Logo ideas.(programming as an educational tool) (column)Robert Lawler.

Logo Ideas

Microworlds And Learning

The central problem of humane education is how to instruct while respecting the self-constructive character of mind. Teachers face a terrible dilemma in motivating children to do schoolwork that is not intrinsically interesting. Either the child must be induced to undertake the work by promise of some reward or must be compelled to do the work under threat of punishment. In neither case does the child focus his attention on the material to be learned. The work is seen as a bad thing because either it is an obstacle blocking the way to a reward or it is the cause of the threatened punishment.

Psychologists know that much of learning is a gradual process, one of familiarization, of stumbling into puzzlements and resolving them by proposing simple hypotheses in which a new problem is seen as similar to others already understood, and of performing simple experiments to test the latest theory.

Microworlds can be seen as worlds designed for virtual, streamlined experiences, worlds with agents and processes one can get to know and understand. Properly designed microworlds embody a lucid representation of the major entities and relations of some domain of experience--geometry and music are two examples--as understood by experts in the domains. This is where the knowledge of the culture is made available in the very terms in which the microworld is defined.

The child's appropriation of that knowledge is made possible by the microworld not being focussed on problems to be done, but on "neat phenomena'--i.e., the primary manifestation of the power made available by knowledge about the domain. If there are neat phenomena, then the challenge to the knowledgeable expert is to formulate so crisp a presentation of the elements of the domain that even a child can grasp its essence. The value of the computer is in building the simplest model which an expert can imagine as an acceptable entry point to his own richer knowledge.

If there are no neat phenomena that a child can appreciate, there is no function that knowledge of the domain can serve for him. He should not be expected to learn about it until he is personally engaged with other tasks which will make the specific knowledge tolerable as a supporting prerequisite to something desirable to know.

The Idea Of A Formalism

A formalism is a set of symbolic objects that are related by the operations or manipulations that can be performed on them. Everyday arithmetic is an example of a formalism: the numbers are related to one another by addition, subtraction and so forth. We often use formalisms, such as arithmetic, without asking what there is about them that really makes them useful in thinking.

The mathematician-philosopher Whitehead raised this question about the calculus, another formalism, and proposed an answer of the following sort: A formalism is useful because it gives you one less thing to worry about. You learn a set of rules of almost mechanical manipulation, then you can concentrate on how to apply them to a specific situation about which you want to know more. You judge the applicability of a mathematical formalism by whether or not its predictions correspond to what happens in the problem domain.

A programming language such as Logo is also a formalism-- but one whose focus is more on its concrete use than on its symbolic prediction. In this sense, the Logo language is a kind of empirical mathematics, one whose value does not depend upon immediately mastering perfectly a set of rules. One can begin with a faulty procedure and perfect it by debugging-- retrying the execution until it produces the intended result or a better one is discovered along the way. Eventually, one may become sufficiently expert to compose perfect code, but it is not necessary that one ever do so.

A relaxed requirement for perfection is one major way that Logo programming contrasts with the child's other experienced formalism, arithmetic. This is important because in the world of turtle geometry, the domain of design is so rich that unintended results can often be more attractive than what the programmer first intended. This is a direct contrast with arithmetic--in which errors are of positive value only to psychologists. There is a second sense, however, in which Logo programming requires perfection as much as any other formalism. When one is committed to a specific result, specific operations must be performed in the correct order to achieve that result. Because of the relative richness of the error paths in turtle geometry, Logo may be a more accessible formalism--and a more attractive one--than children commonly met before the advent of computers.