learning and teaching Turtle Art

Turtle Art is a deliberately minimalist design of Logo by Brian Silverman and Paula Bonta of the Playful Invention Company. By minimalist I mean it sticks to the principles outlined by Mitch Resnick and Brian Silverman in their 2005 article, “Some Reflections on Designing Construction Kits for Kids”, namely

• Make it as Simple as Possible – and Maybe Even Simpler
• A Little Bit of Programming Goes a Long Way

The Turtle Art sessions were the starting point of a bigger project. The students began by designing interesting and artistic geometric shapes. They then exported an SVG of their shape into Tinkercad. From Tinkercad they saved an STL and then 3D printed the shape. Next they used the shape to imprint a clay tablet and finally they painted the tablet.

Following a well worn path I began with the square. The Turtle Art defaults are setup for drawing a square. Once a square is drawn you can then show how to “black box” it with a named hat. This creates a brand new block which can now be used later as part of a larger design.

This starting shape is a good one to role play with a student acting as a robot and another as the controller. This gels with the body syntonic principle (Seymour Papert, MindStorms) and hopefully gets students thinking in terms of “I am the turtle, what do I need to do to make this shape”

I then challenged the students to create the shapes shown (page 1 starters). I witnessed some students completing the square where the turtle begins and returns to the centre whilst others struggled to do this.

In my experience some things have to be taught whilst others are more likely to be picked up naturally in a well constructed learning environment like Turtle Art. My goal is for students to become fluent in their ability to make complex, artistic geometric patterns.

The principle I talk up at the start is turtle state. When you make a shape make sure the turtle ends up in the same position and heading (direction) as where it began.

Later on I talk a lot about 360 / N where N is the number of repetitions needed. For example, say you want to make this shape

First make a midpoint square, remembering that the turtle must start and finish in the same state

Then count the number of repetitions (5) and work out the angle 360 / 5 = 72. Use the midpoint square hat as a building block for the more complex shape

I had a number of regular polygons on my starter page (square, triangle, pentagon, hexagon, octagon). The 360/N formula produces the external angles of these shapes, not the internal angles. I did talk briefly about that showing a diagram on the board with internal and external angles. In this class I never got around to showing how to do variables so to draw all these shapes with one equation. I could have done that but
(a) it wasn't strictly necessary, and
(b)I’ve found in the past after showing this that students often don’t use it anyway. Many prefer the simpler version!

One of my triangles was right angled. Most students worked it out using a guess and test method. I asked the maths co-ordinator if they had done Pythagoras’ theorem yet and she said it would happen a bit later in the year. I decided to go ahead and show how to get the exact lengths using Pythagoras. The hypotenuse is 141.4 if the other two sides are 100 each. A few of the more capable students picked up on this but when I checked later for some of the others if they remembered me teaching Pythagoras I received some blank looks!

I’m not too fussed about this. On the one hand some students are doing it by tinkering which is another word for guess and test. Perhaps they are learning some perseverance as well. Others are learning the more traditional way and getting a more precise answer. For the purposes of what we are trying to achieve here – make interesting and artistic geometric shapes – both methods work fine.

From the page 1 starter shapes I then suggested some pathways that students could go down to produce more interesting and artistic shapes

I did make efforts to setup a situation where students worked in groups and helped each other. They nominated their preferred partners, I then set up groups. I also sometimes asked them to fill out a planning sheet at the start of lesson (questions like ‘Which shapes do you plan to make today?’) and end of lesson (questions like ‘Who helped you?’, ‘Who did you help?’ and ‘Give some details of the help’). I make this part of the assessment criteria. Some students emerged as brilliant helpers of others while some others learnt to find the right person to ask.

A few students managed to complete all my challenges before the others and so I gave them some harder challenges (shapes 36 and 40) from Barry Newell’s original booklet, Turtle Confusion. His hardest shape is shape 40. I had three students successfully do that one and one of them went on with it as his shape to 3D print.

A handful of students went their own way and developed their own shapes at some point. I didn’t push particularly hard for this but did praise it when I saw it happening

As the process continued students finished up with a variety of 3D prints that looked like this:

And painted clay tiles that looked like this:

And yet, this is only covers a tiny fraction of what you can do with Turtle Art. I hope to write some notes in the future about how to teach the many other artistic elements of the program.

Reference:
Burker, Josh Invent to Learn Guide to Fun (2015), pp. 107-113
Newell, Barry. Turtle Confusion (1988)
Papert,Seymour. Mindstorms (1980)
Stager, Gary & Martinez, Sylvia. Turtle Art Tiles Project Guide (adapted from the original Josh Burker article)

Software:
Turtle Art https://www.playfulinvention.com/webturtleart/

(earlier blogs on this project)
Turtle Art Tile Project Conclusion
Working with Acrylics
Working with Clay
Scaffold for Turtle Art Tiles Project
Turtle Art Tiles Project