# 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 on  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.

# Mathimals

## March 6, 2015

Manimals is a good educational game for several reasons.

First off, the rules are stupid simple. If you’re going to use a game in your classroom, it better have simple rules. I learned this the hard way last Fall when I tried to use Sid Sackson’s, Can’t Stop, to explain relative frequencies in statistics. (I stole the idea from this guy.) The lesson was a raging success, but the rules explanation was not. Think about how hard it is to teach the rules of a board game to friends who’ve volunteered to play the game, and imagine that confusion multiplied across 25 restless students who do not want to be there.

The board in Can’t Stop even looks like a histogram…this just screams relative frequencies!

But forget simplicity, the best quality of Manimals is that it’s actually fun! A lot of educational games feel like homework…this one does not. The artwork is also gorgeous, and it packs up compactly. Manimals has a real-time, “race to be first” aspect to it, which will appeal to some of your more kinesthetically inclined and/or competitive students, but you don’t have to be fast to be successful.

This game is a versatile, educational tool. Instead of animals, you could use any concept that you wanted to teach. I’m imagining cards with different representations of functions on them (graphs, tables, equations, a description in words, etc.) and on the back would be icons representing properties of this function like “is linear,” “has an x-intercept,” “is always increasing,” “is one-to-one,” “domain contains [1, 3),” “is transcendental,” “has a vertical asymptote,” and so on. The game would otherwise be played exactly the same way!

It even gets more interesting because sometimes the representation may not provide enough information to determine if the function has the trait or not. This could be indicated on the back of the card with a broken icon, and the student could get 2 points (rather than 1) if they explain why there’s not enough information. This chance for extra points starts a conversation. Your classmates want to win. They’re going to challenge your explanation, and you better be ready to defend it.

Another reason I like this activity is because it reminds me a lot of Bruner’s Concept Attainment, which is a well-tested and widely used technique. We also know from APOS Theory that students struggle to think of functions as objects. By printing a different function on each card, you are basically presenting the functions as objects out of the box. A student can pick up and manipulate this card like a real-world physical object. One of the main weaknesses of APOS Theory is that it really only offers one intervention (computer programming with ISETL) for moving students to an object understanding of functions. This could be another intervention.

A lot has been written about the gamification of learning. I won’t rehash that literature here, but I will say that you can get a lot of mileage out of a simple game and your students will engage in ways you never imagined. That lesson on relative frequencies that didn’t go so well? I was out at a bar one night when my colleague called me from the office. My students were there, and they wanted her to lend them my copy of Can’t Stop. They chose to play a math game in their free time!