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.
People have struggled with the idea of creating educational video games for many years. A few companies have made some progress in this field but for the most part there has not been much study into the game’s effectiveness.
Speaking from experience I would argue that games, such as the ones created by MECC in the 80’s, are effective. I remember playing “Number Munchers” and memorizing my multiplication tables faster than I would have in a lecture setting. I remember assuming the role of a fish in “Odell Down Under” and learning about how I (my fish) fit into the food web. These experiences have stuck with me and to my knowledge it has also stuck with my friends who have also played these games. Obviously, MECC was onto something. Unfortunately that something must have been magic to them as well, as evident by their closure in 1999. So what is this magic? And if we can find it, what do we do with it?
Today educational video games lead a cursed life. For the most part they are loved by parents and loathed by kids. This is not surprising considering that the most popular (at least for parents and educators) educational video games follow a prize winning formula. They make academics explicit. Math formulas are plastered all over the front of box. Claims that students need practice are slathered on the back. If one didn’t know any better they might think their holding the very essence of the subject they want to study. Once the actual program is booted up the user is bombarded with questions, sometimes in exchange for an animation of some sort that disappears only to be seen when another question is answered. They feature academics so well that they forget it’s an educational game, not a virtual worksheet. The parents are over joyed, they feel they got what they paid for. The kids feel slighted, weren’t they supposed to be playing a game?
Unfortunately, there is a disconnect between how much an game sells, and how much it gets used. I’ve noticed quite a few times how kids get bored with an educational video game that forgets it’s a game. I would argue that this is probably the reason those games fail in the first place. Why should Batman waste time answering the question “2+2 = ?” ? Almost any kid knows that Batman much smarter and much too important to waste his time on such things.
So what are we to do? Well, why don’t we set the game up so that the skills desired must be applied in order to win? Say you wanted to teach english. Why not create a world where the student is a proofreader at a local paper. They are given a few articles that need corrections and must make the correct decisions before their deadline. Now the subject and the game are one. If a student wants to beat the game (they usually do) they must acquire the skills needed to be a proficient proofreader. Spelling, grammar, reading comprehension, anything a proofreader encounters can be inserted into the game. So proofreader doesn’t get you excited? Well then why not use Batman a better way? Batman is a detective . Thus students who play the game should also assume the role of a detective. Say you want to find the joker. Why not have the students analyze a letter from the joker to find out where he strikes next? If Batman needs to get into a room with a combination why not have the students crack that code? Cryptography involves many subjects including Math. In both this case and the previously mentioned case students must use math to advance the game. But only in this one do they not feel like it’s irrelevant.
Allowing the student to assume various roles in order to learn? What an odd idea? It’s not like someone’s already proposed learning through experience… What a strange idea to be applied to video games.
On Informal Learning
The relationship between informal learning and more traditional lecture style learning is a strained one. Lecture style learning has been around for a while, it’s been there done that and has taught millions. For lecture style learning, order and timelines are important. Informal learning, on the other hand, plays by it’s own rules. Informal learning is messy, fun, and a bit of a slacker. You would think that if these two were people they wouldn’t get along very well. Their personalities clash, they have different our looks on life and have different methods for achieving success. And yet we cannot resist getting them together.
I have to admit, I’m guilty of trying to use informal learning in a formal learning environment (In fact I still think it can be done). This is perhaps why one of Papert’s statement really jumped out to me. Papert states “[Discovery learning] is disempowered in part because discovery stops being discovery when it is orchestrated to happen on the preset agenda of a curriculum”. Here Papert argues that there is disconnect with the idea of discovering something that has already been found, or in this case is meant to be found. This presents a problem considering the fact that schools today must ensure that key concepts are being taught. There are no guarantees with true discovery learning, but that simply cannot exist in a standards based curriculum.
Further more, Papert puts forth the idea that it is not enough to learn through discovery if what the student discovers is of no use or interest to them. The ideas used and the ideas formed must be appealing to the students. The problem is: What idea is big enough to encompass the interests of all students? I love to learn about animals and the various defensive strategies they’ve evolved over millions of year, but others can’t even make it to the end of that statement without nodding off. This is exactly why there is so much interest in computers as educational tools.
There seems to be a misguided idea of what educational technology is, and at what point it is useful. Everyone seems to be waiting for that new program that can teach anyone anything. The truth is it will never come. Computers are seen as these magical creature that help people learn through their programs. The reality is that computers are no more than an evolution of paper. They are merely tools that display what others have created. If we take this a step further programs can then be seen as books, or pieces of artwork created on this paper. But just like in real life, some books really connect with the readers and expands their minds, and other don’t.
Perhaps this is why Papert believed Logo to be an excellent learning tool. Logo, as any other programming language, allows students to write and draw on this new paper. Now, I’m not saying that programming is the only option but I agree with the logic behind it. Allow the student to create what they want with a computer. If logo allows them to explore their Ideas, then great. If Microsoft Word allows students to express their ideas, then allow them to be used! The beauty of computers is that they are flexible enough to become whatever the student needs. Maybe Resnick said it best when he noted that “These new technologies should provide children with design leverage, enabling them to create things that would have been difficult for them to create in the past”.
While I agree that a child who grows up in france will learn french easier than say a person living in America I’m not quite sure that this is enough. Speaking french is quite different from say analyzing french poetry. Papert’s “math world” does get the children associated with some ideas of geometry but does it teach them poetry? I remember playing with logo, and I also remember others who did the same. We made some cool pictures, but only a few of us sought to make these pictures on purpose. Furthermore, I find it a bit difficult to say that everyone could express those ideas in terms of geometry.
If we agree to abide by the language analogy we will soon run into the problem of translation. A great french scholar may be crippled if he is forced to express those ideas in another language. At some point or another the children need to leave the math world. When then do they need to make sure that they can express the ideas they learn in the non math world. If they cannot translate these ideas and use it in other contexts they are at a disadvantage.
Gears of my childhood
I am constantly amazed by the way that video games command attention. People willingly play video games for hours without becoming bored. I can’t blame them, I do the same. However, what excites me is the fact that some children who generally do not do well with memorization can recite the names of hundreds of Pokemon while also listing some of their characteristics. Obviously something is happening that allows these kids to learn and recall this information easily or at least willingly. Something that occurs while they’re playing the game. If we can harness this medium to create effective educational tools the results would be very valuable. The question is, how?
My fascination for using games to promote learning came at an early age. My mother helped me understand that education unleashes potential and that the first step towards fulfilling any dream is to learn about it. Coming from a low income neighborhood however, did not provide many opportunities to seek additional tutoring. My mother met this challenge by creating simple educational games that we would then play together. I remember playing a wide variety of games each with an underlying educational concept that I could use in my studies. I appreciated how much my mother worked with me and since that time I wished to do the same for others.
Growing up, everything was a game to me. I remember doing inequalities and pretending the greater than or less than sign was the mouth of an alligator. To win this game I had to feed the alligator the biggest number I had. I remember taking tests and pretending that I was on a quiz show. The more questions I got right, the more money I got. These little games helped me to focus on the tasks and motivated me to do my best. They also added a bit of excitement to what would otherwise be repetitive tasks.
When I was 16 my love of games introduced me to programming. I remember finding the program GameMaker and being amazed by the fact that I could make things move across a screen by issuing simple commands. It wasn’t long before I had things moving across the screen and crashing into one another. I also remember what didn’t work, and the hours I spent debugging my code. But instead of loathing the debugging process I found myself looking forward to it. I found that I treated debugging much like a riddle that I was eager to solve. I continued to develop my game until one day I was selected to represent my region in the Intel Teen Technology summit. Because of my game I was also featured in a New York Times article showcasing youth and technology. I’ve been programming ever since.
Even now it baffles me that people don’t actively create little games to help them learn. I firmly believe that making small games has helped to me achieve the success I have today. But, even with the advent of Sesame Street, some people still cling to the antiquated idea that if someone is laughing, they probably aren’t learning. This was especially relevant during the time I volunteered at the intel teen technology clubhouse. During that time the card game YU-GI-OH! was very popular. Almost every student that came to the club house was familiar with the game and enjoyed playing it. The coordinators of the teen technology clubhouse, however, saw the card game a a nuisance and tried to ban it. Being the proponent of games I argued that the students were actually learning while they played the game. The coordinators seemed intrigued by this idea and asked me to put together a small presentation about what the students learned while playing the game.
At first I wasn’t sure what I was going to present. Obviously the game required knowledge of addition and subtraction during the “battle” phase, but I wasn’t sure what else. However, as I studied the game with the lens of an educator I began to see multiplication, division, probability, strategy, reading comprehension, and even economics being used while playing the game. What was more exciting was that some of these concepts had not been taught at school meaning that the student had learned that skill simply so that they would be good at the game. The game had served as a tool to encourage learning. I was excited by what I had discovered and the coordinators were impressed that these concepts were present in what they had assumed to be a frivolous activity. Needless to say, the game was not banned.
When I think back to these experiences I can’t help but get excited. I only wish I knew more about effective educational games. There is great power in learning through play, and I can’t thank my mom enough for introducing me that idea.