I’m finally getting around to reading Mindstorms by Seymour Papert. I’ve enjoyed his writing before so was looking forward to this seminal work on computing education. I’m surprised by the first chapter though.
In a typical experiment in combinatorial thinking, children are asked to form all the possible combinations (or “families”) of beads of assorted colors. It really is quite remarkable that most children are unable to do this systematically and accurately until
they are in the fifth or sixth grades. Why should this be? Why does this task seem to be so much more difficult than the intellectual feats accomplished by seven and eight year old children? Is its logical structure essentially more complex? Can it possibly require a neurological mechanism that does not mature until the approach of puberty? I think that a more likely explanation is provided by looking at the nature of the culture. The task of making the families of beads can be looked at as constructing and executing a program, a very common sort of program, in which two loops are nested: Fix a first color and run through all the possible second colors, then repeat until all possible first colors have been run through. For someone who is thoroughly used to computers and programming there is nothing “formal” or abstract about this task. For a child in a computer culture it would be as concrete as matching up knives and forks at the dinner table. Even the common “bug” of including some families twice (for example, red-blue and blue-red) would be well-known. Our culture is rich in pairs, couples, and one-to-one correspondences of all sorts, and it is rich in language for talking about such things. This richness provides both the incentive and a supply of models and tools for children to build ways to think about such issues as whether three large pieces of candy are more or less than four much smaller pieces. For such problems our children acquire an excellent intuitive sense of quantity. But our culture is relatively poor in models of systematic procedures. Until recently there was not even a name in popular language for programming, let alone for the ideas needed to do so successfully. There is no word for “nested loops” and no word for the double-counting bug. Indeed, there are no words for the powerful ideas computerists refer to as “bug” and “debugging.”
This just seems really a strange point of view. People have been making combinations of beads for a very long time, surely. Clearly “nested loops” are extremely common in textiles, and the double-counting bug simply doesn’t arise when sorting beads physically, unless you treat them as ordered pairs… and surely this kind of mathematics is very old. The text continues to describe all this as a new style of thinking, arguing that this is the first time we have the tools to think about thinking… Just what??
I’ll carry on reading but would love to hear what others think about the book, or join folks for a reading group discussion around the book if some of you aren’t completely zoomed out by now…