Graphical Calculators

[Samsonknight]

Are they worth the cash? As I would like to minipulate graphs visually in my
spare time.
Or am I better off downloading and using a mathematical graphics program (if
you know of one please tell me)

Thanks

[H Bergeron]

On Mon, 4 Apr 2005 16:28:31 +0000 (UTC), "Samsonknight"

Post by Samsonknight
Are they worth the cash? As I would like to minipulate graphs visually in my
spare time.
Or am I better off downloading and using a mathematical graphics program (if
you know of one please tell me)
Thanks

Even a freeware computer program is likely to outperform a graphics
calculator for speed and ease of viewing. Quality of documentation is
another matter (though it needn't be wonderful to beat the manuals of
most calculators). There are tons out there if you Google, but I don't
know any well enough to recommend.

We use Autograph 3, which is pretty good, but costs about £50 to buy
for a single-user licence. However there is a free 30-day trial at
http://tinyurl.co.uk/s0p3

The main reason to buy a graphics calculator is for exam purposes,
where it can generate all kinds of answers - solutions of equations,
definite integrals and so on. Of course, these answers should gain no
credit without proper methods, but they can be useful checks.

(This can cut both ways though: you know you have used the right
method for that integration, but your GC tells you that you have the
answer wrong - do you invest time in finding the error, or go on to
new things, but with dented confidence?).

GCs also tend to let you enter stats data in a form where you can view
and edit data in a tabular form, which does tend to help avoid errors
in data entry.

[Alun Harford]

Post by H Bergeron
The main reason to buy a graphics calculator is for exam purposes,
where it can generate all kinds of answers - solutions of equations,
definite integrals and so on. Of course, these answers should gain no
credit without proper methods, but they can be useful checks.

I don't know about now, but in my day calculators that could do definate
integrals were not allowed in any exam in which they might be useful.

Alun Harford

[H Bergeron]

On Tue, 5 Apr 2005 21:14:12 +0000 (UTC), "Alun Harford"

Post by Alun Harford

Post by H Bergeron
The main reason to buy a graphics calculator is for exam purposes,
where it can generate all kinds of answers - solutions of equations,
definite integrals and so on. Of course, these answers should gain no
credit without proper methods, but they can be useful checks.

I don't know about now, but in my day calculators that could do definate
integrals were not allowed in any exam in which they might be useful.
Alun Harford

If you mean at A level, I suspect you did them fairly recently.
TTBOMK the only "graphical calculator" ban there has ever been was the
one that began with the C2K syllabuses in 2001 and is disappearing
this summer as the old specifications give way to the new.

Did you do your A levels in that time frame?

[Stuart Williams]

In article <***@4ax.com>, ***@thank.you
says...

Post by H Bergeron
On Tue, 5 Apr 2005 21:14:12 +0000 (UTC), "Alun Harford"

Post by Alun Harford

Post by H Bergeron
The main reason to buy a graphics calculator is for exam purposes,
where it can generate all kinds of answers - solutions of equations,
definite integrals and so on. Of course, these answers should gain no
credit without proper methods, but they can be useful checks.

I don't know about now, but in my day calculators that could do definate
integrals were not allowed in any exam in which they might be useful.
Alun Harford

If you mean at A level, I suspect you did them fairly recently.
TTBOMK the only "graphical calculator" ban there has ever been was the
one that began with the C2K syllabuses in 2001 and is disappearing
this summer as the old specifications give way to the new.
Did you do your A levels in that time frame?

From the Edexcel website:

Calculators:
Rules on calculators have been amended for the new specification: Unit C1
is now entirely non-calculator. In all other units, any calculators may
be used which are allowed by the Joint Council for Qualifications (these
can be found under paragraph 3 of the Instructions for the
Conduct of Examinations)

From the JC(G)Q website:

3.2.1 Calculators designed or adapted to offer any of the following
facilities are prohibited:
=3F language translators
=3F symbolic algebra manipulation
=3F symbolic differentiation or integration
=3F capability of remote communication with other machines or the World
Wide Web.

It goes on to say

3.3 Calculators with graphic displays and programmable calculators are
permitted if they conform to the above restrictions, unless prohibited in
the specification.

3.4 For GCE Advanced Subsidiary and Advanced Mathematics examinations,
only those calculators specified by the Qualifications and Curriculum
Authority may be used in certain Pure Mathematics unit examinations as
stipulated in the relevant specification. [Regulation 3.4 applies to
specifications whose last full A level examination is in June 2005; for
revised specifications for first teaching from September 2004, regulation
3.4 does not apply.]

So I guess that sophisticated graphics calculators are forbidden. If you
produced an indefinite integral from one of these - well, your exam
officer's head is on the block. Are there any calculators that solve
equations or evaluate definite integrals without also having the
capabilities forbidden by the regulations?

SW

[H Bergeron]

On Wed, 6 Apr 2005 19:56:10 +0100, Stuart Williams

Post by Stuart Williams
says...

Post by H Bergeron
On Tue, 5 Apr 2005 21:14:12 +0000 (UTC), "Alun Harford"

Post by Alun Harford

Post by H Bergeron
The main reason to buy a graphics calculator is for exam purposes,
where it can generate all kinds of answers - solutions of equations,
definite integrals and so on. Of course, these answers should gain no
credit without proper methods, but they can be useful checks.

I don't know about now, but in my day calculators that could do definate
integrals were not allowed in any exam in which they might be useful.
Alun Harford

If you mean at A level, I suspect you did them fairly recently.
TTBOMK the only "graphical calculator" ban there has ever been was the
one that began with the C2K syllabuses in 2001 and is disappearing
this summer as the old specifications give way to the new.
Did you do your A levels in that time frame?

Rules on calculators have been amended for the new specification: Unit C1
is now entirely non-calculator. In all other units, any calculators may
be used which are allowed by the Joint Council for Qualifications (these
can be found under paragraph 3 of the Instructions for the
Conduct of Examinations)
3.2.1 Calculators designed or adapted to offer any of the following
=3F language translators
=3F symbolic algebra manipulation
=3F symbolic differentiation or integration

Yes, symbolic algebra and calculus have always been forbidden.

Post by Stuart Williams
=3F capability of remote communication with other machines or the World
Wide Web.
It goes on to say
3.3 Calculators with graphic displays and programmable calculators are
permitted if they conform to the above restrictions, unless prohibited in
the specification.
3.4 For GCE Advanced Subsidiary and Advanced Mathematics examinations,
only those calculators specified by the Qualifications and Curriculum
Authority may be used in certain Pure Mathematics unit examinations as
stipulated in the relevant specification. [Regulation 3.4 applies to
specifications whose last full A level examination is in June 2005; for
revised specifications for first teaching from September 2004, regulation
3.4 does not apply.]

Yes, this is the rule that came in with C2K and is now being dropped
again.

Post by Stuart Williams
So I guess that sophisticated graphics calculators are forbidden.

True, though not because they are graphical, but because they do
symbolic manipulation.

Post by Stuart Williams
If you
produced an indefinite integral from one of these - well, your exam
officer's head is on the block. Are there any calculators that solve
equations or evaluate definite integrals without also having the
capabilities forbidden by the regulations?

Probably the majority do. For example, Sharp's entry-level GC, the
EL-9450 (costing about £25), lets you type in definite integrals
exactly as they are printed and it evaluates them for you. And to
solve, say, cos2x+sinx=0 on 0<x<2*pi you can simply plot the graph of
y=cos2x+sinx, and at the press of a button you can locate the
x-intercepts one after another. (Actually, in this example, the
"x-intercept" method fails to pick up the solution where the graph
touches the x-axis at a local minimum. But there is another button for
finding minima that does the job.)

In all cases, you certainly don't get the answers as fractions, surds,
multiples of pi, etc, but as decimals correct to 8 s.f. or more.

[Stuart Williams]

In article <***@4ax.com>, ***@thank.you
says...

Post by H Bergeron

Post by Stuart Williams
So I guess that sophisticated graphics calculators are forbidden.

True, though not because they are graphical, but because they do
symbolic manipulation.

Post by Stuart Williams
If you
produced an indefinite integral from one of these - well, your exam
officer's head is on the block. Are there any calculators that solve
equations or evaluate definite integrals without also having the
capabilities forbidden by the regulations?

Probably the majority do. For example, Sharp's entry-level GC, the
EL-9450 (costing about £25), lets you type in definite integrals
exactly as they are printed and it evaluates them for you. And to
solve, say, cos2x+sinx=0 on 0<x<2*pi you can simply plot the graph of
y=cos2x+sinx, and at the press of a button you can locate the
x-intercepts one after another. (Actually, in this example, the
"x-intercept" method fails to pick up the solution where the graph
touches the x-axis at a local minimum. But there is another button for
finding minima that does the job.)

Forgive the ignorance, but I don't use a calculator when doing maths: if
the machine can't produce indefinite integrals, does it evaluate definite
integrals by, as it were, drawing a graph and "counting squares"?

SW

[John Porcella]

Forgive the ignorance, but I don't use a calculator when doing maths: if
the machine can't produce indefinite integrals, does it evaluate definite
integrals by, as it were, drawing a graph and "counting squares"?

No, it produces the answer by going through algorithms. Without looking up
the booklet, Newton rings a bell.

[H Bergeron]

On Fri, 8 Apr 2005 10:46:09 +0100, Stuart Williams

Post by Stuart Williams
says...

Post by H Bergeron

Post by Stuart Williams
So I guess that sophisticated graphics calculators are forbidden.

True, though not because they are graphical, but because they do
symbolic manipulation.

Post by Stuart Williams
If you
produced an indefinite integral from one of these - well, your exam
officer's head is on the block. Are there any calculators that solve
equations or evaluate definite integrals without also having the
capabilities forbidden by the regulations?

Probably the majority do. For example, Sharp's entry-level GC, the
EL-9450 (costing about £25), lets you type in definite integrals
exactly as they are printed and it evaluates them for you. And to
solve, say, cos2x+sinx=0 on 0<x<2*pi you can simply plot the graph of
y=cos2x+sinx, and at the press of a button you can locate the
x-intercepts one after another. (Actually, in this example, the
"x-intercept" method fails to pick up the solution where the graph
touches the x-axis at a local minimum. But there is another button for
finding minima that does the job.)

Forgive the ignorance, but I don't use a calculator when doing maths: if
the machine can't produce indefinite integrals, does it evaluate definite
integrals by, as it were, drawing a graph and "counting squares"?

Yes, in the sense that it uses a purely numerical method. Numerical
methods for integration depend on dividing the area to be found into
vertical strips and the using a formula to find the total area of the
strips, based on some assumption about their shape - for example in
the simplest cases you might assume the strips are rectangles. The
discrepancy between the actual and assumed shapes introduces an error,
but the size of the error can be reduced by increasing the number of
strips.

Which of the various numerical methods are used in graphical
calculators I don't know: probably not the trapezium rule or the
mid-ordinate rule which are second-order methods - meaning that their
accuracy increases relatively slowly as the number of divisions
increases.

I would guess that either Simpson's rule (fourth order) or 3-point
Gauss method (sixth order) is more likely.

However, the method used does fix the maximum error, not the number of
strips. Thus a well-behaved graph (smooth, little change in gradient)
can be integrated much faster than a badly-behaved one (this is
particularly noticeable when the graph has a point where the gradient
approaches infinity). This probably means the calculator uses some
kind of iterative approach, estimating the error after each of a
successively improving sequence of approximations.

[Samsonknight]

Post by H Bergeron
On Mon, 4 Apr 2005 16:28:31 +0000 (UTC), "Samsonknight"

Post by Samsonknight
Are they worth the cash? As I would like to minipulate graphs visually in my
spare time.
Or am I better off downloading and using a mathematical graphics program (if
you know of one please tell me)
Thanks

Even a freeware computer program is likely to outperform a graphics
calculator for speed and ease of viewing. Quality of documentation is
another matter (though it needn't be wonderful to beat the manuals of
most calculators). There are tons out there if you Google, but I don't
know any well enough to recommend.
We use Autograph 3, which is pretty good, but costs about £50 to buy
for a single-user licence. However there is a free 30-day trial at
http://tinyurl.co.uk/s0p3

Thanks Mr Bergeron, this piece of software is great! More students should
use this as this I can imagine would improve problem solving skills - as
Mathematics becomes more visual as a result.

Post by H Bergeron
The main reason to buy a graphics calculator is for exam purposes,
where it can generate all kinds of answers - solutions of equations,
definite integrals and so on. Of course, these answers should gain no
credit without proper methods, but they can be useful checks.
(This can cut both ways though: you know you have used the right
method for that integration, but your GC tells you that you have the
answer wrong - do you invest time in finding the error, or go on to
new things, but with dented confidence?).

Such as in the Trapezium rule, where the GC gives you an approximate answer,
whilst we are expected to get an estimated answer?