Pythagorean Exploration

I don’t love this textbook task.

Too many substeps before students return to the question: what’s the relationship between the length of the sides of a right triangle?

“For each right triangle, write an addition statement…”? C’mon!

But I’m hesitant to join the down with textbooks revolution; I don’t want to associate myself with the back to basics movement. So in conversations where the suggested alternative is more worked examples, I soften my criticism.

Besides, it gives me something to modify. Instead of completing the table, I could challenge students to find right triangles and ask “What do you notice?”

One problem: this requires “attend to precision” to do some heavy lifting.

4-7-8
The 4-7-8 Right Triangle

This leads to some truly awkward feedback: “Are you sure it’s a right triangle? You might want to measure again.”

GeoGebra may provide a solution.

4-7-8 GGB
Click to view on GeoGebraTube

Revisiting GeoGebra

Four years ago I learned about GeoGebra and made some applets to be used in my classroom. I started by creating applets that demonstrated the effect changing slider values had on the graphs of trigonometric functions. I’d change a value and then ask the class to describe what happened to the graph. These constructions made excellent demonstrations. But that was the problem. The spectator experience was improved, but students remained spectators. (SMART Board fans take note: having one student at a time come to the front of the class does not change this.)

I also posted these applets on my class website. I thought students would try them at home to reinforce learning and check for understanding. They didn’t.

I wanted to move more towards having students themselves do the investigating. I constructed dynamic worksheets to explore slope and circle geometry in Math 10 and 11. Twice, I threw in the towel halfway through the period because of technical difficulties. The 15 laptops had to remain plugged in because their batteries no longer held a charge. The wireless network couldn’t handle having 15 laptops on it. The files were copied from my flash drive to desktops but only worked on some of the computers.

So, we went back to pencil and paper. Each student drew and then measured his or her own angles. Some students immediately observed the relationship. Others observed it after seeing the results of each group member. They asked “What if we move the inscribed angle off to the side more?” and “What if the central angle is larger?” Then, they set off to find the answers. Listening to these conversations, I wondered what this would have looked like had I been able to carry out my lesson plan.

In the four years since then, I’ve seen several GeoGebra/Sketchpad constructions created by other math teachers but very little that really excites me. A new tool to use while I stand and deliver? An e-version of an investigation that my students do using pencil and paper? Okay. I guess. Just don’t try to sell it to me as being more than what it is.

I want to incorporate technology into my teaching in meaningful ways. Here’s something from David Cox that could get me back on the GeoGebra bandwagon. It starts with a great problem that is enhanced because it is posed using GeoGebra. Students continue to interact with the applet as they attempt to solve the problem.

I uploaded some of my dynamic worksheets to GeoGebraTube and was very pleased to see that they worked on my iPad. I’d love some feedback on them. Was my assessment of them correct or are they salvageable? Also, I’m willing to give GeoGebra another try. Can you point me to exemplars?