That reminds me of the difference between live theater and film. I almost always prefer film to theater which is maybe why I like multimedia so much.

@Sylvia – I dont know if Gary told you but I’m “interviewing” him on Math 2.0 Elluminate on 10/13. Maybe you want to join us for what promises to be a lively discussion of our vision of math learning in this Web 2.0 world?

And learning which consumes the product during the learning experience (cut up a paper circle…oops, wrong number of pieces…cut up another one…oops, wrong again…cut up a third one…) teaches some valuable lessons about why we need to be able to represent some objects in order to measure, learn, test them.

When possible, use the physical objects. When that becomes impossible (which is often more a limitation of our creativity than a genuine restraint) or harmful (we don’t destroy functioning buildings to measure them), use the best representation possible…assuming the technology is available to your students. And it still is not in many schools.

Don’t get me wrong, I agree that good use of media is a great tool to make data and reality accessible in the classroom. But the roll of tickets example is relatively easy to swap in direct access to reality. I tend to think that if you can bring in the real thing without too much fuss, that’s going to trump the indirect representation most of the time in terms of engagement and usefulness.

Obviously this doesn’t work with everything. I’m not bringing in a half-dozen hoses and giant water jugs. Plus, it may be harder to set those specific constraints that make the problem interesting (ie. pressing the pause button at the right time). And with an actual roll, you have to convince them that they’re not allowed to just, you know, unroll it or something.

Also, reality is easier for students to work with as they don’t have the intermediate step of dealing with scaled photographs. (Which is either a pro or a con, depending on what you want them to practice / demonstrate.)

Until about two years ago, I wasn’t doing much mathematical problem-solving, certainly not as a regular/weekly activity. If there was something interesting that came out of what I was teaching, I’d play with it. But that didn’t happen often.

It took finding a community of people online, who enjoy thinking together, to get me into doing math for fun on a regular basis. Before that happened, I played free cell and sudoku when I felt like exercising that part of my brain.

The biggest change for me was going to the Math Circle Summer Institute. For a week, I got to have this kind of community, and it was in person!

Maria, don’t the people doing Sudoku and KenKen – and other puzzles – count? And people playing chess? I’d expect the total to be higher than 5%. (Although perhaps not more than 10%. And of course I’ve been known to be wildly, inaccurately optimistic.)