you guessed 100 eggs too high or 100 eggs too low. For our purposes, those two people tiedThis is a good companion exercise, in that sense, to How Old Is Tiger Woods?.

Two students were so close to constructing that operation themselves I had to bite off my tongue to keep from spelling the whole thing out (“ABSOLUTE VALUE! SUBTRACT AND THEN TAKE THE ABSOLUTE VALUE!!”) and then the bell rang. We didn’t graph anything. We didn’t get to percent error. Half the groups got to absolute value.

Off moments like this, I have determined my constructivism multiplier to be four, which is to say it takes me four times longer to bring a student to conceptual understanding through conversation and questioning in a social situation the student helped create than it does to get up in front of the class and simply give it to them straight, no chaser, through direct instruction and a handout of questions I wrote.

What I find maddening about conversations with committed constructivists (cf. the conversation here) is the reflexive assumption that educators choose direct instruction because they’re either power-drunk or self-obsessed or because they lack faith, courage, or high expectations. I can’t, personally, wave so dismissively at the massive institutional impediments to student-constructed learning.

Interesting Pictures

Percent Error By Grade Level

Percent Error By Guess Type

It’s worth pointing out here that “Math Computation” isn’t the same thing as “Correct Math Computation.” The most accurate guessers verified their correct math computation with a visual estimate.

Percent Error By Math Class

Percent Error By Job Description

That last graph is what I meant at TEDx when I said that math gives your intuition a certain vocabulary. The math teachers have a more descriptive vocabulary for expressing their own intuitions than the students do. This is also a fair answer to the question, “when will I ever use math?” You might not. You can live without it. But it makes a lot of intuitive tasks a lot easier. And you should also understand the risk that you’ll one day be fleeced by or passed over for those who know how to speak with that vocabulary.

The Creative Feedback Loop Of Teaching

Where else can you get this? In all of the creative fields that have ever tempted me professionally — I’m talking about graphic design, screenwriting, and filmmaking — ideas often take months to generate and refine, years to produce, and, in many cases, you can’t do anything with the feedback except hope it’s good enough to get you your next job.

With teaching, you can get any old harebrained idea on Friday, challenge your students with it Monday morning, then adapt it for your afternoon class based on feedback from the morning. The feedback loop is fast enough to give you whiplash. It’s so much fun, this job, it seems impossible sometimes that anyone could ever walk away from classroom teaching.

The Grand Prize

Not those horrid malted eggs, that’s for sure.

Blogging So I Don’t Have To

I’m drafting a longer post right now on a recent classroom exercise. (Teaser!) Meanwhile, here’s some stellar work from around the edublogosphere:

Scott Elias writes up what you need to know when you’re done with teacher school, a list that rings true to my own experience, especially his advice to “be interested.”

No, that’s not a typo. I don’t want you to worry too much about being interesting because that’ll take care of itself. And, let’s be honest, you just can’t force that. So start out your first year in the classroom by being interested — really interested. And please, for the students’ sake, show them that you’re interested in more than just your content area. You’ve got a passion (presumably) so don’t be afraid to let it come out in who you are in the classroom.

Megan Golding and Nick Hershman invigorate two of the most contrived content standards in all of the high school mathematics (as far as I’m concerned) — combined rates for Megan, ie. “How long does it take Timmy and Marsha to mow the grass if it takes Timmy 2 hours on his own and Marsha 1.5 hours on her own?”; systems of equations for Nick, ie. “A train leaves Philadelphia at noon, etc.”. These concepts are incomprehensible to students as words on a page but enjoy the difference when Megan and Nick first a) visualize the problem with multimedia and then b) access student intuition. I love, also, what Nick says about making the WCYDWT media:

As I’ve been editing them I can’t shake the feeling of being frequently rewarded when a calculation adds a meaningful piece of info into the scene or turning pixels roughly into meters and determining a subjects’ speed by calculating the difference in location over time. The math feels really useful. It’s hard to get that by having them watch the video. I had it by making it.

Sam Shah opens up his unit on area under the curve by giving his students a visual question and then asking them to simply get their hands dirty:

What was interesting to me was how hard it was for them. Not the estimating, or the making of triangles and rectangles and other smaller pieces. What was hard for them was being asked to do something that they didn’t know how to do. It happened multiple times that kids were sheepishly telling me that they didn’t know how to start, that they were doing it wrong, that they didn’t know the right way. They were telling me this to assuage some part of their psyche that was telling them that they had to be right. I told them to STOP BEING CONCERNED ABOUT KNOWING THE RIGHT WAY and just TRY SOMETHING! Then they did.

This last link has nothing to do with anything except for the fact that I’ve listened to this mashup track featuring Lil Wayne and The Office (called Office Musik) about a million and a half times tonight. Not safe for a) work or b) people who don’t have awesome taste in music and tv.

Working At Google v. Working At A Public High School

I carried a pedometer in my pocket all day every day from January 1, 2010, up until March 6, 2010, when I lost it somewhere in the New York City subway system. My 2010 Annual Report will be all the worse but I could at least salvage one interesting infographic:

Posted without comment, though if you’re into this kind of commentary, you can find more spread throughout this thread.

Easy. Fun. Free.

Here is one of my private assumptions about education innovation that could use some public criticism:

If [x] is going to change teaching practice at scale, then [x] needs to be easy, fun, and free for both the teacher and her students. [x] needs to be all three of those things at the same time.

Realize that if you’re a teacher and you’re reading a blog post, you’re automatically seeded in the top 10% of innovative educators. You’ll try anything once. Let’s also go with Jack Welch and assume that 10% of educators are hopelessly and/or willfully incompetent.

Convince yourself, then, that 80% of teachers exist on a sliding scale of innovation and are basically up for grabs. Those who don’t want to try [x] aren’t necessarily bad educators. They may have made a rational calculation that [x] isn’t easy enough, fun enough, or free enough to adopt.

There are implications here, some obvious, some subtle:

  • “Good” doesn’t matter. This is a little sad. But most of those 80% already have [y], which they consider “good enough.” They won’t pick up [x], however superior it is to [y], unless it is easier or more fun. This puts the burden on the reformer to make something easy, fun, and free that is also good. Good is the Trojan horse of education innovation.
  • You’ll have to package [x] for Internet distribution. Because it’s the only way to distribute at scale for (nearly) free.
  • Learning should always be fun, though I’m not talking about “fun” as it exists in “unlimited rides and deep-fried Oreos at Six Flags.” Rather I’m talking about the profound sense of satisfaction and accomplishment inherent to good learning. Just to be clear.
  • Learning isn’t always easy but learning tools should be. Just for instance, last week, I saw groups of students clicking the same download link over and over again in Safari not realizing that they had already downloaded the attachment. The download window was open but obscured by the browser. Anecdotes like this make me skeptical of Scott McLeod’s argument that computers are to teachers what checkout registers are to grocers. Many of you have vastly overrated the ease of educational computing.

The field of easy, fun, and free innovations that are also good for students isn’t exactly crowded but, for the record, I have bet on two horses. I expect these picks to strike certain readers as simultaneously naive, deranged, or self-obsessed but these innovations, more than any other I’ve used or observed, are ones that sell themselves:

  1. Google Reader.
  2. What Can You Do With This.

No further comment.