Wednesday, August 22, 2012

[NBI] Modeling Temperatures with GeoGebra

This post is part of the new blogger initiative.

The more that I grow as a teacher, the more I believe in teaching modeling with mathematics.

That might sound somewhat silly. I've always known, in some sense, that modeling is a good idea. They certainly encouraged it in my prep program and it's a significant part of the Common Core. However, when you're actually making instructional decisions for the day or week, modeling can be tough to choose. It takes more class time, and in some ways, can seem "softer".

But every time I have my students complete a good modeling activity, those thoughts just seem ridiculous. I see real struggle. I see connections get made and broken. I see students conjecture. I see them contextualize and decontextualize. Beyond the truly deep learning, I haven't encountered a better assessment tool.

Monthly temperatures in Wisconsin

One of the better lessons that I taught during my first year of teaching was a modeling lesson. We were finishing up a unit on trig functions and I *thought* that my students had learned the transformations. I wanted them to see that what we learned really does show up in the world, so I grabbed the last five years of monthly temperatures in Wisconsin from the Online Climate Data Directory. I then entered that data in the spreadsheet of GeoGebra, created a list of points, and distributed the GeoGebra file to my student. (I would love for my students to be able to handle the data, but I made an executive decision based on time-constraints).
I know that it's supposed to look like this, but it still kind of amazes me. 
For the activity itself, I distributed the following halfsheets to guide students through the techy aspects of the activity:
Temperature Directions

Basically, I wanted students to find an equation that fits the data as accurately as possible, interpret the different parts of their equation in the context of monthly temperatures, and present their work in a professional looking document. As we had done very little work of this type, I created a template with Google Docs to use.
Temperature in Wisconsin


It wasn't perfect, but it was good. The insights into students' thinking were amazing. For example, it turned out to be very difficult for my students to interpret the period as one year, or that the midline represents the average temperature. I had a number of very good conversations trying to help students make these connections.

Additionally, I really enjoyed watching students while they were fitting equations to their data. I had considered setting up the equation for them with sliders, but I'm glad that I didn't. There was value in having them manually type in and change constants in the appropriate places in their equation. Students were checking their notebooks to figure out how to change the amplitude, or just tinkering to see if it worked. Really, either was fine with me. 

In the end, I hope trig was a bit more concrete, and I had a much better idea of what my student understood.

Next time

Instead of ending the unit with this, I will start with it. Trig would then come from the real world and students would be playing with all of the transformations before I teach the vocabulary. We could then discuss the ideas of trig transformations with a solid context to refer to and draw comparisons to other places in the world - "How do you think the amplitude of the monthly temperatures in Wisconsin compares to Cuba's? Why? What about the period?"

Next time.


  1. Great, and fascinating, blog. Hoping to use GeoGebra with the IB HL Physics... they need to model a lot more than is currently taught. Just hope my brain is still up to it!

    1. Thanks! I'm going to try to blog a lot more of my ideas and activities this year. If anyone else finds it useful or interesting, all the better!

      As for GeoGebra, just play with it. It's a very rich environment - you can do a lot just playing with it. If you need some ideas [read: you want to steal from other smart people], check out GeoGebraTube! Here's the link to the material tagged with 'physics':

  2. Thanks for the post! I've been using Geogebra as an algebra/analytic geometry teaching tool, but you've inspired me to check out the spreadsheet functionality for investigating data. Keep up the good work! -Paul

    1. That's one thing that makes GeoGebra great - it's such a rich environment. I'll keep an eye on your blog to see what you do with it!

  3. Thanks for the post and good ideas. I have a similar project, but I like your idea of having several years of data. Even with one year of data, though, my students struggle with the period being one year. Hmm. Still trying to figure out GeoGebra, too. With so many other tools available - that my students and I already know how to use really well - it's difficult to motivate myself to learn something new.

    1. I agree, it's hard to pick and choose tools, and I think it's important to focus on a few. I find that GeoGebra is so versatile that it fits in very well with this strategy.

      Which tools have you been using for projects like this?