Review by: Reichert, Raimond (2004-08-10)

The mathematician, computer scientist, and psychologist Seymour Papert conducted renowned projects in the 1970s at the Massachusetts Institute of Technology with the goal of making children the “builders” of their own intellectual “buildings”. In this book, he outlines his vision of “constructionism”, a variant of constructivism where children should be enabled to “learn by making”. In Papert’s view, this is qualitatively different from learning by doing.

In particular, the goal was to enable children to discover geometric knowledge on their own. The computer was to serve as a powerful tool with which the children could formulate algorithms to create certain patterns and test these algorithms. The point here is that children program the computer, that the children are in control of what they do. In most educational situations where children come into contact with computers – i. e. programmed instruction, computer aided instruction – the relationship is reversed: The computer programs the child.

The language Logo was created as a dialect of the LISP programming language. Logo is a general-purpose language; to adapt it for the purpose of teaching geometry, a subset was used in a particular micro world setting. The resulting “Turtle Geometry” involves programming a turtle, either a robotic one drawing on the ground, or a virtual one drawing on the screen.

Papert intended Turtle Geometry to be a mathematics learning environment for children. He observed that a child who has difficulties with mathematics is often labeled mathematically untalented. However, a child having trouble learning a foreign language like French is not labeled untalented for French. We know that if the child had grown up in France, it would have learned French without any conscious effort. Papert argued that in “Math Land”, children would learn mathematics as naturally as their mother tongue. Logo and the Turtle Geometry were his vision of Math Land.

The turtle has a position and faces a direction, specified in degrees. These two properties fully describe the state of the turtle and can be easily visualized. The commands understood by the turtle are also simple. It can move forward, painting its trail, or turn at its current position. Logo supports recursion, which makes it possible to formulate algorithms concisely. As a general-purpose language, Logo also has variables, parameters, branches, repeat statements, blocks, and much more. Logo is more powerful than a first glance reveals. It was Papert’s intention to design “a computer language that would be suitable for children. This did not mean that it should be a ‘toy’ language. On the contrary, I wanted it to have the power of professional programming languages, but I also wanted it to have easy entry routes for nonmathematical beginners”.

Papert also argued that using the Turtle as an “object to think” with would affect learning in a broader sense. Critiques feared that teaching children programming would instill “mechanical” thinking. He argued that on the contrary, without having a personal experience in what it means to program a mechanical device, children can develop no sense of what “mechanical” thinking is. He suggested making the thought processes required when programming an educational goal. His idea is eloquently expressed by Donald Knuth (1974): “It has often been said that a person does not really understand something until he teaches it to someone else. Actually a person does not really understand something until he can teach it to a computer, i. e., express it as an algorithm. […] The attempt to formalize things as algorithms leads to a much deeper understanding than if we simply try to comprehend things in the traditional way.”

It is interesting to view Papert’s work on Logo more than twenty years later, in the context of e-learning. It would seem that his point that in educational settings, it is too often the computer that is in control, is still valid. One could also argue that the full potential of his constructionist ideas, of learning by making, and of using computer-based micro worlds to this end, has not yet been realized.