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, 13:08, 28 June 2011
Long before children can use written language or a computer keyboard, they can do Turtle Art in the classroom on an open expanse of carpet, with a set of colored ribbons and tacks or masking tape. One child is the turtle, others fix the ribbons in place, and someone gives directions. Initially, this would be the teacher, but soon the children will want to take over. The Turtle on one run should be given the opportunity to be the direction-giver.
Start simply with Forward [number of steps], Right 90, Left 90. You can draw a surprising variety of patterns with just these. Gradually add commands, such as Back, Pen Up and Pen Down, SetColor (change ribbon), Repeat (have one child keep the count), Right/Left 45/60/120/135, Store Value in Box (have a student keep track of that value), and whatever else the children show readiness for.
Children can start by giving any sequence of directions they like, but after a while, they should be challenged to make particular patterns and to generalize. Can you make a polygon of any number of sides? How do you express the angles? Can you make star shapes? Can you invent directions? How can a child walk in an accurate circle? (Hint: Euclid) How about a quarter circle?
At this point, we are in a research project, specifically Seymour Papert's project from the 1960s, which asks whether we can make it as natural for children to learn math as language. You be the Turtle has not been done enough to know what preschool children can understand immediately, what they need hints for, what they have to be shown, and how far they can go. We do not know what levels of art or programming or math they can achieve in Turtle Art or otherwise. We do know that it is more than they have been supported in doing so far.