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Algebra
Posted:
Jun 18, 2001 11:11 PM


Deemphasized 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 yearlong AP calculus classes at Ursuline Academy (both in/near Cincinnati). The Ursuline students will have TI83's I'm told. Expect a mix at RWC, I'm told.
The TI83 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. "Singleargument 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 "TI83 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 TI83 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 seencalculus 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 TI83 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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