On the Shoulders of Technology

As I walked into this session, the presenter Frank Sobierajski had a video of a first date between and pi, which was interesting. He then showed us how he modeled a problem using Geometer's Sketchpad, where you could determine the minimum and maximum distance to place drinks on the edge of a pool, where the distance is determined on where the two friends are in the pool. It was quite neat.

Frank talked about how he was going to show us many interesting things that we may not know. He begins by showing how to create a scroll bar to adjust values in cells in Excel. He mentions that most of what he is showing he learned by playing around, including noticing that if you change the b value in a standard form equation, the vertex traces another parabola! There are many uses of sliders in Excel. He also shows how they can be used with functions to compare graphs.

He next moves into Geometer's Sketchpad and show sliders as well. This is truly amazing stuff. He started from scratch and ended up with sliders that graph a line in slope-intercept form.

Moving on to Word, we look at putting a grid in and make a triangle in it. In the end, we will have a fractal. From there, he follows the 3 r's of fractals: Reduce, replicate, repeat. Back in Sketchpad, he moves to Sierpinski's Triangle. He breezes through creating it, and it's flooring me. This is such a great constructivist session. With tools like this, you can definitely imagine having more explorations into fractals in today's classrooms. I am so glad that Frank says that we're going to get this information at the end of the session.

I'm sitting next to Pat from West Shore (he didn't even see me when he sat down), and we're constantly turning to each other and saying "Wow!" I wonder how many non-math teachers are in this session. It would be great to get their reactions.

Next is The Chaos Game, back in Excel. Basically, you plot three points to form a triangle. Then, generate (randomly) a fourth point, then plot points that are between there, finding out that if you plot enough points, you see Sierpinski's again.

Next, we see stop signs in Sketchpad. Starting with a square, give the students a chance to turn it into a stop sign, letting them explore how to do so, without previous knowledge of the details.

Moving on, we see finding the angle of descent on Millennium Force, again with Sketchpad. Following that, we see some interesting signing in hotels, schools, and hospitals. Who does this? Obviously not mathematicians!

Next, we see great ways to include photography into math lessons. Take pictures of water coming out of hoses or water fountains and have kids fit curves to it. You can even do it with so many everyday objects and apply so many different mathematical concepts to them. Why don't we all do more of this? If you want to talk about getting the real-world connections for your students, this is how.

Another way to use photography in a math class is to have a scavenger hunt having kids find cases of math in their world. Logos also have many interesting mathematical characteristics, as well.

In the end, Frank gave us a handout with an email address to access to access his content from today. Send an email to fsobierajski@nrwcs.org with subject necc08, and an instant response will be sent to allow you to access the info.

If you know anyone who wants to include more technology in their mathematics, or even if you just want to wow some friends or colleagues, check out his material. You'll see what I mean.