Subject: Seymour Papert and Mathetics

Posted by Neha Celik on 12/9/2010

Message:

Dr. Forrester and Dr. Papert make a perfect full circle. I think Seymour Papert’s wonderful book ‘’Mindstorms: Children, Computers, and Powerful Ideas’’ has a lot to offer to the discussion that has been going on for a while about System Dynamics, innovation, and mathematics. Here are some samples from the book ‘’Mindstorms.’’


PLATO WROTE over his door, "Let only geometers enter." Times have changed. Most of those who now seek to enter Plato's intellectual world neither know mathematics nor sense the least contradiction in their disregard for his injunction. Our culture's schizophrenic split between "humanities" and "science" supports their sense of security. Plato was a philosopher, and philosophy belongs to the humanities as surely as mathematics belongs to the sciences.


The status of mathematics in contemporary culture is one of the most acute symptoms of its dissociation. The emergence of a "humanistic" mathematics, one that is not perceived as separated from the study of man and "the humanities," might well be the sign that a change is in sight. So in this book I try to show how the computer presence can bring children into a more humanistic as well as a more humane relationship with mathematics. In doing so I shall have to go beyond d discussion of mathematics. I shall have to develop a new perspective on the process of learning itself.


To my ear the word "mathophobia" has two associations. One of these is a widespread fear of mathematics, which often has the intensity of a real phobia. The other comes from the meaning of the stem "math." In Greek it means "learning" in a general sense.* In our culture, fear of learning is no less endemic (although more frequently disguised) than fear of mathematics. Children begin their lives as eager and competent learners. They have to learn to have trouble with learning in general and mathematics in particular. In both senses of "math" there is a shift from mathophile to mathophobe, from lover of mathematics and of learning to a person fearful of both. (*The original meaning is present in the word "polymath," a person of many learnings. A less well-known word with the same stem which I shall use in later chapters is "mathetic," having to do with learning.)


…But utility was only one of the historical reasons for school math. Others were of a mathetic nature. Mathetics is the set of guiding principles that govern learning. Some of the historical reasons for school math had to do with what was learnable and teachable in the precomputer epoch. As I see it, a major factor that determined what mathematics went into school math was what could be done in the setting of school classrooms with the primitive technology of pencil and paper. For example, children can draw graphs with pencil and paper. So it was decided to let children draw many graphs.


Another mathetic factor in the social construction of school math is the technology of grading. A living language is learned by speaking and does not need a teacher to verify and grade each sentence. A dead language requires constant "feedback" from a teacher. The activity known as "sums" performs this feedback function in school math. These absurd little repetitive exercises have only one merit: They are easy to grade. But this merit has bought them a firm place at the center of school math. In brief, I maintain that construction of school math is strongly influenced by what seemed to be teachable when math was taught as a "dead" subject, using the primitive, passive technologies of sticks and sand, chalk and blackboard, pencil and paper. The result was an intellectually incoherent set of topics that violates the most elementary mathetic principles of what makes certain material easy to learn and some almost impossible.


Neha Celik
nehace@yahoo.com

Follow Ups:

Seymour Papert and Mathetics - Michael Round 12/10/2010