On the face of it, formal education would seem the antithesis of intuitive learning.
And the large majority of formal education is exactly that, an impediment to learning.
But there are a few exceptions.
And  of much greater importance  the objectives of formal education can be most successfully
met by a curriculum based on intuitive learning.
Put a student in a classroom in which any form of mathematics is being taught, and more likely than
not the teacher will warn about the consequences of wrong answers.
When the numbers are wrong,
 the medicine might kill the patient.
 the bridge might collapse.
 the plane could fall out of the sign.
Imagine the child's terror of and guilt about getting a wrong answer.
Now add to this, the thought that only careful thinking will avoid a wrong answer; intuition
has no place in mathematics.
I used to poll my mathematics students with a single question: How many of them never really
listened to their math teachers?
After a certain edginess, and looking around at other students, a lot of them would raise their hands.
These students knew what I meant without my adding anything to the question. These were the
students who would work problems without showing their work, then  sometimes  recopy the problem showing their work so
they could get credit. The quality of their work depended in large part on their intuition.
And these students  the ones with their hands up, the ones who didn't listen  these were my best
students. Not only did they make the highest grades in my class, but also earned the highest ratings in the ACT, PSAT,
and SAT tests.
And those students whose hands were not raised, who always listened to their teachers, these sweet
attentive schoolboys and schoolgirls  they were the ones struggling to succeed (and more often than not failing).
They were the ones with math and test anxiety. They were the ones without confidence.
Most math teachers are teaching their students to fail.
Any teacher who expects his students to succeed when the motivation is anxiety will only fail himself.
Success both depends on confidence and is the result of confidence. And confidence can be measured by one's reliance on intuition.
Whether or not they have articulated it, every person knows that whatever he or she does well, he or she does intuitively.
And it is in our awareness that we can tap that intuition that we achieve confidence.
It doesn't only happen in mathematics.
It happens in science classes and liberal arts classes.
It happens in social studies classes.
And, most startling, it happens in foreign language classes.
Why is it so startling? Because there is so much evidence, so much documentation that the way
to master a foreign language is by immersion in that language. Once a student can be somewhat comfortable hearing and
speaking that language, then that student possesses sufficient examples to examine under the microscope of syntax, of grammar,
of spelling and punctuation rules. With the illumination provided by those examples, the student is ready to delve into
the depths of that language. Understanding starts not with rules, but with practice.
It doesn't happen in physical education. Virtually every coach realizes that physical activity
requires intuition.
It doesn't happen in vocational education. If you're going to learn to use a tool, you must
be able to use it intuitively or you're going to hurt yourself.
It would be easy to blame the teachers and leave it at that.
But that ignores the larger part of the problem.
Motivation.
Remember the first essential to a child learning language: Incentive to learn it.
Many students arrive at educational institutions with little or no motivation to learn. Many
more students arrive with motivation and have that motivation killed by encountering bad teachers or being forced in inappropriate
programs.
The question faced by every good teacher is what to do about the unmotivated student. The greatest
temptation for many of us is to ignore that student. If the student becomes disruptive, force him out of class.
But that solution does not work for the good teacher. By their very definition, good teachers want all their students
to succeed.
Yet what is the teacher to do when after being told he does not have to show his work, the student
hands in a list of answers unrelated to the problems? Or hands in answers obviously copied from another student's paper?
The teacher might realize that a little effort can avoid a great effort, but too many students
today don't get it. Studies show that young people usually don't intuitively grasp the concept of delayed gratification
 that is, they understand it intellectually, but not emotionally. These become our "lazy" students.
True, we can explain their behavior: They would rather have fun today than more fun tomorrow.
Fun today is almost tangible; more fun tomorrow is too nebulous to sacrifce for some slight benefit today.
This is the conflict that all teachers encounter. A classroom divided is a classroom divided
against itself. A teacher trying to teach two curriculums may not succeed in teaching either.
Does the teacher teach to the "good" students, those who are already intuitive learners or does the
teacher teach to the "bad" students, they melange of angry, distracted, confused, resentful, and/or worried students who just
don't seem to get it?
But this is only one part of the problem.
There is the state: Federal and State Government. Coming from above  from people with
no knowledge of how to teach  come all sorts of rules designed to result in better students.
And as each set of rules fails, rather than being removed from legislation, they get added to.
Politicians are loathe to admit their errors, better to cover them up with further legislation.
(That's ranting, and I apologize for it.)
The fact is, like everything else, good teaching is an intuitive process. The more a teacher tries to follow an
imposed guideline, the less that teacher is functioning at the height of her skills.
It is one thing to have an objective toward which we are to teach  providing those are good objectives  but it is
quite something else when we are told the route by which we are to get there.
I have diverged from the strategy of a colleague, teaching a particular class in my special way only to find that my
colleague has matched my success with his own strategy, one which I had disdained. All that mattered here was that both
strategies be good ones and that we were confident in using them.
Concentration blocks Intuition.
A good teacher relies on intuition.
