GeoGebra with a Purpose

(Lost the source of this!)

I got to give a whiz-bang 60 minute (with an option for 30 extra minutes) intro to GeoGebra at the New Tech network conference this week. 50 plus tech-savvy teachers... so it was good. I am always worried that people expect me to tell them about GeoGebra for an hour, when purpose is to get them started using it on the spot, in ways that make sense of their potential use. (Note that if you are in driving distance, I am more than happy to come do this at your school. No GeoGebra lectures, however.)

Purposes. So what are the ways that people make use of it? Oh, let me count them:

1. World's best graphing calculator. (A little weak on statistics and CAS, but that's improving quickly.) For you and your students. For algebra, calculus, or geometry.
2. Mathematical image editor. For uses in reports, papers, handouts or assessments.
3. Demonstration tool. Project a great visualization on your screen to show to or discuss with students.
4. Focused mathematical activity for students.
5. Open-ended inquiry tool. Pose a question and let students investigate.

Requirements. The AMAZING thing about this tool is that with version 4.0, all of these are accessible to teachers in that 60-90 minute start up.

1. Open the program, start typing equations on the input bar.
2. Needs some quick familiarity with the tool bar to make your image, then File > Export > Graphics View As A Picture.
3. GeoGebraTube. If you have not looked at this, you are missing out. 14,000 sketches and counting; free accounts, search, likes, tagging and you can collect them in teacher mode or show collections in student friendly mode. This is why you need minimal expertise to start using the program deeply. If you can run YouTube and you are a teacher, you can do this.
4. See #3. 
5. Students today are geared for this kind of tool. You give them access, they'll figure things out about it that I don't know.

Really, any training beyond that first 90 min. is about if you want to become proficient in number 5, or if you want to be designing your own activities. Some teachers are doing that anyway by the end of an hour, most by the end of a half day.  Once you start using it, there's a big danger of being sucked in by the possibilities of what you can make. The power of dynamic examples is as much greater than static electronic images as static electronic images were than hand drawn. (My opinion. No research. Actually yes research, but they would never quantify so crazily.)

After my session, I got to go to Geoff Krall's (@emergentmath) session on formative assessment. He was using the MARS  MAP (Mathematics Assessment Resource Service - Mathematics Assessment Project) materials.  In particular, he used the Ferris Wheel lesson to get us collaborating and specific in discussion.

As we discussed, it really got me thinking about how I would use the task early on. It would make a good project or assessment, I think, but what about as an inquiry? The basic problem was to make a symbolic model [find a, b and c for a+b*cos(ct)] for the height of a car on a specific Ferris wheel. Then there was a card sort which got students comparing context, equation and graphs.

I've given many explorations before that got students experimenting with parameters to see the effect on graphs, but I love the idea of tying it to a context. That doubles up on the intuition they can apply - physical and visual. If the students had access to that, they might be able to do enough trials to start to generalize. Even without much trigonometry understanding, it's a nice context for graph transformations. For me, these kind of thoughts now lead to GeoGebra. I made a quick sketch, with the Ferris wheel in a 2nd graphics window, and was delighted to find that even the 2nd window worked on GeoGebraTube.

But since then I thought it would be worthwhile to develop a bit more. Both to familiarize myself with using the 2nd graphics window and to make the single model into a reusable activity. I knew I wanted to have either a customizable or random Ferris wheel, some animation of the situation and a way for the students to enter the equation.

That bore some thought: sliders, input boxes for parameters or an input box for the function?  Sliders are best for seeing continuously linked examples, but can make a problem like this too easy! The input boxes for the parameters helped support the idea of structure, require some thinking before making a new guess, and don't require as much typing as entering the whole function. Plus you can isolate one parameter and just adjust that. That might be a positive or negative.  It feels like a support for learners early in this, by encouraging them to focus on one parameter at a time.

The trick to working on two graphics views is the advanced tab of object properties. You can use any tools from the main window. Just select the tool and then use it in the 2nd graphics window. The objects you make there show up in the algebra view. But when you edit things, or create them in the input bar, they migrate or appear in the first graphics window. The solution is in the object properties, advanced tab; just check the box you need. Note that you can have something appear in both ... there just has to be a cool use of that.

I don't think there's anything else too tricky about the sketch. I used the Function[ , , ] to get the modeled equation to move with the tracing point, the ZoomIn[1] command on the button to clear traces, and the UpdateConstruction[] command to reset the Ferris wheel dimensions. (I had slick graphics window dimensions based on the Ferris wheel, but then the ZoomIn[1] command doesn't work. Ultimately I thought it was better to see the Ferris wheel changing sizes anyway.)




 The sketch is on GeoGebraTube: Teacher page for download or Student worksheet for in browser use. You have to click in the main window to get the animation button to show.