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Authored by: Anonymous on Wednesday, April 17 2013 @ 01:11 AM EDT |
There is a big difference between those who plan to make mathematics the
cornerstone of their life, and those who have the need to use mathematics. For
the former, it's extremely important to understand how to derive mathematics,
because they will eventually be working with mathematics for which no one has
already solved the problem. But for the later, which is the majority of people
taking mathematics, learning how to use Wolfram Alpha is a more productive use
of their time. That doesn't mean there is no problem solving, as knowing the
right question is more important than ever, but knowing how to personally solve
the question has become less important, at least once one gets out of college.
Just because I learned programming by reading language specs and having to
memorize function arguments does not mean that my children should learn this
way. Search engines are wonderful things, and there is no way I could continue
to do my job without them. Students are expected to know more and more
information, but still finish high school in 4 years and college in about 4
years. But, as long as we keep teaching the same material in the same way,
imparting knowledge will continue to be as slow as ever. It's almost like the
hazing done when joining a sports team. All the team members were hazed when
they joined, so all the new members need to be hazed. That's the way we teach
college mathematics. An engineering student has to take 4 courses of calculus
taught the old fashioned way, because that's how everyone else was taught.
Additionally, since the physics teachers don't want online tools used for their
final, everyone has to learn calculus the hard way, since they will have to do
it by hand on the physics final.
We need to move curriculum towards being able to understand the problem, and to
formulate the problem in a way so that tools can be used to solve the problem.
This still means knowing calculus for certain as needed, but being able to get
the final result without a computer shouldn't be required. So, the students
should be able to calculate the speed at which a shadow gets longer as a person
walks away from a light using computer assistance. But, is it important to know
how to set up the problem, or just that one can find out how to do so by
searching for the term: rate of change shadow length?
[ Reply to This | Parent | # ]
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- Re: I have not tutored, but I teach. - Authored by: mpellatt on Wednesday, April 17 2013 @ 07:12 AM EDT
- Re: I have not tutored, but I teach. - Authored by: lnuss on Wednesday, April 17 2013 @ 07:47 AM EDT
- Re: I have not tutored, but I teach. - Authored by: JamesK on Wednesday, April 17 2013 @ 11:49 AM EDT
- Amen. - Authored by: Anonymous on Wednesday, April 17 2013 @ 12:50 PM EDT
- But, is it important to know how to set up the problem, or just that one can ... search - Authored by: Anonymous on Wednesday, April 17 2013 @ 01:26 PM EDT
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Authored by: JamesK on Wednesday, April 17 2013 @ 11:43 AM EDT |
{
In particular, they can't solve a quadratic equation and get the right answer.
}
I used to enjoy doing quadratic equations. However, it's been about a quarter
century since the last time I did one, so I may have forgotten a few things.
However, I certainly agree with the general lack of education in so many areas
these days. For example, I have a friend who has a PhD in psychology, but she
has extremely poor knowledge of history or even current events. Then we get to
store clerks who can't even do simple addition & subtraction...
---
The following program contains immature subject matter.
Viewer discretion is advised.[ Reply to This | Parent | # ]
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Authored by: Anonymous on Wednesday, April 17 2013 @ 01:02 PM EDT |
When you are in a math series, your ability to do math correctly and well is
always one course level behind the one you are in. Your arithmetic gets good in
algebra. Your algebra gets good in trig. Your trig gets good in calculus.
Your calculus gets good in DiffEq. It goes on and on from there.
The reason is the difference between LEARNING a skill and USING a skill. When
the skill is required for solving a higher order problem, that is where you
really get the reps down to own the earlier skill.
As to tables, I learned, and understand, the solution of the various integrals.
Many require memorizing Well Known Tricks (tm). If I am going to memorize
something, it will be the table. (I am a recent engineer graduate) If I need
the WKT, I can find it on the net, (They seldom appear in any textbook). What
may be a drawback to initial learning is usually the greatest value as a
reference. At $200+ for a book, I want it around for later use! (I refer to my
textbooks often. They are more familiar to me than a website. I know exactly
what I am looking for, and usually, where it is in the book)
-- Alma[ Reply to This | Parent | # ]
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