Which calculator

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Which calculator

I have been reading this thread about which calculator for about a week, and
of course everyone has their own opinion, as do I.


There is absolutely no benefit to the student for any calculator beyond a
simple scientific for any course before second year algebra.  Students need
to know how to draw their own graphs and need to learn the important
concepts of slope and intercepts by looking at the equation, or factoring,
or whatever.  I know, "why should we teach factoring if the calculator can
do it for us?"  By that same reasoning, "why should we teach anything?  I
can always go out and hire someone who knows the subject."


It's just that the process of doing the factoring and doing the symbol
manipulation is an important component in the learning process.  As a
California high school teacher (not really something to be proud of), I am
using the CPM materials in teaching mathematics, so an understanding of
families of equations is not expected until the third year.  It is at this
point that the graphing calculators become an important component, not
because it makes it easier for students to do their work, but rather because
the investigations presented in the more up-to-date textbooks, utilize the
calculator's graphing capabilities to more quickly, and perhaps more
efficiently, teach the concept.  In effect, there is absolutely no point in
having students compute and graph and endless number of points and graphs,
when the concept being taught has nothing to do with the graphing process,
but is primarily concerned with an understanding of the general appearance
of a graph if one is given an equation.  For those using a more traditional
curriculum, this concept is not presented until Trig, thus the graphing
calculator serves no real purpose until these investigations are presented.


So now we get to Cabri geometry.  Unless teachers have been writing their
own curriculum, there are virtually no textbooks on the market whose lessons
are tailored toward teaching geometric concepts using Cabri.  That is not to
say that Cabri has no use, but rather that it has little if any value in
teaching students geometry (you know, proofs, congruence, and all that
stuff).  However, a teacher utilizing an overhead unit would be able to
present great demonstrations to a class using Cabri.  So, in my opinion, it
is the teacher who should have this calculator, not the students.


As to derive, give me a break.  A first year algebra student could probably
pass a class without knowing anything, and I am sure that with the 92 out
there, many may have already done so.  Many a parent could easily justify
the cost of a 92 when compared to the cost of long term tutoring, and many a
student could also do so rather than studying and learning the material.


As to calculus, the same applies.  Most of us who teach calculus never had
the benefit of these sophisticated tools.  Some of us older ones even had to
do our work with slide rules and trig tables.  We simply learned the
material.  Our calculus students should not be using these calculators as a
substitute for learning, but rather as a tool for learning; and for the most
part, that is simply not happening.  Most teachers have neither the time or
the initiative to design tests which are not calculator biased.  ETS is
having trouble keeping up with the technology, and has not, as yet, come up
with a new AP that does not give 92 users an advantage.


At a recent SAT seminar, the presenter stated that it was an important goal
that the SAT not be calculator biased, but privately admitted that students
utilizing calculators had a distinct advantage.  Students taking the AP are
permitted to utilize two calculators; and their memories loaded with
formulae and programs are not cleared.


So which calculator should one recommend?  It really depends upon the
curriculum.  Things being as they are, the 85 and 83 are probably more than
sufficient for college, with the 85 being significantly more powerful, while
the 83 is a bit easier to use and having the benefit of the statistical and
financial functions.  Under no circumstances would I recommend that students
get 92's unless (1) they really don't want to learn anything, (2) they want
to spend endless time and energy waiting for fargo so they can play games,
or (3) the curriculum has been designed to utilize the 92 as a teaching tool
and not as a substitute for real learning.


Now I guess I can sit back and get flamed.  Please, however, remember.  As a
courtesy to others, don't reply publically unless you think that everyone
will benefit.


Bernard Domroy
High School Math Teacher