Re: need help with homework

On Sep 24, 6:56 am, rem6...@xxxxxxxxx (Robert Maas, see http://tinyurl.com/uh3t)
wrote:
From: Scena <metarell...@xxxxxxxxx>
Bryana says that the teacher was teaching about inverses of functions


and then that night for homework, she gave the students a work***
with problems that she had NOT taught the students how to do.

That's a strange way of putting it. For a complete idiot (per mathematics)
who needs to learn how to balance a checkbook or run a cash register
without any understanding of the arithmetic involved, perhaps
teaching by drill how to mechanically solve a fixed set of types of
"problems" might suffice. But that's not math, that's job training.
So why did the teacher *ever* teach the students how to solve
specific problems, as you seem to imply? Maybe you worded it wrong.
Maybe the students were coached how to figure out themselves how to
solve various kinds of problems, being spoon-fed exactly the needed
clues at precisely the appropriate time in the process of solving
the problem-of-the-day? And of course you mean "type of problems"
instead of "problems", right?


Actually, Robert, the majority of the class did not understand the
problem(s) given on this particular work***. Infact, the teacher
realized after that, that she needed to give a quick review of
geometry. Bryana took geometry three years ago! So.....it wasn't
just Bryana that didn't "get it".





So first I made sure she understood all the really basic ideas
(part in my listing of questions earlier, part I omitted and hinted
at in the above paragraph and should directly address later), and
after I'm sure all the prerequisites are fresh in her mind, then I
can start teasing her to figure out how to put them together
(perhaps Polya-esque) toward the full solution to the problem.


Bryana wasn't too sure about the "circuiting" concepts that you were
trying to explain However, she does understand that the "problem"
given by the teacher was to be answered with a hypothetical equation,
rather than with concrete numbers, which is what she learned to do in
geometry.


I didn't have time to finish this reply Sunday night, so I'm
finishing Monday morning. I'll check to see if you posted a
followup telling how she did with answering my questions Sunday
afternoon ... nope, nothing posted by you since your Saturday reply
to somebody else where you said "The course does have a textbook
but Bryana says that those problems weren't in the textbook. ..."


Oh, I'm sorry! I thought you just wanted me to go over those
questions with Bryana, not type them out here. Bryana is studying for
a math exam tonight, but I will have her answer your questions when
she gets a chance.


Note there's a good reason for the teacher to include problems that
aren't in the textbook: Because some students **CHEAT** their
entire way through high school by purchasing the teacher's edition
of the textbooks which contains answers to all the problems in the
textbook. (Sometimes the teacher's edition has answers to only the
odd-numbered problems, but then somebody separately publishes and
sells answers to *ALL* the rest of the problems. You may have seen
threads in the newsgroup looking for various solution books?)

Yeah, I did see that. Some idiot going to USC wanted a solution
manual. What's the point in that? Why even bother going to school if
you don't want to learn. A degree is just a piece of paper.


These
not-in-book questions are the only way to easily detect and
eliminate such cheating. Also I rather like this particular problem
because it combines two standard concepts (compounding functions
and cross-circuiting one value for two uses) and two standard
formulas (area of circle and volume of general cylinder). The
teacher may be a really good teacher who likes this kind of problem
but discovered that the book doesn't have any problem like this,
and so including it in an extra work *** would be valuable.


Bryana feels that she is a good teacher but moves a little too fast.


By the way, it occurs to me now that since this material is really
elementary, yet the particular problem is interesting in its
combination of several elementary concepts/formulas, *you* the
parent might take this opportunity to learn the material too.
(But if you succeed, please don't *TELL* your daughter how to solve
the problem, destroying her chance to be coached toward figuring
out the specific solution herself.) For *you*, I have these very
elementary geometry questions. These are "diagnostic", i.e. to
determine your level of prior knowledge so that I know which stuff
you already know and which stuff I need to teach you before proceeding:
- Do you know the formula for area of a rectangle? (Hint: Count rows,columns.)

Base X Height (b x h)



- Do you know the formula for area of a triangle? (Hint: Decompose rectangle.)


1/2 b(h)


- Do you know the formula for circumference of circle? (Hint: Definition!!)

2 pi x r


- I hope you know the relation between radius and diameter!!

radius is half of the diameter.


- Do you know how to use the triangle-area formula together with the
circumference formula to approximate the area of a circle, first
expressed as function of diameter, then converted to function of
radius where it becomes simpler and easier to remember?


no.


(I'm assuming you don't remember the formula for area of a circle,
or maybe you already looked it up and/or memorized it but it's a
mystery why the formula is like that and you really should learn
the rationale for it if you didn't learn that already.)

Don't know this either.


- Extra credit, can you guess who first proved somewhat rigorously
that the weird/sloppy pseudo-triangle-approximation for area of
circle in fact gave *exactly* the correct answer?

No.


Later, after you've informally derived the area of circle formula
yourself, I'll coach you toward the formula for area of trapezoid,
and then the general formula for volume of cylinder (even a
trapezoidal cylinder with non-circular weird-shaped base!).

So I'm awaiting back from you:
- Update on how coaching your daughter with my earlier message went
Sunday afternoon (her answers to my questions, and any additional
remarks that came up).
- Any remarks you have in response to the main part of my reply above.
- Your answers to my questions in the previous questions, me
coaching you this time!

Ok, sir! Bryana will get back to you asap.


No, I'm not going to try to coach you to catch up with *all* of
high-school math, after you said "the highest that I sent [sic "went"]
in math was Algebra I!" But once in a while there's something
really easy to understand and fun to derive, and this is one of
those cases where you *can* get a feel for what's going on with
this specific problem and this kind of problem more generally.
Although you apparently didn't take a formal geometry class, I
presume you have picked up some general concepts, such as counting
objects in retangular arrays (which is actually the *definition* of
multiplication of integers in non-rigorous math) and the analagous
formula for area of rectangle, and the basic concept of circles
with radius diameter and circumference, right? That's all the
geometry you need for this problem and for the more basic questions
I asked you, so I'm sure you can work it out with my coaching.


Last math class I took was college level Algebra 1 in 1997. I did
pretty good (B+), but I had to study like crazy. We did go over some
basic geometry in one chapter.

.

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