# Space Gate

What: Concept for an educational game (topic: mathematical differentiation)

Where: Merz Akademie in Stuttgart, Germany

When: Summer semester 2009

As a practical component for my diploma project, I chose to devise the concept for an educational game. I picked the mathematical differentiation as the educational material the game would attempt to convey, since I was personally familiar with that topic and it would be a bit of a challenge.

f(x) = 2x³  ==>  f’(x) = 6x²

Well then: How does one create a game that educates about differentiation without explicitly having the player differentiate a mathematical function? One doesn’t. Differentiation is too complex for it to be simplified and abstracted into other activities that could be employed in a game, and for the skills developed during abstracted activities to then be translated back to the solving of differentiation exercises. (At least it was in my opinion, a modest person would probably say.) Instead, I chose a different approach, and attempted to make the solving of differentiation exercises itself an enjoyable task.

If the popularity of sudoku puzzles has shown anything, then it is that number puzzles can be seen as enjoyable. My goal for this game was to present the differentiation of a function more as a puzzle, rather than a dry chore. In order to achieve that, the game concept employed two main strategies:

Interface: In this game concept, the derivative function is constructed with the mouse only. Parts of the original function can be selected and dragged over to the derivative function. Numbers are increased or decreased by left or right clicking on them. I did not want the player to type in any numbers or parts of the function with the keyboard, because that would feel like solving an exercise in a training software. Instead, he would be manipulating “puzzle elements” with the mouse.

Click the image for a short animation of the interface.

Context: The “differentiation puzzles” are solved in a sci-fi adventure setting. The objective of the player is to figure out a discovered alien artefact, and he has to solve the differentiation puzzles in order to do so. That was meant to create an environment where the player would perceive the “math” puzzles as a natural and obvious activity. The player is attempting to decipher alien technology/language/programming, so of course complex puzzles are the expected activity.

In the game, the player boards a Nasa Space Station where he finds an alien artefact, the eponymous “Space Gate”. In order to activate it, he has to decipher the encryption on each activation stone. Completely deciphering one ring of stones enables the character to travel to a new strange alien planet, where he will find instructions on how to decypher the next ring (using an additional differentiation rule to do so).

An interior concept for the space station airlock chamber.

Coming up with a sci-fi scenario was of course a major part of the fun in this project, even if that was not the focus of my diploma. But constructing an educational game around such a complex topic was in itself a very interesting challenge as well.