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Tuesday, April 12, 2011


This year I look forward to and dread at the same time broaching binomial expansion/bernoulli trials/pascal's triangle in Algebra 2. (They are so stickily intertwined, their little tentacles all wrapped up around each other.)

I'm looking forward to it because I have a problem to pose that the kids will dig. That I am shamelessly stealing from Jason Dyer.

See QBert.

See him hop. Hop, QBert, hop. 8-bit music is rad. Kids will be amazed that I have an Atari. And brought it in. And let them play it. (Side note: saw a kid in Learning Support today playing Google Pac Man. Way to get around the filters, kid! Well played.)

I'm sure you see where this is going. QBert starts at the top. How many ways to get to any block? I used Geometer's Sketchpad and made them a beautiful blank QBert board to scribble on. I figured out how to do it with iterated transformations. It was exhilarating.

In an ideal world the curious cherubs will count pathways and write them down and notice some patterns! And think it's cool and try to explain mathematically where those patterns came from and everything will be lovely and we will break into song like we're in a Disney TV film about a high school where everyone is happy all the time and even when they are not happy they only have problems which you might describe as adorable.

I dread it because this is what will happen in my world: they will get confused looks on their faces for 5 seconds. Then they will start talking about unrelated topics. I will say "How can I help you?" They will want me to show them what to do. I will resist. I will say "How many paths can he take to this close block right here?" They will say 2. They will write it down. They will get confused looks on their faces for 5 seconds. They will start talking about unrelated topics. I will try to prod them along to listing out the rights and lefts. I will say the words "right" and "left" approximately 900,000 times. Each.

We will waste 20 minutes.

I will feel like the world's crappiest math teacher.

I will whine about it on my blog.

I will try something similar next week.


  1. Thanks for this post. My classes go the same way so often and sometimes I wonder if the magical blog community never has those problems. Good luck!

  2. I'll try something similar next week! Someday they will let me kick the football...

  3. Clearly the solution is to only allow one question for each completed level of Q*Bert. Each additional question can only be asked after completing the next level, which will be progressively more difficult.

    At the very least, they will quickly develop an appreciation for the fancy > 4-color palettes and full symphonic scores of modern video games. ;)

  4. Well done for your efforts. Even though sometimes it seems as though they are wasted. Big sigh. I am frustrated from teaching about geometric and arithmetic sequences for three weeks and then the test showing that we have learned very little. The test review lesson was today and I was still dragging them along. Sigh.

    But I have to believe that it's not always this way. And choose to remember some better days!

  5. With regards to your last set of comments, I'm with you. Sometimes one section of kids will buy in to what I think is a neat activity, while another section seems bored and distracted.

    This job is easy. Right?

  6. You are all very kind. Thanks for indulging my moment of mope.

  7. Two things I noticed:
    1) Oh boy, even the famous Kate Nowak has cool lessons that are disintegrated by kids un-persistence. I feel better now.

    2) It sounds like your kids, like most of the ones I work with, really really struggle with the "Solve a Simpler Problem" strategy. They don't think they're allowed to go step-by-step, or they don't see the value in it, or they don't record their work and exploit patterns in the previous stages.

    Sometimes explicit instruction in the simpler problem strategy can help... "What makes this problem hard?" -- generate a list. "How can we change it to make it easier?" -- make another list. Often I have to start this list and help add to it and kids say, "we can do that?!?" Then help them try the simpler versions and RECORD what they do. Come back together and discuss: what did we learn? Does any of it have to do with the original problem?

  8. The challenge I see in selling this is that you have to sell them on the coolness of a 2-D game from twenty five years ago AND on spending twenty minutes analyzing the game by determining the number of pathways to each square.

    I could be completely and utterly wrong with this suggestion, but I'd suggest providing homework the day before the lesson for the students to play a few games of QBert online. Here's a link to a Sony version:

    Then, for those who tried it, the lesson becomes one of figuring out strategy using math, even if it really is more about math than about strategy.

    Paul Hawking
    The Challenge of Teaching Math
    Latest Post:
    Creating a culture of double-checking your work

  9. I have seen his problem years ago, but it was asking for the number of cubes.

  10. I have seen this problem years ago but it was asking for the number of cubes. Anyway, the video is very cute.


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