I’m a long-time user of interactive geometry software, of which the dominant instance these days is GeoGebra. Here are some ways it’s enhanced my teaching over the years.

- Most obviously, it provides an environment for students to explore geometry and geometric construction. I’ve written much about it on this blog, and shared some curriculum on my site ( 8th grade | 9th-10th grade).
- It makes transformational geometry much more accessible — my Space course was revolutionized by this software.
- It is a powerful platform to create special-purpose applets that can enhance the teaching of many math topics in geometry, algebra, trigonometry, and calculus.

One perhaps underused feature of GeoGebra is the ability to have two graphics panes in the GeoGebra window. This turned out to be quite useful in setting up my arithmetic games (Signed Numbers | Complex Numbers). The game interface is in one pane, and the graphical representation is in the other. I also made use of the two panes in Doctor Dimension. This is an environment to explore and discuss rate of change, using a geometric situation in one pane and the corresponding graph in the other. Another possible use which I read about (but have not tried) is to display a graph in one pane, and a zoomed-in part of it in the other.

### Making a Slide Show

My most recent use of the two panes is in creating a slide show about an unorthodox path to the quadratic formula. (The video is a little over 11 minutes, so you might take a look now. It will help you follow the instructions I share below.)

I already had a silent slide show on this, but I thought it may be a good idea to add a narration to it. Instead of using Apple’s Keynote this time, I decided to re-create the entire slide show in GeoGebra. This way of using GeoGebra may be useful to others, so I’ll share how I did it in this blog post. (There are several versions of GeoGebra. I used GeoGebra Classic 5 on my computer. I welcome information on how this would work in GeoGebra 6, and in the various online and in-device versions.)

1. Making a slide show in GeoGebra is of course mostly relevant if your key arguments are best made using GeoGebra. In this case, it did make sense, because I needed to make a graphing / geometry connection, and animations were an essential part of my presentation. I started by creating a .ggb file to illustrate the proof, using the Geometry perspective, but showing the axes. This included lines, hyperbolas, various rectangles, sliders, and text boxes. The plan was to make those items appear or disappear as needed as I talked through the slides, matching what was visible to the slide I was on and the accompanying narration.

2. To show the second pane, I selected **Graphics 2** in the **View** menu. Once that pane is visible, it can be dragged to be above, below, or to the left of the first Graphics pane — or it can be left on the right. I put it on the left, and in it, I made a slider which I would use to navigate from slide to slide. I called it **Slides**, and had it range from 1 to 12, with an increment of 1. I later found out that I actually needed 14 slides, but that was easy enough to change in the **Slider** panel of the slider’s preferences.

3. I pasted the content of the slides as images, in the same pane, using **Insert Image From…Clipboard** in the **Edit** menu. This is in because I already had those images, and didn’t want to remake them. If they didn’t already exist, I could either make them in other software and copy-paste this way, or create them right within GeoGebra. In the preferences for each such image (or such text created within GeoGebra), I went to the **Advanced** panel, and entered **Slides = **[the appropriate slide number] under **Condition to Show Object.**

4. For each slide, I used the same method to show or hide the items in the original pane (lines, hyperbolas, rectangles, etc.) If an item needs to appear with multiple slides, the **Condition to Show Object** needs to be more complicated, using **or** and/or **and** (heh) as needed. Another reason you might need those operators is if an item’s appearance / disappearance also depends on the value of another slider. Here is how you enter the various logical operations:

(I no longer remember where I got this table. On geogebra.org, presumably.)

5. Once all this was set up, I could advance through the slides and the accompanying graphics by using the slider. I rehearsed the slide show, making sure that the right items appeared in both panes for each slide. To add the narration, I used my Mac’s QuickTime Player to record part of the screen.

I think that’s all you need to know!