Discussion:  All Topics in Algebra 
Topic:  Algebra Textbook Recommendation 
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Subject:  RE: Algebra Textbook Recommendation 
Author:  markovchaney 
Date:  Jul 7 2007 
> 1. A
> quote from John Saxon's literature: "Do not try to teach
> your
> students to think. Practice, practice, practice.
> Eventually they
> will get it." I couldn't disagree more. I have
> two passions, which
> drive all of my work. The first is, I must
> make sure students
> understand "why" the mathematics is what it
> is. Not just why we
> "do" it the way we do, but why it even makes
> sense to CONSIDER doing
> it that way.
4. As "certified"
> mathematics teachers, we have the
> potential of being some of the
> most arrogant teachers in education.
> We "know" a subject with
> which many people have trouble. And we
> don't often let you
> forget that. When a math teacher looks at my
> material (this
> actually happened) and says that it has the most
> detailed
> conceptual explanations she has ever seen, and the most
> vivid
> graphics clarifying the concept, and then says, "There's no
> way I
> would use this in my classroom", that pretty much makes the
> case.
> The followup was, "I will never use anything in my classroom
>
> that can do a better job than I can." Case closed.
I have to
> totally disagree with you on point #1  the "WHY" is exacely what
> Saxon student learn. This I know, because I experienced it myself;
> my blood boiled over and over again all throught the years that we
> studied Saxon math when I realized over and over again the why of so
> many concepts that I never learned in school; without that
> understanding, math just doesn't work!
Perhaps it would be useful to all of us if you could cite in some detail a few
specific examples of exactly how Saxon did this for you on a couple of points.
Any level or topic would be fine. I would be very interested to see what you
mean, as perhaps your notions on this and mine are quite different, and that
would account for my feeling that Saxon Math is the antithesis of focusing on
understanding.
I was educated in the 1950s and '60s, and Saxon didn't exist. Neither did the
kinds of studentcentered, investigative, discoveryoriented,
conceptuallybased, or applicationsfocused books generally lumped together
today as either "reform" or "fuzzy" depending upon whom is doing the lumping. :)
I was a very facile student of arithmetic and algebra, but my facility in
getting all the problems right, faster than everyone, did not promote any
enjoyment in or love for mathematics, and by my midteens I had completely
lost any interest in math. I went through high school math classes (all four
years) in a kind of fog, and it was only in my 30s that I revisited algebra 2,
finally learned trig, took precalculus and calculus, and eventually completed
all the course work for the equivalent of a BS in mathematics (as well as
getting certified in secondary math in addition to my alreadyearned
certification in secondary English). I went on to do graduate work in
mathematics education at the University of Michigan and earn a masters degree
from there. I was lucky enough to have teachers during my second encounter with
math who valued real mathematical thinking, who were not afraid to see
technology used to help students play with real mathematics (my calculus 2
teacher, not a young man at all, gave many computerbased assignments that
were extremely challenging and enlightening, and my calculus 3 teacher let us
use computer software to help us visualize and play with multivariate calculus
problems that would have been very hard for me without some tool like that,
given the very limited teaching of solid geometry that remains a major problem
in most American high school math programs).
As for point #4, I
> couldn't agree with you more! :)
I agree that there is a good deal of arrogance among math professors and some
among high school math teachers, though it is not always all that
wellfounded. It is this arrogance and, more importantly, lack of empathy for
students to whom math comes less easily that makes many wouldbe and
practicing high school math teachers less effective than they might be. In my
experience as a supervisor of secondary math student teachers at U of M, I found
many of them puzzled at why students struggled with ideas and procedures that
were "obvious." Of course, the word "obvious" is one I would ban from math
teaching.
As for the mathematicians at the university level, I think for many their high
level of accomplishment makes them less interested in issues of teaching than
should be the case for people who are expected to instruct, and it makes many of
them VERY poor judges of K12 mathematics teaching issues. Unfortunately, many
of those who choose to engage in the "Math Wars" debates seem to be drawn from
this large subset of the mathematical community, and they believe that subject
matter expertise is the sole requirement for effective math teaching. Thus, they
decry reform books that focus a great deal on process, discovery, group
learning, mathematical communication, etc., and believe that a
mathematicallyknowledgeable engineer would be a better high school math
teacher than would be someone coming out of a school of education. Of course, in
any given instance, this might well be true, that would be on my view more a
matter of individual skills in teaching than due to the mathematical knowledge
alone.
 
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