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The Penny Determination Algorithm

Some of my students fabricated their data, that much was obvious. The question was, which ones? I passed this graph out to my students and asked them to come up with a definition for cheating.

Most of them circled the same four extraordinary outliers but very few students could come close to verbalizing why they chose those outliers. It was just … obvious. The formula for statistical error was so intuitive they couldn’t verbalize it.

Something I enjoy about computational thinking (the focus of my position with Google) is that it asks you to explicitly verbalize processes that may only exist in your intuition, processes that are too obvious for words.

Case in point: which of these is a US penny?

100% of my students would correctly select I. But if I asked them, “Why? How do you know?” and requested a “Penny Determination Algorithm,” the sort of thing you could give to an alien race to identify our one-cent currency, it would drive them crazy.

“I don’t know. It’s just … obvious.”

My particular students may not be ready for that conversation but it would be a good one. We’d prioritize algorithms that used cheap inputs. After all, we could scan every coin and apply some kind of edge-finding filter in Photoshop, but that would be too expensive and time-consuming for the machine that counts your change at the supermarket. Once students completed their algorithms, we’d trade them around the room and try to throw exceptions at each other.

These conversations are very difficult to have with students whose teachers for the last eight years have a) defined the inputs for their students (“The area of a triangle depends on its base and its height.”) and b) given them the algorithms (“The area is half the product of the base and height.”).

Those students just want you to give them a sack of thirty objects so they can use the algorithm you gave them to answer the question, “which of these is a penny?” They don’t want to answer the question, “how do you know?” They wouldn’t know where to start.

Save The BetterLesson Blog!

Eight of the last ten BetterLesson blog posts have been teacher interviews. “Interview” is a misnomer, though, since the prefix “inter-” implies some kind of dialogue between two parties. These are “surveys,” a one-way conversation between a person and an fixed list of ten questions. (eg. “Coffee, tea, or caffeine free?”)

I’m not even skimming them anymore so let me drop some public encouragement into their suggestion box: if you see someone upload an exceptional lesson, ask the teacher how she did it. Ask her to describe her motivation and creative process. Or, if you see someone using your site exceptionally well โ€“ downloading lots of material, leaving comments everywhere, ratcheting her “impact” rating past “high” all the way to “jackhammer” โ€“ interview her about that.

I’m pretty sure I’m ripping off Kathy Sierra here but it seems empirically true to me that the point of your company blog should be to make your users more powerful, more enthusiastic, and happier about whatever brought them to your site in the first place. They should walk away from an entry on the BetterLesson blog inspired, excited about their career choice, and eager to reach “jackhammer” status on your site.

If this doesn’t make sense, check out Kickstarter which has โ€“ bar none โ€“ the best company blog around โ€“ killer interviews, tutorials, and podcasts, all of which make you want to sign up and get that hard cider business out of your head and funded on their site.

Nothing but love, BL buddies. Stay strong.

Is This What Lemov Means By “No Opt-Out?”

Someone, if not Lemov, ought to film this exchange. David Cox takes a student from “I have no idea.” to “Oh that’s how you do it.” without asking a single content question, just a series of Jedi meta-cognitive mind tricks that amount, basically, to this:

  1. What is the question asking you to do?
  2. What do you know about what it’s asking you to do?
  3. Do you notice any patterns about what you know about what it’s asking you to do?
  4. How can you use that pattern about what you know about what it’s asking you to do to answer the question?

Yo Dave: record that patter to MP3; sync to every portable music device in the classroom; take the day off.

BTW: Tom Woodward pulls a clip out of his vault that illustrates, if not this exact line of questioning, its tone.

My comment there:

If “feign the curiosity of a novice” isn’t an element of Lemov’s Taxonomy, he needs to get started on the second edition pronto. I think it’s a very small subset of educators who attempt this kind of assessment at all (ie. “waitaminit … walk me through this … “) and an even smaller subset of those educators who can pull it off without it seeming campy or in on their own joke.

This Is Why We Can’t Assign Nice Things

Fresh off our success decoding airline flight tables, I promised them we were going to crack the secrets of grocery stores wide open but to do so we’d need a lot of data. If we each sampled three data points, that’d suffice.

I gave them the weekend. I gave them a week’s worth of homework credit. I let them work with a partner.

33% of the class submitted data. That’s a pity. Even worse is the difference between the data I personally gathered last September (blue diamonds) and the noise my students submitted (pink squares) some of which was almost laughably fabricated. (As in, I laughed when I saw it.)

For perspective, I have one really exceptional outlier out of the thirty-six transactions I recorded: the person who took six minutes to purchase twenty items. It was a disastrous exchange featuring a price check and a ripped register tape. It was so bad that people happily fled that customer’s line for longer ones.

Out of my students’ thirty-two data points, they observed six transactions that were even more abnormal than that one, including one incredible checker who managed to ring up one hundred items in just eighty-one seconds.

Exactly one hundred items, right?