Stitching away

ellice wrote:

Just what I was going to say. Even in subjects like geometry or trig, they
can do more with a calulator. The bigger problem is the kids that don't
understand the basics of algebra, or actual arithmetic. Even when I went to
school, I had to have a slide rule in high school for calculus and AP
Physics & Chem. Don't need a calculator IMHO for algebra, geometry or trig
- but it definitely helps with trig.

Based on what my kids have used calculators for (through
geometry, at this point), it's not that they use the calculator
instead of learning to solve things the "old fashioned way."
It's true they don't use a slide rule and they don't use logarithms
much, but they also have a much heavier emphasis on real world
sorts of problems where the math doesn't work itself out nicely.
They still learn the usual methods, and work the practice problems
sans calculators, but then they go on to do more applied problems
for which they are more likely to use the calculator. I don't
have any objections to that, and actually think that it improves
the program to have them do more real world sorts of problems.
I'd say that to date, the kids have only used calculators for
maybe 10-20 percent of their math classes, but the use has seemed
quite sensible to me. Once the basic ability to solve a particular
type of problem has been mastered, the important thing is to get
a lot of practice figuring out when to apply that technique and
using it to solve a variety of problems.

There are definitely kids who don't understand basic
arithmetic or algebra or whatever the topic is at hand--but
I don't think that's because they've used calculators. There
were kids who didn't master arithmetic or algebra or what
have you before calculators as well ;-) Not only are more
things being covered in these math courses, but many more
students are taking higher level math courses than previously,
which would also lead one to expect some dilution in accomplishments.
There may be some kids who aren't getting algebra all that well,
but a generation ago, they might not have even attempted algebra.
Whether that's a good thing or a bad thing can, of course, be
debated ;-)

Best wishes,
Ericka

Olwyn.Mary wrote:
How on earth did I manage to study algebra, geometry and trigonometry
with only a pencil, noteboook and set of log tables????????

Same here except that later on we were taught to use a slide rule,
usually referred to as a "guessing stick" g
--
Bruce Fletcher
Stronsay, Orkney UK
"My friend had a pet rock, he called it Trelawney"

While some of that applied math is okay, the method my kids were
taught didn't teach the basics nearly well enough. I've said it
before he they can tell you five different ways to figure out what
a 15% tip should be, but can't tell you what the actual answer is!
(Doesn't help most cell phones actually come with a tip calculator).

The parents finally had enough and they are now going to start
teaching more traditional methods of rote memorization. To this day,
I am not sure my kids can do long division manually. And I know my
son's biggest mistakes in algebra were math errors - because they just
don't do enough practice.

linda

On 8/6/09 8:08 PM, "Dr_brat" wrote:

On Aug 6, 6:32*pm, "Olwyn.Mary" wrote:
Dr_brat wrote:
On Aug 6, 11:03 am, Cheryl Isaak wrote:

Don't get me started. DS is required to have a $100 calculator for
pre-calculus. A different one from all his other courses.

My mother had six kinds of hissy over buying me a TI30 in 1978. *Guess
which calculator I'm still using for my grades all these years later?

Elizabeth

Welcome back, Elizabeth. *I was just wondering this morning where you
were. *After all, academics are supposed to have lots of free time in
the summer. *(One friend of mine in the college town where we lived
always said "There are three reasons to remain in teaching. *June, July
and August.")

Hi Olwyn Mary,

I have a sick DH and had a very sick dog, so I've been busy. The sick
dog has been taken care of by removing his right front leg, which was
traumatic for all involved, but doesn't seem to be bothering Harry in
the least any more. He just does whatever he wants to do and, except
for tiring relatively quickly (it's only been 2 weeks since the
surgery), is very much himself.

My DH, on the other hand, requires much management, as we have no idea
what's wrong with him and it's starting to wear on his every nerve.
Stress levels are high and I find that I'm not a very nice person to
have on rctn when I'm stressed.

Elizabeth

Sorry to hear of all these woes for you, Elizabeth. Glad to hear that Harry
is coping, and hope that somehow the situation with your DH improves.
Medical mysteries are very tough on everyone, sending good thoughts your
way.

Ellice

On 8/6/09 11:58 PM, "Ericka Kammerer" wrote:

ellice wrote:

Just what I was going to say. Even in subjects like geometry or trig, they
can do more with a calulator. The bigger problem is the kids that don't
understand the basics of algebra, or actual arithmetic. Even when I went to
school, I had to have a slide rule in high school for calculus and AP
Physics & Chem. Don't need a calculator IMHO for algebra, geometry or trig
- but it definitely helps with trig.

Based on what my kids have used calculators for (through
geometry, at this point), it's not that they use the calculator
instead of learning to solve things the "old fashioned way."
It's true they don't use a slide rule and they don't use logarithms
much, but they also have a much heavier emphasis on real world
sorts of problems where the math doesn't work itself out nicely.
They still learn the usual methods, and work the practice problems
sans calculators, but then they go on to do more applied problems
for which they are more likely to use the calculator. I don't
have any objections to that, and actually think that it improves
the program to have them do more real world sorts of problems.
I'd say that to date, the kids have only used calculators for
maybe 10-20 percent of their math classes, but the use has seemed
quite sensible to me. Once the basic ability to solve a particular
type of problem has been mastered, the important thing is to get
a lot of practice figuring out when to apply that technique and
using it to solve a variety of problems.

The way you describe your kids usage makes sense to me. They just don't
have to spend the time doing the math, so to speak. Which, OTOH, translates
into the problem seen all over of not recognizing a wrong math solution
because that familiarity with number relations, manipulation is not gained
(the repetition, practice thing even with math). So often what ends up
missing later on is that recognition of a solution being slightly, or even
order of magnitude, off.

There are definitely kids who don't understand basic
arithmetic or algebra or whatever the topic is at hand--but
I don't think that's because they've used calculators. There
were kids who didn't master arithmetic or algebra or what
have you before calculators as well ;-) Not only are more
things being covered in these math courses, but many more
students are taking higher level math courses than previously,
which would also lead one to expect some dilution in accomplishments.
There may be some kids who aren't getting algebra all that well,
but a generation ago, they might not have even attempted algebra.
Whether that's a good thing or a bad thing can, of course, be
debated ;-)

I think the difference in how much, how far in math type education kids go
now compared to 20 or 40 years ago really depends on school systems.
Honestly, compared to my high school the average kid takes less math
nowadays. Our system required math thru Algebra II - IIRC those who were
really struggling would perhaps go to a business math class instead. I had
friends in the then Honors program who weren't heading for science careers
and much to the shock of our classmates dropped math after Algebra II (only
to later discover they had to take more math in university). Depending on
where you fell on the scale WRT Math/Science programs kids would go thru
Trig/analyt or Calculus, some with a 2nd year of calculus or some other math
development. Educational strategies are always interesting. Having close
friends that are academics in the science/engineering world we end up
talking about the math thing a lot. Even from work - it is interesting to
me that interplay between math and its applications. People doing fabulous
calculational simulations - but they don't have the right science background
to know that while their math is right the physics is off. Then the
converse, people who are certain of the physics involved, but have no
inherent feel for the numbers. I guess part of that is in some advanced
math stuff - well - the numbers don't come into it - until you're in the
real world trying to apply complex equations, and then the real part of
things kicks in. It's all pretty interesting how things change, and in some
ways remain the same.

Ellice

On 8/7/09 10:16 AM, " wrote:

While some of that applied math is okay, the method my kids were
taught didn't teach the basics nearly well enough. I've said it
before he they can tell you five different ways to figure out what
a 15% tip should be, but can't tell you what the actual answer is!
(Doesn't help most cell phones actually come with a tip calculator).

The parents finally had enough and they are now going to start
teaching more traditional methods of rote memorization. To this day,
I am not sure my kids can do long division manually. And I know my
son's biggest mistakes in algebra were math errors - because they just
don't do enough practice.

linda


I am so with you on this. My favorite example - I taught a 300 level
engineering class when my last year in grad school. Homework counted.
Thermo calculations mean doing real numbers, and the kids could use
calculators for tests. I would get homework turned in from a certain group
of frat boys that clearly had an old copy of the answer manual. Now, the
text is a classic, and the manual had been written by some similar grad
student so had plenty of errors in it. Which meant that when I graded I
would have to redo all the problems for correct answers - especially the
math errors in the manual. The idiot kids would turn in their homework with
the copied work - and not even bother to check the math. So, they'd get "0"
and finally I put a note on saying "if you're going to cheat, at least be
smart enough to check the math" . If work was presented so I could figure
out that they at least had the right path working, they'd get most of the
credit, with minimal math points off (depending). It amazed me, both for
laziness, and stupidity - things as simple as 5X2=7 . And they'd just copy
it. The moral of the story - those three did so poorly on the exams
(despite their lovely, neat, presentations) that they had to retake the
class to graduate. Yup.

Anyhow, sadly, it's the kind of thing that would happen with my co-op
students, young engineers - they just hadn't enough work with the basics in
a problem and would be so fast to grab a calculator, or look in the back of
some book that they had to learn the hard way to check their work for maybe
a misentered number.

Ellice

wrote:
While some of that applied math is okay, the method my kids were
taught didn't teach the basics nearly well enough. I've said it
before he they can tell you five different ways to figure out what
a 15% tip should be, but can't tell you what the actual answer is!
(Doesn't help most cell phones actually come with a tip calculator).

The parents finally had enough and they are now going to start
teaching more traditional methods of rote memorization. To this day,
I am not sure my kids can do long division manually. And I know my
son's biggest mistakes in algebra were math errors - because they just
don't do enough practice.

That hasn't been much of an issue for us. I will
say that one teacher, in my opinion, taught too many ways
to solve some kinds of problems. However, there was always
plenty of practice and an expectation that basic math facts
were memorized and readily at hand.

And frankly, while I think there is some value in
memorizing basic math facts so that one is not completely
incapacitated without a calculator, I do believe that there
is little learning accomplished with rote memorization.
As soon as you get past grade school math, if you don't
really understand what you're doing and why (and have the
ability to apply it to novel situations), then you're not
going to get very far, no matter how quickly you can rattle
of multiplication tables.

Best wishes,
Ericka

ellice wrote:

I think the difference in how much, how far in math type education kids go
now compared to 20 or 40 years ago really depends on school systems.
Honestly, compared to my high school the average kid takes less math
nowadays. Our system required math thru Algebra II - IIRC those who were
really struggling would perhaps go to a business math class instead.

If you look at national numbers:

% HS students
completing
through: 1986 2004
-------------------------------------------------
Algebra I 79 94
Geometry 59 83
Algebra II 44 69
Pre-calc/Calc 7 18

So, significant increases even just over the last 20 years. There
was a huge push in the 90s to get 8th graders into algebra, and
it did result in a large increase in the proportion of 8th graders
taking algebra. It's unclear whether this has been a good thing.
On the one hand, it's greatly increased the number of students
taking calculus in high school, but some argue that it has
resulted in less proficiency (either because kids were pushed
to take math classes before they were really developmentally
ready, or because the courses were being "dumbed down" once
they were no longer being taught only to the most elite HS
students). Some say that the rush to get 8th graders into
algebra has meant short-changing kids on basic math in the
earlier grades.

Best wishes,
Ericka

On 8/6/09 5:22 PM, in article
, "Dr_brat"
wrote:

On Aug 6, 11:03*am, Cheryl Isaak wrote:


Don't get me started. DS is required to have a $100 calculator for
pre-calculus. A different one from all his other courses.

My mother had six kinds of hissy over buying me a TI30 in 1978. Guess
which calculator I'm still using for my grades all these years later?

Elizabeth

Those were little power houses. Still love my Casio for stats...

Cheryl

On 8/7/09 2:19 PM, "Ericka Kammerer" wrote:

ellice wrote:

I think the difference in how much, how far in math type education kids go
now compared to 20 or 40 years ago really depends on school systems.
Honestly, compared to my high school the average kid takes less math
nowadays. Our system required math thru Algebra II - IIRC those who were
really struggling would perhaps go to a business math class instead.

If you look at national numbers:

% HS students
completing
through: 1986 2004
-------------------------------------------------
Algebra I 79 94
Geometry 59 83
Algebra II 44 69
Pre-calc/Calc 7 18

So, significant increases even just over the last 20 years. There
was a huge push in the 90s to get 8th graders into algebra, and
it did result in a large increase in the proportion of 8th graders
taking algebra. It's unclear whether this has been a good thing.
On the one hand, it's greatly increased the number of students
taking calculus in high school, but some argue that it has
resulted in less proficiency (either because kids were pushed
to take math classes before they were really developmentally
ready, or because the courses were being "dumbed down" once
they were no longer being taught only to the most elite HS
students). Some say that the rush to get 8th graders into
algebra has meant short-changing kids on basic math in the
earlier grades.


Again, I'd say that the variations in school systems 40 or 20 years ago was
much wider than it is today. From my personal experience alone I can say
that when I was in elementary school and went from Nassau Cty NY to Dade Cty
(Miami) Fl, I had to be put forward 4 grades for math and reading - so for
reading in 3rd grade - seriously - I spent the year reading the
encyclopedia, and sat in math class with some 6th graders. The next year
there were some reforms made in curricula, and a new elem school - so
several of us were put into their version of a G&T - would spend 2 hours a
day in the library doing special projects. This continued for me - I
actually worked in the office for an hour a day instead of going to reading
class.

However, as math & science classes progressed - Dade County made huge
strides then, so the standards for math to graduate high school were 3
years. While my math/science group was ahead of the norm - all taking
calculus in high school - I think the standard was people took Alg I in
either 9th, the ahead of that taking it in 8th, and the accelerated programs
taking it in 7th. Going to a summer camp away we'd all talk about school,
and then university away - even at an engineering/science uni - there were
huge differences in the math, science and language requirements and
opportunities in different parts of the country.

As you know - statistics can be interpreted oh so many ways. I have no
issue with the national average of math classes changing. My point is that
the changes may be less of a greater requirement, or essentially none, to
even a lesser requirement, in different areas. The education requirements
are much more standardized now across the country than they were thru the
70s.

I totally agree with the arguments about rushing kids. In real life, it's
so much more important to actually understand math concepts, and algebra
than pressure many to take a calculus course. If you don't really get
algebra, trigonometry and geometry then basic calculus is just memorizing
some formulas that you will never understand or be able to actually apply.
Even kids doing AP calc, when they get to university, for the most part what
that does is give you a leg up with the true university course, perhaps
getting you out of 1 term, or in my case (the school didn't accept AP then)
sticking you into an honors I must be crazy to be in this class I'm not a
math major. It does help with having put the concepts in front of the
student. But dumbed down math just to expose kids kind of short-changes
them. Calculus is a great tool, and a gateway to so much, if you do
engineering/physics/statistics. But, honestly, it doesn't help you figure
out which product to buy in the grocery store, and most people even with
college degrees, don't need years of it - but they do need some. Just my
nickel's worth.

Ellice