## Why Retro Desmos

Like many of my generation, I grew up coming home from school each day turning my television set to channel three and firing up my Nintendo to play the newest video game.  Video games challenged me to solve problems, discover patterns and react to a variety of situations.  The visible representations of movement and action combined with a level of intellectual undertaking would keep me occupied for hours.

I believe mathematics instruction should be akin to this “video game” experience with regard to visual representation and cognitive engagement. Teaching in this way removes many of the barriers found in traditional mathematics instruction.  It creates an open learning environment where students are tasked to discover patterns and problem-solve free from the limitations of “follow me” mathematics in which students mimic teacher steps.  When math is taught in such a traditional rote manner, only students that follow the specified “rules” are successful.

So then, how can we use video games to transform classroom mathematics? Mathematics should be presented in a way that enables students to connect math concepts to visual action.  Everyone can see an action and interpret it.  When someone runs or jumps, it can be understood in any language.  Video games have the power to show mathematical concepts in the form of a specified type of action.

An Example

Let’s look at this geometry problem on changing dimension effects on a cube or rectangular prism.

Standard problem: Three dimensions of a cube are reduced to one-half their original length. If its original volume was 256 cubic units, what is its new volume?

In order to be able to solve this problem, a student would have to know the formula for the volume of a cube and if they did, compute it correctly by using the quantity (1/2) cubed in some sort of way to get the correct answer of 32.  This a procedural based approach that only works with cubes.

Video game approach:

So, what happened?   Almost every student can see or tell you that the shape was cut in half.  From there meaningful mathematical discourse can be established by asking questions, such as:  What happened to the volume? the length? the width? the height?  Students can develop a conceptual understanding of change in dimension when mathematics are presented through this type of action.  In this example students are not constrained to formulas or algebraic symbols or even numbers.  It is about constructing mathematical knowledge and understanding that can be applied to any type of situation.

I posed this question to a group of seventh grade students. I showed them a video of Mario smashing the block in half and asked them what happened.  Every one of them had the understanding that if the volume of a shape is cut in half only one dimension is changed because they could see it and there were no numbers or symbols getting in the way of processing the action.  Some sample student responses:

It is in this way that visual representations through the action in video games allows conceptual understanding and personal meaning to take root.

## The Power of Desmos

Desmos also has the ability to create situations for students in which they can easily generate their own data.  When students have a level of engagement with or attachment to data, the situation in which the math is presented takes on a different level of meaning.  Desmos has a variety of activities in which students have such an opportunity. Here’s an example of a video game-based activity I created in which students make their own data.

Students play through the boxing game and generate points in each level by fighting various boxers.  Thus, each set of data is created from individual experiences in the game.  In this activity students are challenged to find the mean, median, range, and mean absolute deviation from the data they created.  This is powerful with a statistical measure such as range in which if a student has a large range they can reflect on the experience of scoring high in one fight or bout versus scoring low in another or likewise having a small range because each fight had similar scores.  This is easily facilitated into the classroom because of the power of Desmos activity builder.

There are other functions in Desmos that allow for improved classroom experiences.  In a recent activity I used the random number generator in the Desmos software to create different numbers or values for students.  This moves the focus of instruction to the process of finding the correct answer instead the value of the current answer.  It pushes students to ask, “How did you get the answer?” instead of “What did you get for the answer?” The power in that subtle change moves students from copying an answer from a peer to having students engaging in mathematical discourse.

In this problem, the percentage is different for each student.  This means every student will have a different correct answer that Desmos can verify is accurate.  It sets the stage to invite collaboration into the classroom because Desmos has removed most opportunities (it is random so repeats could happen) in which students can copy each other’s answers.  For even more variability, the random number generator could also be applied to the water depth along with the percentage.  The focus in math should be on how you get the answer and not on what you got for the answer.

It is time to move past the old traditions of math classrooms and move to a place where math engages students cognitively, removes barriers of language and background, and creates a classroom that values process and individual experiences.  Desmos has the power to make this a reality and video games provide a format in which to present traditional mathematics content in a new and more engaging way.