Calculus Or Algebra -http://www.freemathhelp.com/forum/threads/97620-Calculus-practic

[HallsofIvy]

How can you say what the person who set the problem intended? As I said before, this problem can be done without any Calculus at all.

 

[Steven G]

How can you say what the person who set the problem intended? As I said before, this problem can be done without any Calculus at all.

The problem comes from the section in a Calculus book entitled Max/Min word problem. Many (MANY) times problems that appear to come from that section, but can be done differently, are put in as an exercise. In this case the problem can be done using Calculus or Algebra.

In my opinion, which method to use is up to the student. If the student is weak in Calculus then they should do the homework problem (not the exam problem) using Calculus to practice max/min problems.

 

[lookagain]

In my opinion, which method to use is up to the student.

If it's a calculus course, and it's an exam, then the method won't be up to the student.

The student will use derivatives (as in calculus), not algebra, as the main tool.

 

[Steven G]

If it's a calculus course, and it's an exam, then the method won't be up to the student.

The student will use derivatives (as in calculus), not algebra, as the main tool.

That depends on the wording of the problem. If it just says to maximize what turns out to be a quadratic equation then Algebra should work.

If 4th grade in the States one is taught that if 12/3 = 4, then 12/4 = 3 as well. Now in Algebra, if you have 12/x = 3 then it is a disaster how it is taught to solve this problem. Personally I just say 12/3 = x, so x=4. This is fine thinking in my mind. I do not think a teacher should ever not allow a student to think. I do agree however that for some problems a teacher can state to solve by using the quotient or by using Calculus.

I recall when I was in graduate school a disagreement I had with my instructor in Linear Algebra Professor. I was asked to show that two (or maybe three) vectors were dependent. I always always spend about 2-3 second to see if I can find a linear combination of the vectors that yield the zero vector. Well on this particular homework problem I saw the combination without doing any work and he marked it wrong. I also recall storming out of his office promising not to ever think again. Later that day he approached me and apologized for marking the problem wrong and encouraged me to see if I could find the solution in my head--another words with a different method. Students should be allowed to use any method they want.

I recall as an undergraduate student having my physics professor always saying when he was going over an exam he had given us that a few of you (which always meant just me) did the problem differently. I thought like a strong math student and not like a physics major. Should I have been marked wrong? It was because of comments like that--saying that I WAS correct in how I solved the problems - and my knowing that it was solved like a math major was the main reason I chose to study math instead of physics. Had my physics teacher marked me wrong I might not have seen that my love was math over physics until later on, if ever.

Let the student think any way they want, as long as they think and their thinking is mathematically sound.

 

[stapel]

If it's a calculus course, and it's an exam, then the method won't be up to the student.

The student will use derivatives (as in calculus), not algebra, as the main tool.

True enough. However, the student seemed to indicate that s/he had no idea even how to get started. Hence, the reference to the algebra that s/he should already know. Once the student sees this connection, the exercise becomes much less onerous.

 

[lookagain]

http://www.freemathhelp.com/forum/threads/97675-Calculus-Or-Algebra-http-www-freemath

That depends on the wording of the problem. If it just says to maximize
what turns out to be a quadratic equation then Algebra should work.

No, it's not about what "should work." The student is in a calculus course, and the student is
required to use the derivative to find the minimum or maximum. That is part of the
requirement of solving this problem in this calculus course. Stating that it can be done other
ways is changing the subject.

-- - -- -- --------------------------------- -- - - - - ----------------------------------- - - - - - - - --

 

[Steven G]

Boy oh boy.......:-(

I agree.

 

[Steven G]

No, it's not about what "should work." The student is in a calculus course, and the student is
required to use the derivative to find the minimum or maximum. That is part of the
requirement of solving this problem in this calculus course. Stating that it can be done other
ways is changing the subject.

-- - -- -- --------------------------------- -- - - - - ----------------------------------- - - - - - - - --

I do not think that we will agree on this topic but I do want to point out one think. Even when you use Calculus in my opinion you still have to add, divide, etc. Is this not allowed, after all this is calculus.