Survey posted 2000-02-27 20:36 by Andy.

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The Evolution of Math Teaching

1960s:
A peasant sells a bag of potatoes for $10. His costs amount to 4/5 of his selling price. What is his profit?

1970s:
A farmer sells a bag of potatoes for $10. His costs amount to 4/5 of his selling price, that is, $8. What is his profit?

1970s (new math):
A farmer exchanges a set P of potatoes with set M of money. The cardinality of the set M is equal to 10, and each element
of M is worth $1. Draw ten big dots representing the elements of M. The set C of production costs is composed of two big
dots less than the set M. Represent C as a subset of M and give the answer to the question: What is the cardinality of the
set of profits?

1980s:
A farmer sells a bag of potatoes for $10. His production costs are $8, and his profit is $2. Underline the word "potatoes"
and discuss with your classmates.

1990s:
A farmer sells a bag of potatoes for $10. His or her production costs are 0.80 of his or her revenue. On your calculator,
graph revenue vs. costs. Run the POTATO program to determine the profit. Discuss the result with students in your group.
Write a brief essay that analyzes this example in the real world of economics.

(Anon: adapted from The American Mathematical Monthly, Vol. 101, No. 5, May 1994 (Reprinted by STan Kelly-Bootle in Unix Review, Oct 94)

ok.......

I am sure that was a very revelent comment and one that definetly needed to be made. When you come up with revelence of it, please post it. I am anxious to read it.

He was trying to illustrate the reliance on calculators that the current math curriculum seems to lean toward, if not push. (Or something like that.)

Your sarcasm fails here.

-meingts. everything that ever was, is, or will be. (sound familiar?)

Also he was pointing out the fact that all classes are being made mucheasier. this is largely a result of the self-esteem age. For some reasopn counsleors think that students are to dependent on what grade they get, so they order easier texts. If you haven't noticed, the average grade is most likely a B instead of a C 20 years ago. I prefer old texts because i leanr alot more that students using new textbooks. He was also pointing the fact that graphing calculators arent always necessary for problems, but most schools some how manage to add a graph to every problem to make studenst and tax-payers believe that buting graphing calcs are necessary for all math classes.

'Course of human progress staggers like a drunk,
Its steps are quick and heavy and its mind is slow and blunt.'
--Operation Ivy (Freeze Up)

LOL.

That was great....

Good thing I took set theory a couple years back...

Incindentally, on the calculator thing...

I'll be shortly getting a TI-89. However, I refuse to let the calculator think for me. I've been through that once before and it was *hell* getting my basic arithmetic skills back.

Man, the 70's were messed up!

This is an awfully broad and awkward question - if the standardized test was a completion of Algebra 1 exam or something, then such a calculator shouldn't be allowed. But for a Calculus exam or the like, it's implied that the test taker has algebra skills, so such a calculator would be okay.

I'm a freshman in college and I own a TI-89. I am allowed to use it on my Calculus homework, but I am only allowed to use a scientific calculator on quizzes and tests. We're expected to know how to do everything by hand except complex number crunching. It was the same in high school. We had tests that were either no calculators or had a no calculator section. If one was expected to know how to solve a problem by hand, but uses a calculator to solve said problem, he's only hurting himself.

But for calculus, you don't want to allow advanced CAS (like on the 89), which makes calc I very easy.

Of course - but the original question asked about calculators with only Algebra Systems.

They do allow the Ti-89s for the Calculus AP exam. In fact, it is an requirement to have a graphing calculator for the test. If they were to put Calculus on the SAT, then I'd agree they should be allowed.

So you disagree with the current state of the SATs where 89s are allowed?
Most of the people at school don't think you can use an 89 on the SAT, until I show them the webpage.
They should make you take a test - without a calc or with just with a scientific calc - before you are allowed to use it.

What I understand by "CAS" is something with symbolic manipulation, not simply a solver.

That is correct. What's your point?

I'm saying that the question asked about Algebra systems, so CAS calculators shouldn't be included in this discussion. I think a calculator that just has Algebra capabilities and not CAS should be allowed on calculus exams. I sure hope anyone taking Calculus knows basic Algebra.

Fool, the question is: "Do you think calculators with computer algebra systems should be allowed on standardized tests?" CAS is an acronym for "computer algebra system". The *whole* discussion should be about CAS.

BTW, I agree about allowing solvers but not symbolic manipulation on the tests.

It's not good to rely so much on CAS calculators. If for some reason you are unable
to use it due do external reasons, you are pretty much screwed. It's better to be
completely familiar with the subject rather than blindly trusting the calculator.

Calculators with CAS capabilities should be allowed and used in class, because it enables the students to get through more material in a one semester math course, without haveing to tediously do the basics over and over. But as for standardized testing, they are used to make sure you know the basics before going on to higher education, and if you use a calculator that does that for you, it kinda defeats the purpose.

Well, in the first place, standardized tests should give you real-world problems (like the lovely word problems we all love :^). Assuming that, you have to know how math "works" to be able to know what function of math to utilize, thereby assuaging the question of utilizing CAS on standardized tests.

<sarcsm>Noo, not word problems</sarcasm>

Anyway, I dislike *some* word problems but I can solve them. Still sometimes its nice to have a calculator to assist you with large numbers.

The question isn't whether of not to allow calculators to +,-,x,/ large numbers. The question is whether or not we should allow calculators than graph lines and solve equations.

Okay already! Stop acting so self richeous!