**
In the classroom there are really only two important ingredients to consider
when trying to achieve learning, the teacher and the student.**

**
For the teacher to be effective he needs to spend as much time during each
lesson/week/term/year in reality. As a model of this situation I have developed
what I refer to as the Reality Quotient. It is a rational expression in
which the denominator is the amount of time spent in abstraction, and the
numerator, of which, is the time spent in reality. The result is that the
more time that a teacher spends in abstraction as compared with the amount
of time he spends in reality the less value the reality quotient has. It
is my belief that the most effective teachers work diligently to spend
as much time as possible in reality. It is my further belief that a great
teacher should constantly be trying to keep his Reality Quotient at a value
that is at least, one. Mathematically, it looks like this:**
**R ³
1,**

**
One of the results of this effort is that good teachers become great teachers,
and once they are great they will be spending at least as much time in
reality in their teaching as they spend in abstraction.**

**
For the student to be effective he needs to spend as much time as possible
during each lesson/week/term/year working beyond his ability. As a model
of this situation I have developed what I refer to as the Achievement Ratio.
It is a rational expression in which the denominator represents the student’s
ability and the numerator is the student’s achievement level. The result
is that the more time that a student spends working at a level that is
above his ability as compared with the amount of time he spends working
at a level that is beneath his ability the less value the achievement ratio
has. It is my belief that the most effective students work diligently to
spend as much time as possible working at a level that is above their ability.
It is my further belief that a great student should constantly be trying
to keep his Achievement Ratio at a value that is at least equal to one.
Mathematically, it looks like this:**
**
A
³ 1,**

**
One of the results of this effort is that the student will constantly be
working hard enough to have a positive impact on his ability resulting
in the need to always work harder still to keep his Achievement Quotient
worth at least one. In the end one would hope to have a student who is
very bright, and always working at his level of ability.**