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 re-reading Lord of the Rings right now). This post, after this short-I-promise 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 longer-lasting. 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
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 self-perpetuating 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 self-reinforcing taboo
- "Cchool math" is not the same as "mathematics"
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
- 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 problem-solving
- 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 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)
- Learn to write subprocedures, aka "mind-sized 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"
- 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 long-standing 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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