Visual Math Instruction: Premium Grade

The more I dig into the question, “How do we turn digital media into learning objects for math students?” the more I’m convinced we need a frameworkor maybe a stylesheet or perhaps a standards & practices document – I’m not sure of the best analogy here. for capturing and mounting that mediaie. “this is how we take a photo when we want to use it as a learning object.”. This is most obvious to me in our classroom conversations, some of which are enduring and propel serious mathematics, others of which are diverting but ephemeral. At whatever point I pin down the difference, I think I’ll have written myself a recipe for a coherent, engaging math curriculum, something that could occupy me for years.

Though neither of the following two curricula have any kind of public outline, they seem extremely self-consistent and they track (unintentionally, of course) extremely closely to the vision I’m chasing.

Problem Pictures

These CD-ROMs (which you can preview here and which Mr. K reviews here) are stocked with images that are each, on some level, “interesting,” and each of which beg a different mathematical question. Mercifully, that question is rarely, “what shapes do you see in this photo?” which is the lowest level of some pyramid which has yet to be named.

Principle Failing: No video, which makes the next entry particularly essential to my investigation.

The Hypertextbook

“Edited by Glenn Elert, written by his students.”

Their investigation of Mario’s acceleration due to gravity may have cropped up on one of your Internets, recently, and was certainly worth your attention. The recipe is consistent throughout Elert’s curriculum:

  1. Extract some video from pop cultureTalkin’ about Batman Begins, Madden 2006, Jackass – this Elert guy is out of control in my opinion..
  2. Use physics, math, Wikipedia, photogrammetry, and estimation to answer an interesting question.

Principle Failing: This document is designed more as a record of student learning than as a curriculum for teachers. The media which would propel this thing into classrooms around the world is either absent (as with the Mario investigation) or was uploaded to YouTube which dutifully scrubbed it (as with the Hulk investigation).

To proliferate as fully as they deserve to, these investigations need a complete multimedia supplement, starting with high-resolution captures. In Mario’s case, you would need:

  1. a clip showing Mario falling from the same height from every Mario game published, edited into a multi-panel split screen. The students would then ask the obvious question, “Why does Mario hit the ground sooner in some games than in others?”
  2. an individual clip for each jump, no decoration.
  3. The same clips with a grid superimposed over the footage for measurements.
  4. A lesson plan with analysis.

Again, we’re working on different projects here, but Elert only includes #4, which means his work will find its way only into the classrooms of the most digitally savvy physics teachers. How many more teachers would benefit had he included the first three? My guess is: a lot.

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


  1. I was thinking the same thing when I saw the lesson. A frame counter would also be helpful.

    In truth, the best thing would be to have the actual game there, not just a video to analyze. Then students could experiment and bring up questions like — what if Mario hits something on the way up? what about the underwater levels? Is there a terminal velocity?

  2. Having the actual game will mainly encourage kids to experiment with “how much playing can I get away with as pretending to do something meaningful?”

  3. I dunno, Jason. Much of this work depends on frame-precision measurement, which seems easier to acquire with QuickTime playback, rather than with real-time. I’ll have to think on it.

  4. Then your smart kids could try to figure out just what the hell was special about Princess in Mario 2, why could she fly? Would her dress really help her that much? At all?

  5. @Dan: I was actually thinking of how emulators have an option for a precise framerate display.

    Now, in terms of practical reality of what teachers would have the tech-savvy to handle, video is certainly the better option.

    @kevin: Yeah, these sorts of assignments can be a classroom management nightmare.

  6. “some pyramid which has yet to be named” – <a href=””<check out the van Hiele’s. OK it’s not a pyramid but I read some of their work in a grad class and it makes alot of sense.

    After seeing I think a link in your comments, I ordered one of the problem pictures CD’s. Can’t wait to check it out.

  7. Elert’s work is amazing. This guy could probably take over the internet during his prep if he wasn’t busy meeting with his students every moment. He’s got a detailed bike journey across the country with all sorts of number crunching. Clips of jackass for physics: raw.