Learning Mathematics by Making Games

“The natural mode of acquiring most knowledge is through use leading to progressively deepening understanding. Only in school and especially in SME is this order systematically inverted. The power principle reinvents the inversion. [Seymour Papert, 1996]”

It is always a treat reading Papert for the way he criticizes so boldly about the wrong perspectives of traditional education methodologies. He is also so good in pointing out explicitly different and much better perspectives for learning. What amuses me most is his tendency of introducing so called complex concepts at much younger aged students.

I was fascinated with the principle “Project before problem” especially it captures so many reasons against traditional methods and so many principles for the types of education we would want in the future. Before stating my idea for learning math I want to again quote from Seymour Papert:

““Kafai's fourth graders did more and better mathematizing and much more problem solving in making video games than all the word problems in all the algebra texts””

The Idea: To make a game that would be predictably played by the gamer.

The game would be about simulating a business. The player (Named: Alice) is about to open a business, a flower shop, starting with a small amount of money and a shop with a number of a type of flower. Customers come at random times but not very frequently. Within the first two minutes after selling to some customers the number of flowers Alice started with is finished and now Alice needs to buy some more flowers.

Alice visits the flower wholesale shop. There Alice would also find that there are other types of flowers which is higher priced but with better yields. Alice would always try to maximize the profit by maintaining the inventory so that the good customers would not go with empty hands and in addition to that to expand the business by introducing new types of flowers.

It is not a good thing for the gamer to have no challenge at all. The game need to produce goals for the gamer to achieve based on which the gamer would level up which would be required to unlock more interesting game features (e.g. Business deals, Plant own flower trees, etc). Some kind of negative event is also a good thing to keep as part of the experience (e.g. like some kind of pesticides which may destroy all the flowers, or maybe some gangster which frequently visits for money etc).

Game Maker’s Point of View:

Now think from the game maker’s point of view, how many types of flowers to keep, how to set the prices, how frequently the customers shall come and for what types of flowers and with what price in mind? These all questions are dependent upon what type of experience the game maker would want for the gamer to have.

The game needs to be set up in a way that the gamer would be busy all the time and has some challenging task to do. Setting up the prices for each of the flower types can be a linear function of time taking into account how much time the gamer would need to earn enough profit including all the facts of negative events.

The two minutes mentioned earlier is actually not so arbitrary, as it would be a very boring game if the player would need to play the sequence of events (i.e. waiting for a customer, sell the item) for too long. On the other hand, it is also not very good a game if the timing of each event be absolutely fixed (i.e. First customer would come at 50 seconds after the starting of the game.), thus requiring the use of probability inevitably.

The goals that the game would produce need to be more interestingly calculated, may be with help of exponential functions again taking account of all the event types.

Conclusion:

This is just a brainstorming as was required for this blog. But I hope it is evident making a game such as a business simulation is a project requiring many of mathematical concepts. And I do like to argue that it would not be harder to make such games if sufficient mathematical functions are provided for the students than learning the same math concepts in the way they are to be learnt in traditional methodologies. At least this experience can be one which lets the students to have a deep connection with the mathematical concepts they would need for the project of making the game predictably engaging for its gamers.