I'm thinking of giving my old HP48SX (since I've updated to the 49G+) to my
16 year-old niece who will be taking a pre-calculus course in high school.

She's a bright student, but I don't know if she'd have trouble using it or
not.

I do have the original user's manual so it should help her out.

Anyone have any comments pro or con?  Any suggestions of links to look for
info that might help her?  I think she used to have a TI-83, which I don't
think can do calculus.

--
Michael C. Polinske
Milwaukee, WI
====================
Come to the WELS for
new life in the living Word
http://www.wels.net

Mike, unless she wants to get into all aspects of programming, I don't 
think that is the best type of machine to give a high school kid, 
especially if she is still doing algebra, trig, etc.  Besides, these 
days, when teachers request the kids go and get a calc, they usually 
mean a TI-83 or such.

I have seen so far only one *college* student even with a HP calc, and 
it's the algebraic HP-39G.  All others are TIs, Casios, and Sharps, or 
the no-name algebraics.

I gave my own son (middle school... sorta like junior high) a 39G.  I 
also forbade him to use it until the teachers require that he does, 
except for programming, figuring that if he figures out how to program 
functions, even if in an effort to be lazy or sneaky, he has learned 
something useful.  So far, he's only pre-algebra!  Anyhow, my 
wind-obscured point is that with all students learning the fundamentals 
of math, it's probably best only to let 'em have a 4-banger.  Too bad no 
one makes a RPN four-banger with only maybe exponentials, several 
registers and enough memory RAM space so that they're FORCED to program 
in sin, log, conversions, etc.

I find that the advent of computers and (especially graphing) 
calculators have contributed to dulling the mathematical wit of most 
American students to the point that one can tell one who has had a 
foreign secondary education by how well they can handle math.

So, teach her to program it, but don't let her do logs, trig, or plot 
anything on it!  Gift wrap it with graph paper adorned with pencils and 
erasers!

Mike Polinske wrote:

> I'm thinking of giving my old HP48SX (since I've updated to the 49G+) to my
> 16 year-old niece who will be taking a pre-calculus course in high school.
> 
> She's a bright student, but I don't know if she'd have trouble using it or
> not.
> 
> I do have the original user's manual so it should help her out.
> 
> Anyone have any comments pro or con?  Any suggestions of links to look for
> info that might help her?  I think she used to have a TI-83, which I don't
> think can do calculus.
> 
> --
> Michael C. Polinske
> Milwaukee, WI
> ====================
> Come to the WELS for
> new life in the living Word
> http://www.wels.net
> 
> 
> 

Hi Ed, I more or less agree with your views on the effects of
calculator technology on people's understanding of mathematics, but
surely you wouldn't make your children go back to using log tables?
You must have a relatively high understanding of math to know how
transcendental functions are calculated anyway, it's better if
students learn how they behave and to let them get a general feel for
what they are.

No electrical engineering students I know chose their field of study
by learning about fourier and laplace transforms when they were 15,
like myself they're at uni because they were inspired by blinking
lights, electric motors, model aeroplanes and crystal radios.

When I started using my first graphing calculator and saw all the
great stuff I could make it do, it was somewhat like playing with
light-bulbs and motors when I was younger. I didn't really understand
how it all worked, but it inspired me to learn more about the subject.
I think if anything technology opens up the worlds of science and
engineering so they're more accessible to people who're really
interested in them.

So I don't think it would be fair to tell a student "Before I let you
use those trig buttons, I'm going to make sure you fully understand
Taylor series and CORDIC vector rotation" :-)

But then again, I'm probably one of the more unique students who take
a genuine, rather than vested interest (ie degree==job ticket) in what
I'm studying :-) This is just my NZ$0.02!




Ed Look <elook@optonline.net> wrote in message news:<3FADB17D.8030609@optonline.net>...
> Mike, unless she wants to get into all aspects of programming, I don't 
> think that is the best type of machine to give a high school kid, 
> especially if she is still doing algebra, trig, etc.  Besides, these 
> days, when teachers request the kids go and get a calc, they usually 
> mean a TI-83 or such.
> 
> I have seen so far only one *college* student even with a HP calc, and 
> it's the algebraic HP-39G.  All others are TIs, Casios, and Sharps, or 
> the no-name algebraics.
> 
> I gave my own son (middle school... sorta like junior high) a 39G.  I 
> also forbade him to use it until the teachers require that he does, 
> except for programming, figuring that if he figures out how to program 
> functions, even if in an effort to be lazy or sneaky, he has learned 
> something useful.  So far, he's only pre-algebra!  Anyhow, my 
> wind-obscured point is that with all students learning the fundamentals 
> of math, it's probably best only to let 'em have a 4-banger.  Too bad no 
> one makes a RPN four-banger with only maybe exponentials, several 
> registers and enough memory RAM space so that they're FORCED to program 
> in sin, log, conversions, etc.
> 
> I find that the advent of computers and (especially graphing) 
> calculators have contributed to dulling the mathematical wit of most 
> American students to the point that one can tell one who has had a 
> foreign secondary education by how well they can handle math.
> 
> So, teach her to program it, but don't let her do logs, trig, or plot 
> anything on it!  Gift wrap it with graph paper adorned with pencils and 
> erasers!
> 
> Mike Polinske wrote:
> 
> > I'm thinking of giving my old HP48SX (since I've updated to the 49G+) to my
> > 16 year-old niece who will be taking a pre-calculus course in high school.
> > 
> > She's a bright student, but I don't know if she'd have trouble using it or
> > not.
> > 
> > I do have the original user's manual so it should help her out.
> > 
> > Anyone have any comments pro or con?  Any suggestions of links to look for
> > info that might help her?  I think she used to have a TI-83, which I don't
> > think can do calculus.
> > 
> > --
> > Michael C. Polinske
> > Milwaukee, WI
> > ====================
> > Come to the WELS for
> > new life in the living Word
> > http://www.wels.net
> > 
> > 
> >

XYZ wrote:
> So I don't think it would be fair to tell a student "Before I let you
> use those trig buttons, I'm going to make sure you fully understand
> Taylor series and CORDIC vector rotation" :-)

Right. They may first treat a hightec calculator as a kind of outlook on
these and other things like Laplace and Fourier tranformation etc. And
even after having learned to use all this stuff, it may still be
pleasant to take a little rest enjoying some game or animation on the
calculator, perhaps asking oneself how the programmer may have realized
it. This may even be more fascinating than blinking lights, electric
motors ...

Look for instance at the animation ORBIT from ANI49 where the earth
turns around the sun, first covering the sun and then, if returning
after half a year on its orbit and being far away, is covered by the
sun.    

- Wolfgang
http://page.mi.fu-berlin.de/~raut/WR49/Ani49.htm

oN 08-Nov-03, Mike Polinske said:

> Anyone have any comments pro or con?  Any suggestions of links to
> look for info that might help her?  I think she used to have a TI-83,
> which I don't think can do calculus.

I know it's not what you want to hear, but the schools in the U.S.
(including colleges) seem all to have standardized on TI calculators.
ANything up to the TI-89 appears to be ok for use on exams, but the
TI-92, and others qith QWERTY keyboard layout are apparently verboten,
as they are simply too easy to use as crib sheets.

While she may be able to use the HP-48 to do the work, she will find
*no* help from any instructor regarding its use, as few will even have
seen one, much less have used one.

-- 
Bill
Posted with XanaNews Version 1.15.7.4

oN 08-Nov-03, Ed Look said:

> I gave my own son (middle school... sorta like junior high) a 39G.  I
> also forbade him to use it until the teachers require that he does

Years ago, I gave my old HP-25 to my younger brothers, with the
stricture that it was only to be used for *checking* their homework. I
further explained to them that learning the underlying solution
processes was critical to a solid understanding of mathematics.

I have heard some (not very bright) teachers claim that there's no need
to learn to manually derive a root, as anyone can use a calculator. I
wonder who they think will design calculators once a real understanding
of mathematics has been lost...

-- 
Bill
Posted with XanaNews Version 1.15.7.4

William, given today's climate, I think no one actually cares, at the 
moment, anyway, about who will design tomorrow's calculators... or auto 
safety features, for that matter.  They think, "some scientist" is gonna 
  do it!  They fail to realize these little nose-picking, girl-teasing, 
my-dog-ate-my-homework-kids are going to be that "some scientist".

But the poster who wrote that it may be too much to ask a child to tough 
out how transcendental functions actually work may also have a point. 
I'm getting old.  I seem to forget when it was that I myself was 
introduced to various things.  But I still think kids should learn log 
table interpolation (good skill for other things, too!), understand by 
the end of high school (if not a bit sooner) that the trig functions are 
more than just SOH CAH TOA.  But most American kids really seem to care 
just about as much their teachers on this.

I told some college students that every time I fuel my car, I try to 
calculate my rough mileage per gallon in my head as I'm leaving the 
filling station, just so I don't lose the skill.  They seriously and 
drily told me I was crazy.  Of course, don't try this if you pulling 
back onto a very busy street or highway!  I think the older generation 
of teachers might have supported such things... and manual calculation 
of square roots, which really is not all that troublesome.

William Meyer wrote:

> oN 08-Nov-03, Ed Look said:
> 
> 
>>I gave my own son (middle school... sorta like junior high) a 39G.  I
>>also forbade him to use it until the teachers require that he does
>>
> 
> Years ago, I gave my old HP-25 to my younger brothers, with the
> stricture that it was only to be used for *checking* their homework. I
> further explained to them that learning the underlying solution
> processes was critical to a solid understanding of mathematics.
> 
> I have heard some (not very bright) teachers claim that there's no need
> to learn to manually derive a root, as anyone can use a calculator. I
> wonder who they think will design calculators once a real understanding
> of mathematics has been lost...
> 
> 

Hi, I might be able to give a unique view on this issue, I am a university
student in Australia studying Mechatronic Engineering. In my high school
years I lived in Western Australia, where we used the 38G and 39G
calculators quite extensively, I also dabbled with the Casio GFX9500+ from
personal interest. I found two things, firstly, the teachers knew very very
little about the operation of the calculators and most of what we learnt was
from the people around who figured it out from the manual. Secondly, some
people have a genuine interest in learning the fundamental theory of
mathematics and others are quite happy to learn the process and apply it
time after time. Fortunately I was interested in the theory because when I
went moved to the Eastern States (New South Wales) to start university I
found that NSW does not use graphic calculators at all. That said, in all of
first year uni, we still have not covered the same amount of maths that we
did in final year of high school.  This is because once we have learnt the
fundamental theory we get bogged down by doing silly things like row
reductions and inverting matrices by hand which are simple to do on advanced
calculators. The point is that I find this sort of thing pointless!! Even
more pointless I think is learning numerical solving methods only to have to
sit and substitute value after value after value with a scientific
calculator when a graphical calculator can do it more quickly and more
accurately than what I would need. Do you honestly think that outside of uni
if I had to find a set of egien values/vectors I would do it by hand? What
is the point? So for those who want to program the calculators and computers
etc (which I enjoy immensely) let them learn the theory, for those who
simply need to do the calculation, just do it on a graphics calculator and
move on, what is the point of having the technology and not using it.

Now as to the use of the HP48SX, I am not familiar with this exact
calculator but I assume that it would take an RPN style entry. If this is
so, then to a highschool student, it would be of very little use, I would
personally suggest something along the lines of the 38G,39G or 39G+ or even
the TI-83 or CasioGFX950+ these are all more suitable for this level of
study. (My personal favorite is the 39G which has some great calculus
functions and there is a great collection of aplets about to help out..see
www.hphomeview.com for more info)

What you say does make some sense, as none of US and you've declared it, 
  too, will go back to doing some things by hand now that we've sweated 
out the countless manual manipulations.  But you do see that your 
physical pencil and paper handling of matrices allows you to be able to 
program a graphing calculator!

Anyway, I suspect you've learned a lot from Colin Croft or his marvelous 
website!

; )

MG wrote:

> Hi, I might be able to give a unique view on this issue, I am a university
> student in Australia studying Mechatronic Engineering. In my high school
> years I lived in Western Australia, where we used the 38G and 39G
> calculators quite extensively, I also dabbled with the Casio GFX9500+ from
> personal interest. I found two things, firstly, the teachers knew very very
> little about the operation of the calculators and most of what we learnt was
> from the people around who figured it out from the manual. Secondly, some
> people have a genuine interest in learning the fundamental theory of
> mathematics and others are quite happy to learn the process and apply it
> time after time. Fortunately I was interested in the theory because when I
> went moved to the Eastern States (New South Wales) to start university I
> found that NSW does not use graphic calculators at all. That said, in all of
> first year uni, we still have not covered the same amount of maths that we
> did in final year of high school.  This is because once we have learnt the
> fundamental theory we get bogged down by doing silly things like row
> reductions and inverting matrices by hand which are simple to do on advanced
> calculators. The point is that I find this sort of thing pointless!! Even
> more pointless I think is learning numerical solving methods only to have to
> sit and substitute value after value after value with a scientific
> calculator when a graphical calculator can do it more quickly and more
> accurately than what I would need. Do you honestly think that outside of uni
> if I had to find a set of egien values/vectors I would do it by hand? What
> is the point? So for those who want to program the calculators and computers
> etc (which I enjoy immensely) let them learn the theory, for those who
> simply need to do the calculation, just do it on a graphics calculator and
> move on, what is the point of having the technology and not using it.
> 
> Now as to the use of the HP48SX, I am not familiar with this exact
> calculator but I assume that it would take an RPN style entry. If this is
> so, then to a highschool student, it would be of very little use, I would
> personally suggest something along the lines of the 38G,39G or 39G+ or even
> the TI-83 or CasioGFX950+ these are all more suitable for this level of
> study. (My personal favorite is the 39G which has some great calculus
> functions and there is a great collection of aplets about to help out..see
> www.hphomeview.com for more info)
> 
> 
> 

I have to agree with MG, even though one has to learn the how most
operations of math works (algebra,trigonometry,calculus), having a
calculator around is good helps in two very important aspects:

1) Having the correct answer to questions give confidence for users
that lack it (such as myself)

2) Curious people will always try to find things on they own and the
calculator are a great way to "explore" the world of math.

In my last calculus exam I had to calculate the limit of the following
fucntion , excuse me for the wrong notation but I have no idea what's
used outside Brazil:

Lim((x-atan(x))/(x^3)),x=0)
As many of you already know, atan(0) is 1 so it was a simply just to
apply L'hospital until you got the result 1/3.

But I have already learned series and my professor told me that many
of the questions involving limits are created by taking a series of a
familiar function and doing some operation with it. This comment is
always on my head and I decided to calculate that limit using series.

I started with what we call "The Geometric Series":
1/(1-x)=1+x+x^2+x^3+...

I then replace x by (-x^2):
1/(1+x^2)=1-x^2+x^4-x^6+...

Following that I calculated the "integral" of both sides:
atan(x)=x-(x^3/3)+(x^5/5)-(x^7/7)+...

Putting a (-) in both sides of the equation:
-(atan(x))=-x+(x^3/3)-(x^5/5)+(x^7/7)+...

Adding x:
x-atan(x)=(x^3/3)-(x^5/5)+(x^7/7)+...

Diving by (x^3):
(x-atan(x))/(x^3)=(1/3)-(x^2/5)+(x^4/7)...

If x=0:
(x-atan(x))/(x^3)=(1/3)

Is it as easy as just doing L'hospital? No.
Is it worth doing limits this way during an exam? No.
Is it interesting to resolve limits using series? Yes.
Is it fun? Hell yeah :P

Conclusion:
A graphing calculator can be good or bad, it's just the way you use it
that adds or subtracts from your mathing skills (pun is not
intentional :P).

| va.va |





"MG" <deadgrey19@hotmail.com> wrote in message news:<bon4bp$m99$1@tomahawk.unsw.edu.au>...
> Hi, I might be able to give a unique view on this issue, I am a university
> student in Australia studying Mechatronic Engineering. In my high school
> years I lived in Western Australia, where we used the 38G and 39G
> calculators quite extensively, I also dabbled with the Casio GFX9500+ from
> personal interest. I found two things, firstly, the teachers knew very very
> little about the operation of the calculators and most of what we learnt was
> from the people around who figured it out from the manual. Secondly, some
> people have a genuine interest in learning the fundamental theory of
> mathematics and others are quite happy to learn the process and apply it
> time after time. Fortunately I was interested in the theory because when I
> went moved to the Eastern States (New South Wales) to start university I
> found that NSW does not use graphic calculators at all. That said, in all of
> first year uni, we still have not covered the same amount of maths that we
> did in final year of high school.  This is because once we have learnt the
> fundamental theory we get bogged down by doing silly things like row
> reductions and inverting matrices by hand which are simple to do on advanced
> calculators. The point is that I find this sort of thing pointless!! Even
> more pointless I think is learning numerical solving methods only to have to
> sit and substitute value after value after value with a scientific
> calculator when a graphical calculator can do it more quickly and more
> accurately than what I would need. Do you honestly think that outside of uni
> if I had to find a set of egien values/vectors I would do it by hand? What
> is the point? So for those who want to program the calculators and computers
> etc (which I enjoy immensely) let them learn the theory, for those who
> simply need to do the calculation, just do it on a graphics calculator and
> move on, what is the point of having the technology and not using it.
> 
> Now as to the use of the HP48SX, I am not familiar with this exact
> calculator but I assume that it would take an RPN style entry. If this is
> so, then to a highschool student, it would be of very little use, I would
> personally suggest something along the lines of the 38G,39G or 39G+ or even
> the TI-83 or CasioGFX950+ these are all more suitable for this level of
> study. (My personal favorite is the 39G which has some great calculus
> functions and there is a great collection of aplets about to help out..see
> www.hphomeview.com for more info)

Ed Look wrote:

> William, given today's climate, I think no one actually cares, at the
> moment, anyway, about who will design tomorrow's calculators... or auto
> safety features, for that matter.  They think, "some scientist" is gonna
>   do it!  They fail to realize these little nose-picking, girl-teasing,
> my-dog-ate-my-homework-kids are going to be that "some scientist".
> 
> But the poster who wrote that it may be too much to ask a child to tough
> out how transcendental functions actually work may also have a point.
> I'm getting old.  I seem to forget when it was that I myself was
> introduced to various things.  But I still think kids should learn log
> table interpolation (good skill for other things, too!), understand by
> the end of high school (if not a bit sooner) that the trig functions are
> more than just SOH CAH TOA.  But most American kids really seem to care
> just about as much their teachers on this.
> 
> I told some college students that every time I fuel my car, I try to
> calculate my rough mileage per gallon in my head as I'm leaving the
> filling station, just so I don't lose the skill.  They seriously and
> drily told me I was crazy.  Of course, don't try this if you pulling
> back onto a very busy street or highway!  I think the older generation
> of teachers might have supported such things... and manual calculation
> of square roots, which really is not all that troublesome.
> 
> William Meyer wrote:
> 
>> oN 08-Nov-03, Ed Look said:
>> 
>> 
>>>I gave my own son (middle school... sorta like junior high) a 39G.  I
>>>also forbade him to use it until the teachers require that he does
>>>
>> 
>> Years ago, I gave my old HP-25 to my younger brothers, with the
>> stricture that it was only to be used for *checking* their homework. I
>> further explained to them that learning the underlying solution
>> processes was critical to a solid understanding of mathematics.
>> 
>> I have heard some (not very bright) teachers claim that there's no need
>> to learn to manually derive a root, as anyone can use a calculator. I
>> wonder who they think will design calculators once a real understanding
>> of mathematics has been lost...
>> 
>>
There needs to be some sort of middle ground.  I have had teachers who
taught the steps by calculator model X so you didn't learn the how and why
and couldn't figure out how to work the problems on a different model
calcualtor.  Then there was the other extreme, the no calculators at all
teachers.  Those would make you show every basic step on the most comlex
problems so you too so long  to work the problems you didn't get to learn
as much either.  I prefer to learn how to do something and practice it a
bit, then use the calculator for that so I can concentrate on learning
somethng more complex.

oN 09-Nov-03, Ed Look said:

> William, given today's climate, I think no one actually cares, at the
> moment, anyway, about who will design tomorrow's calculators... or
> auto safety features, for that matter.  They think, "some scientist"
> is gonna   do it!  They fail to realize these little nose-picking,
> girl-teasing, my-dog-ate-my-homework-kids are going to be that "some
> scientist".

Agreed, but that doesn't mean *we* have to buy into their idiocy!
 
> But the poster who wrote that it may be too much to ask a child to
> tough out how transcendental functions actually work may also have a
> point. I'm getting old.  I seem to forget when it was that I myself
> was introduced to various things.  But I still think kids should
> learn log table interpolation (good skill for other things, too!),
> understand by the end of high school (if not a bit sooner) that the
> trig functions are more than just SOH CAH TOA.  But most American
> kids really seem to care just about as much their teachers on this.

My step-daughter (just turned 14, newly arrived from China, and
struggling with English) was recently pointing out my errors in
pre-calculus homework while reading my work upside down from across the
table, so while I'm getting old, I have a lot of respect for what kids
can do. During my high school years, I fell victim to the "new math",
and that soured me on math studies for a long time. I've recently taken
them up again, and am enjoying it much, though I'm also (unfortunately)
getting the idea that my short-term memory may not be what it once was!

> I told some college students that every time I fuel my car, I try to
> calculate my rough mileage per gallon in my head as I'm leaving the
> filling station, just so I don't lose the skill.  They seriously and
> drily told me I was crazy.  Of course, don't try this if you pulling
> back onto a very busy street or highway!  I think the older
> generation of teachers might have supported such things... and manual
> calculation of square roots, which really is not all that troublesome.

My grandfather was of the opinion that any child who couldn't multiply
5 digit numbers in his head ("his" being the inclusive pronoun, in that
era), was only marginally acquainted with arithmetic. I have been
surprised to discover that intermediate algebra does not address the
manual calculation of a square root, although it *does* review numerous
far simpler processes.

Though I dove back into math studies (after a 35 year hiatus) in order
to meet the pre-reqs for some software classes I wanted, I think I've
now decided to pass on the software classes in favor of continuing
math. The software classes I did take were of uneven quality, and
pretty boring. But then, I've been coding for over 27 years...

-- 
Bill
Posted with XanaNews Version 1.15.7.4

Ah Eugene!

How could you (not you, Eugene, but the proverbial, rhetorical, plural 
you) not learn anything when you did your calculations manually?  If you 
think that as a student, especially a beginning one, you will miss out 
on "the important stuff" because you're slogging through the division 
part of complicated algebraic set up, you're missing the point!  All 
that manual labor conditions one to properly execute more complex 
operations.  Try forgetting your algebra or simple multiplication tables 
  if you want to reduce some symmetry representation or other such stuff 
(often necessary before one can get at the science behind a phenomenon), 
you'll screw it up!

Middle ground??  How did those poor pre-electronics people do it?  It 
makes for greater mental agility later when the taskmas... uh, 
schoolmasters make you "do it the hard way" first.  When the student 
goes to college, then I'd say a powerful programmable scientific (RPN, 
as I'm biased) is appropriate.  A graphing one, maybe later with more 
advanced studies, but even then...

Eugene wrote:

> Ed Look wrote:
> 
> 
>>William, given today's climate, I think no one actually cares, at the
>>moment, anyway, about who will design tomorrow's calculators... or auto
>>safety features, for that matter.  They think, "some scientist" is gonna
>>  do it!  They fail to realize these little nose-picking, girl-teasing,
>>my-dog-ate-my-homework-kids are going to be that "some scientist".
>>
>>But the poster who wrote that it may be too much to ask a child to tough
>>out how transcendental functions actually work may also have a point.
>>I'm getting old.  I seem to forget when it was that I myself was
>>introduced to various things.  But I still think kids should learn log
>>table interpolation (good skill for other things, too!), understand by
>>the end of high school (if not a bit sooner) that the trig functions are
>>more than just SOH CAH TOA.  But most American kids really seem to care
>>just about as much their teachers on this.
>>
>>I told some college students that every time I fuel my car, I try to
>>calculate my rough mileage per gallon in my head as I'm leaving the
>>filling station, just so I don't lose the skill.  They seriously and
>>drily told me I was crazy.  Of course, don't try this if you pulling
>>back onto a very busy street or highway!  I think the older generation
>>of teachers might have supported such things... and manual calculation
>>of square roots, which really is not all that troublesome.
>>
>>William Meyer wrote:
>>
>>
>>>oN 08-Nov-03, Ed Look said:
>>>
>>>
>>>
>>>>I gave my own son (middle school... sorta like junior high) a 39G.  I
>>>>also forbade him to use it until the teachers require that he does
>>>>
>>>>
>>>Years ago, I gave my old HP-25 to my younger brothers, with the
>>>stricture that it was only to be used for *checking* their homework. I
>>>further explained to them that learning the underlying solution
>>>processes was critical to a solid understanding of mathematics.
>>>
>>>I have heard some (not very bright) teachers claim that there's no need
>>>to learn to manually derive a root, as anyone can use a calculator. I
>>>wonder who they think will design calculators once a real understanding
>>>of mathematics has been lost...
>>>
>>>
>>>
> There needs to be some sort of middle ground.  I have had teachers who
> taught the steps by calculator model X so you didn't learn the how and why
> and couldn't figure out how to work the problems on a different model
> calcualtor.  Then there was the other extreme, the no calculators at all
> teachers.  Those would make you show every basic step on the most comlex
> problems so you too so long  to work the problems you didn't get to learn
> as much either.  I prefer to learn how to do something and practice it a
> bit, then use the calculator for that so I can concentrate on learning
> somethng more complex.
> 

But you seem to know your math quite well.  For you, there is no 
argument; use whatever calculator you like (of course we here hope it is 
a HP RPN model), for you don't look like the type that will allow a 
skill to go rusty.  But for many students, they can benefit by doing the 
manual steps.  I will admit however, that on an exam, there is a need 
for time, so if your instructor allows it, use the calculator!  But on 
homework or practice, I'd do it by hand, doing only what a simple 
4-function calculator... well, maybe simple scientific... can do in the 
calculator.  Enjoy your studies!

va.va wrote:

> I have to agree with MG, even though one has to learn the how most
> operations of math works (algebra,trigonometry,calculus), having a
> calculator around is good helps in two very important aspects:
> 
> 1) Having the correct answer to questions give confidence for users
> that lack it (such as myself)
> 
> 2) Curious people will always try to find things on they own and the
> calculator are a great way to "explore" the world of math.
> 
> In my last calculus exam I had to calculate the limit of the following
> fucntion , excuse me for the wrong notation but I have no idea what's
> used outside Brazil:
> 
> Lim((x-atan(x))/(x^3)),x=0)
> As many of you already know, atan(0) is 1 so it was a simply just to
> apply L'hospital until you got the result 1/3.
> 
> But I have already learned series and my professor told me that many
> of the questions involving limits are created by taking a series of a
> familiar function and doing some operation with it. This comment is
> always on my head and I decided to calculate that limit using series.
> 
> I started with what we call "The Geometric Series":
> 1/(1-x)=1+x+x^2+x^3+...
> 
> I then replace x by (-x^2):
> 1/(1+x^2)=1-x^2+x^4-x^6+...
> 
> Following that I calculated the "integral" of both sides:
> atan(x)=x-(x^3/3)+(x^5/5)-(x^7/7)+...
> 
> Putting a (-) in both sides of the equation:
> -(atan(x))=-x+(x^3/3)-(x^5/5)+(x^7/7)+...
> 
> Adding x:
> x-atan(x)=(x^3/3)-(x^5/5)+(x^7/7)+...
> 
> Diving by (x^3):
> (x-atan(x))/(x^3)=(1/3)-(x^2/5)+(x^4/7)...
> 
> If x=0:
> (x-atan(x))/(x^3)=(1/3)
> 
> Is it as easy as just doing L'hospital? No.
> Is it worth doing limits this way during an exam? No.
> Is it interesting to resolve limits using series? Yes.
> Is it fun? Hell yeah :P
> 
> Conclusion:
> A graphing calculator can be good or bad, it's just the way you use it
> that adds or subtracts from your mathing skills (pun is not
> intentional :P).
> 
> | va.va |
> 
> 
> 
> 
> 
> "MG" <deadgrey19@hotmail.com> wrote in message news:<bon4bp$m99$1@tomahawk.unsw.edu.au>...
> 
>>Hi, I might be able to give a unique view on this issue, I am a university
>>student in Australia studying Mechatronic Engineering. In my high school
>>years I lived in Western Australia, where we used the 38G and 39G
>>calculators quite extensively, I also dabbled with the Casio GFX9500+ from
>>personal interest. I found two things, firstly, the teachers knew very very
>>little about the operation of the calculators and most of what we learnt was
>>from the people around who figured it out from the manual. Secondly, some
>>people have a genuine interest in learning the fundamental theory of
>>mathematics and others are quite happy to learn the process and apply it
>>time after time. Fortunately I was interested in the theory because when I
>>went moved to the Eastern States (New South Wales) to start university I
>>found that NSW does not use graphic calculators at all. That said, in all of
>>first year uni, we still have not covered the same amount of maths that we
>>did in final year of high school.  This is because once we have learnt the
>>fundamental theory we get bogged down by doing silly things like row
>>reductions and inverting matrices by hand which are simple to do on advanced
>>calculators. The point is that I find this sort of thing pointless!! Even
>>more pointless I think is learning numerical solving methods only to have to
>>sit and substitute value after value after value with a scientific
>>calculator when a graphical calculator can do it more quickly and more
>>accurately than what I would need. Do you honestly think that outside of uni
>>if I had to find a set of egien values/vectors I would do it by hand? What
>>is the point? So for those who want to program the calculators and computers
>>etc (which I enjoy immensely) let them learn the theory, for those who
>>simply need to do the calculation, just do it on a graphics calculator and
>>move on, what is the point of having the technology and not using it.
>>
>>Now as to the use of the HP48SX, I am not familiar with this exact
>>calculator but I assume that it would take an RPN style entry. If this is
>>so, then to a highschool student, it would be of very little use, I would
>>personally suggest something along the lines of the 38G,39G or 39G+ or even
>>the TI-83 or CasioGFX950+ these are all more suitable for this level of
>>study. (My personal favorite is the 39G which has some great calculus
>>functions and there is a great collection of aplets about to help out..see
>>www.hphomeview.com for more info)
>>

I must agree with va.va. After having my graphics calculator for only a
short time I discovered that if I manipulated the coeffients the right way,
I could make an x^3 graph look like a SIN(x) graph. To my amazemnet in 1'st
year univeristy I discovered that what I had done ,with no mathematical
knowlege, was to derive a simple Taylor expansion of SIN(x). The point is
that I didnt have to know any complex maths to do it, it didnt take me hours
to do beacuse I could plot each function in a matter of seconds, and I
learnt by exploration the Taylor Series. I am now very greatfull that I
learnt it this way because I have a personal understanding for the Taylor
Series not just some mathematical mumbo jumbo that the lecturer taught us.
To me that is the real power of a graphics calculator in learning.

M@

"Ed Look" <elook@optonline.net> wrote in message
news:3FB07441.8020302@optonline.net...
> But you seem to know your math quite well.  For you, there is no
> argument; use whatever calculator you like (of course we here hope it is
> a HP RPN model), for you don't look like the type that will allow a
> skill to go rusty.  But for many students, they can benefit by doing the
> manual steps.  I will admit however, that on an exam, there is a need
> for time, so if your instructor allows it, use the calculator!  But on
> homework or practice, I'd do it by hand, doing only what a simple
> 4-function calculator... well, maybe simple scientific... can do in the
> calculator.  Enjoy your studies!
>
> va.va wrote:
>
> > I have to agree with MG, even though one has to learn the how most
> > operations of math works (algebra,trigonometry,calculus), having a
> > calculator around is good helps in two very important aspects:
> >
> > 1) Having the correct answer to questions give confidence for users
> > that lack it (such as myself)
> >
> > 2) Curious people will always try to find things on they own and the
> > calculator are a great way to "explore" the world of math.
> >
> > In my last calculus exam I had to calculate the limit of the following
> > fucntion , excuse me for the wrong notation but I have no idea what's
> > used outside Brazil:
> >
> > Lim((x-atan(x))/(x^3)),x=0)
> > As many of you already know, atan(0) is 1 so it was a simply just to
> > apply L'hospital until you got the result 1/3.
> >
> > But I have already learned series and my professor told me that many
> > of the questions involving limits are created by taking a series of a
> > familiar function and doing some operation with it. This comment is
> > always on my head and I decided to calculate that limit using series.
> >
> > I started with what we call "The Geometric Series":
> > 1/(1-x)=1+x+x^2+x^3+...
> >
> > I then replace x by (-x^2):
> > 1/(1+x^2)=1-x^2+x^4-x^6+...
> >
> > Following that I calculated the "integral" of both sides:
> > atan(x)=x-(x^3/3)+(x^5/5)-(x^7/7)+...
> >
> > Putting a (-) in both sides of the equation:
> > -(atan(x))=-x+(x^3/3)-(x^5/5)+(x^7/7)+...
> >
> > Adding x:
> > x-atan(x)=(x^3/3)-(x^5/5)+(x^7/7)+...
> >
> > Diving by (x^3):
> > (x-atan(x))/(x^3)=(1/3)-(x^2/5)+(x^4/7)...
> >
> > If x=0:
> > (x-atan(x))/(x^3)=(1/3)
> >
> > Is it as easy as just doing L'hospital? No.
> > Is it worth doing limits this way during an exam? No.
> > Is it interesting to resolve limits using series? Yes.
> > Is it fun? Hell yeah :P
> >
> > Conclusion:
> > A graphing calculator can be good or bad, it's just the way you use it
> > that adds or subtracts from your mathing skills (pun is not
> > intentional :P).
> >
> > | va.va |
> >
> >
> >
> >
> >
> > "MG" <deadgrey19@hotmail.com> wrote in message
news:<bon4bp$m99$1@tomahawk.unsw.edu.au>...
> >
> >>Hi, I might be able to give a unique view on this issue, I am a
university
> >>student in Australia studying Mechatronic Engineering. In my high school
> >>years I lived in Western Australia, where we used the 38G and 39G
> >>calculators quite extensively, I also dabbled with the Casio GFX9500+
from
> >>personal interest. I found two things, firstly, the teachers knew very
very
> >>little about the operation of the calculators and most of what we learnt
was
> >>from the people around who figured it out from the manual. Secondly,
some
> >>people have a genuine interest in learning the fundamental theory of
> >>mathematics and others are quite happy to learn the process and apply it
> >>time after time. Fortunately I was interested in the theory because when
I
> >>went moved to the Eastern States (New South Wales) to start university I
> >>found that NSW does not use graphic calculators at all. That said, in
all of
> >>first year uni, we still have not covered the same amount of maths that
we
> >>did in final year of high school.  This is because once we have learnt
the
> >>fundamental theory we get bogged down by doing silly things like row
> >>reductions and inverting matrices by hand which are simple to do on
advanced
> >>calculators. The point is that I find this sort of thing pointless!!
Even
> >>more pointless I think is learning numerical solving methods only to
have to
> >>sit and substitute value after value after value with a scientific
> >>calculator when a graphical calculator can do it more quickly and more
> >>accurately than what I would need. Do you honestly think that outside of
uni
> >>if I had to find a set of egien values/vectors I would do it by hand?
What
> >>is the point? So for those who want to program the calculators and
computers
> >>etc (which I enjoy immensely) let them learn the theory, for those who
> >>simply need to do the calculation, just do it on a graphics calculator
and
> >>move on, what is the point of having the technology and not using it.
> >>
> >>Now as to the use of the HP48SX, I am not familiar with this exact
> >>calculator but I assume that it would take an RPN style entry. If this
is
> >>so, then to a highschool student, it would be of very little use, I
would
> >>personally suggest something along the lines of the 38G,39G or 39G+ or
even
> >>the TI-83 or CasioGFX950+ these are all more suitable for this level of
> >>study. (My personal favorite is the 39G which has some great calculus
> >>functions and there is a great collection of aplets about to help
out..see
> >>www.hphomeview.com for more info)
> >>
>

Ha ha ha ha!

Not laughing at you, but am amused by all this!  We used to make similar 
discoveries with a pencil and paper... and lots of erasers!

Again, as I said earlier either to you or another in this thread, you 
obviously have a more in depth understanding of and appreciation for 
math than many (most?) other students.  For you, use of a graphing calc 
is a nonissue.  For the rest... well, they ought not to rest...


MG wrote:

> I must agree with va.va. After having my graphics calculator for only a
> short time I discovered that if I manipulated the coeffients the right way,
> I could make an x^3 graph look like a SIN(x) graph. To my amazemnet in 1'st
> year univeristy I discovered that what I had done ,with no mathematical
> knowlege, was to derive a simple Taylor expansion of SIN(x). The point is
> that I didnt have to know any complex maths to do it, it didnt take me hours
> to do beacuse I could plot each function in a matter of seconds, and I
> learnt by exploration the Taylor Series. I am now very greatfull that I
> learnt it this way because I have a personal understanding for the Taylor
> Series not just some mathematical mumbo jumbo that the lecturer taught us.
> To me that is the real power of a graphics calculator in learning.
> 
> M@
> 
> "Ed Look" <elook@optonline.net> wrote in message
> news:3FB07441.8020302@optonline.net...
> 
>>But you seem to know your math quite well.  For you, there is no
>>argument; use whatever calculator you like (of course we here hope it is
>>a HP RPN model), for you don't look like the type that will allow a
>>skill to go rusty.  But for many students, they can benefit by doing the
>>manual steps.  I will admit however, that on an exam, there is a need
>>for time, so if your instructor allows it, use the calculator!  But on
>>homework or practice, I'd do it by hand, doing only what a simple
>>4-function calculator... well, maybe simple scientific... can do in the
>>calculator.  Enjoy your studies!
>>
>>va.va wrote:
>>
>>
>>>I have to agree with MG, even though one has to learn the how most
>>>operations of math works (algebra,trigonometry,calculus), having a
>>>calculator around is good helps in two very important aspects:
>>>
>>>1) Having the correct answer to questions give confidence for users
>>>that lack it (such as myself)
>>>
>>>2) Curious people will always try to find things on they own and the
>>>calculator are a great way to "explore" the world of math.
>>>
>>>In my last calculus exam I had to calculate the limit of the following
>>>fucntion , excuse me for the wrong notation but I have no idea what's
>>>used outside Brazil:
>>>
>>>Lim((x-atan(x))/(x^3)),x=0)
>>>As many of you already know, atan(0) is 1 so it was a simply just to
>>>apply L'hospital until you got the result 1/3.
>>>
>>>But I have already learned series and my professor told me that many
>>>of the questions involving limits are created by taking a series of a
>>>familiar function and doing some operation with it. This comment is
>>>always on my head and I decided to calculate that limit using series.
>>>
>>>I started with what we call "The Geometric Series":
>>>1/(1-x)=1+x+x^2+x^3+...
>>>
>>>I then replace x by (-x^2):
>>>1/(1+x^2)=1-x^2+x^4-x^6+...
>>>
>>>Following that I calculated the "integral" of both sides:
>>>atan(x)=x-(x^3/3)+(x^5/5)-(x^7/7)+...
>>>
>>>Putting a (-) in both sides of the equation:
>>>-(atan(x))=-x+(x^3/3)-(x^5/5)+(x^7/7)+...
>>>
>>>Adding x:
>>>x-atan(x)=(x^3/3)-(x^5/5)+(x^7/7)+...
>>>
>>>Diving by (x^3):
>>>(x-atan(x))/(x^3)=(1/3)-(x^2/5)+(x^4/7)...
>>>
>>>If x=0:
>>>(x-atan(x))/(x^3)=(1/3)
>>>
>>>Is it as easy as just doing L'hospital? No.
>>>Is it worth doing limits this way during an exam? No.
>>>Is it interesting to resolve limits using series? Yes.
>>>Is it fun? Hell yeah :P
>>>
>>>Conclusion:
>>>A graphing calculator can be good or bad, it's just the way you use it
>>>that adds or subtracts from your mathing skills (pun is not
>>>intentional :P).
>>>
>>>| va.va |
>>>
>>>
>>>
>>>
>>>
>>>"MG" <deadgrey19@hotmail.com> wrote in message
>>>
> news:<bon4bp$m99$1@tomahawk.unsw.edu.au>...
> 
>>>>Hi, I might be able to give a unique view on this issue, I am a
>>>>
> university
> 
>>>>student in Australia studying Mechatronic Engineering. In my high school
>>>>years I lived in Western Australia, where we used the 38G and 39G
>>>>calculators quite extensively, I also dabbled with the Casio GFX9500+
>>>>
> from
> 
>>>>personal interest. I found two things, firstly, the teachers knew very
>>>>
> very
> 
>>>>little about the operation of the calculators and most of what we learnt
>>>>
> was
> 
>>>>from the people around who figured it out from the manual. Secondly,
>>>
> some
> 
>>>>people have a genuine interest in learning the fundamental theory of
>>>>mathematics and others are quite happy to learn the process and apply it
>>>>time after time. Fortunately I was interested in the theory because when
>>>>
> I
> 
>>>>went moved to the Eastern States (New South Wales) to start university I
>>>>found that NSW does not use graphic calculators at all. That said, in
>>>>
> all of
> 
>>>>first year uni, we still have not covered the same amount of maths that
>>>>
> we
> 
>>>>did in final year of high school.  This is because once we have learnt
>>>>
> the
> 
>>>>fundamental theory we get bogged down by doing silly things like row
>>>>reductions and inverting matrices by hand which are simple to do on
>>>>
> advanced
> 
>>>>calculators. The point is that I find this sort of thing pointless!!
>>>>
> Even
> 
>>>>more pointless I think is learning numerical solving methods only to
>>>>
> have to
> 
>>>>sit and substitute value after value after value with a scientific
>>>>calculator when a graphical calculator can do it more quickly and more
>>>>accurately than what I would need. Do you honestly think that outside of
>>>>
> uni
> 
>>>>if I had to find a set of egien values/vectors I would do it by hand?
>>>>
> What
> 
>>>>is the point? So for those who want to program the calculators and
>>>>
> computers
> 
>>>>etc (which I enjoy immensely) let them learn the theory, for those who
>>>>simply need to do the calculation, just do it on a graphics calculator
>>>>
> and
> 
>>>>move on, what is the point of having the technology and not using it.
>>>>
>>>>Now as to the use of the HP48SX, I am not familiar with this exact
>>>>calculator but I assume that it would take an RPN style entry. If this
>>>>
> is
> 
>>>>so, then to a highschool student, it would be of very little use, I
>>>>
> would
> 
>>>>personally suggest something along the lines of the 38G,39G or 39G+ or
>>>>
> even
> 
>>>>the TI-83 or CasioGFX950+ these are all more suitable for this level of
>>>>study. (My personal favorite is the 39G which has some great calculus
>>>>functions and there is a great collection of aplets about to help
>>>>
> out..see
> 
>>>>www.hphomeview.com for more info)
>>>>
>>>>
> 
> 

| va.va |

"MG" <deadgrey19@hotmail.com> wrote in message news:<bon4bp$m99$1@tomahawk.unsw.edu.au>...
> Hi, I might be able to give a unique view on this issue, I am a university
> student in Australia studying Mechatronic Engineering. In my high school
> years I lived in Western Australia, where we used the 38G and 39G
> calculators quite extensively, I also dabbled with the Casio GFX9500+ from
> personal interest. I found two things, firstly, the teachers knew very very
> little about the operation of the calculators and most of what we learnt was
> from the people around who figured it out from the manual. Secondly, some
> people have a genuine interest in learning the fundamental theory of
> mathematics and others are quite happy to learn the process and apply it
> time after time. Fortunately I was interested in the theory because when I
> went moved to the Eastern States (New South Wales) to start university I
> found that NSW does not use graphic calculators at all. That said, in all of
> first year uni, we still have not covered the same amount of maths that we
> did in final year of high school.  This is because once we have learnt the
> fundamental theory we get bogged down by doing silly things like row
> reductions and inverting matrices by hand which are simple to do on advanced
> calculators. The point is that I find this sort of thing pointless!! Even
> more pointless I think is learning numerical solving methods only to have to
> sit and substitute value after value after value with a scientific
> calculator when a graphical calculator can do it more quickly and more
> accurately than what I would need. Do you honestly think that outside of uni
> if I had to find a set of egien values/vectors I would do it by hand? What
> is the point? So for those who want to program the calculators and computers
> etc (which I enjoy immensely) let them learn the theory, for those who
> simply need to do the calculation, just do it on a graphics calculator and
> move on, what is the point of having the technology and not using it.
> 
> Now as to the use of the HP48SX, I am not familiar with this exact
> calculator but I assume that it would take an RPN style entry. If this is
> so, then to a highschool student, it would be of very little use, I would
> personally suggest something along the lines of the 38G,39G or 39G+ or even
> the TI-83 or CasioGFX950+ these are all more suitable for this level of
> study. (My personal favorite is the 39G which has some great calculus
> functions and there is a great collection of aplets about to help out..see
> www.hphomeview.com for more info)

> I must agree with va.va. After having my graphics calculator for only a
> short time I discovered that if I manipulated the coeffients the right way,
> I could make an x^3 graph look like a SIN(x) graph. To my amazemnet in 1'st
> year univeristy I discovered that what I had done ,with no mathematical
> knowlege, was to derive a simple Taylor expansion of SIN(x). The point is
> that I didnt have to know any complex maths to do it, it didnt take me hours
> to do beacuse I could plot each function in a matter of seconds, and I
> learnt by exploration the Taylor Series. I am now very greatfull that I
> learnt it this way because I have a personal understanding for the Taylor
> Series not just some mathematical mumbo jumbo that the lecturer taught us.
> To me that is the real power of a graphics calculator in learning.

     I've had a similar experience.  When I was in the 6th grade, was
playing around with a four funtion calculator.  I realized that (in
the language of the math that I new at the time) that the difference
between a number times its self and a number one smaller times itself
was twice the number is twice the smaller number plus one.  It took
until the 9th grade when I taught myself calculus to realize that I
had "discovered" the concept behind the derivative way back in 6th
grade.
     In the 8th grade I played around with a emulated TI-89.  I had no
idea what the symbolic integrate and differentiate functions did, and
wanting to now this is why I picked up a calculus textbook.
     I do not believe that now, in the 10th grade I was in any way
"hurt" by using calculators.  I use an underpowered but required TI 83
for my school math class but eagerly await the arrival of my HP-49g+
so I can explore some more.  I now routinely use my copy of
Mathematical to investigate mathematical oddities so I can explore the
often unexpected but correct results.
     I agree that the use of any type of calculator may hurt the
weaker students who have not mastered the concepts the calculator is
used for.  However, occasional use of a symbolic manipulator for
exploration will help all students expand their knowledge.
     As for the original posters question, my school is so TI
dependent that I am the only students who (soon will have) has an HP
calculator.  I have always been insulted when teachers spend class
time explaining how to use a calculator they barely understand
themselves, but that is a reality I face.  I know how to use my TI 83
better then any student or teacher else in my two kid high school even
though I use it only in class; preferring Mathematical or a symbolic
calculator to complete homework exercises of skills I have long since
mastered.  even though I rarely do my homework manually, I scored a 98
on New York's "flawed" June 2003 math A regents' exam with but a
scientific calculator.  I have no regrets to my use of a of powerful
tools that and often do  have amazing benefits.

Whilst I agree with you entirley, I think that the people on this group do
have a point, that is, for you or I, the usage of the calculator itself is a
non issue. We feel comfortable exploring our way around it and learning
almost by trial and error. But many people (I dont see how) find the use of
the calculators themselves a great challange. Thus the amount of leaning
that they gain is limited mainly because they use only what they have been
taught (badly) by teachers and have little understanding of what they are
doing.

BTW, I think that this discussion has driffted quite drastically from the
original topic! That said, I would like to reafirm the 38G/39G as excelent
highschool g-calculators.

M@

"Bill Pike" <Bill_h_pike@yahoo.ca> wrote in message
news:1ab089aa.0311111107.24f7a5a1@posting.google.com...
> > I must agree with va.va. After having my graphics calculator for only a
> > short time I discovered that if I manipulated the coeffients the right
way,
> > I could make an x^3 graph look like a SIN(x) graph. To my amazemnet in
1'st
> > year univeristy I discovered that what I had done ,with no mathematical
> > knowlege, was to derive a simple Taylor expansion of SIN(x). The point
is
> > that I didnt have to know any complex maths to do it, it didnt take me
hours
> > to do beacuse I could plot each function in a matter of seconds, and I
> > learnt by exploration the Taylor Series. I am now very greatfull that I
> > learnt it this way because I have a personal understanding for the
Taylor
> > Series not just some mathematical mumbo jumbo that the lecturer taught
us.
> > To me that is the real power of a graphics calculator in learning.
>
>      I've had a similar experience.  When I was in the 6th grade, was
> playing around with a four funtion calculator.  I realized that (in
> the language of the math that I new at the time) that the difference
> between a number times its self and a number one smaller times itself
> was twice the number is twice the smaller number plus one.  It took
> until the 9th grade when I taught myself calculus to realize that I
> had "discovered" the concept behind the derivative way back in 6th
> grade.
>      In the 8th grade I played around with a emulated TI-89.  I had no
> idea what the symbolic integrate and differentiate functions did, and
> wanting to now this is why I picked up a calculus textbook.
>      I do not believe that now, in the 10th grade I was in any way
> "hurt" by using calculators.  I use an underpowered but required TI 83
> for my school math class but eagerly await the arrival of my HP-49g+
> so I can explore some more.  I now routinely use my copy of
> Mathematical to investigate mathematical oddities so I can explore the
> often unexpected but correct results.
>      I agree that the use of any type of calculator may hurt the
> weaker students who have not mastered the concepts the calculator is
> used for.  However, occasional use of a symbolic manipulator for
> exploration will help all students expand their knowledge.
>      As for the original posters question, my school is so TI
> dependent that I am the only students who (soon will have) has an HP
> calculator.  I have always been insulted when teachers spend class
> time explaining how to use a calculator they barely understand
> themselves, but that is a reality I face.  I know how to use my TI 83
> better then any student or teacher else in my two kid high school even
> though I use it only in class; preferring Mathematical or a symbolic
> calculator to complete homework exercises of skills I have long since
> mastered.  even though I rarely do my homework manually, I scored a 98
> on New York's "flawed" June 2003 math A regents' exam with but a
> scientific calculator.  I have no regrets to my use of a of powerful
> tools that and often do  have amazing benefits.