|
|
|
| Authored by: PJ on Tuesday, April 16 2013 @ 10:26 PM EDT |
I wonder if it's worth while to contact the publisher
and express concerns?[ Reply to This | Parent | # ]
|
| |
| Authored by: Anonymous on Tuesday, April 16 2013 @ 11:05 PM EDT |
To use an integral table, or a book of integral tables, after having actually
learned the subject of calculus is one thing. When I say that all of the
calculus texts with those tables in them ought to go in the fire, the remark is
not directed to those who have completed the course and gone on to other things,
especially in other fields. There are many aspects to growing up, after all, and
we all agree that there are topics which are suitable for adults but not for the
young.
Nevertheless, the context of my remarks was with regard to learning calculus,
specifically in the calculus course. In this context, I will stick to what I
said. And so here is some further explanation.
To use those tables of integrals while learning the subject of calculus is very
very very bad. It is the short cut which many students want, or think that they
want. But it is nothing more nor less than learning to walk on crutches. Such a
start leads inevitably to the situation which is what actually exists all around
us -- that too many of the students learn for the test and not in order to
master the subject. Then when they are in the next course and they need to *use*
what they just learned in the previous one, they just look blankly at the
professor and say, "Sir, it has been a long time since we studied
that."
Here are a couple more examples of what is happening. The problem is not
confined to calculus, but in fact long precedes it:
Too many students who are taking even a sophomore-level differential equations
course cannot do algebra. In particular, they can't solve a quadratic equation
and get the right answer. I trust you are aware how relevant this is in a
differential equations course.
Too many students are fundamentally illiterate in the subject of trigonometry.
The above two examples are items which every high school graduate is supposed to
know, and in particular the students who enter the university where I work are
supposed to know those things and have previous academic credit therefor. But
too many of them did not retain the knowledge which they have allegedly studied
and learned. Why?
I humbly submit that there is in fact only one way actually to learn
mathematics. Learn the basics, and learn how all else follows from those basics.
If you forget something which you learned recently, make yourself go back and
derive it. Then you will tend to forget less often. Moreover, there is even a
shorter list of those things that one actually needs to learn. Things get much
easier in the long run. What is needed is practice. We would not expect anyone
to become a musician or an athlete without practice. How come that society
expects people cam just have knowledge of some "math facts" poured
into their heads and then be able to use it?
[ Reply to This | Parent | # ]
|
- Re: I have not tutored, but I teach. - Authored by: Anonymous on Wednesday, April 17 2013 @ 01:11 AM EDT
- 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
- Re: I have not tutored, but I teach. - Authored by: JamesK on Wednesday, April 17 2013 @ 11:43 AM EDT
- Math Skills Always Lag Current Course - Authored by: Anonymous on Wednesday, April 17 2013 @ 01:02 PM EDT
| |
| Authored by: Anonymous on Wednesday, April 17 2013 @ 09:03 AM EDT |
Is this guy for real?
one does not learn how to swim from the blackboard alone ,
- one must also jump into the swimming pool, sometime ![ Reply to This | Parent | # ]
|
| |
| Authored by: JamesK on Wednesday, April 17 2013 @ 01:37 PM EDT |
{
Students need to learn how to problem solve
}
Quite so. They have to know enough to understand if the result is valid. While
I often use a calculator, I may also run through the calculation in my head. If
I'm not in the same ballpark as the calculator, I made a mistake somewhere.
Back in the days of slide rules, this was essential, so that you didn't
accidentally lose track of decimal places or refer to the wrong scale etc.
Those clerks I mentioned in another post couldn't recognize their errors,
because they didn't understand what they were doing.
---
The following program contains immature subject matter.
Viewer discretion is advised.[ Reply to This | Parent | # ]
|
|
|
|
|
