Thoughts on Papert, Coding, and Math

Prior to reading Seymour Papert's book, Mindstorms: Children, Computers, and Powerful Ideas, I had the benefit of trying out coding with the Logo computer language. Logo was developed by Papert, along with his colleagues at MIT, because they believed that, "[C]hildren can use computers in a masterful way, and that learning to use computers can change the way they learned everything else." I experienced first-hand, the exact examples that Papert expressed in Mindstorms which are required for this learning process. Papert emphasizes the importance of making, fixing, and learning from mistakes, which he calls "debugging." Logo helps to support and develop new ways of thinking. It's through this process a powerful thing occurs-learning. Like Piaget, Papert believed in the theory of "learning without being taught" and learning through doing. Since programming is mainly a self-directed activity, children learn at their own pace through their own trial-and-error. It's this process of doing that is the basis for learning. I would not have been able to simply read about coding or watch my professor code then set out to write a program on my own; I needed the opportunity to code to learn how to code. The process of writing smaller programs, or as Papert calls them "structured programming' is a big help with coding. By dividing a program into parts when coding, it becomes much easier to find and correct mistakes. It also allows the programmer to incorporate previously written program code into new code which saves time, especially when the pre-written code has already been debugged of errors. In my case, I wrote a code to make a square then added code for a triangle to make a house. The code for the square was written separately, as was the code for the triangle, but added together, they created a program for a house. But trust me, this was not an easy process. it took a lot of trial-and-error. However, once the program for the house was run, and an actual house was created, I can't even describe the feeling of accomplishment that occurred!

"Mathophobia," or the fear of math, is a big part of why Logo was created. Children are taught early on (most likely from a parent or a teacher) that they are either "good" or "bad" at math, which sets their identity on their ability to learn math. Those who are "bad" at math think that no matter how hard they work at it, they aren't going to "get it" anyway and will always be "bad" at math. Papert believed that teaching rote mathematics was completely the wrong way to teach math or anything else for that matter (Papert was also an opponent on using standardized testing to measure what a child understands and knows). Papert's aptly named Turtle geometry incorporates learning principles which have "more structure to the concept of an appropriable mathematics." In traditional Euclid's geometry, which is taught in schools, a point is defined as "a primitive notion upon which the geometry is built. Being a primitive notion means that a point cannot be defined in terms of previously defined objects." WHAT?! Can you imagine trying to teach this abstract concept to any student? It is done each and every day in schools. Turtle geometry is a "computational" type of geometry. It's a different way that children can learn math, because they identify with the Turtle. The Turtle (it resembles a triangle-shaped cursor) "serves no purpose other than of being good to program and good to think with."  Children learn to control the Turtle because it becomes an object they can control and think with, thus making their thinking visible. 

"One learns that the most powerful idea of all is the idea of powerful ideas."

~Seymour Papert