Month: January 2011

Total 18 Posts

[WCYDWT] Orbeez

I’m really grateful for the deep bench I have on this blog, the readers who take the time to share with me the mathematical objects that intrigue them. Adam Poetzel, secondary math ed prof at the University of Illinois, sent along Orbeez, which is pretty aptly described by this commercial:

Basically, small things that grow big in water. The Orbeez website puts the volume increase at a factor of 100 while the instructional manual puts it at 150. Controversy! Which is right? Or are they both wrong?

I went to Toys R Us and bought a starter pack for $8.00.

I dunked ’em for a few hours and got this:

A few ideas here. Start informally. Move from the concrete to the abstract. The informal question is, “how many times bigger is it, really?” Ask the students to write down guesses. Write a few up on the board. Perhaps print that photo out and have them draw what they think “150 times the volume” would look like. (Am I alone in thinking this looks way way smaller than 150 times bigger?)

Ask them what information they need to answer the question exactly. Put up this photo.

Here’s the math:

Okay, Orbeez, just watch yourself, that’s all I’m saying.

Ideally, you’ll move from the relatively laborious calculation of volume to the relatively simple comparison of the diameters using scale proportions. ie. if the large volume is really 150 times the small, then the large radius has to be at least 150^(1/3) = 5.3 times the small.

The Goods

The problem archive, including:

  1. the commercial,
  2. the manual,
  3. the website screenshot,
  4. before / after photo of Orbeez,
  5. before / after photo of Orbeez with ruler.
  6. Orbeez’ internal expansion measurements (given different water sources) [see this post].


This is the rare WCYDWT investigation that would be even better with real stuff rather than all these digital replications of real stuff. Buy some Orbeez off Amazon. Let your students dunk their own Orbeez on day one. Perform the investigation on day two.

2011 Jan 11: Sharon Cohen, the brand manager of Orbeez, stops by to drop some knowledge on us all.

Kate’s Urban Legend

Kate Nowak, on the grand finale of Pseudocontext Saturday:

I realize this is going to sound urban legendy, but I know someone who knows the teacher who wrote this question [..] And, the story goes she wrote this question as a joke. As in, as a lark she wrote something so bad and ridiculous that it would never be used. And then they put it on the exam.

Nope nope nope. No way. Not buying.

[PS] The End

This is completely subjective, but Peter Brouwer sent in the problem that I thought satisfied both halves of the working definition of pseudocontext in the most spectacular fashion. This is it. This is as bad as it gets.

From the June 2001 Math B New York Regents examination [PDF]:

Jo Boaler gets the last word:

Students do however become trained and skillful at engaging in the make-believe of school mathematics questions at exactly the “right” level. They believe what they are told within the confines of the task and do not question its distance from reality. This probably contributes to students’ dichotomous view of situations as requiring either school mathematics or their own methods. Contexts such as the above [pseudocontext], merely perpetuate the mysterious image of school mathematics.

That’s it. Thanks for pitching in.

Students Tweeting About Clickers

I find it hard to get worked up one way or the other over clickers (or “student response systems” or what-have-you) but something I definitely don’t hate is Derek Bruff’s weekly roundup of student clicker tweets.

For instance:

@jackiesayswhat I need to buy a clicker? seriously? during my last semester?

@hornylizard Man who got a clicker that they aint using this semester and wouldn’t mind letting me use?

@Thee_JadeE Oooohhhh I’m bout to drop this psych class! Something told me I was gunna have to buy a clicker!

You start to get a pretty strong sense of the student response to student response systems.

Pro Tip

Anytime anybody asserts anything disparaging (or affirming) about contextual problem solving in mathematics, it’s helpful to ask “what representation of problem solving are you talking about?” Because a) unless the student is actually outside the classroom in the context, you (or more likely your textbook’s publisher) have had to represent that context somehow for use in the classroom, and b) not all representations are created equal. Also, not to get too big for my first-year PhD student britches either but this seems like a blind spot in the existing research.