This is a difficult goal to present to teachers, coming as it does at a time when education is under attack from many quarters. But our society is changing rapidly and the difficulties of foreseeing what kinds of skills future generations will require are increasing. Although we have so far depended on the rational, left half of the human brain to plan our children's future and to solve the problems they might encounter on the way to that future, the onslaught of profound change is shaking our confidence in technological thinking and in the old methdods of education. Without abandoning training in tradtional verbal and computational skills, concerned teachers are looking for teaching techniques that will enchance children's intuitive and creative powers, thus preparing students to meet new challenges with flexibility, inventiveness, and imagination and with the ability to grasp complex arrays of interconnected ideas and facts, to perceive underlying patterns of events, and to see old problems in new ways.

There is no way to tell whether the patterns extracted by the right hemisphere are real or imagined without subjecting them to left-hemisphere scrutiny. On the other hand, mere critical thinking, without creative and intuitive insights, without the search for new patterns, is sterile and doomed. To solve complex problems in changing circumstances requires the activity of both cerebral hemispheres: the path to the future lies through the corpus callosum.

Teachers should be able to help learners to efficiently communicate to other numerical ideas and to make connection with real-life problems in the areas chosen for their eventual career. Training only on subject matter is definitely not going to bring about this expertise. There must be more emphasis on coaching and facilitating techniques. In their normal practices, teachers must see very clearly where each individual learner stands on the learning continuum of that particular development, what problems and difficulties he or she is going to face and what lies ahead on that learning continuum to be walked by the learner. Teachers should be trained to be a master of how to help each and every learn to walk through the learning task. Going through the learning task is a necessary and essential aspect of teacher training but it is not sufficient to make them good and effective teachers.

Teachers need to be trained on how children learn, not only how to solve mathematical problems. They must know how to make learners well understand the New Math and enable them to solve mathematical problems.

The most necessary task of civilization is to teach people how to think. It should be the primary purpose of our public schools. The mind of a child is naturally active, it develops through exercise. Give a child plenty of exercise, for body and brain. The trouble with our way of educating is that it does not give elasticity to the mind. It casts the brain into a mold. It insists that the child must accept. It does not encourage original thought or reasoning, and it lays more stress on memory than observation.

My suggestion is that at each state the proper order of operation of the mind requires an overall grasp of what is generally known, not only in formal logical, mathematical terms, but also intuitively, in images, feelings, poetic usage of language, etc. (Perhaps we could say that this is what is involved in harmony between the 'left brain' and the 'right brain'). This kind of overall way of thinking is not only a fertile source of new theoretical ideas: it is needed for the human mind to function in a generally harmonious way, which could in turn help to make possible an orderly and stable society.

On the other hand, mere critical thinking, without creative and intuitive insights, without the search for new patterns, is sterile and doomed. To solve complex problems in changing circumstances requires the activity of both cerebral hemispheres: the path to the future lies through the corpus callosum.

I always believed that at some time fate would take from me the terrible effort and duty of educating myself. I believed that, when the time came, I would discover a philosopher to educate me, a true philosopher whom one could follow without any misgiving because one would have more faith in him than one had in oneself. Then I asked myself: what would be the principles by which he would educate you?—and I reflected on what he might say about the two educational maxims which are being hatched in our time. One of them demands that the educator should quickly recognize the real strength of his pupil and then direct all his efforts and energy and heat at them so as to help that one virtue to attain true maturity and fruitfulness. The other maxim, on the contrary, requires that the educator should draw forth and nourish all the forces which exist in his pupil and bring them to a harmonious relationship with one another. ... But where do we discover a harmonious whole at all, a simultaneous sounding of many voice in one nature, if not in such men as Cellini, men in whom everything, knowledge, desire, love, hate, strives towards a central point, a root force, and where a harmonious system is constructed through the compelling domination of this living centre? And so perhaps these two maxims are not opposites at all? Perhaps the one simply says that man should have a center and the other than he should also have a periphery? That educating philosopher of whom I dreamed would, I came to think, not only discover the central force, he would also know how to prevent its acting destructively on the other forces: his educational task would, it seemed to me, be to mould the whole man into a living solar and planetary system and to understand its higher laws of motion.

The most important part of teaching is to teach what it is to know.

I know of no significant advance in science that did not require major inputs from both cerebral hemispheres. This is not true for art, where apparently there are no experiments by which capable, dedicated and unbiased observers can determine to their mutual satisfaction which works are great.

between the ‘left brain’ and the ‘right brain’.) This kind of overall way of thinking is not only a fertile source of new theoretical ideas: it is needed for the human mind to function in a generally harmonious way, which could in turn help to make possible an orderly and stable society.

The task we all face as human beings ... is to find and become who we are. The task teachers face is to find their own way of teaching, one that manifests who they are.

To teach is to learn twice.

Train assiduously, with the teacher serving as the needle and the student as the thread.31