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[Phys-L] Re: student mathematical capabilities



Hi all-
Thanks to all who responded to my suggestion. I should have
anticipated the first question: what standards exist?
The NCTM (Nat. Council Teachers of Math, www.nctm.org) published
in 2000 <Principles and Standards for School Mathematics>. My impression
is that most elementary and secondary math teachers are familiar with the
book, and most administrators give it lip service at the very least.
____________________________________________________________________
The algebra standard for grades pre-K through 12 reads (as to goals):
Understand patterns, relations, and functions;
Represent and analyze mathematical situations and structures using
algebraic symbols;
Use mathematical models to represent and understand quantitative
relationships;
Analyze change in various contexts.
-------------------------------------------------------------------
The next 343 pages of the book purport to flesh out these
principles.
I will let this information soak in before I comment on it,
although I invite comments.
The topics listed for pre-K through Grade 12 standards are:
Numbers and Operations
Algebra
Geometry
Measurement
Data Analysis and Probability
Problem Solving
Reasoning and Proof
Communication
Connections
Representation

On the topic of problem solving, the authors write: "Effective
problem solvers plan frequently." (on p.54)
_____________________________________________________________________
I have taught introductory calculus at a community college (as a
result of that experience I am writing my own text). I have taught
college Junior-level physics (statics) to students who have had three
semesters of calculus. In both cases I found myself confronted with
students who couldn't do algebra. Example: divide a-cubed + b-cubed by
a+b (presented symbollically). Answer: a-cubed/a + b-cubed/b =
a^{2} + b^{2}.
I conclude that our mathematics peers are passing students through
calculus courses without challenging the students' algebra skills.
Regards,
Jack





On Mon, 19 Sep 2005, Hugh Haskell wrote:

At 13:54 -0500 9/19/05, Jack Uretsky wrote:

I suggest the latter, the first immediate goal being a statement
from the AAPT on the teaching of math.
Our clout (a local Chicago word) out to be great. The ultimate
sanction being the takeover of math preparation of students who are
interested in careers in the Physical and Biological sciences.
My suggestion for a starting point is a statement of proposed
outcomes, at the end of grade 12, in the subjects of algebra, geometry and
pre-calculus - without limiting ourselves to bureaucratic definitions of
those topics.

Sounds like a great idea to me. I would suggest that any such
statement include the need for students coming out of high school
math (which should just be reinforcement of the same goals set for
elementary and middle school) to have an understanding of the role of
units with numbers, thought (or more commonly, "story") problems--how
to take a verbal description of a situation and translate it into the
necessary equations--, graphing real data (including the idea that in
real data, "outliers" are not necessarily errors, but may indicate
something new) and interpreting the graphs in physical terms
including the understanding of the physical significance of some
common mathematical functions (trig, inverse and direct square,
exponential, etc.), scaling laws, and finally approximate
arithmetic--estimating answers to about an order of magnitude.

They don't have to be expert at these things, but they need to
appreciate their value and not be surprised when they see their
professors in college apply these ideas routinely in class.

Hugh
--

Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

(919) 467-7610

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