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Re: Rules and Formulas  Supplied or Not?
Posted:
May 29, 1995 1:32 PM


Rex Boggs writes,
>Should we supply on the exam paper such things as >sin^2 + cos^2 = 1, (ab)^n = a^n b^n, log(ab) = log a + log b, the chain >rule for differential calculus, etc,, and concentrate on whether students >can apply the correct rule correctly. Or are these part of the body of >mathematical knowledge that a good student should have at their fingertips? > >In Queensland, we have external exams for mature age learners. The Maths in >Society exam has the formulas supplied, the Maths B and Maths C exams >(roughly equivalent to Algebra II, and Calculus and Analytical Geometry) >don't. So even within our system there appears to be differing attitudes.
I am not a teacher at this level, but I have had a number of semitechnical jobs and hobbies where algebraic manipulation was necessary. If I did not know the formulas you give, I would be in sad shape. Or rather, I would, through practice, quickly learn them. I would hope that the course they took gave them enough practice so you wouldn't have to give them formulas like this. If they don't know that (ab)^n = a^n b^n or log(ab) = log a + log b, then how can you say they really know exponents or logarithms?
In the case of sin^2 + cos^2 = 1, this one is pretty basic to doing any kind of trig calculations, but for trig identities in general, there are so many of them and they are so interrelated that no one can expect to know them all. Maybe give them the standard identities, but problems that depend not on those, but identities that can be derived from them.
In the case of the chain rule, and in general, the answer depends on what you want them to know when the course is over. If the Maths in Society course  like many similarlynamed courses in the USA  is intended for people who are going no further with math, giving them the formulas may be appropriate. If you are training scientists and engineers, they obviously need to know the chain rule after their first calculus course; they will need it soon and often.
Amos Newcombe  Voice (914) 3390582  The world's biggest fool CyberMath  Fax (914) 3312697  can say the sun is shining, Manor Lake #2  Email: amos@cerf.net,  but that doesn't make it Kingston NY 12401  76324.3313@compuserve.com  dark out.  Robert Pirsig



