Month: November 2010

Total 14 Posts

Multimedia Inoculates Pseudocontext

I owe Brian Caine a debt of gratitude for flipping my switch on the question of “what is multimedia doing for us, anyway?

Multimedia makes it really, really hard to lie.

Witness David Cox’s toaster regression. It doesn’t work. We thought it was linear. It isn’t. It isn’t worthless for classroom inquiry. Maybe it’s exponential. But the linear model is a dead end.

If you’re writing the problem in a textbook, though, it isn’t a dead end. You grab some clip art of a toaster. You create a table with values that are linear because who’s going to stop you? Even though the real context isn’t linear, you’re the god of your textbook’s pseudocontext.

Then you fabricate a conclusion that supports the pseudocontext.

For whatever other good it does for problem posing, multimedia keeps you honest. How do you (easily) film pseudocontext? How do you take a picture of a premise that is false? Even harder, how do you take a picture of the conclusion of that false premise in a way that doesn’t belie the premise itself?

[PS] Swedish Yoghurt

Arla, a Swedish yogurt producer.


You catch a pike but the scales are broken. The pike weighs two kilograms plus half its weight. How much does it weigh?


At this point I’m comfortable with two definitions of pseudocontext:

  1. context that is flatly untrue: “a basketball team scores two points every minute for the duration of the game.”
  2. operations that have nothing to do with the given context: “the age of Mark’s dad is three more than four times Mark’s age.”

We’ve worked hard for those two categories. We’ve digested some really untasty mathematics in their development. They indicate problems that aren’t just boring or irritating but problems that are actually alienating, problems that disrupt a student’s innate and true sense of the world.

Pseudocontext Saturdays will run their course eventually. For now, though, the intellectual challenge of identifying different levels of badness (and, in many cases, redeeming it) is too invigorating to give them up. Those of you who have invested time and effort on these features in the comments and in your submissions — thanks.


  1. Scan an example of pseudocontext.
  2. Email it to
  3. List the textbook title, edition, and publisher.
  4. Give me your interpretation of the term “pseudocontext.”
  5. Let me know if you’d like credit (name, blog or twitter) or if you’d prefer anonymity.

[HOWTO] Projectile Motion Strobe Effect

I had a few requests for a tutorial for this treatment. Here goes. Also, a text summary after the jump.

Projectile Motion Strobe Effect from Dan Meyer on Vimeo.

1. Record video from a stationary source. Like a Flip cam on a tripod, for instance.

2. Trim the video to one shot.

3. Export that clip to an image sequence. 15 frames per second gets you pretty clean motion.

4. Load those images into a stack in Photoshop.

5. Mask off the basketballs. (It’s tough for me to explain this step without video.)

6. Import all these resources into Adobe AfterEffects.

7. Extend the masked basketball layers to the end of the composition. Otherwise they won’t hover in mid-air. They’ll just disappear after two frames.

8. Keyframe the brightness of each basketball layer to give yourself one frame of pure white at the start of each layer.

2013 Mar 18. Chris McCaffrey offers a less expensive method for creating the images (if not the video also).

[WCYDWT] Will It Hit The Hoop?

Is he going to make it? Can you draw me the path of a shot that will make it? That will miss it?

How about now? Can you draw me the path of a shot that will make it? That will miss it?

How about now? Can you draw me the path of a shot that will make it? That will miss it?

A little more obvious, isn’t it? And like that, we’ve derived illustrated the fact that, while one point is enough to define a point, and while two points are enough to define a line, you need three points to define a parabola.

Basketball Strobes — Full Take 4 from Dan Meyer on Vimeo.

Here are seven versions of the same problem. Each one contains:

  1. the half video, for asking the question,
  2. the half photo, for giving the students something to work with,
  3. the geogebra file, one use for the half photo, featuring a dynamic parabola in vertex form.
  4. the full video, for showing the answer,


[PS] Midterm — Solution Key

[see midterm]

1. Which of Will’s commenters has suggested a pseudocontextual problem?

Very few of them, it turns out. Which isn’t to say that all of the suggested problems are good problems, just that our worst tendency in these discussions is to conflate the term “pseudocontext” with “problems I don’t much care for.” Pseudocontext uses the full authority of the teacher or the textbook or of grades to force a connection between The Math and The Context that doesn’t naturally exist. This is a separate matter from “Do professionals really use math in that way within that context?” or “Will my students care at all about the math, even though it exists naturally in this context?”

Spot check me here but I find it pretty easy to divide the suggestions at Will’s place into four categories:

Valid Context, Of Inherent Interest To Basketball Professionals

These questions are ideal, and really hard to find. Will is probably better off asking a basketball player, a coach, or a sportscaster because they won’t waste his time (or, especially, theirs) with pseudocontext.


You can probably set up different metrics – basically giving different weights to things like free throw percentage, scoring, rebounds, steals, etc. – and compare players and be able to claim “I can prove that Kobe is better than Lebron” or whoever else you want to compare. This would also extend to comparing teams and stuff.

Have you seen John Hollinger’s formula for player efficiency? It’s gargantuan. Have your students create their own, balancing factors however they choose, checking the results against their intuitive sense of the best basketball players. (ie. “I know Kobe’s the best but my formula is coming up with Lebron.” So you rebalance.)

George Woodbury:

There are some probability applications. If a free throw shooter has a 75% chance of making a free throw, what are the chances that he or she makes 2 free throws? 1 of 2? 0 of 2?

Pair with video clips of different shooters at the line. Given their overall average, place bets on which players will hit both, which will hit one, and which will miss both. Then show the answers.

Valid Context, Uninteresting To Basketball Professionals But Interesting To Students If We Develop It Well

Do basketball players need to know anything about 3D vectors? When they go for jumpshots are they converting force to acceleration and then solving the quadratic formula to see if the ball will land? No, but these problems are of interest to students. Especially if we visualize them well, if we present them in a format that appeals first to intuition (“do you think it goes in?”) that only later uses math to formalize that intuition.

Angie B:

Dan Meyer’s dy/dan blog had this on it.


How about studying the lines and shapes on the court? A little bit of geometry there.

I like the challenge here. There is a lot of geometry in the lines and shapes on the court. But the hard work remains. What question do you ask? What problem do you pose to get students diving into the geometry of a basketball court, wondering “what kind of shape is the three-point line anyway?”

One idea: I draw two points on a piece of paper. The line between them is the baseline on one side of the court. Can you draw a scale replica of the rest of the basketball court. Bonus: do it with a compass and straightedge alone. Extra bonus: write a program that accepts two mouse clicks and does the rest automatically.

Valid Context, Uninteresting To Basketball Professionals, Also Uninteresting To Students

It’s within your professional jurisdiction to ask these questions, but these questions only appeal to math teachers. Not basketball professionals, and certainly not students. But they aren’t pseudocontextual. These problems have an inherent connection to basketball. If anybody is selling a term to describe these problems (ideally something more descriptive than “lame”) I’m buying.

Lyn Hilt:

Incorporate geography…calculating traveling distances/methods to visit arenas and attend games.

Jason Kornoely:

If it takes one player an average of 15 seconds to dribble across the field, how much time would it take for a team of x to finish?


[What is the] volume of skin making up ball assuming skin is 1/16 th thick?


Jason Kornoely:

Determine the hypotenuse using the distance from the free throw line to the center of the hoop and the height of the hoop.

This was the only response I could call pseudocontext with absolute certainty. The Pythagorean theorem has no use or meaning here. The teacher is imposing the theorem on a context that doesn’t want or need it.

2. Create a math problem in response to Will that would be pseudocontextual.

Chris Sears:

Kentucky and UCLA have appeared in the NCAA Division I men’s basketball tournament 80 times, with Kentucky appearing 8 more times than UCLA. How many times has each team appeared in this tournament?