MariaD’s blog

This is an experiment for Twitter-like communication in a more permanent medium. Here is the original, created by John Faig.

This parking meter is a contribution to What Can You Do With This, or WCYDWT, project. Dor Abrahamson sent it to me, together with this story for WCYDWT people:

“I’m co-teaching w/ Prof. Alan Schoenfeld an undergraduate course for future teachers, at UC Berkeley. It’s a problem-solving based course, and the problems are often based on mundane situations. We used this authentic document - a Berkeley parking meter - to explore multiplicative structure and rational numbers. Rate, I guess. Basically, we show this picture and ask what the best bang for the buck is. To our great surprise there was much confusion in terms of concepts, notation, vocabulary. Diverse approaches, some we couldn’t make sense of.

Judging by your blog, I need not demonstrate what a talented math teacher could do with this material. The mind reels, right? One of the interesting angles here is that some kids calculate min/cent, and others go for cent/min. We all wish to equalize the “denominator” so that we can compare the “numerators” directly. However, for me the min/cent feels intuitive, b/c I want to know how much bang I get for the buck. And yet, think of those ‘value’ numbers we see in the supermarket, which help us choose between comparable products that come in different volumes — they tell you, e.g,. 39c/ounce. So the equivalent here would be cent/min, right?

And so on. We played with polynomials so as to figure out what exact minute totals we could produce and how much they would cost us.

Time is money.

Oh, and the person whose image we can just discern in the display area of the parking meter is Becky Blessing — this is her, errr, reflection piece.”

UPDATE: Becky already submitted this picture in February, and there is a very nice discussion there at dy/dan blog.

In an overview of the Natural Math project, an audience member asked why we are doing such diverse things. Why work, all at once, on mathematical art, programming-based math, algebra for toddlers, meta-cognition and quite a few other directions we pursue at the same time? These are necessary tools for a gradual, gentle cultural change we are making.

The future is already here, it’s just not evenly distributed. The future where toddlers and their parents play with algebraic ideas, where kids contribute to real work as apprentices, where everybody is able to create or improve mathematical conjectures, definitions and metaphors. We are working on inviting more and more people to work and play in this future, now. This mind map shows some of our tools.

Full screen view.

This Saturday, I participated in a wonderful workshop on real time collaboration. Here is the mind map summarizing it, with links to appropriate sites and details:

It is shared under Creative Commons license by Change Management Community.