Q&A #16699

Teachers' Lounge Discussion: Teaching mathematics

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From: Susan

To: Teacher2Teacher Public Discussion
Date: 2006022402:58:54
Subject: Re:  Teaching mathematics

I am currently a high school math and science teacher, teaching Alg 1
to ninth and 10th graders.  I did not come into teaching with an
education degree, but instead with degrees in both math and science
with an additional 12 hours of graduate study mathematics.  I also
taught both Alg 1 and Intermediate Algebra in the college setting.  I
was quite shocked at how many students coming into high school are not
prepared to take algebra, especially in understanding basic math
skills such as fraction manipulation, an extremely important element
in solving algebraic equations.    

Many students were very "calculator" dependent.  I found this to be
the case for many beginning college students as well when I taught at
the college level, a frustration for many of my college colleagues,
too.  In the college I taught at, many of the first weeks were spent
retraining students who had been trained by elementary and high school
teachers that when they are weak in an area that they were just to
fall back on using a calculator to complete simple mathematic basics. 
It appeared as if the calculator was a crutch not only for the
student, but for the Elementary or High School teacher as well.  And
what I and my colleagues found, too, is that because these students
entered a college algebra class without any of those basic skills
grounded in their brains, that they really did not possess the skills
needed to complete an algebra course at the pace required at the
college level.

My opinion this is this.  That a calculator in mathematics is a
powerful tool.  However, a tool is only as good as the operator using
it.  Meaning, if the operator does not have a good understanding about
what he/she is calculating, then all that he/she is doing is plugging
numbers in with a hope of getting the correct answer. This is what I
found that many of students were doing, plugging in numbers with no
real understanding of the mathematic manipulations involved.  I found,
too, that when I did not allow students to use a calculator, some had
difficulty even doing basic multiplication and division.  They also
found adding simple negative number problems especially a challenge. 
I have been amazed at how many students would panic at not having a
calculator so that they could add something like 5-7 or -5-7. I was
told by most of these students that their previous teachers had
encouraged them to use the calculator for these simple functions,
rather having an expectation that the student needed to know these
things without the use of a calculator.  Mental math appears to have
gone out the door.  This is disheartening.  As with needing exercise
for our bodies, our brains also need that mental exercise.  It helps
with mental alertness abilities, as well as with deductive reasoning
skills.  Thus, to me, basic math skills need to be taught without the
use of a calculator and the calculator only being used when the
algebra becomes such that a student can relate the basics mentally
first.  Thus, I do not allow my students to use calculators,
especially in the beginning of Alg 1. 

Another aspect I have found with students at the high school level and
sometimes even at the beginning college level is the maturity level of
the students, especially in the lower high school grades.  At the
ninth and tenth grade ages many students are more into the social
scene than sitting down and taking the time to learn math.  They want
minimal homework and they want to learn everything in the classroom
setting.  They are still not at an understanding of what individual
responsibility is all about or that learning algebra requires
discipline much like that of an athelete.  It is funny how many high
school students are willing to put in hours to train their bodies for
a sport, but are not willing to put forth the effort to train their
minds for something like algebra.  A skill that they will use for the
rest of their lives.

Which brings me to one more statement on your question.  Most of the
students I have taught at the high school level do not believe that
what they are learning will be of a value to them after high school. 
Alot of times, too, their parents don't believe this either.  Because
of this belief, they do not think that they need to have homework or
have to work at learning the subject.  They do not really take what
they are learning seriously.  Also, in this day and age, everything
has to be a game or a theatrical production.  This is what our
American society does put value on.  And it is because of this that
America is starting to give up it's lead in mathematics and science.  

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