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Do yourself a BIG favour - Get a GDC

Well yet again I've said to one of my students "let's look at this on the TI-Nspire". There is so much it can help you with, if you know how to use it well.

Why then are most UK students so stupid as to not invest in something that could well push their A-level results up a grade? Surely they can't be so mean that they would sacrifice a better grade to save a little money. Or maybe they are naive enough to listen to a lying teacher who tells them that the calculator is not allowed (only true for Core 1, which doesn't allow any calculator), or that they offer no advantage. And, you will generally find that teachers who say this have no, or very little, experience of using a GDC.

To take just one example of how useful a GDC can be, consider the normal distribution. Students often experience difficulty working out probabilities when a boundary is less than the mean (i.e. negative for the standard normal distribution), and make mistakes. You can look this up directly on a GDC. This is just one example of many.

If you want to get a better maths A-level, do yourself a big favour and get a GDC: the TI-Nspire CX is one of the best (the CAS model is not allowed in exams). Don't listen to your maths teacher: these days most of them are pretty useless.

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Reply 1
Original post by David Getling
Well yet again I've said to one of my students "let's look at this on the TI-Nspire". There is so much it can help you with, if you know how to use it well.

Why then are most UK students so stupid as to not invest in something that could well push their A-level results up a grade? Surely they can't be so mean that they would sacrifice a better grade to save a little money. Or maybe they are naive enough to listen to a lying teacher who tells them that the calculator is not allowed (only true for Core 1, which doesn't allow any calculator), or that they offer no advantage. And, you will generally find that teachers who say this have no, or very little, experience of using a GDC.

To take just one example of how useful a GDC can be, consider the normal distribution. Students often experience difficulty working out probabilities when a boundary is less than the mean (i.e. negative for the standard normal distribution), and make mistakes. You can look this up directly on a GDC. This is just one example of many.

If you want to get a better maths A-level, do yourself a big favour and get a GDC: the TI-Nspire CX is one of the best (the CAS model is not allowed in exams). Don't listen to your maths teacher: these days most of them are pretty useless.



Which school do you teach at if you do not mind asking?
I'll be interested to see where this thread goes. I'm an American who came over to England about a little over a month ago to do a PGDipEd in Secondary Maths. Graphing Calculators are found in the school bags of most American students once they begin algebra, usually a TI-84.

They're wonderful tools, but they can also allow students to be incredibly lazy. I don't think there's a thing wrong with the statistics example that you mentioned, but I've seen students resort to graphing really basic polynomials on them. Do you really need a calculator to graph y=2(x-4)^2-1? I want students to understand at a glance what transformations have taken place. Likewise, I know quite a few students who think factorising a quadratic means graphing it and finding the x-intercepts using the calculator. An answer can be found easily if the quadratic has a leading coefficient of 1 and integer roots, but I've seen students write (x-0.166666667) as a factor and argue that it must be right because that's what their calculator said was the x-intercept.

As with many tools, it's a balance of know when it's appropriate to use calculators. My experience with students in the US is that they struggle to find that balance. I'm looking forward to seeing the difference in calculator usage between the two countries firsthand.
Original post by ktalexander

As with many tools, it's a balance of know when it's appropriate to use calculators.


This is the main argument against their use

A Level maths does not need a graphical Calculator

The timing of the exam papers gives students more than enough time to calculate and check everything they need

The example suggested in the OP regarding the normal distribution suggests using the calculator rather than teaching a better understanding



I fully understand the OPs point - whist graphical calculators are allowed in school exams some students will find themselves advantaged if they use one
(edited 9 years ago)
Is there really any advantage of the Nspire CX over a GDC half its price? I was intending on getting a GDC and was planning on going for the Casio FX-9750GII since I really don't particularly want to be spending over £100 on something which I'm dubious about its use anyway.

Also, how is the CX allowed in exams when it allows you to import images? What's to stop you from storing formulae?
(edited 9 years ago)
Original post by TenOfThem
example suggested in the OP regarding the normal distribution suggests using the calculator rather than teaching a better understanding

A better understanding of what, using tables? Are tables really the end-all, be-all of statistical understanding?

I definitely think that students need to understand z-scores as how many standard deviations a value is away from the mean. I think they should be able to calculate those values as well and have found that if you start with values that can be done intuitively, a formula is easily derived. Understanding comes from applying the numbers to make useful inferences, not from being able to look up numbers on a table. Let the calculator do the mindless stuff and have the students do the reasoning on what those numbers actually mean within the context of the problem.
Original post by ktalexander
A better understanding of what, using tables? Are tables really the end-all, be-all of statistical understanding?

I definitely think that students need to understand z-scores as how many standard deviations a value is away from the mean. I think they should be able to calculate those values as well and have found that if you start with values that can be done intuitively, a formula is easily derived. Understanding comes from applying the numbers to make useful inferences, not from being able to look up numbers on a table. Let the calculator do the mindless stuff and have the students do the reasoning on what those numbers actually mean within the context of the problem.


The example given was that students fail to understand when the boundary is less than the mean - students should have no more difficulty with this than with a boundary above the mean - if the OP were saying "use the calculator instead of the tables" that would be very different
Reply 7
Just my two cents, as an IB student, graphical calculators are mandatory for all the Math courses, be it the Higher or Standard levels. In our programme, it is meant to complement our understanding. Students are not able to get away with not understanding something and simply plugging numbers into the GDC. The bulk of the work, especially the conceptual part is done by the student. The GDC is simply there to facilitate the number crunching.

However, as I have some experience with the A-level course, students are able to get away with using the GDC's to get away with not completely understanding something or turning them lazy. My opinion is that the use of a GDC is good, as long as the teacher is able to control the usage and guide the students into using the GDC only for the boring number crunching and letting the students use do all the conceptual work. How this could be implemented, I do not know, I leave that for teachers with much more experience and knowledge to work something out. :smile:
Original post by Zacken
Just my two cents, as an IB student, graphical calculators are mandatory for all the Math courses, be it the Higher or Standard levels. In our programme, it is meant to complement our understanding. Students are not able to get away with not understanding something and simply plugging numbers into the GDC. The bulk of the work, especially the conceptual part is done by the student. The GDC is simply there to facilitate the number crunching.

However, as I have some experience with the A-level course, students are able to get away with using the GDC's to get away with not completely understanding something or turning them lazy. My opinion is that the use of a GDC is good, as long as the teacher is able to control the usage and guide the students into using the GDC only for the boring number crunching and letting the students use do all the conceptual work. How this could be implemented, I do not know, I leave that for teachers with much more experience and knowledge to work something out. :smile:


The standard approach in exam questions is to ask for exact answers, i.e. answers including ln 2 or pi for instance. Edexcel have also started saying "using algebraic integration" in their Mechanics papers and the sentence "Solutions based entirely on graphical or numerical methods are not acceptable." in their Pure papers.
To answer a few points. K T Alexander, what you say about most students in the US packing a GDC doesn't come as any surprise. I came across them being used with students in New Zealand who were taking the equivalent of GCSE, never mind A-level.

The comments about students being lazy or not needing them are valid, BUT since they are allowed in exams, and DO confer an advantage it's silly not to use one. They shouldn't be a substitute for understanding, but when you are in an exam and after that A grade anything that you are allowed to do goes. If using a graph or polyroots helps you get the answer quicker, or make sure that you have got it right, then go for it - there are no marks for heroic effort.

Chlorophile, I have taught students to use the Casio that you mentioned, and the TI-83 and TI-84, so I can say beyond a shadow of a doubt that the TI-Nspire is much better. Yes it costs more, but you get what you pay for. Isn't it worth the extra money if it might get you a few more marks in your exams? The CX is definitely allowed. However, for A-level exams, it is your responsibility to clear the memory before entering the exam. For I.B. exams this is the responsibility of the invigilator.

Hobbit, even if Edexcel is trying to negate the advantage of using a GDC they are kidding themselves. They can only reduce it a bit without radically changing their exams. For example, are they going to get rid of graph sketching? Are they going to dock marks from students who look up binomial values with p > 0.5, rather than buggering around by turning the question into one about failures? And, if nothing else, even if lots of working, or an exact solution, must be given a GDC can often tell you very quickly whether you have got the right answer.
Original post by David Getling
To answer a few points. K T Alexander, what you say about most students in the US packing a GDC doesn't come as any surprise. I came across them being used with students in New Zealand who were taking the equivalent of GCSE, never mind A-level.

The comments about students being lazy or not needing them are valid, BUT since they are allowed in exams, and DO confer an advantage it's silly not to use one. They shouldn't be a substitute for understanding, but when you are in an exam and after that A grade anything that you are allowed to do goes. If using a graph or polyroots helps you get the answer quicker, or make sure that you have got it right, then go for it - there are no marks for heroic effort.

Chlorophile, I have taught students to use the Casio that you mentioned, and the TI-83 and TI-84, so I can say beyond a shadow of a doubt that the TI-Nspire is much better. Yes it costs more, but you get what you pay for. Isn't it worth the extra money if it might get you a few more marks in your exams? The CX is definitely allowed. However, for A-level exams, it is your responsibility to clear the memory before entering the exam. For I.B. exams this is the responsibility of the invigilator.

Hobbit, even if Edexcel is trying to negate the advantage of using a GDC they are kidding themselves. They can only reduce it a bit without radically changing their exams. For example, are they going to get rid of graph sketching? Are they going to dock marks from students who look up binomial values with p > 0.5, rather than buggering around by turning the question into one about failures? And, if nothing else, even if lots of working, or an exact solution, must be given a GDC can often tell you very quickly whether you have got the right answer.


Original post by tiny hobbit
The standard approach in exam questions is to ask for exact answers, i.e. answers including ln 2 or pi for instance. Edexcel have also started saying "using algebraic integration" in their Mechanics papers and the sentence "Solutions based entirely on graphical or numerical methods are not acceptable." in their Pure papers.


Original post by Zacken
Just my two cents, as an IB student, graphical calculators are mandatory for all the Math courses, be it the Higher or Standard levels. In our programme, it is meant to complement our understanding. Students are not able to get away with not understanding something and simply plugging numbers into the GDC. The bulk of the work, especially the conceptual part is done by the student. The GDC is simply there to facilitate the number crunching.

However, as I have some experience with the A-level course, students are able to get away with using the GDC's to get away with not completely understanding something or turning them lazy. My opinion is that the use of a GDC is good, as long as the teacher is able to control the usage and guide the students into using the GDC only for the boring number crunching and letting the students use do all the conceptual work. How this could be implemented, I do not know, I leave that for teachers with much more experience and knowledge to work something out. :smile:


Original post by TenOfThem
The example given was that students fail to understand when the boundary is less than the mean - students should have no more difficulty with this than with a boundary above the mean - if the OP were saying "use the calculator instead of the tables" that would be very different


Original post by ktalexander
A better understanding of what, using tables? Are tables really the end-all, be-all of statistical understanding?

I definitely think that students need to understand z-scores as how many standard deviations a value is away from the mean. I think they should be able to calculate those values as well and have found that if you start with values that can be done intuitively, a formula is easily derived. Understanding comes from applying the numbers to make useful inferences, not from being able to look up numbers on a table. Let the calculator do the mindless stuff and have the students do the reasoning on what those numbers actually mean within the context of the problem.


Original post by Chlorophile
Is there really any advantage of the Nspire CX over a GDC half its price? I was intending on getting a GDC and was planning on going for the Casio FX-9750GII since I really don't particularly want to be spending over £100 on something which I'm dubious about its use anyway.

Also, how is the CX allowed in exams when it allows you to import images? What's to stop you from storing formulae?



I just wanted to ask, what graphical calculators are allowed in alevel exams that you can use to draw frequency tables, find z values and things like that? The best calculator.

Thanks!
Reply 11
Original post by David Getling
To answer a few points. K T Alexander, what you say about most students in the US packing a GDC doesn't come as any surprise. I came across them being used with students in New Zealand who were taking the equivalent of GCSE, never mind A-level.

The comments about students being lazy or not needing them are valid, BUT since they are allowed in exams, and DO confer an advantage it's silly not to use one. They shouldn't be a substitute for understanding, but when you are in an exam and after that A grade anything that you are allowed to do goes. If using a graph or polyroots helps you get the answer quicker, or make sure that you have got it right, then go for it - there are no marks for heroic effort.

Chlorophile, I have taught students to use the Casio that you mentioned, and the TI-83 and TI-84, so I can say beyond a shadow of a doubt that the TI-Nspire is much better. Yes it costs more, but you get what you pay for. Isn't it worth the extra money if it might get you a few more marks in your exams? The CX is definitely allowed. However, for A-level exams, it is your responsibility to clear the memory before entering the exam. For I.B. exams this is the responsibility of the invigilator.

Hobbit, even if Edexcel is trying to negate the advantage of using a GDC they are kidding themselves. They can only reduce it a bit without radically changing their exams. For example, are they going to get rid of graph sketching? Are they going to dock marks from students who look up binomial values with p > 0.5, rather than buggering around by turning the question into one about failures? And, if nothing else, even if lots of working, or an exact solution, must be given a GDC can often tell you very quickly whether you have got the right answer.


I went to university in the eighties when only scientific calculators were around. (if graphics ones just started coming out I do not know but certainly I do not remember seeing one back then.)

To my shock, as a naive first year student then, I could not fathom how calculations were to be made without a calculator! (UCL still to this day DOE NOT allow the use of any calculation aid in their exams)

The points that Davidgetling is trying to make are these

point one

If the "system" allows the use of such aid you will be foolish not to use one, if you can afford it and it is going to help you by checking answers (or by checking the answers or graphs you can reconstruct the solution)
To this point I fully agree.


point two

why do we have to use normal tables, binomial tables, etc some with very limited values for the parameters.
How is that different form using tables for trigonometric ratios, logarithms etc.?
Shall we even bring back tables for square roots, cube roots etc (I actually own a booklet with such tables).
A calculator should be able to give values for all probability distributions as well as some special functions such as gamma, beta, bessel to name a few.

The point I disagree is the use of calculators that factorize, solve simultaneous equations etc

In my opinion topics should be grouped in such a way so you have more non calculator papers.
Advanced mechanics papers should be all be non calculator demanding exact answers in terms of constants
Further pure should all be non calculator (I do not include FP1 in this list as this is "Mickey Mouse Maths" and was introduced in its current form in 2009 for "educationally political" reasons).

The boards will do nothing as most of them are run like business.
Top universities already pick candidates for maths and strong science degrees on non calculator papers such as Step, AEA, Oxford entry etc. (the A* is a given)
Everybody is happy, why rock the boat?
Allow graphic calculators, allow computer algebra systems, allow "ask a friend" ...
Soon everybody will be getting A* ( as a God given right) and eventually" A level Mathematics" will renamed as "A level" in "Shoe lacing techniques".
(look as an analogy the use of the word "Pure". "A level Maths" had pure topics in 60s but not now)
It is all political.
We are a developed country, we need only produce a handful of top brains to replace the deceased, and if we experience a shortage we can always import scientists from a developing country instead of investing in the education here.

I am getting off the subject but I got some things off my chest ...

(Apologies for my rant)
Original post by TenOfThem
X


This feature is also available on many standard scientific calculators, for example the Casio fx-991ES, which I use, has that technique for probability distribution functions. Knowing how to use a calculator is useful provided you also know how to do the maths underneath.
Original post by David Getling
To answer a few points. K T Alexander, what you say about most students in the US packing a GDC doesn't come as any surprise. I came across them being used with students in New Zealand who were taking the equivalent of GCSE, never mind A-level.

The comments about students being lazy or not needing them are valid, BUT since they are allowed in exams, and DO confer an advantage it's silly not to use one. They shouldn't be a substitute for understanding, but when you are in an exam and after that A grade anything that you are allowed to do goes. If using a graph or polyroots helps you get the answer quicker, or make sure that you have got it right, then go for it - there are no marks for heroic effort.

Chlorophile, I have taught students to use the Casio that you mentioned, and the TI-83 and TI-84, so I can say beyond a shadow of a doubt that the TI-Nspire is much better. Yes it costs more, but you get what you pay for. Isn't it worth the extra money if it might get you a few more marks in your exams? The CX is definitely allowed. However, for A-level exams, it is your responsibility to clear the memory before entering the exam. For I.B. exams this is the responsibility of the invigilator.

Hobbit, even if Edexcel is trying to negate the advantage of using a GDC they are kidding themselves. They can only reduce it a bit without radically changing their exams. For example, are they going to get rid of graph sketching? Are they going to dock marks from students who look up binomial values with p > 0.5, rather than buggering around by turning the question into one about failures? And, if nothing else, even if lots of working, or an exact solution, must be given a GDC can often tell you very quickly whether you have got the right answer.


The thing is, I'm dubious that it would get me extra marks. I mean the GDC looks cool but I've never had a situation where I've thought "my life would be so much easier with a graphics calculator". I've not done FP2 or FP3 yet but I have done C1-4 all the other X1 modules and I seriously don't see how a GDC would be of serious use. Maybe I'm wrong, but I've been pretty happy with my FX991ES.
Reply 14
Original post by Chlorophile
The thing is, I'm dubious that it would get me extra marks. I mean the GDC looks cool but I've never had a situation where I've thought "my life would be so much easier with a graphics calculator". I've not done FP2 or FP3 yet but I have done C1-4 all the other X1 modules and I seriously don't see how a GDC would be of serious use. Maybe I'm wrong, but I've been pretty happy with my FX991ES.


if you are a "serious candidate" there is no advantage ...
for the weaker students in straight maths there is a small advantage.
Original post by Chlorophile
The thing is, I'm dubious that it would get me extra marks. Maybe I'm wrong, but I've been pretty happy with my FX991ES.


GDCs, and especially the TI-Nspire are sophisticated tools, that take substantial effort to get to know well. Like any sophisticated tool until you have become very familiar with it, like me, you are quite incapable of judging just how powerful and useful it can be. I could show you numerous places in C2 to C4 (no calculators in C1) where a GDC could help you, and for statistics I've written 70 pages on the subject.

While I don't question TeeEm's maths expertise, I do wonder just how much experience he has of using GDCs.

Any sensible student recognizes that because they don't possess the necessary experience they need to trust and be guided by someone that does. Unfortunately, when it comes to GDCs, very few maths teachers in this country have anywhere near enough experience to make an accurate appraisal of how useful they might be to their students. Even worse, they aren't honest enough to admit this.
Original post by David Getling
GDCs, and especially the TI-Nspire are sophisticated tools, that take substantial effort to get to know well. Like any sophisticated tool until you have become very familiar with it, like me, you are quite incapable of judging just how powerful and useful it can be. I could show you numerous places in C2 to C4 (no calculators in C1) where a GDC could help you, and for statistics I've written 70 pages on the subject.Well, how about actually giving some of these examples, so we can get an idea of exactly what you're talking about?
Original post by DFranklin
Well, how about actually giving some of these examples, so we can get an idea of exactly what you're talking about?


Bad mistake - here comes the advert for his wondrous books on the benefits of GDCs. Relentless advertising got him banned from the TES website.

I've no desire to publicise those books but I did enjoy the Amazon reviews for another of his less-than-weighty tomes.

Earlier thread from TSR
(edited 9 years ago)
Original post by Mr M
...


You're a mine of information - PRSOM.
Reply 19
Original post by Mr M
Bad mistake - here comes the advert for his wondrous books on the benefits of GDCs. Relentless advertising got him banned from the TES website.

I've no desire to publicise those books but I did enjoy the Amazon reviews for another of his less-than-weighty tomes.

Earlier thread from TSR


I think everybody should click on Mr M's link to Amazon reviews!

Some of them are quite funny

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