different perspectives, different ways of thinking
“. . . . But in these first simple number sums there is one very important consideration. It will make a great difference to the tendency of his thinking for the rest of his life whether you fill the child’s mind with the idea that one and one and one make three, or whether you start with three and break it into its parts. Ultimately and logically the first leads to the idea that the universe is composed of atoms. The second, the grasping of the whole before the parts, is the way of imagination, and leads to the view that it is only the whole which gives meaning and existence to the parts. The difference is as subtle as it is profound.
“Starting with the whole makes it possible also to introduce another gesture into arithmetic. Addition, the adding of unit to unit, always contains something of the suggestion that the object is to get more and more. Subtraction leads readily to the picture of giving away to others. So, if it is to be a gardener with a bunch of roses he has grown, let him be thinking: if he has twenty roses and gives a beautiful bunch of six to his neighbor and seven to his wife, how many will there be left over for his friend’s little girl who is very ill in bed? . . . . The children should only know that they are learning about numbers. Actually they are learning something of far greater importance — a moral attitude to life. . . .”
This quote is from p. 104 -5 of The Recovery of Man in Childhood, by A. C. Harwood, copyright 1958 by The Myrin Institute of New York, eighth impression 1992. (The subtitle only appearing on the main title page is “A Study in the Educational Work of Rudolf Steiner”.)
I am currently browsing through this book during intermittent periods of lucidity.
How and what we teach our children will have very important consequences for the future of our world.
There is a practical benefit to making use of different perspectives. From the days when I was a problem solver, working on contract with various companies, I know it is true that viewing a problem from a different angle(s), so to speak, can help in arriving at solutions. Many evenings upon leaving work, it would seem that no solution could be found to a problem (or, if you prefer, a challenge). Perhaps, the unconscious was involved here in ways that I did not suspect. In many instances, the next morning when I arrived and began the day’s work, another way of viewing the problem would suggest itself quite quickly. Then, when viewed from a different perspective, the solution, or at least, a solution jumped up at me. Possibly, doing some individual brain storming may also help to generate ideas and possible solutions. (Being on contract often to work on “special projects” precluded including other employees in such brain storming as they had no time to spare for it.) As well, this approach is even applicable to improvising solutions to mechanical problems around the house when there is no help available. Relax the constraints on your mind, be less rigid in your thinking, and constructive solutions can be found.
Shadows on pavement (July, 2013).
As the subtitle suggests, this book is based on the work of Rudolf Steiner (1861 – 1925), an Austrian philosopher and scientist. I may have come across his name before in my wide ranging reading, but I was not familiar with his writings. He was an ardent admirer of the German writer, Goethe (1749 – 1832). Now some German writers and philosophers can be terribly difficult to read. I recall suffering through Immanuel Kant in college days. Nietzsche (1844 – 1900) was easier to read (The Birth of Tragedy, Beyond Good and Evil) in recent years, but he plays the role of social critic as much as he does of philosopher. Perhaps, social criticism is simply the other side of the coin of philosophy. (Bertrand Russell (1872 – 1970) said that Nietzsche was the successor to Arthur Schopenhauer, but that he did not present a new philosophy.)