The Relative Emphasis Upon Mechanical Skill and Applications of Elementary Mathematics
The teaching of elementary mathematics has two distinct purposes, quite closely connected with each other and yet easily distinguished. The pupil must develop a skill in the manipulation of the symbols of elementary mathematics and he must develop a power to apply them to the solution of life problems. By special emphasis upon either phase of the subject an ability can be developed in it without a corresponding ability in the other phase, and sometimes at the expense of ability in the other phase. It is easy to develop in pupils a high degree of skill in the mechanical processes of computation with almost no ability to decide in a particular problem what process is to be used. And in pioneer days many men were quite able to solve the problems met in daily life though knowing nothing of the use of figures for purposes of computation. It has been very interesting to me to note that pupils in the third and fourth grades, utterly innocent of the use of the symbols in division of fractions, will frequently solve problems involving division of fractious more readily than will those same pupils after they have been taught to “invert the divisor and multiply.” This does not mean that skill in computation with figures stands in the way of solving concrete problems, but that during the time devoted to acquiring the skill they have lost power in thinking number relations, possibly through a transfer of interest.