Do we live in math world?
While reading Eisenberg’s paper I was captivated by the description of a real life mathland. Mostly, I mused on the fact that many of these things can be, and in some places are, used today. If you want to get technical about it almost everything requires some amount of math to create. Chairs, beds, windows are all composed of geometric shapes. We live in a math world. But, that doesn’t mean that we speak math. A chair is not a construct made of polygons, it’s a chair. Unless, someone can show us otherwise.
This lack of speaking math seems to spread onto the other examples that Eisenberg provides including his paper tape. Sure, you CAN develop the ideas of privative simple commands creating a more complex program. But when you’re simply playing with paper tape it’s hard to come up with that idea on your own. This is true for most transitional items and application. Unless someone help people find similarities, or there is incentive, the paper tape will probably end up being a testament to the user’s skill with paper tape. Not his geometric ability.
Microworlds vs Video Games: Why can’t we just get along.
When reading the Edwards paper I was continually reminded what defined a micro world. A microworld is a subset of known actions or commands that represent real life ideas. These actions and commands can then can be built upon or used to obtain a goal. Obviously, logo is a good example of a mathematical/programming microworld. In logo a turtle knows a few basic commands that make up it’s world. The user can then use those known commands to create almost anything, provided it doesn’t violate the existing rules.
With this definition in mind I submit that all video games are in fact micro worlds. Take the game pac man. Pac man’s “world” is composed of a few simple actions: turn left, turn right, go up, go down and eat. Using these actions players can then construct more sophisticated maneuvers such as eat all pellets, avoid enemies, and eat ghosts. Yet, people are hesitant to associate microworlds with video games seeing the former as academic and the latter as frivolous. This is very unfortunate since a well constructed video game, in my opinion, would probably serve as a very powerful microworld.
Anyone can ask a physics question and present multiple outcomes. However, if the user is immersed in the problem and is given the freedom to explore the possible outcomes themselves then learning can occur. For example, let’s place the user in a scenario where they are stranded on an island and need a way to get off. Suddenly, a question about buoyancy and engineering becomes much more involved. If executed correctly the user will be able to test different materials with know densities, and through trial and error come to the conclusion that a lower density correlates to a better floating raft. Yes, a problem about buoyancy is not explicitly presented, but the concept will be. Once the user understands the concept their understanding of the formulas that go with it will also increase.