# Space Range-r

## September 18, 2016

Today, I’m releasing an early prototype of a new math game I’m making in GeoGebra. Introducing… Space Range…er. (It’s a pun. Get it?)

The idea for this game has been rolling around in the back of my head for a good 9 months. I thought I’d need Javascript to make it happen, but on Friday, I thought of an easier way. This version took me only one afternoon of work. GeoGebra makes it easy to quickly prototype new ideas!

Space Range-r prepares students to evaluate functions graphically and talk about their domain and range. It follows my idea of “messing around,” an idea I wrote about earlier on this blog and recently presented onĀ at the 4th Annual Southern Connecticut GeoGebra Conference. I’ve also written an article about this concept, which will appear in the conference proceedings; stay tuned for more info.

In the game, you control a space ship that moves back and forth along the x-axis. A button on the right lets you “fire your lasers,” which basically amounts to evaluating the function. Explosive stars appear along the y-axis. They heat up; turn red, and begin throbbing. If you don’t disarm them with your lasers, they’ll explode!

To win this game, one needs a keen understanding of how function evaluation works. That might seem like a simple thing, but even Calculus students have difficulty coordinating changes in the x-axis with changes in the y-axis. This leads to a lot of confusion when you introduce a concept like piecewise functions and ask a student a question like “what’s the range of this function?”

This is a very early version of the game, and also a very unplayable version. I need to do some work smoothing out the controls. One of the game’s key mechanics has not even been implemented yet. In the upper right corner, you will be able to switch between three different “weapons.” Each “weapon” switches to a different graph. Some graphs will be better than others for shooting at certain y-values. In most levels, some of the graphs will be piecewise functions or parabolas whose range doesn’t even include all the y-values shown in the image. Students need to make quick, smart decisions about which graph is best at which moment in time.

Here are a few other features I plan to implement:

- Difficulty controls. A slider on the start screen will let you change the difficulty level. At higher difficulty levels, there will be more exploding stars and they’ll blow up quicker.
- Accuracy controls. Right now, you have to be very precise with your shot, which can be frustrating. Students who want to play a more forgiving game will be able to use a slider to give themselves more leeway in their shots.
- Music. Sound effects. Stars floating by in the background. I have to be careful about lag time over the internet, but some of this stuff is necessary to make the game feel alive.
- A proper “you win!” screen!
- Multiple levels with different combinations of graphs available to the player.
- More ambitious ideas that may not happen:
- More types of enemies. I want to add red herrings that look like stars but cause you to lose if you shoot them. Maybe some enemies will move around? Maybe others will shoot back at you? That could be a fun way to introduce the idea of inverse functions. I’m thinking about having later levels where you can transform the functions. I also was toying the idea of enemies that can shoot a hole in your graph, making it no longer use-able. I would love it if you could grab power-ups that float down.
- Boss enemies. That would be really cool!
- A story line?

The coolest thing about GeoGebra though is that it’s open source software. I encourage you to download it, mess around, and make your own levels! At the very least, stay tuned for more updates in the near future.

# Messing Around in GeoGebra

## August 16, 2016

This blog has basically become a last-minute repository for all my talks. I’m not happy about that; I’m going to start blogging for real again, but in the meantime, here’s another talk for the repository.

I’m speaking tomorrow (today?) at the Fourth Annual Southern Connecticut GeoGebra Conference. This is an exciting talk for me for a lot of reasons. It’s inspired by a blog post I wrote back in February (back when I still wrote blog posts,) and it will be part of the conference proceedings. Most importantly though, I gave a talk at last year’s conference, which set in motion several exciting collaborations with some really wonderful people. Wow, I cannot believe it’s only been a year! It feels like a decades. In any case, here are my slides. I hope the coming ~~decade~~ year can be every bit as meangingful as the last one.

# Southern Connecticut GeoGebra Conference

## August 24, 2015

I’ll be giving a short presentation tomorrow at the 3rd annual GeoGebra Conference of Southern Connecticut. I’m really looking forward to meeting other folks in the GeoGebra community and hearing what they’ve been doing.

In my talk, I’ll be presenting an activity that I use in my Statistics class at Guttman. It’s based on APOS Theory, and uses a GeoGebra worksheet to help students make sense of the mean and median as objects. As students drag and drop dots on a dotplot, the mean and median dynamically change in response to their manipulations. The slides, handouts, and GeoGebra worksheet can all be found below.