Chapter Three and Four
Turtle Geometry: A Mathematics Made For Learning, Languages for Computers and for People
“An important part of becoming a good learner is learning how to push out the frontier of what we can describe with words.”
Here are some things to think about as you read these chapters:
The LOGO Turtle taps into children’s ‘body knowledge’, i.e. their sense of how to move with their bodies. What’s an example of something that makes learning a task easier by tapping into body knowledge?
Papert talks about 3 kinds of mathematical knowledge: ‘school math’ (selected to be the core knowledge everyone should learn), ‘proto-math’ (background that’s assumed without being explicitly stated), and a third category of knowledge that’s neither selected not assumed, but ought to be included in education. Drawing from any field you’re familiar with, what are examples of these different kinds of knowledge?
Papert writes, “You learn in the deepest way when something happens that makes you fall in love with a particular piece of knowledge.” In Mindstorms, Papert describes how many children came to LOGO hating numbers as ‘alien objects’ and left loving them. Think back to an experience of falling in love with an idea. What features of it led to this feeling? Or conversely, what barriers prevented you from falling in love with an idea?
Papert describes how drawing spirals with LOGO is more empowering than solving algebra problems, or how making computer poetry is more empowering than memorizing parts of speech. Drawing from any field you’re familiar with, how could we teach a piece of knowledge so that it more readily empowers the learner?
In Chapter 4, Papert describes how to teach juggling more efficiently by ‘thinking computationally’ (e.g. thinking in terms of procedures, breaking a problem into parts, debugging individual parts, etc.) Think back to learning a complex skill with your body (such as swimming, dancing, juggling, riding a bicycle, etc.) Did computational thinking help you learn this skill more effectively? If not, how might it?
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