Lecture Four

When I begin this way with the total actually in front of me, and then go on to the numbers to be added together, I am sticking with reality; I proceed from the whole, which is constant, to its parts. The parts can be grouped in various ways—for example, \(10 = 2+2+3+3\)—but the whole is constant and invariable, and this is the greater reality. Thus, I must teach children to add by proceeding from the whole to the parts. Genuine knowledge of the human being shows us that, at this age, a child will have nothing to do with abstractions, such as addenda, but wants everything concrete; and this requires a reversal of the usual method of teaching mathematics. In teaching addition, we have to proceed from the whole to the parts, showing that it can be divided in various ways. This is the best method to help us awaken forces of observation in children, and it is truly in keeping with their nature. This applies also to the other rules of mathematics. If you say, “What must we take away from \(5\) in order to leave \(2\)?” you will arouse much more interest in children than if you say, “Take \(3\) from \(5\).” And the first question is also much closer to real life. These things happen in real life, and in your teaching methods you can awaken a sense of reality in children at this age.