Here was my follow-up, which provided valuable information regarding function misconceptions. I would provide a graph, then challenge students to write a plausible story which could be modeled by the given graph. Usually, I was looking for a story which made use of the intercept and slope, but some students would look at starting and end points. Other students would simply place the given numbers in a story without concern, and we would critique all of these. These story-writing experiences were done through the year, and were adapted as we learned new functions, function notation, domain and range. Also, it was easy to bring in vocabulary like independent, dependent, domain, range.

The day I shot this video of me sliding down the slide, I went to the park early in the morning when the park was free of people. As I took several “takes” of the video – trying to get the timing right, adjusting the camera, etc – a few moms and their young children started to arrive at the park. Needless to say, I received some strange and slightly unnerved looks by the protective mothers wondering why a grown man was recording himself go down the slide again and again. After I got the video I needed, I started to leave and walked past one of the mothers. Wanting to explain, I said “I was just making a video for a math lesson”. The look on her face told me she now thought I was even more strange than she had previously assumed :)

As for curriculum, what I am developing is not question based, it is design based. There are certainly well defined objectives, like “create a dynamic point in GeoGebra that moves through the path that Adam’s waist moves through in the video as a function of t, where t is the time from the beginning of Adam’s journey to the end of it.” But the purpose of the task is not simply to complete it (although that is certainly one the the activities that drives learning). It is also to better understand Adam’s sliding experience and be able to interact with it in creatively valuable ways that are unique to each learner.

As for my own home, I’m working on that now. Thank you for the encouragement. I hope you won’t mind if I continue to interact with you guys here until I get mine up and running.

Thanks, again.

Instead of the goal of the activity being an end product, the static height vs. time graph, let it be a spatially tangible model, a structure, created in GeoGebra. Here’s what I made in response to this newly defined task:

https://www.dropbox.com/s/rm08u0wjiurmzya/AdamSlidePlus.ggb

To start, I sketched the height vs. time graph using the freehand function tool and called it p(x). Then I also sketched the horizontal position from the starting point vs. time with the freehand function tool and called it q(x). Then I made a slider for the time variable called t, ranging from 1 to 15 seconds, and created a parametrically defined point (q(t), p(t)) and boom, now I’ve got a spatially tangible version of Adam’s slide experience that I can *handle* and *use*.

Tracing the point while animating the slider, t, allows us to perceive Adam’s relative velocity throughout the sliding experience in one image, here:

https://www.dropbox.com/s/ifpikfse7mv6p31/AdamSlide-VisibleVelocity

Then I started playing around with transforming q(t) and p(t) with the intention of finding ways to creatively reimagine the experience. The point (2*q(t), 2*p(t)) traces out a path that suggests an extreme version of the slide design (could be fun), while (0.3*q(t), 0.3*p(t)) suggests including a toddler slide in the park. The point (q(2*t), p(2*t)) traces out the same path, but twice as fast. Timed slide races, maybe?

This version of the activity blurs the lines between using context to understand mathematics and using mathematics to understand context. They become one and the same.

PS. You shouldn’t be wasting all of this thoughtful analysis in the comment section of some guy’s blog. Think about getting an online home of your own and posting it there.