[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

Results

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.

The Coming Year - Technology In My Classroom

In a little more than a month, I will begin my first year as a high school math teacher. Having a vague understanding of how challenging it is going to be, as well as knowing my tendency to take on too much, one of my goals before the year starts is to have a plan for the technology I am going to use, its purpose, and how I am going to incorporate it into my teaching.

In choosing which technologies I will use, I am using the following as my requirements:

• Free to use as in cost. Truly free software is a bonus.
• Cross-platform. Works with Windows, Mac, and Linux without a fight.
• No downloads or installations required, other than a reasonably modern browser.
• Limited number of registrations and sign ups.
• Ease of use. I want to teach math, not technology.

That being said, here are the weapons I plan on brandishing:

GeoGebra

Absolutely amazing mathematics software designed for teaching and learning mathematics. While it's not always the most intuitive software to use, its dynamic and interactive nature make it a powerful tool in the classroom. There are loads of tutorials and ready-to-use materials on the main website.

Python

I absolutely agree with Conrad Wolfram that teaching a bit of programming is crucial in teaching mathematics in the twenty first century. Python is my programming language of choice for many reasons. Also, Google's Exploring Computational Thinking is a great resource (and they even posted one of my lessons from my student teaching!).

Google Docs

If you have never used Google Docs before, I highly recommend it. I often hear it described as Microsoft Office in the cloud, but it is much more than that. It puts collaboration and sharing at the center of the process. Students are able to work on the same document at the same time, chat online together, track who made changes and when, and so much more. And it keeps getting better.

Twitter/Google+

For most of the summer, I simply assumed that I would be using Twitter, but the recent (beta) release of Google+ has been rethinking that. I love the idea of back-channeling, communication, and collaboration inside and outside of the classroom, as well as giving students a different way to contribute. Circles, hangouts, and sparks (Google+ features) are promising features. Here is an evolving presentation on some potential uses of Google+ in education (and a great example of Google Docs in action!).

The math and tech geek in me is excited. These tools have the potential to engage students with mathematics at a level far beyond my high school experience, and that was not all that long ago.

Oh, and please leave comments! I would love to hear your thoughts and suggestions and learn about new resources.

Next post: How I plan on using technology for continual professional development and reflection.