Thinking and learning to think

by Nathan Christ Schaeffer

Mechanical memory.

The verbal memory is but one form of the mechanical memory. There is no necessary connection between persons and their names, between events and dates, between things and their symbols; these must be learned by bringing them together before the mind until by the law of association, called contiguity in time and place, the link that binds them is forged; or, to change the figure, until they occupy places side by side on the tablets of the mechanical memory. It is sometimes supposed that there is a necessary connection between the two factors and their result in the multiplication table. But the moment we construct an arithmetical scale based on the dozen instead of ten, 7 × 8 = 48 instead of 56 (the former combination of figures signifying four twelves and eight ones), and the arbitrary character of the combinations in the Arabic notation becomes apparent at a glance. Sometimes a peculiarity in a rule like that for the middle and the opposite parts in the right-angled spherical triangle may assist the memory; but in most cases the formulas which are in constant use in the higher mathematics must be fixed by the methods of drill appropriate for the mechanical memory.

Pestalozzi’s mistake.

It is a mistake in teaching as well as in practical life to neglect the mechanical memory. In many directions it takes care of itself through the conditions and requirements of a person’s daily occupation. The salesman in a large store, the conductor on a railway, the politician on the hustings remembers many things in this way, and not because they are bound together by a logical nexus like that which binds together the thoughts of a geometrical proof. Many things which the pupil must carry from the school into practical life must be retained through drill and repetition. Pestalozzi imagined that if he taught pupils how to construct the multiplication table it would not be necessary for them to commit it to memory. The Swiss teachers long ago found out the insufficiency of his method; found out that, whilst it pays to let a pupil construct the table for himself, because it increases his interest in the combinations, and thus lightens the burden of the mechanical memory, the drill must be kept up until the sight of two factors suggests their product with infallible accuracy. Valuable time can be saved if the teacher will make a list of things that must be fixed in the mechanical memory for the purpose of facilitating the thought-processes in more advanced stages of instruction and in the discharge of the duties of practical life. The following are typical examples of what should be lodged in the mechanical memory:

1. A reasonable vocabulary of words in the mother tongue.

2. A working vocabulary of words in the foreign languages which the circumstances or occupation of a student will compel him to use.

3. The combinations of addition up to one hundred, the multiplication table, and the tables of weights and measures.

4. Algebraic and other formulas which constantly recur in the higher mathematics.

5. The fundamental formulas in chemistry, physics, and other sciences.