The Psychology of Number and Its Applications to Methods of Teaching Arithmetic

Excerpt from The Psychology of Number and Its Applications to Methods of Teaching Arithmetic

In presenting this book on the Psychology of dumber it is believed that a special want is supplied. There is no subject taught in the elementary schools that taxes the teacher's resources as to methods and devices to a greater extent than arithmetic. There is no subject taught that is more dangerous to the pupil in the way of deadening his mind and arresting its development, if bad methods are used. The mechanical side of training must be joined to the intellectual in such a form as to prevent the fixing of the mind in thoughtless habits. While the mere processes become mechanical, the mind should by ever-deepening insight continually increase its power to grasp details in more extensive combinations.

Methods must be chosen and justified, if they can be justified at all, on psychological grounds. The concept of number will at first be grasped by the pupil imperfectly. He will see some phases of it and neglect others. Later on he will arrive at operations which demand a view of all that number implies. Each and every number is an implied ratio, but it does not express the ratio as simple number. The German language is fortunate in having terms that express the two aspects of numerical quantity.

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