There has been a lot of forward looking contemplation in the game development community about whether educational games will eliminate the need for teachers.  Afterall, an aptly constructed game that challenges a student at their ability level and offers immediate feedback on their performance with built-in explanations of the problems offers faster and better differentiation than a human teacher could.

Salman Khan is testing his video-based tutoring program with differentiated practice problems in many school districts including mine.  My district currently uses the online ALEKS tutoring program, which offers students the incentive of filling in pieces of a pie that represent different mathematical topics as they successfully answer practice problems.

Many teachers use ALEKS as a teaching tool without any human interaction involved, whatsoever. In these cases, the program really is acting as the teacher and the man or woman in the room who goes by the title of “teacher” is really just the supervisor who tells everyone to be quiet and stop playing solitaire.

During this week off from school, I am leading an optional tutoring program in the math computer lab on campus for students who want more practice with ALEKS.  As you might expect, the student turn-out is low.  Actually, I have only one pupil who is attending these extra practice sessions at the school.

The two of us are working on filling in the pieces of the pie in his account.  He practices the problems and I give him verbal feedback and explanations to support the automated responses.  Over and over, the student proclaimed, “We’re getting so much done!”  Out of curiousity, he clicked on the report that ALEKS provides of the number of topics that he has learned over time.  I was surprised to see that he was learning 7 times as many topics an hour working with me than working on his own!

There is a feeling by some that the pace set by teachers slows down the advanced students and that they ought to be replaced with faster computer games and programs.  My position is that games that differentiate and offer feedback and motivation for students are valuable but are far more so with the support of a knowledgable and caring person to aid the learner. Rather than replace teachers with games, we can use educational games to enhance the skills that teachers have to offer.

Please support gameful member Scott Laidlaw and “APPLAUD”  his entry in the STEM challenge for innovative education!

http://cooney-stem.skild.com/ConceptDetails.jsp?pId=5601

Ko’s Journey is the story of a young woman who is granted the living magic of mathematics as a gift from her ancestors as she journeys alone. Ko’s Journey is also the story of a math teacher who spent years crafting games so that each of his students might find their own way to the mathematics they inherit from their ancestors.

As a young fool finding my way through the language of gameful education, I know Scott Laidlaw’s game is a living novel that I want as many students to cherish as possible. Math education has been a dustbowl for decades; most people don’t know what sustainable growth in this field will even look like. I’m not claiming Scott’s game is a snake oil cure-all, but it’s a gameful grove children already flock to and eagerly listen to the riddles of the world.

So blog, tweet, post, rant, tell your friends, tell your mom, tell your friend’s mom… something this innovative shouldn’t go unnoticed, especially by the secret headquarters of gameful education!

So, it’s time for another blog post where I share my thoughts on the teaching of math-related subjects, and how that might improve… maybe even become fun to learn. But to be honest, today I’m inspired to write about how the traditional methods fail.

Antecedents

This weekend was the Global Game Jam! Although I wasn’t able to participate, I followed you guys through twitter and some streams; tonight I’ll play some of your projects, it’s amazing to see what you managed to develop in such a short time.
Oh, but well… While everyone else was having fun, I had to stay a bit away because it was… Math homework time! By the way, it wasn’t just a common homework.

The traditional method

According to what my professor told me today, the teaching method in my school -and nationwide, from what I know- is based in the following structure:

Every week (5 classes a week), we learn from one to two new mathematic methods, for a small variety of cases. Every class, we do a small set of exercises and if we fail to solve them on class time, we bring them home, and at the end of each week we receive a super homework in order to “reinforce our knowledge” during the weekend. That way -according to my professor- they ensure that students manage to remember the things that we learned during the week and polish our problem-solving skills.

*Glossary:

-Mathematic method : A specific set of steps to get a solution. Think of it as an algorithm or “recipe” that you apply to a specific math question to solve it.
-Case : Every “recipe” has slight variations depending on the nature of the problem, and these variations are named “cases”.
-Super Homework : A long series of exercises that we must solve for next Monday, they range from 100 to 350 different questions or problems.

Well, that is the professors’ particular viewpoint on the subject. However, in my humble opinion, this structure is a complete failure.

How it fails?

As I couldn’t shake my head off the GGJ this weekend, even while I solved one after another of the questions in my “super homework”; I decided to do something gameful in order to keep the spirit. 

So, I decided took my own homework and analyze it as if it were a game, adding to my “review” a few conclusions that started to come to my mind as I progressed. Here are my results, plotted with the aid of Minitab:

First of all, I created the above graphs by taking a sample of 86 different math problems, numbered from 96 to 182 in the professor’s text book, which represent a section of this week’s “super homework”. The first one shows each one of these math problems with their corresponding difficulty level… and as you can see, we get the first failure from a game designer’s viewpoint. Imagine a game whose first levels are fairly easy, then you get to a boss battle! And after beating the boss, back to more easy levels intersected randomly with challenging ones. Would you enjoy it?

So, whoever wrote this book and arranged the problems in the order they appear, obviously fails at designing a difficulty curve.

However, they are not arranged randomly. When solving each one of the problems, I noticed a pattern on them – The first one could be solved by using a direct integration formula, then the second one requires the same formula plus a slight algebraic transformation. The next one requires the previous two elements and another transformation, and the pattern goings on until you reach a problem that is completely different from the previous one, and that you can’t solve by using any hints given by the surrounding problems – you can visualize them as “spikes” on the graph. After looking at this pattern, I immediately thought of a broken SIMON game that keeps resetting itself after suddenly changing the game pattern to a more difficult one.

Second issue – The time. You would think that the relation between difficulty and average time to solve a problem is proportional. However, as you can see on the second graph, this is not always the case. Some problems that are easy to understand can be very time consuming because of their lenght, as you are required to write every step to the solution, no matter how trivial it might be.

Anyways, no matter how easy the problems might seem to a student, their considerable amount will make you spend more than an hour and a half solving them. I started to notice that, after this amount of time, my mind started pondering unrelated things, and my math solving skill had become a mechanical ability more than the reason-based one that it should be. What is the point on making the students solve such an unreasonable amount of math problems? Is there any evidence that learning progress is proportional to the number of math problems assigned? What I was able to find is that, when you get to a certain point, your brain interprets this as a source of stress and actively tries to suppress your will to continue. You know that you need to solve them all in order to get a good grade, but your brain tells you that it isn’t interested in keeping up with such purpose: You start to associate math with stress and frustration.

Okay, you get up, take a breath and do some other things to relax, and then you get back to work. Then, after a while you notice that you have reached your break point sooner than before: This is called Repetitive Stress, and it’s a real health issue; even videogames have a warning against it printed on the manual and some have taken very creative measures to prevent it.

Conclusions

In the end, I think it was a fairly good analysis, which manages to summarize pretty well what is failed on the teaching method that we are forced to endure:

- Repetitive and prolonged tasks != learning experience
- Failure to make a reasonable difficulty curve = frustration and stress
- Problems could be arranged in a more logical way, but this is ignored (see the last graph)
- In the end, responsibility isn’t a big deal. The homework was cancelled as no one but me made it.

Antecedents

Lately, it has been great to see games and websites that attempt -sometimes, very successfully- to teach, and not only to entertain. However, up to this moment I haven’t had the opportunity to know of a game focused in any branch of Mathematics that accomplishes the goal of being entertaining.

In fact, game designers aren’t the only ones who have faced this issue; countless generations of teachers have also dealt with it, trying to teach Math-related subjects to a public that almost unanimously show no interest on learning them.

So… what is going on there? Is there any hope to figure a way to make Math accessible to students through videogames? Today, something happened to me that motivated me to write on this topic for my first blog post in Gameful – a Diagnostic Test.

Motivation and Memory

At the start of our course on Integral Calculus, my group was treated to a Diagnostic Test, featuring topics that we should be already familiar with, after being through Differential Calculus and Basic Algebra. Luckily, it wasn’t part of our grades, as we failed it with no exception! But what was interesting to see is that not everyone of us got the same answers wrong…

My classmates weren’t so eager to share their motives of remembering function analysis while ignoring how to actually graph a function, but I noted something interesting on my test – I was unable to remember trigonometrical identities, how to factorize a simple equation and some definitions, but curiously, got all the Application Problems right! Everyone said that it was the most difficult part of the test, most of my classmates weren’t able to even put the problem in algebraic terms, but it was very obvious to me. Why?

Then I realized something: I was able to recall the process on how to solve these problems because they had a goal! In my mind, they served a direct purpose and were important, so my brain put them in the “priority list” of memories. Factorizations and definitions were abstract, distant things memorized only because the professor said so… I’m not kidding, at that time, when I asked the professor why Sin, Cos, Tan and all trigonometric definitions stemmed from a circle and a triangle, his only answer was: ”Because this is the way it is”.

Digging through my old math books in order to remember all these concepts again, I noticed how none of them focused on the origins of math, even the ones for Primaria [lit. "Primary", that's how the mexican education system refers to Junior schools] – the books only limited themselves to explain the operations, provide a few examples, and repeat the same definitions over and over. Where did these things came from? Why are they so important? The other day, I watched on the TV a guy predicting that a kicked ball would hit a certain window with math. Cool! Can I do that? If you are a child looking for an answer, you’ll never get a good one for the first two questions and you’ll have to wait for a few years until you reach Dynamics to do that trick.

Conclusion

To be honest, I was the kid who thought that math would be fun because it would let me predict things and take decisions. These things were, and are important to me, that’s why I cared to remember them instead of concepts that the professor classified as “basic” and “easy”.

It seems that, in order to not only learn, but actually remember the acquired skill or knowledge, it’s important to associate it with a feeling or purpose - In this particular case, a student could say: “Yeah, I remember how to obtain the maximum and minimum values of a function, it helps you to build a soda can without wasting too much metal”

By the way, I also found something interesting while checking out different math-related books: I expected that every of them would be as cold, devoid of any relation with the real world as the ones I had already read, but one of them stood out: Calculus, by James Stewart. This book not only teaches concepts and the way to do things, it also provides real-life examples supported by evidence and actual cases were a certain math skill was used in order to successfully overcome a problem. I would recommend it to any student facing troubles in this subject.