[comp.edu] Teaching Math. was: Subtle Math Questions

mdhutton@cs.toronto.edu (Mike Hutton) (05/03/91)

In article <1991May2.133856.8338@psych.toronto.edu> grant@psych.toronto.edu (Stuart Grant) writes:
>... _Any_ math course taught at a college or university will be at  
>least as sophisticated as what teachers will be teaching in primary and
>secondary schools. Not knowing how to do differential equations is not
>the greatest problem math teachers have.
>
>Calling the education faculty math courses wimpy, and making math teachers
>take "regular" math courses is not the answer. The quality of math 
>instruction will improve if teachers are given more training in the 
>teaching of math. Teaching math is difficult, Motivating students and
>getting across abstract concepts that the students have not used before
>is, I believe, the greatest difficulty.
>
>So, I think math instruction can be best improved not by teaching the 
>teachers more math, but by giving them more teaching skills, including
>additinal training in how to teach math.  

I think that the primary skill required for a good teacher is the 
*desire* to teach, which consists largely in liking the material 
themselves, and wanting to pass this feeling on to the students.  
This desire comes from understanding more about the subject, and
*wanting* to understand more about the subject.  The teacher's 
motivation is the student's motivation, and motivation is the
key to any learning.

One of the biggest problems in high-school today is that the teachers 
are only one level above the classroom.  This makes it next to
impossible for the teacher to instill any kind of motivation 
or excitement in the students.  How can one teach how to 
graph a function, or do elementary calculus if they have never
extended these concepts to interesting applications and higher
math?  Even determining the equation of a line is a useless exercise
unless the teacher *feels* the uses of understanding linear
relationships between things (a more abstract concept).  

I think that teachers should be further beyond their students.  To
teach math, one should take a degree in a math-related field, then
learn how to teach (the Waterloo Math: teaching-option progrem has been 
mentioned before).  Then the motivation and the skills both exist.  The
US system, and more and more the Canadian system does it backwards;
they make teachers into subject-teachers.  Except for OAC, almost
anyone can teach math because it is considered 'basic' to teachers at
the high-school level.   My father (a math teacher) considers it a joke
that his certificate states he is 'qualified' to teach every subject
except French.  This is total garbage; he is a great math teacher, but
he would be a lousy history teacher.

If you want a good math teacher, train a mathematician to be a teacher,
not the other way around.  There is no wonder-training that can make
someone who doesn't like math teach it well.

Mike.