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Algebra
Posted:
Jun 18, 2001 11:11 PM
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De-emphasized or not, algebra is still a stumbling block for calculus
students. And lack of understanding of the order of operations is a big part
of it.
I am about to teach two summer courses at Raymond Walters College, after
which I will teach two year-long AP calculus classes at Ursuline Academy
(both in/near Cincinnati). The Ursuline students will have TI-83's I'm told.
Expect a mix at RWC, I'm told.
The TI-83 Guidebook states, in so many words, that the order of operations
is:
1. postfix operators (the book calls these "functions")
2. powers (and roots)
3. "Single-argument functions that precede the argument (e.g., the square
root symbol, sin, log)." (I think they include all prefix operators in here.
It isn't clear.)
4. Permutations (nPr) and combinations (nCr) (special infix operators on
most TI calculators)
...and then what you'd expect.
As a programming teacher, I always found "unary minus" in books at "TI-83
level 3", after exponentiation and before mult & div. Fine.
But I think TI's order (1 2 3 4 above) is WRONG, because, if (in degree
mode) I compute SIN(30)^2, I get .25.
I think the TI-83 CLEARLY does powers BEFORE "...functions that precede the
argument..." I think the list above is ordered 1 3 2 4, not 1 2 3 4.
Meanwhile, Derive 5.0's stated operation precedence just lists expo; * or /;
+ or -. No placement of unary minus. No functions. But when I do
SIN(pi/6)^2, I get .25 and when I do -3^2, I get -9. Fine.
But I am aware of NO math book (none *I*'ve ever seen--calculus or
otherwise) that clearly tells students where functions are evaluated.
All of which has made me write this venerable list for help.
First, what am I missing? Why keep something as important as the complete
order of operations a secret? Are our students THAT smart that they will
just figure it out?
Second, am I missing something with respect to the TI-83 Guidebook? What, in
the 1 2 3 4 list above, makes me know that, in evaluating SIN(30)^2,
squaring comes AFTER taking the sine? Based on what I read, I expected to
get 0 (sine of 900).
And many/most/all algebra I texts state that FIRST we do PARENTHESES; THEN
we do expo; * or /; + or -. But aren't parentheses an AFTERTHOUGHT?Shouldn't
we state the order of operations FULLY, THEN say, Oh, yeah, you can override
this order by using parentheses?
Dave Slomer
David.Slomer@uc.edu is an alias
for slomerdd@ucmail.uc.edu
Web page:
http://homepages.uc.edu/~slomerdd/
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