Computers are rather good at math. Here's how they can give students new perspectives on the problem solving process, while providing feedback and support.

How the CPU Changes the Math Problem

How the CPU Changes the Math Problem


June 28, 2020

Author: Victoria

The central processing unit, and its arithmetic logic units, can perform the same math operations a person can. Where a textbook can only describe a math problem, a computer can simulate, solve and assess a players performance on a problem.

CPUs as Training Wheels

Kids often learn to ride a bike with the use of training wheels. The training wheels are temporary and to be removed one day, giving the rider the full power of the bicycle, but they do get the beginner started.

Math is a challenging skill that involves comprehending abstract scenarios and complex operations. By having a computer automate or handle parts of the problem solving process, the player’s cognitive load is reduced, freeing them focus on aspects of the problem. For players that find math operations frustrating, automating them can remove a barrier to entry, allowing the anxious to improve other skills that would otherwise atrophy until operation mastery is achieved (if ever).

Persistent Problems in Math

According to researchers and groups like the National Council of Teachers of Mathematics, a persistent problem in math education over the last century is the tendency of students to think math is just a series of procedures. Schoenfeld (1992) listed a number of harmful attitudes in regards to math, one being the common belief that ‘ordinary students cannot expect to understand mathematics; they expect simply to memorize it and apply what they have learned mechanically without understanding’. (Brook, 2014) Exactly what leads to this common opinion is beyond the scope of this post, but people who view math in this way are not difficulty to find (I have a full post on the matter here):

subreddit: r/dyscalculia

"I've ALWAYS viewed math as a sequence of events to be memorized. Math to me is just memorizing calculations, I can't comprehend it the way I can comprehend a poem for example."

subreddit: r/learnmath

"I've been planning to relearn math via Khan Academy from the 1+1 level, as i am horrible, horrible at math. However, just like in school i do not really understand what is going on, only following the formulas like a robot."

subreddit: r/offmychest

"I know someone on here will say that doing algebra is about critical thinking. That is a total lie. It's about memorization and regurgitation . And boredom. I'm only at the halfway point in the semester and want to scream. Real screaming, not the pretend screaming I do in my head."

Too many people aren’t seeing the forest for the tree’s in maths.

Math education is an area of active research, having innovated a number of methods like rote-learning, discovery math, new math and standards-based math, to name a few. Yet the unpleasant aftertaste of math persists in many people.

Computer Based Math Education

The idea of computer based math is not new.

Math programs are routinely used by professionals to solve problems. Developing math problems where the CPU handles the basic operations for struggling students, may not only allow players to experience different aspects the problem solving process that they were otherwise unable to, it may actually be a more authentic preparation for professional life.

The CPU would act as a set of training wheels in math problems, handling some parts of the problem, reducing the cognitive load on weaker players. Shifting the focus away from basic procedures towards strategic selection of math tools, directly contradicts that common belief that math is just a series of procedures. Where frustration might cause neglect of these higher order skills, assisted exercise with the digital equivalent of training wheels, eventually strengthens the players skills to the degree they no longer need assistance.

A New Perspective On Math

Having computers handle part of the problem solving process creates a new design question of game based learning design. Which parts of the problem are most beneficial for the player to focus on? Is it exploration of simulated environments, learning how experimentation and measurement can be used to understand the situation? Is it the connection of different inputs and functions to search for an answer the player decides is good enough?

The speed at which a CPU can crunch numbers gives players a different perspective on math, one that is easy to miss when busy performing calculations yourself. A game that enables rapid mixing of inputs and functions can show students the very different numerical outcomes of their choices, with no fear of errors. This shifts focus away from ‘did I calculate that correctly’ to ‘is that the right operation to use? Does the answer look right?’ When placed in the context of a simulation that changes with the players choices, and then wrapped in a story that adds meaning to different simulation states, the player can start to say which formulas answers are ‘better’ and which are ‘worse’.

Assessment and Support in Math

Of particular importance for the math anxious, is the level of support the CPU can provide in problem solving. Since the system has full access to the simulation state, it can reveal parts of the problem to the player, while hiding others. An example of this would be a game that exposes soil nutrient composition and plant growth rates to the player, while hiding the specific equations that calculate plant growth from fertilizer levels, leaving the player to infer it from the data. The players decision on which information is relevant, their selection of tools to transform this information into answers, and their application of these answers to the simulation state, can all be compared against the complete set of information the program has. Does the player understand the fertilizer has a multiplicative relationship with plant growth? Have they found all the nutrient variables that are used to calculate plant growth? How similar are the outputs of the players equation compared to the simulation equation? The player can be assessed by the accuracy of their answers against the secret values in the simulation. When wrong, the game can give instant feedback, or change the games content to give the player extra support in overcoming the problem.

Summary

While CPU’s provide many new possibilities in helping people master math, they don’t replace traditional text books, collaborative project based learning or even rote-learning. The CPU’s ability to simulate a problem, shift the players focus to specific aspects of a problem, assess their performance and provide instant feedback and support where necessary, make them a handy new tool that should be quite effective to some math beginners.

References

Brook, Ellen. May, 2014. INVESTIGATING THE ADULT LEARNERS’ EXPRERIENCE WHEN SOLVING MATHEMATICAL WORD PROBLEMS, Kent State University College of Education, Health, and Human Services, https://etd.ohiolink.edu/!etd.send_file?accession=kent1394513871&disposition=inline