# Mathematics and Turtle Art

## Body

We’re a K–12 school, with K–12 makers, and we treat that making as a way of driving student learning, rather than simply showcasing it. What that means is that we let students tinker, discover, and hit walls with a project before giving them instruction, then use these successes and setbacks as learning tools. Driving our curriculum through our making requires shifting our roles as educators. We often take a step back from teaching directly, so students can teach themselves.

We use Turtle Art—free software that lets users draw using block programming— to introduce our fifth and sixth graders to programming, and explore mathematical concepts. The basics are easy. Want to make the turtle draw a line? Click the block labeled *Forward*. How long should the line be? *Forward 100* (meaning pixels). It's pretty easy to see how Turtle Art works to teach students programming, and a quick glance at the Turtle Art image gallery is proof enough of the opportunity to expand into complex designs. But how do we use it to teach math?

One of our early lessons in Turtle Art might prompt students to spend five minutes exploring the different tools on their own. They often initially think that the *Right *and *Left* commands mean the turtle will move those directions (they actually mean the turtle will rotate those directions), which leads to confusion on their part when the turtle stays put. So we come together for discussion, and define what the different commands do as a class: "*Forward* must not mean up. It looks like it means whatever direction the turtle is facing. And when we click *Right* and *Left*, the turtle seems to be turning those directions, not moving them." Once students discover that they can make the turtle turn “sideways” by entering *Right 90*, (for 90 degrees), teachers can start a discussion on angles. “What happens when you enter 180? What about 360?” And then, “Can you use what we’ve learned to draw a square?” Some students will inevitably struggle with putting these pieces together, but one trick to help them conceptualize the turtle’s movement is to have them physically walk out a path around the classroom while describing the steps they are taking.

Students typically work with Turtle Art for several weeks, each class building on the one before it. We cover angles, distance, area, perimeter...we’ve found Turtle Art particularly useful for engaging students in learning about the Cartesian coordinate system. As students experiment with changing ‘x’ and ‘y’ values to move the turtle, teachers can challenge them with questions like, “What do we have to enter to put the turtle back in the center of the screen?” The point with all of this being that we want to keep the students engaged through their inquiry and critical thinking. Then, once students have a basic understanding of the concepts being covered, we can further test their comprehension by asking them to draw a shape in each of the four quadrants, or some other challenge based on the day’s lesson. But the important aspect is the method of using Turtle Art to drive the lesson through discovery and discussion, not Turtle Art in and of itself (though it is a helpful tool).

Our aim is to give students ownership of their learning. Often that comes with great frustration on their part. But by putting them in charge, and giving them the freedom to learn through a creative outlet, more often than not, they take it upon themselves to push through any roadblocks, and ultimately walk away with both a deeper conceptualization and an eagerness to continue learning.