Additional Comments: Your Teachers!
Finally, here are some points to watch for when you
 a. watch your teachers solve problems or
 b. read the problems with solutions in your text book.
Problem number 1
Teachers are experienced problem solvers in the areas in which
they teach. In their teaching areas, teachers are experts.
Some consequences of this are:
 a. As an expert, the teacher tends to use an abbreviated
form of problem solving, taking several steps at once. You, as a
beginner, or in a new area, must take new steps one at a time.
 b. As an expert, the teacher may take many steps mentally 
often only writing down the calculations at Step 3.
You must write down on paper most steps  especially as
you start to use this problemsolving technique or as you start a
new area of study.
 c. The subject matter is well known and readily accessible
to the teacher who may therefore underestimate the difficulties
you have in getting around in the subject matter.
Problem number 2
For teachers, almost all problems presented to students are
routine.
Some consequences of this are:
 a. Teachers tend to skip the planning stages (Steps 1 and 2)
emphasizing only the calculation step. This step, Step 3, is after
the problem has been solved  so if you have a difficulty as to how
a particular solution was arrived at by the teacher, now you know
why  you weren't shown how to solve the problem at all, you were
merely show the solution in the form of the final calculation!
 b. For routine problems, forward reasoning is most efficient
and so teachers tend to show you solutions to problems by forward
reasoning. This, of course, leads you to believe that forward
reasoning is the most efficient method and to strengthen your
resistance to backward reasoning. You must resist reaching this
conclusion as experts agree: backward reasoning is the most
efficient method when the problem is not routine.
Using this information
These pointers may help you analyze why you are having
difficulties in understanding how some of your teachers arrive at
solutions to problems. If you understand where your difficulties
seem to lie you can begin to ask relevant questions of your
teachers, asking perhaps for a full approach to solving a problem
or for a demonstration of backward reasoning through a problem.
What if the teacher is a text book?
If the teacher is a text book, you cannot ask it questions,
but you can:
 use another text or
 ask your 'live' teacher to reason through a problem that is
not well illustrated by the text or
 ask peers to listen to you reason through a problem and help
you with that reasoning.
A thru E Index
