The Construction Zone

Occasional thoughts about education and 'who is in charge of the learning'

Drawing Kids Into Being Mathematicians with Turtle Art


Let your students amaze you with their mathematical minds as they create art with turtle geometry!

This is a three-part post.

I have set it apart from the blog because of its currency and practical nature.

  1. What is Turtle Geometry? Getting Started.

  2. Constructivism & Constructionism

  3. The Issue of Transfer


1. What is Turtle Geometry?

You give a turtle a sequence of commands and it draws for you! These commands are specified by snapping together puzzle-like blocks. The turtle then draws lines and arcs, goes to a specific place on the screen, etc. Some blocks let you repeat or name sequences. Other blocks perform logical operations.

Many students have difficulty understanding & enjoying mathematics. But many students enjoy drawing and making. As they create art with turtle geometry, students will come to understand coordinate geometry, angles, operations, variables, and distances as they draw their way into being mathematicians.

“…students will come to understand…as they draw their way into being mathematicians.”

Turtle geometry arose out of the tradition of the LOGO programming language invented (in 1967) by Seymour Papert, Cynthia Solomon, Wally Feurzig and Daniel Bobrow.

Programming? That’s Hard!

Programming? Coding? Don’t worry! These tools are designed to be easy enough for children and yet powerful enough for all ages. Turtle geometry in available in a number of LOGO style programming languages. Here we will explore Turtle Art—but, it is very similar in Scratch and other turtle-based programming languages. I like Turtle Art for this purpose because there are fewer distractions than in other programs. Students are able to better focus on the art and the mathematics.

First…a Little History & Theoretical Overview

Seymour Papert was the father of educational computing; the genius behind ‘constructionism’ and the originator of the digital age ‘maker movement’.  As you watch the following movies, I ask you to think about these questions:

What resonates with you?

What surprises you?

What do you find interesting?


This is incredible history. A groundwork never to be forgotten and one upon which to build. I believe that this pedagogical framework must be brought to our classrooms and to our schools for any of the current maker and ‘coding’ movement to have traction in developing deep understandings and to support students in being mathematicians.

Getting Started with Turtle Art

First of all, you need to download the program—Turtle Art. It is a free program and is not designed to be commercial. Go to and click email us. Just request the download link for Mac or Windows from Brian Silverman and Artemis Papert. They simply want to have some sense of who is using Turtle Art. There is no need to worry about spam or commercial interests on their part. (You can also get the TurtleArt app from the App Store.)

When you open the program, this is the screen you will see the following.



Now watch this short video for an overview.

Play Turtle

Because this is such a wonderful geometric activity based on relative movements… playing turtle can be wonderful.

A great activity for the classroom, hallway, outside, or gym. Once the kids have the basic commands, they can team up and issue commands to each other to accomplish certain tasks:

  • Making geometric shapes (squares, triangles, etc.)
  • Following a preset path
  • Obstacle course
  • Turtle could be blindfolded
  • Turtle could have an RT and an LT on their hands if need be

Now that you have seen the basics of turtle art—I want you to watch another video related to how and why turtle geometry is so very relevant for kids in learning mathematics. As you are watching, I want you to ask yourself:

Which ideas really mean something for you and for your students?

How might this be different, or similar, to other things you are doing in your classroom?

We’ll come back to Turtle Art shortly and delve much more deeply!

In Drawing Kids into Mathematics (Part 2), we will explore constructivism and constructionism and their usefulness as pedagogies in implementing a culture for Turtle Art.

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