Re: Prolems in Mathematics Education

On Aug 29, 4:16?pm, hru...@xxxxxxxxxxxxxxxxxxxx (Herman Rubin) wrote:
In article <1188415451.246010.56...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,

porky_pig...@xxxxxxxxxxx <porky_pig...@xxxxxxxxxxx> wrote:
On Aug 28, 10:44 pm, Tim Norfolk <timsn...@xxxxxxx> wrote:

<> 1. A significant number of freshmen come to us with high GPA's,
<> including in
<> mathematics courses, and claim to have taken a calculus course in high
<> school,
<> yet place into our Intermediate Algebra (basically an Algebra I
<> course), on
<> several measures, including ACT, SAT, COMPASS test, and our old
<> department
<> placement test.





Yes, this is like a chain reaction. First it's a school which says
that kids don't really need to know math (or give them the inflated
grades so they can graduate), so the colleges are on the receiving
end. Then it's a college which says that students don't really need to
know math, unless they are doing some engineering or like. What's
next? Students engineers who don't really need to know math? Yes, I
already saw something of that kind.
As far as school cirriculum, I would have it consolidated with the
emphasis on solid high-school algebra, geometry and trigonometry. With
that type of background, you can start the college right with Calculus
1. That was in my case, by the way. Pre-calculus is sort of a 'grey
area'. You can learn this staff as you go along learning Calculus. I
think in case of exceptionally bright students, they probably can
attend pre-calculus, so in college they start with something like
'Honor Calculus' or 'Calculus with Theory', like they have in few
schools (normally, using Apostol's Calculus as a textbook). Other than
that, the path 'Solid algebra, geometry, trigonometry in school ->
Calculus in College' is the most practical. It's a shame nowdays
colleges have to waste their time teaching the students what they were
supposed to learn in high school (and never did).

Make it a GOOD algebra course, using many variables
from the beginning, and a GOOD geometry course, the
old "Euclid" course with proofs, and stress understanding,
not quick arithmetic. Also, induction needs to be
included somewhere; it is not difficult if the teacher
understands it, and the students have been allowed to
think, rather than use algorithms to get "right answers".

BTW, any of these courses can be taught, to those who
can understand them, not later than "middle school".

--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hru...@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558- Hide quoted text -

- Show quoted text -

Herman;

I actually had you in mind when I wrote this last night.

For the following, I wish I had the apocryphal third hand of the
economists.

On one hand, I started 6th grade in the UK in 1968 at a selective
grammar school for one year, then 2.5 years at a school for military
kids in Cyprus, 0.5 years off school in Germany (where I worked my way
through a couple of calculus books from the library), and then 1.5
more years at a selective grammar school back in the UK, terminating
in the 'O'-levels.

I can only suppose that the curriculum was similar throughout Britain
at that time, although they have gutted it all since I left, and the
system now under-performs the US in most studies.

6th grade was simple set theory and algebra.
7th and 8th grades were algebra/trig/geometry, including constructions
and proofs AND induction!
9th and 10th grades were calculus I and analytical geometry.

However, probably less than 15% of students passed 'O'-level maths,
and only 3-5% went on to higher education.

On the other hand, I have taught mathematics and physics for 29 years,
as well as tutoring both, teaching boy scouts, and teaching martial
arts, to students from age 5 to 75.

In that time, I have had about 4,000 students. While not common
(because of the placement procedures that we have tried to perfect), I
have had a small handful of students who couldn't "get it", no matter
what either of us did. Those are the ones that I lose sleep over. I
feel for them, but feel an obligation for the veracity of the
certification that I give. This small number has come at all levels,
from remediation to graduate work in analysis. My personal conclusion
is that there is a spectrum of mathematical ability, due to genetics
or early conditioning (I favour the former, but am biased, as I breed
animals as a hobby). If correct, this means that each of us has a
mathematical "Peter Principle Plateau", beyond which we cannot go. My
personal one was the humility of working on the Riemann Hypothesis
with Richard Varga (with some success), and on the Collatz Conjecture
(with none).

On the third hand, most students who have failed in my classes have
not put forth the effort required. I am convinced that 95% of the US
population could learn more mathematics, were it not cool to be "bad
at math".

My fundamental thesis is that the leadership of the US mathematical
community will not get listened to, as the politicians and pundits
only defer on educational policy (if at all) to colleges of education,
who have the peculiar and fanatical philosophical view that one can
train a teacher without regard to subject matter.

However, a nationally-recognized test in College Algebra, and another
in PreCalculus, would at least get some reasonable standards and
advantages for the students and teachers who did work hard and care
about learning.

.

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