On Fri, 17 May 2013 21:41:06 +0100, Martin Brown
wrote:

On 17/05/2013 19:40, Jim Thompson wrote:
I'm fighting the school system with, now, the 5th granddaughter, 6th
Grade.

Last week they were peddling how to cut corners out of a piece of
cardboard to form a box with the maximum volume, with no established
skill set.... "guess" your way to the solution :-(

To be fair to the teacher - giving them two pins, a length of string and
the challenge to construct an ellipse is actually a *very* good test of
innate mathematical intuition.

That I'm OK with.


I think the reasoning for the biggest cardboard box one is similar.

But you can't "reason" your way to a numerical answer. You can reason
that the flat piece of cardboard has no volume, and that cutting away
all the cardboard yields no volume. But you have to plot it to find
the maximum.


You can pick out the geniuses more easily with tests that are beyond the
reach of linear progression from what has been actually taught.

Another really good test is:

given a^2 + b^2 = c^2 where a,b,c are integers

can you construct A^2 + B^2 = 2c^2 and state A, B

You can either see the answer to this instantly or not at all.
(this latter is more applicable to university entrance for maths)

As soon as you state "integers" it becomes a guessing game. I "guess"
the engineer in me frowns on guessing.

I took the exam and was admitted to Mensa (at age 30), but most of the
exam questions were guessing.


This week they suddenly jumped to Algebra, simultaneous equations,
without even any single variable background.

Clearly madness if it is as you reported it.

Yep. I've already ordered several of the recommended books to make
sure she has a solid background in Algebra.


I got into trouble at school once by framing quadratic equations as
untaught non-linear two variable problems. I got the right answer but
ignored the teachers hint how to do it. He was not amused.

I've "unamused" a number of teachers along the way.


And she says her teacher is already using the word "Calculus". I
guess that's the leftist way anymore, speaking the words makes you
expert :-(

No idea what 6th grade US is so cannot comment.
In my day basic calculus was taught about age 14 ish. We did a lot of
spherical trig first for navigating around the empire on great circles.

"In my day" we had Algebra, Plane Geometry, Trigonometry and Solid
Geometry in High School. My first exposure to Calculus was my
Freshman year at M.I.T. By then it was easy for me to understand. I
ended up taking 6 semesters of Calculus... all the way up to Tensors.

Modern "education" seems to think quantity is better than quality...
just because you've taken a course labeled "Calculus" makes everything
all marvelous.


It would be a sad day indeed if a teacher of mathematics did not fully
understand both integral and differential calculus. I'd expect most of
them to understand the finesse of calculus of variations as well.

My first year undergraduate maths for physicists course was something of
a notorious baptism of fire starting as it did with differential vector
calculus and assuming everything that went before it. The pure
mathematicians meanwhile spent most of that term proving that 0 != 1.

I truanted my last year of maths classes at high school as complete
waste of my time.

No wonder US students rank so low, worldwide, in math (and science).

Fortunately the school year is almost over, and she'll be with us for
a month in July.

So my question...

Can anyone recommend an available Algebra book that instructs in the
old fashioned sequential way... lots of one variable word problems
first, then go on to more advanced topics?

I'll become teacher of the month ;-)

The compendium of Lewis Carroll's works and Martin Gardener books are
much more fun to learn from and far more educational. Maybe just a bit
beyond the reach of your ward.

She's up to it. The reason she's visiting us this summer is that we
pay her way every year to Phoenix Valley Youth Theater Summer Camp.
She's been three years now... and has managed to be the star in their
final performance every time. She's quite the thespian and she's an
honor student... in spite of my fuming over the teaching methods.

Another really tricky one is construct a
triangle given only two sides and the radius of the inscribed circle
using ruler and compasses only. Algebra needed to work out what to do
unless you really are true genius level at physical geometry intuition.

I'm a master of those games... I still remember how to construct a
pentagon with compass and straight-edge ;-)


(I taught math back in 1964-65 to disadvantaged youth (aka "thugs")
from South Phoenix with a very high success rate :-)

...Jim Thompson

Make it fun and you don't have to teach it.

Certainly! Make it fun, and you don't ever have to "work". I've
never worked a day in my life ;-)


Why is this cross posted to alt.binaries.*.* ?

It's not. Just to circuit groups.

...Jim Thompson
--
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