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Math and Game Programming

Overview
Just before the start of the semester I came across the Level Up project at the Scholastic website.  There, several lesson plans are listed that combine content with video game programming. 

I was immediately intrigued by the resources that they used for making the games.  For the beginners they use Gamestar Mechanic and for the intermediate students they use Gamemaker.  I took some time to try both of these resources and I also contacted Merry Lenz, a fifth grade teacher in my district who is always quick to use new technology in her classroom.

Merry immediately embraced the idea of trying something involving video game design with her students.  After evaluating the sample math lesson from Scholastic, though, I decided I would make my own lesson.  I was not impressed with the superficial blending of the game design tools with the content, especially in the math and science lessons.  Merry wanted to keep the ratio and proportion content in my activity, so I attempted to make a game design assignment that required a better understanding of those concepts in creating the games.  The worksheet packet that I developed for this is attached below.

After working with Merry's fifth grade students for a few days, I also began working with four sixth grade students from a math intervention class at the middle school.


Literacy and Learning Principles
Active, Critical Learning Principle
All aspects of the the learning environment (including ways in which the semiotic domain is designed and presented) are set up to encourage active and critical, not passive, learning.

Design Principle
Learning about and coming to appreciate design and design principles is core to the learning experience.

Semiotic Principle
Learning about and coming to appreciate interrelations within and across multiple sign systems (images, words, actions, symbols, artifacts, etc.) as a complex system is core to the learning experience.

Semiotic Domains Principle
Learning involves mastering, at some level, semiotic domains, and being able to participate, at some level, in the affinity group or groups connected to them.

Meta-level thinking about Semiotic Domain Principle
Learning involves active and critical thinking about the relationships of the semiotic domain being learned to other semiotic domains

Identity Principle
Learning involves taking on and playing with identities in such a a way that the learner has real choices (in developing the virtual identity) and ample opportunity to meditate on the relationship between new identities and old ones. There is a tripartite play of identities as learners relate, and reflect on, their multiple real-world identities, a virtual identity, and a projective identity.

"Regime of Competence" Principle 
(This principle is not evident in the components of this learning activity, but it was discussed as an important aspect of any good game.) 
The learner gets ample opportunity to operate within, but at the outer edge of, his or her resources, so that at those points things are felt as challenging but not "Undoable". 

Incremental Principle
  (This principle would come into play in a course designed as described in the Further Explorations section below.)
Learning situations are ordered in the early stages so that earlier cases lead to generalizations that are fruitful for later cases. When learners face more complex cases later, the learning space (the number and type of guess the learner can make) is constrained by the sorts of fruitful patterns or generalizations the learned has founded earlier. 

Insider Principle
The learner is an "insider," "teacher," and "producer" (not just a consumer) able to customize the learning experience and the domain/game from the beginning and throughout the experience.


Classroom Experience
I followed this general outline when presenting this lesson to the two classes.
  • I spoke to the students for 15 minutes about my experiences with board and card game design.  From there, we talked briefly about what makes games fun.  For our purposes, I summed it up by saying games need an element of surprise and a doable challenge.
  • Students accessed the Gamestar Mechanic site after that.  They created accounts and began playing through the initial levels.
  • On a following class period, I had students start the worksheet packet.  At first it involves a review of ratios, decimals, percents and proportions.  The goal for this first period was to finish the first page of the packet.  It provided a review, some practice and a couple questions involving a template game from the game site.
  • For the next meeting, students would complete the lesson by finishing the worksheet packet.
Working with the fifth grade class
Merry and I introduced her entire class to the project as planned.  The students enjoyed listening to my experiences in game design and they had several questions.  They enthusiastically discussed what makes a good game and what they enjoy about games of all types. 

We spent about 20 minutes in the computer lab after that and they were thrilled to begin working through the levels of Gamestar Mechanic.  Some students progressed rapidly and began editing or making their own games even in that short time.  A few students had explored the site already on their own from home, since Merry showed it to them briefly a couple days earlier.  Those students were quite advanced and they helped other students become familiar with the games and the site.

Do to conflicts with our schedules, I was not able to get back to Merry's class for about ten days.  In that time, she decided it would be best to have me work with a small group of students on this math and game design experiment.  By that time, many of her students had worked through all of the Gamestar Mechanic levels on their own.  From those who had done so, she chose eight to work with me.  I was not aware of all the factors that went into the selection of the students, but she said most of them were chosen because they had high math skills.

When I met with these eight students (seven boys and one girl) in the computer lab, they were anxious to get started on the game design aspects.  I assured them the math was more important to me than game programming and we spent the majority of our 45-minute session reviewing the basic concepts and doing the practice problems from the first page of the worksheets.  The students were engaged, but I found I had to help them to understand the definitions that they wrote down from the online glossary.  I also had to remind many of them to read my directions.  Most of them skipped the requirement of putting the definition in their own words and providing an example of the term.  Some had trouble converting the fractions to decimals even though I was letting them use a calculator.

In the final ten minutes, I let them sign into the Gamestar Mechanic site and answer the ratio questions that required them to count elements in a template game.

Before our next meeting, I checked their worksheets and made some notes to go over with them before continuing. 

Two days later I returned to the computer lab and met with them again for a final 45-minute session.  We took about 10 minutes at the start to talk about their common mistakes.  I also gave them a short talk about literacy and the importance of being able to communicate about math and to apply it to other areas.  After that, I let them continue at their own pace through the remaining questions on the worksheet.


The questions required them to do a combination of some simple math procedures or experiments with the game template (shown above) from the game design site.  Almost all of them worked steadily through the questions, going back and forth between the math and the games.  I only had to talk to one student who was spending too much time just playing with the game design elements.

Almost all of the students completed the worksheet or at least got to the final questions involving proportions.  Merry and I were not able to coordinate further meetings with our schedule, so we decided the students completed enough of the worksheet packet for this initial experiment. 

Working with the sixth grade class

As mentioned above, this was a small class of only four students, one girl and three boys.  I learned from the teacher that they are usually unmotivated and their math skills are low. 

As with the fifth graders, the students were very interested in my presentation about game design.  The asked questions and contributed to the discussion about what makes a good game.  I could tell, though, even with just four of them, that it was hard to keep their attention as a group for any length of time.

As planned, I started them off on the Gamestar Mechanic site after that introduction.  In this case, the students had not visited the site previously.  They enjoyed playing the games, but no one got far enough into the levels to begin editing or making games.  At one point I had to work with the female student to encourage her not to give up on a level.  She had great difficulty getting through one maze that involved the hero sprite exiting the screen on one side and entering on the direct opposite side.  That particular level was a minor challenge to many students, but I was very surprised how much trouble she had with it.  She almost gave up a couple times and I had to help her predict where the sprite would enter the screen and how to navigate through the maze a little more than I thought I should.

I returned a couple days later to begin working on the worksheets.  These students had the same difficulty with following directions that the fifth graders did, but they worked more slowly and were more likely to have incorrect calculations in their work.  One of the male students was nearly resistant when it came to doing the math practice on the early problems.

At the end of this class period three of the four students started answering the questions about ratios that related to the game design templates.  They needed a little more help than the fifth grade students, but they quickly got the idea.

When I came in for the final day, we started with a discussion of some of the common mistakes they made on the worksheet.  After that I let them sign onto the laptops and continue working on the worksheets.

I soon became aware of one oversight in my lesson.  The early questions on the worksheet involving ratios required the students to use a timer resource, but these students hadn't progressed far enough in the levels on the site to acquire that element.  Unlike the fifth graders, none of these students worked on the levels outside of class.  So, they needed about another 20 minutes to get to that point in the levels.  When they finally did it was difficult to get them all working on the worksheet.  They preferred to keep playing and editing the levels rather than doing any of the math.  By the end of the class period they had not progressed far on the concepts of proportions.  Most had only completed about half of the questions from the lesson.

All things considered for her class, the teacher and I decided it was best to end the experiment at that point. 


Reflections
I have found it difficult to reach a firm conclusion on this experiment with game design and math.  While the students all enjoyed the game design elements and they were more than willing to do most of the math, I was not happy with how much time it took to reach the point where they could begin programming.  Some of this may be attributed to the way the levels are set up at Gamestar Mechanic, but it's a simple fact that any degree of programming will take time to learn.  Most teachers feel there isn't enough time to get to the content as it is, let alone having to introduce basic programming into the course.

Beyond the issue of time, I am quite sure it is possible to integrate more math concepts fully into the game design assignments, but given this short experiment in both classes, I was barely able to evaluate that.  Students were only beginning to get used to my style of teaching and my expectations.  It became clear to me that they were not only learning (or reviewing) math concepts.  They were also learning things like how to use the game site, how to follow directions from a worksheet and how to monitor their own progress and understanding.  Needless to say their math skills did not improve much in the few hours I was with them.  They made the same kinds of mistakes on their work that students did in the regular classroom. 

I also found it very challenging to spend time individually with even eight students to help them objectively consider the math and game design concepts while they worked.  All things considered, I gained very little insight into the benefits of pairing content and game design.

On the positive side, I was encouraged by the engagement that I saw from the students most of the time.  The teachers, especially the sixth grade teacher, commented on this as well.  The novelty of the game elements made it more interesting than the lessons that they were used to.  Also, I found it very enjoyable to encourage their creative pursuits.  When working with the fifth graders that worked ahead on their own at the Gamestar Mechanic site, it was wonderful to see the challenges that they created using the tools there.  I found out at the end of the experiment that the eight students who worked with me for the final two days did so knowing that they also had to keep up with the lessons the rest of the class was doing at that time.  I thought they were getting out of routine work, but instead, they enjoyed the experiment enough to do it in addition to the other responsibilities.

Because of this, I definitely want to continue exploring this idea as much as possible.  I believe there is great promise here, but with all such novel approaches, I think it will require a radical change to the way we usually do school rather than trying to fit it within the old model.
 

For Further Exploration
I want to explore other game design tools.  I liked the simplicity of the tools at the Gamestar Mechanic site, but it required too much time of just playing games before students could begin making their own.  Also, the number of ways one can create challenges is limited, since only mazes and platform game formats are available.  On the other hand, the Gamemaker software is far more flexible, but also considerably more difficult to use.  I have recently done some work with Stencyl and Scratch which may be better options for future experiments.

As Gee touched on parts of his book, I also want to incorporate programming to teach math concepts.  If I can make programming a regular part of a course, it seems logical that basic programming could be integrated into some basic concepts.  Then as the year goes on, the content and the programming can be made more complex, at which point some game design elements in the more flexible development tools would be appropriate.

The director of our alternative high school has asked me and the math teacher there to develop a course involving multimedia presentations and other technology.  We are planning for the course this summer with the intent of incorporating programming and game design.  That course should provide more than enough time to better explore the possibilities that this experiment only hinted at.

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Mike Petty,
Jun 25, 2011, 1:00 PM