Mindstorms
20200503
Mindstorms by Seymour Papert is a book written in 1980 about how children can learn with computers  and learn to fall in love with learning along the way.
I read Mindstorms, and fell in love with the book. My own mind was besieged, stormed, and ultimately broken  only to be reforged anew like Andúril from the shards of Narsil (sorry, I'm rereading Lord of the Rings right now). This post, after this shortIpromise expository intro, contains my book notes.
You may have heard of Papert's LOGO programming language before, which issues commands to an adorable round robot called a Turtle. Papert designed LOGO and the Turtle in the late 1960s to help children learn how to learn with computers. Here's a photo of Papert and his robotic operating buddy:
The popular Lego Mindstorms products are inspired by Papert and this book, along with many other cute robot learning toys for children, like my good friend Cozmo the Robot or the insanely cute Cubetto from Primo Toys:
When you conjure up an image of "learning with computers", you might think of a rote "quiz app" or "flashcard app"  but Papert suggests that it can be more  more creative, more exploratory, more fun, and longerlasting. I think about how I took Calc AB and Calc BC in high school, and I was pretty good at them, too, but I had no idea what I was really doing. I knew the mechanics, not the meaning. When Papert connects teaching the Turtle to move in a cirle and the principals of differential calculus  measuring growth by movement at the growing tip  all I can say is 🤯.
There's obviously also a reference to George Polya in here, too  always a good sign!
And now, onto the notes!
Learning with computers
Mathophobia
The Turtle
Teaching without curriculum
Why is it hard to change education

Radical change is possible, directly tied to the impact of the computer
 Unfortunately, conservatism in the world of education is a selfperpetuating social phenomenon
 But as individuals get computers, education can become a private act, an open marketplace, a Renaissance of thinking about education

Our culture has unneeded split between "humanities" and "science"
 Computer can break down this line

"Math" just means "learning" in Greek
 e.g. "polymath" is a person of many learnings
 "Mathetic" means "having to do with "learning"
 Children begin their lives as eager and competant learners. They have to learn to have trouble with learning in general and mathematics in particular

Conservation of liquids example from Piaget
 Children take a while to learn this principle
 They have their own coherent world view (taller glass must have more liquid)
 This model was spontaneously developed by them
 Mathophobia limit's people's lives. Deficiency becomes part of their identity. It is a selfreinforcing taboo
 "Cchool math" is not the same as "mathematics"
Turtle geometry

There are multiple types of geometry
 Turtle geometry = computational (tracks Position and Heading of the Turtle)
 Euclidean geometry = logical (tracks Position and Point)
 Descartes geometry = algebraic

Geometry arises when child asks "How can I make the Turtle draw a circle?"
 A good teacher doesn't answer the question, but encourages the student to act it out. Literally, to have the child "play Turtle" themselves. What steps do they take to move in a circle?
 Learning to "program computers" is done by teaching the Turtle a new word (aka subroutine / function) like CIRCLE, SQUARE, TRIANGLE
 Along the way, students learn about modularity and state
 Don't forget the error  instead study the bugs!
 Try to make sense of what you want to learn

Syntonic learning
 The Turtle is body syntonic  firmly related to child's sense and knowledge about their own bodies
 Also is "ego syntonic"  the Turtle is coherent with child's sense of themselves with things like (e.g. intentions, goals, desires, dislikes)
 Turtle geometry is learnable because it is syntonic.
 Turtle geometry encourages deliberate use of problemsolving

George Polya
 Came up with a general method for problem solving
 Turtle geometry lends itself well to Polya's methods (e.g. "look for something like it")
 Turtle geometry is great for learning heuristic thinking
 Disassociative learning is something like memorizing the multiplication tables

Bill, a fifth grader, suggests this unfortunate way to learn multiplication tables
 "Make your mind a blank and saying it over and over until you know it"
 Turtle geometry on the other hand has rhythm, movement, navigational knowledger

Differential Calculus
 Differential calculus is ability to describe growth by what is happening at the growing tip
 Newton modeled the motions of the planets with it
 The Turtle's circle program ( FORWARD 1, RIGHTTURN 1) is a set of DIFFERENTIAL instructions!

Many students come to Turtle geometry hating numbers as alien concepts, and leave it loving them. For example, angles.
 Turtle geometry shows students that angles have body syntoncity with compass navigation. The Turtle parallels this
 Idea of a "variable" in programming: using a symbol to name an unknown entity

Idea of "recursion" in programming: a never ending process.
 Kids already love the idea / fantasy of something "going on forever" (with 2 wishes, always use the second wish to wish for two more wishes!)3

The Total Turtle Trip Theorem
 If a Turtle tasks a trip around the boundaries of any area and ends up in the state in which it started (direction and place), then the sum of all the turns will be 360 degrees
 One learns to enjoy and to respect the power of powerful ideas. One learns that the most powerful idea is the idea of powerful ideas.
 Computers can influence the language we use to talk about ourselves (e.g. input, output, feedback)
Structure programming
 Learn to write subprocedures, aka "mindsized bites"
 It's possible to build a large intellectual system without ever making a step that cannot be comprehended, using hierachy of subprocedures
 Example of teaching the Turtle to draw a person can use multiple subprocedures, each of which is easily understood
 Computers give enough flexibility and power so that child's exploration can be genuine and their own
 "Brute force" would be trying to have the Turtle draw the person without any subprocedures  the straight line approach.
 Brute force with no internal structure is not a good model for computer programming
 For example, in real life, juggling is actually composed of many subroutines
 Introduces notion of timing:
`* parallel processes vs serial processes
 Introduce notion of condition logic with The "WHEN demon"
 "When something happens, the demon pounces out and does its own action"
Debugging
 Children seem to have a resistance to debugging
 They would rather "throw it out" and start over
 Seemingly, they want to do it correctly in one shot
 We can empathize, because a bug seems like WRONG or MISTAKE or BAG
 Kids like that computers can remove any trace of their errors
 But errors and debugging are good!
 We must learn to study what happened and understand what went wrong. Through that understanding, we can fix the bug.
 Computers will help children "believe in" debugging
 Contact with LOGO and the Turtle eventually, gradually, underminds the longstanding resistance to debugging and subprocedures
 With LOGO, the teacher is also a learner, and everyone makes mistakes
 Children know when teacher "fakes it" with "let's try this one together"  they see right through this.
 But LOGO makes that situation feel genuine, because the teacher is trying to figure it out, too, and they make mistakes together
 Real intellectual collaboration  together they try to understand the computer and get it to do what they want
 Affirmation of the power of ideas and the power of the mind!
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