Compounding Fun with Vector HD

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Today we have a guest blogger, Josh Giesbrecht, a high school math and information technology teacher in Abbotsford, BC, Canada.  He recently transitioned to teaching from a software development career where he worked primarily in game development.

Vector TD is a stylish but standard entry into the tower defense genre of videogames. However, a few specific design features make it stand out as a potential math lesson waiting to happen.

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Quick intro: Tower defense games are popular in the free web-game space, where they made their big debut as standalone games.  The first tower-defense gameplay was created by people making custom maps for real-time strategy games like Starcraft.   The TD gameplay is an exercise in resource management. The games consist of a map with some kind of a path from start to finish that the bad guys will try to cross. Your job is to build towers that shoot the waves of bad guys down before they get to their destination. The challenge comes from deciding what to build, where to place it, and (most importantly for our purposes) when to buy it.

Before I spoil things any further, go play it. If you have time, try to beat all 50 waves on an easy map; if you’re impatient, at least play for 10 rounds. Or if you want the primer, here’s a short playthrough video of a few rounds.

Clearly, math is key when designing and balancing the gameplay for a game like this. Math also comes into play, usually at an intuitive level, for deciding which towers will give them the most bang for their buck. However, Vector TD stands out to me as a potential stealth-math-lesson for another reason: compound interest.

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If players are stingy and can hoard cash between waves, they earn some amount of interest between waves. Even more importantly, the player is given the choice to allocate scarce bonus points into increasing the interest rate. This isn’t unique to Vector TD; many games in the genre include earned interest, and some also allow you to upgrade your interest rate. Ironically, the reason I’d suggest Vector TD is that the choices it presents aren’t well-balanced.

By placing all of your bonus points into increasing your interest rate, you can get to an absurd 24% interest rate by wave 35 (of 50), and up to a maximum of 30% for the last few waves. While other choices for spending bonus points are more effective in the short term, the combination of a high interest rate and stinginess in spending will give you a glut of money to spend on the most expensive and powerful towers during the endgame. This may not be the only way to complete all 50 waves, but it’s by far the most effective. (Other games in the genre tend to be more balanced, with a lower max interest rate and effective alternatives.)

Implementation

So this game makes compound interest look pretty attractive, and may even help kids catch onto the value in delayed gratification (maybe). So how do we connect it to the classroom? This isn’t an “edugame”; it doesn’t dive straight into teaching interest rates and doesn’t ask students to actually work out any numerical solutions.

(Disclaimer: I haven’t tried this yet. Highly experimental suggestions follow.)

In-class Activity: Here, you could take advantage of cooperative learning and play, letting students who aren’t as game-literate work together with others and get the hang of the basics. The mixed advantage/temptation would also be that you can observe and interact with the students, but try to keep it to a minimum. Don’t be too helpful. Just tell students this is an exercise in finding logic and math in a fun game, ask them to figure out how to beat all 50 waves, and then discuss the winning strategies at the end. The biggest problem: this game takes a while to complete, even if you already know how to beat it. It may take students two or more hours to get enough experimentation under their belt to pull out the “good stuff” on their own.

Homework Assignment: Give students the task of playing and beating the game on their own time. At a secondary level, this has the danger of parental incredulity (“That’s not homework!”) and student abuse (playing it for longer than needed, neglecting other tasks and blaming the teacher). It may also be tricky to account for differing levels of game-literacy in students; some may be completely disengaged or overwhelmed by the task.

Still, a big advantage here is that it could be assigned as a long-term task, something due in a week or two rather than next class. This gives students the space to play and discover things on their own.

Follow-up: In the discussion afterward, you could connect the game’s internal lessons to personal economics. For example, you could ask what the effects of a 24% interest rate would be on a savings account vs on a loan. Or, to draw out the idea of delayed gratification and how that works in your favor, you could ask something like: “Did your buying habits have to change to make this strategy work? Could the same approach have a positive effect in real-life budgeting?”

Thanks Josh, for a great post about Play and Learning.  You can find Josh on twitter @joshgiesbrecht or visit his blog, Josh G’s Notes.  If you’ve got a game that you think would provide good play for learning, and you’d like to write a guest post, send me an email with your idea.

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Chain Factor

For the last week, in between hours of dissertation work, I’ve been trying to figure out best strategies for the game Chain Factor.chain-factor1

I’m still trying to figure this one out, but there’s got to be a way to turn the analysis of this game into an assignment for a math class.  In particular, I’m thinking about doing some mathematical analysis of games in my Honors Calculus class this winter semester.

For the first six days, I just played in Basic Mode to try to figure out some general strategies.  It seems like it would be a very simple game, but it’s much more complex than it looks.  After a week of play, I still can’t come up with hard and fast strategies that work consistently.

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Tonight I started playing in Power Mode and this adds a whole new set of logic and mathematical strategies to the game.  When is the optimum time or situation in which to use each power?  Which are the best powers to choose so that you have a way “out” of any threatening situation?

I’m thinking that, at the very least, it would be an interesting assignment to have students do an analysis of each of the powers, when they are useful, and when using them will actually hurt you.

Another interesting assignment would be to determine a strategy for stacking columns so that you get the best “chains” when they are set off.

The nice thing about the game is that it’s addicting, but just frustrating enough that you can’t just keep playing all day. :)

Please let me know if you come up with any interesting ideas for assigning this game!

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