Date: Jul 23, 2001 8:48 AM
Subject: Re: List of 'good' geometry textbooks
Ah, it seems like I have created a little stir, due to my sloppiness
with words! Hopefully this will clarify some things, but maybe not!!
> I just wanted to day how saddened I am by the proposed constraints
> within which a geometry book should be 'good'.
Sorry for the term 'good'! I deliberately put this in quotes to show
that this was a subjective opinion. I am looking for a book that
stresses formal proof so this is 'good' for me. Another teacher with a
different approach would want a different type of book. I am in no way
saying that other approaches are bad. In fact, I think that it is a
wonderful that they're many approaches to choose from because
different teachers teach in different ways. What works for one teacher
might not work for another. In no way am I saying that this is a
definitive list or the only good books. I am just trying to be helpful
to others that are looking for what I seek. I can debate what the
right teaching method is but ultimately it is in the results that I
get with the students that matters (more on this below). I may find
that a textbook has great success in my class, but the same text falls
flat in another. The proof is in the pudding! (pun intended)
> Formal proof IS a piece of mathematics - but only a piece.
Yes this is quite true. There is some proof in the algebra I teach
(the Students explore and derive everything in class themselves) but I
wanted to have proof presented in a formal mathematical way and in my
opinion geometry is a good place to do this (less abstract than
building algebra from the ground up)
> I hate to see a classroom that tastes like a medicine cabinet rather
> that the life of mathematics.
You should see my class. I am teaching an algebra 1 class for ages
11-13 where we meet once a week for 3 hours and the students are
having a great time. One mother told me a story where her son told her
about a nightmare he had where in his bad dream my math class had been
replaced by soccer! The parents are ecstatic that math can be so much
fun. Half of the students are doing extra homework just because they
love it (and the regular load of homework is around 160-200 problems a
week and we are using a college text). I was skeptical that students
between the ages of 11-13 could pay attention for 3 hours, but the
energy in the class is fantastic and they are able to stay on top of
it. We have a lot of fun. For example, we were discussing Cantors
proof of why the rational numbers are the same order of infinity as
the positive integers and the students were able to derive a symbolic
formula of how to calculate the integer pairing for any square in the
table. And they did this in about 30 minuets! Wow I was impressed. And
I could go on and on and on, I am so proud of them. (By the way, this
is not a special upper track math class, I have a wide range of
student's). I am using a dreadfully boring drill and kill college
algebra book that works perfectly with my style.
>It is particularly sad when a rich
> and important subject like geometry is pushed into a box of
> formal proof. Probably means very little transformations
> (probably the key part of applications of geometry) and very
> little 3-D geometry - at least until the students have been
> so saturated in plane games that they have lost touch with
> the world they live in.
A book is a springboard for a teacher like me. My whole class is
taught using the Socratic method so the students are doing a lot of
thinking out of the box all the time. We are constantly doing puzzlers
and brainteaser that are woven into class. We also do physics
experiments, etc. My point is that I start with the book and do a lot
of enrichment way beyond the scope of the book which would be 3-D
geometry, etc. I could go on about my philosophy of teaching, but what
matters to me is what works for me as a teacher and produces results.
When I say results, I mean that I am expanding the students minds to
think creatively out of the box visa vie math, have a firm
understanding of why things work they way they do (so they are not
just memorizing rules), they are getting excited about math and be
prepared to do problems (lets say problems from a physics textbook). I
have found that the exploratory textbooks that for example Key
Curriculum Press publishes, don't work for me and therefore don't work
in my classroom. But when I use the 'medicine cabinet' books I get
results as defined above. Remember what works for me might not work
for the next teacher. Teaching is an art, not a science and there is
room form many different and divergent approaches to math. And I
firmly believe that there is no one right approach.
You might ask, why don't you use an exploratory book since your class
is in this direction. To answer this question lets take algebra as an
example. What I have found out for me is that the old drill and kill
approach has merit and I want the students to go home and drill. The
exploratory books I have reviewed and used don't do enough drill for
me. By the way, I supplement their homework with explorations.
Remember, the proof is in the pudding, and if I had a class of bored
students or students that were not learning I would change in a
heartbeat. The parents are paying me to teach their children and if
this was a mediocre or average class they would leave, I assure you!
Diversity of opinion is what makes the world a great place. The same
is true of teachers and teaching methods.
PS: missed 2 suggested books
A Course in Geometry: Plane & Solid" by Weeks and Adkins.
Books by Welchons and Krickenberger