Asilomar #5: What Can We Do With This?

Session Title

Lights, Camera, Action! Fun And Success For All In Algebra


Allan Bellman, Supervisor of Teacher Education, UC Davis


“Why would we want to teach with digital images?” he asked and then answered, “Because it’s better to watch it than read about it.” where “it” referred to any generic textbook problem.

I had no disagreement insofar as we keep text on the table as an option for those who do find it better to read about it than watch it. Math education, however, is not suffering from a surplus of visual representations.

I’m naturally inclined to this kind of discussion. He pointed at an image on the screen and asked, “What can we do with this?” which is obv. one of my favorite questions to pose, discuss, or answer. Bellman and I answer that question differently, however.

The image was of a Volkswagen Bug and he wanted us to point out all the mathematical shapes we could see on its frame. We eventually settled on the parabola that formed its canopy. He passed out a printout of a Volkswagen Bug and a transparency of graph paper. He asked us to find the equation of that parabola.

We could position the car wherever we wanted. Some positioned it upright. Others upside-down. Some defined the origin of their coordinate system at the top of the car. Others at the bottom. We all derived our equations.

Then he put a transparent Bug on top of a TI ViewScreen panel connected to a TI-84 Plus. He put the Bug in different positions and we had to modify our parabolic equation each time to match it, which was an interesting exercise in transformations.

Then we reworked the same exercise with an advertisement ripped from a magazine that featured lines, parabolas, and sinusoids. There were TI-Navigators on every table connected to hubs which were connected to some Windows software that would graph the equations we submitted after we logged in.

I graphed y = 4, which traced a horizontal line across a rooftop, and looked smugly at my tablemates.

Bellman then put up a picture of a golf course. He draw a ball next to the ninth hole and asked us to determine the equation of the line that went through those two points. He challenged us to find a quadratic model that fit to those two points. He mentioned that we could even ask our students for an exponential model.

And this is where my purpose splits from his on using digital media in the classroom:

Neither that line, that quadratic model, nor that exponential model have anything whatsoever to do with golf. If we’re going to use an image of a golf course we need to ask a question that clarifies or has even a glancing connection to golf itself.

  1. Will she sink the putt?
  2. How far has she hit the ball off the tee?
  3. Which club should she use here?
  4. How fast is the club head moving?

By setting the background of a coordinate plane to an image of a golf course, we may engage a few more students than if we used a plain plane but I think we’ll also lose a few students on the other end who recognize the arbitrary, artificial nature of the setup. (ie. “Why not a picture of a baseball diamond?”) I worry that if we use digital media in our classrooms like this, we’ll define mathematics even more as an abstract thing rather than as a tool for explaining our own lives.

Bellman then brought up a video of a basketball player shooting a jump shot. We used Logger Pro to pull down some coordinates from the first half of the ball’s arc. Then we answered the question, “will he make the basket?” which is exactly the approach I’d like to see to digital media in the math classroom.


Some PowerPoint. A lot of modeling.


Transparencies and paper to push around and play with.


  • Someone asked him “How long does it take you to come up with all of this?” and he nodded at the difficulty of assembling all this digital material but pointed out (rightly) that you only have to develop it once.
  • “There are two kinds of video. The kind you make and the kind you get from Blockbuster.” Someone asked him how you extract a clip from a DVD and his status as a paid TI rep forced him to play it coy. I am not likewise burdened so here: Handbrake.
  • Bellman kept a running tally of the cost of his setup over the course of his presentation, beginning with a $100 video camera. Clearly, it balloons as you start deploying TI equipment and I’d like to open the floor here to a cost-benefit analysis.
  • In general, I admit to some cynicism about graphing calculators, which occupy a strange corner of the edtech market. The equipment is cumbersome to set up. (Bellman had two lackeys there from TI to help him install those hubs.) It doesn’t come with a web browser. The resolution on its black-and-white screen is worse than the cell phone in my pocket. Can anyone explain to me how graphing calculators are going to avoid getting crushed in the tightening vise between cell phones and netbooks?
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.


  1. Please let the graphing calculators be crushed in the tightening vise between cell phones and netbooks, or between apps on whatever platform (for me preferably a web browser?).

    Ever since the liquid crystal failed on my old HP 41-CV (circa late 1980’s), I have not come to grips with the usefulness of graphing calculators.

  2. Graphing Calculators are going to be tied with standardized tests, as long as they have no internet capabilities.

  3. I have a Navigator system in my room (our school got one, through particular circumstances, for free) and while I do use the picture-matching thing, I find the most wildly effective use this years has been what I might call Coordinate Grid Musical Chairs.

    Set all students on “coordinate point” mode, and also make sure the setting is on so each has a unique shape. (The like this mode; when you first turn this on, they’re happy to spend 5 minutes just chasing each other around.) Write coordinate point on board, count down. Whoever doesn’t reach point in time is out. Coordinate points start easy (“(4, 5)”) and gradually gets harder (“(3, 5) reflected over the x-axis”) and yet harder (“(log base 5 of 5, cube root of -8)”). Last one standing is the winner. Rule sets can vary, of course.

    What I don’t get is how it took him so long to collect media since he’s not using it in relation to the content, just the picture. I have a collection that took me 10 minutes at most to gather, and if I run short I ask the students for a word to search for on Google Images and just toss whatever interesting pops up on.

  4. TI’s calculator monopoly has completely stifled their development. When I saw the new N-spire ones I was amazed… no color screen, no touch screen, networking…but only with their equipment, not any standard. Oh, and buy their extra proprietary hardware if you want to use them for data collection in labs. Yet they have such a stranglehold that they still sell what are 1980s-level technology (the 80s and 90s series) for $75 and those are often still listed as course requirements for college course.

    When my students ask what sort of calculator they should buy for college, I tell them to just buy an app for their phone or for only slightly more than a TI, buy a netbook (my Eee was $185, vs. $150 for an Nspire CAS). I keep hoping that Nintento (or a third party) puts out a calculator program for the DS or similar hardware and sets the Calculator market out of its stupor.

  5. I agree with @Cassidy: as long as cell phones are technologica nongrata in schools and laptops are banned from exams, the GDC will continue to be an important piece of kit.

  6. I have my students complete an activity similar to this but with a few twists. I have the students search the Internet for pictures of real life items that have a parabolic shape. (Ex. The arch in St. Louis)

    I then have the students paste the picture into Geometer’s Sketchpad, turn on the grid and then determine a number of points on the object.

    Finally they determine the equation of the parabolic shape.

    Students like working with all of the different tools. It is a totally engaging activity.

  7. Have to agree about the use of the golf course in that situation. Why not show a ground level view and duplicate the basketball shot with the golf shot? In the end, this is the kind of thing that gets teachers moving towards your side but only because they are using pictures instead of textbook problems. I can already picture the golf problem on a textbook page in my head.

  8. I loev my netbook (got an Asus Eee about 2 years ago) and have been trying to talk our Technology people into getting some. Since we are a low-income district I’m trying to get a set as “loaners” that the students can check out from the library since many don’t have computers at home.

  9. I second the caveat about the St. Louis Arch. I have a science and math supply catalog with some smart-alex “Dr. Science” guy on the cover with the Arch in the background. The piece of paper he’s holding has “Ax^2 + Bx + C = 0”.


  10. I am all in favor of the netbook / cell phone / iPod revolution wiping away the overpriced calculators, but I don’t see anyone here coming up with a solution to the standardized tests problem.

    My students aren’t allowed to use any device capable of networking during a provincial exam. The unfortunate truth is that unless the nature of those exams is turned on its head, I *need* to teach them how to solve things using the overpriced calculators because they’re the only things left that are archaic enough to be offline.

    (Which is not to say I won’t teach them to use other technology as well, but it means they’re stuck paying for it.)

  11. About the TI-calculators, I just can’t believe that:
    1. the technology is so dated
    2. the cost is so high

    I mean, the technology in a TI-84 Plus Silver Mega Titanium (I’m half-joking with the name) is like 1% more advanced than the TIs I used in high school 16 years ago. And yet the price is still $100+. That’s ridiculous.

    I teach IMP, so we do a lot with the calculators, and when I show stuff to the kids, you’d think they were using an abacus. “Why isn’t the line straight?” is a common question. Additionally, the kids want to know where the equal sign is and why when tracing a line on a graph the coordinates displayed represent the points of the pixel and not the points on the line. They dig the capabilities of what the calculators can do, but are frustrated with using them.

    I feel bad making them mandatory because I feel like I’m upholding the TI monopoly.

  12. Can anyone explain to me how graphing calculators are going to avoid getting crushed in the tightening vise between cell phones and netbooks?

    I love my graphing calculator, and my TI-85 has been with me since Junior year of high school (a little over 17 years), BUT the crushing vice for me will eventually include a netbook with Mathematica, Matlab, PowerToy Calculator, SAGE, and/or Maxima installed on it.