Academics denounce maths A-level

Academics denounce maths A-level

news.bbc.co.uk

Dozens of university academics have put their names to calls for a new maths A-level in England to be scrapped.

Educators for Reform, a think tank offshoot, say "use of mathematics" is not of A-level standard.

They argue it will mislead students from poor backgrounds and will not prepare people for university study.

The Qualifications and Curriculum Authority said a consultation on the new course was just ending but it was meant to supplement existing A-levels.

(visit the link for the full news article)

I saw the interview between one university professor against this mickey-mouse maths, and the headteacher in favour of it. And one example of this is that trigonometry functions & other functions can be calculated on a graphical calculator for the A level Maths exam when it changes in 2011.

This will lead to university students without these basic abilities which IMO are easier to just calculate on paper anyway and sketch the graph. I am gobsmacked that graphics calculators could be used as anything more than to check answers or for the occasional too difficult equation. This would produce mindless robots whilst at school, and students unable to manipulate the maths at university level.

The headmaster was recommending these graphical calculators or software packages be used in class.

I can't see why the teachers or tutors can't just explain this on a whiteboard. The world has gone bananas.

Even linear functions at GCSE level were suggested to require a graphics calculator. For example: y=2x+1 to draw on (y vs x) axis. At that level school kids should be able to sketch that in less than 30 seconds on piece of paper IMO, not wasting time on graphical calculators.

What wrong with using a pen & paper?!! And I'm in my mid-twenties as well, I'm not an old man! The generation below me will become mindless zombies at this current rate of dumbing down!

news.bbc.co.uk
(visit the link for the full news article)


[edit on 9-7-2009 by john124]

My little brother has to type reports and now also has to send them to their teachers attached in an email.

That is now how his school turns in their reports and essays.

It's to prepare them for the work world where email rules aparantly.

And each time I read the word "maths", my brain hurt a little lol.

I weep for the future of this planet.....

Originally posted by breakingdradles
My little brother has to type reports and now also has to send them to their teachers attached in an email.

That is now how his school turns in their reports and essays.

It's to prepare them for the work world where email rules aparantly.

And each time I read the word "maths", my brain hurt a little lol.

Well that's not so bad if they learn a few IT skills. There are useful IT skills that are vital to be learnt at an early age, but they should still be supplemented with traditional methods, especially in Maths. As these traditional methods cannot be substituted at university and in real-life skills. Humans tend to learn through a process, and if the process if bypassed then we would all become robots!

IMO I think school work should be handed in physically on paper, or maybe some form of media. But email's can be lost, or deleted or just not read. I wouldn't trust emails for anything vital.

A couple of points to make...

Most people function very well in life and can become hugely successful with only a 13 year-old understanding of basic mathematics. After around Year 8, Mathematics starts to specialise beyond the capability of lots of people to understand.

Years ago, before calculators, people had to learn algorithms for finding square roots. They had to use tables for trigonometric and logarithmic calculations. They had to know time consuming processes such as long division.

With the introduction of the basic calculator, there was no longer a need to learn how to approximate square roots. The technology helped the user to progress beyond the trivial and to concentrate on using the square root. Would anyone argue that we should do away with basic calculators and return to using tables? Of course not, it's a ridiculous notion.

I'm not intending to write a referenced essay here, though I could, so I'm only listing some simple examples.

The fear and paranoia regarding graphics and CAS calculators today, is due to the pace of the technology being introduced. Before some educators can become competent with one model of calculator, the next model has already been released, surpassing the junk. Naturally, many educators would not have had time to adapt their curriculums and examine what they consider should be important to teach. The introduction of Year 12 courses with an assumed CAS competent has been delayed by a year in Victoria. There are not enough schools or educators who will be ready to introduce it next year, as was initially planned. Texas Instruments are still tweaking their TI n-spire CAS model. The latest software update was not long ago.

The most important aspect of graphics and CAS calculators is to make sure that they are used effectively. Students need to be taught when it should be appropriate to either use a CAS and when to ignore it.

Resorting to a CAS calculator to quickly sketch y = 2x + 1 is dependent upon the mathematical experience of the user. Younger students might be exposed to this using technology, however, older students in the A streams should not need to use a CAS. However, sketching something like y = e^x * cos (3x^2 - 4) does justify the use of a CAS, to help a student gain an immediate visual. Sure, it's possible to sketch by hand and can be tried, but it will take time.

Efficient use of technology is the key to a better mathematical understanding.

Also, the content taught can not be planned in isolation of the assessment methods that will be used. An old phrase is 'that the assessment tail wags the curriculum dog'.

Appropriate forms of assessment need to be used. In Victoria, the A stream courses have two final exams. The first, is technology free for one hour. Students must know 'required' processes by-hand. The second, is graphics calculator active, for two hours. Students must know how to effectively use their technology.

The debate centres around which processes should be required, by-hand.

Summarising - education departments are in a state of flux and don't know how to approach the onslaught of technology. Many educators don't know how to approach the onslaught of technology. Many parents have no idea about how much Mathematics has developed, so they don't know how to approach the onslaught of technology. Students are in the best position to embrace the technology, provided they are taught how to judiciously use it and not use it.

Here's a quick example to consider:
Part of a problem requires the following simultaneous equations to be solved...

2w + 3x - 5y + 6z = 7
-3w - 4x + 7y + 8z = 9
6w + x - 8y - 2z = -4
w - 4x - 6y + 3z = -22

I'll use a calculator, taking 30 seconds to tell you that

w = 6498/2081
x = 5804/2081
y = 6041/2081
z = 2394/2081

You get your pen and paper out, enjoy your next hour working out determinants, while I've already moved on to the next part of the problem that required this solution.

Stating that graphics and CAS calculators have no place in Mathematics education is extremely short-sighted and wrong.

The film idiocracy springs to mind.

Very, very scary.

You can be sure the Chinese and the Russians aren't dumbing down their kids! Where is this going to leave the world?

Originally posted by YourForever
You can be sure the Chinese and the Russians aren't dumbing down their kids! Where is this going to leave the world?

I can tell you for a fact that some Chinese students do not know how to use the CAS calculators and they are at a disadvantage in different ways.

They would get out their pen and paper and solve those simultaneous equations by-hand. Meanwhile, the rest of the class has moved on...

Do some research and see exactly how the Chinese and Russians educate their students.

Who really needs to take Calculus anymore when we have graphing calculators and such? Rubbish/

Originally posted by hermantinkly
Who really needs to take Calculus anymore when we have graphing calculators and such? Rubbish/

Humans do maths. The calculators only do what humans tell them to do. Calculators are only good for performing calculations, believe it or not.

It's not that important whether you can evaluate an integral on your own, as being able to recognise when you might need to use that integral as part of a solution procedure.

Think of it like this:
Would you ban students from using spelling and grammar checks in MSWord? Personally, my writing has improved, as a result of using Word. When I see the red and green lines, I know that something may be wrong with my spelling or grammar. Word does not write my essay, but it sure helps me.

Similarly, the CAS calculators, when used effectively, are a good tool to assist learning. They are not a substitute for learning.

Of course there is a place for graphical calculators, but not on A-Level Exams, as this likely prevents many A level students from gaining the expertise to be able to do simple algebraic and trig equations on paper. And this is absolutely necessary for Maths, Physics, Engineering and other science courses at University level. You won't have the graphics calculator in your exam at degree level, and to be frank there is no need for it if you learn the relevant techniques.

Employers like science, engineering and maths degrees because the graduates have shown themselves capable of showing problem solving techniques, and so will adapt in real life situations. This really can't be denied. Employers for top jobs don't look for robots, they want innovative and highly intelligent people.

Of course there are uses for graphical calculators and software packages involving more difficult equations such as with coursework.

University level exams don't waste time with long multiplication techniques, the assessment is on application of the equations and such including learning them. The same should be for A Level Maths at that level, and not bypassing this and creating robots.

And yes you're right people can cope very well without hardly any Maths, and they do. But for University places at decent Uni's to do science or maths courses they require students to have a reasonable level of understanding of A Level maths. That was the issue at hand. I apologise if you got the wrong impression that this thread was intended to bash graphical calcs as a whole, as I have used the equivalent software packages myself occasionally.

And the problem people have with maths beyond yr 8 level is they assume it's too difficult so refuse to accept they can ever understand it. There's been many documented adult learners who have had this problem due to poor teaching at their school or other problems involving confidence. The problem is once they get older it's extremely difficult to take anything in that's new to them.

The y=2x+1 was the example I saw teachers in a school on the news showing students on a graphical calculator. I reckon I could teach any 15-16 yr old how to draw the graph of this who are willing to learn this within 5 minutes on a whiteboard, and visually this is better than on a touch screen.

Using the graphical calculator just adds unnecessary jargon into their heads at this level, and overcomplicates the situation. Of course introduce this later, but I wouldn't recommend using it as the primary method of teaching as they were demonstrating on the news. The kids looked bemused from what I saw, and I'm not surprised.



[edit on 9-7-2009 by john124]

Originally posted by john124
Of course there is a place for graphical calculators, but not on A-Level Exams, as this likely prevents many A level students from gaining the expertise to be able to do simple algebraic and trig equations on paper.

There are other ways to effectively assess students. You must have skipped over the part where I explained how assessment can be both technology free and active.

Originally posted by john124
Employers like science, engineering and maths degrees because the graduates have shown themselves capable of showing problem solving techniques, and so will adapt in real life situations. This really can't be denied. Employers for top jobs don't look for robots, they want innovative and highly intelligent people.

Have you thought this through to its obvious conclusion? Employers want people who can solve their problems. I guarantee you that very few people will solve engineering problems using pen and paper. They'll use computers, with CAS algorithms. Graduates, with little exposure to CAS will not be as versatile as those who are competent with them.

Originally posted by john124
But for University places at decent Uni's to do science or maths courses they require students to have a reasonable level of understanding of A Level maths. That was the issue at hand.

Yes, they do. Therefore, schools need to ensure that they hire good teachers who are able to embrace the technology to effectively help students learn.

The root of the problem starts in the early years. Many Primary School teachers are not confident with their own mathematical ability. Research for pre-service teachers shows that some of them struggle to cope with basic concepts that a Grade 6 student should know. By the time some students reach high school age, it's too late for them. They don't have the skills to progress to anything more than replicating the four operations of a basic calculator.

Originally posted by john124
And the problem people have with maths beyond yr 8 level is they assume it's too difficult so refuse to accept they can ever understand it.

It is too difficult for lots of people. The majority of people shouldn't try to progress to A level Maths. There's a sad delusion in society that anyone can do anything if they try hard enough. This is not so. For lots of people, the ability to competently progress into quadratic algebra and beyond, is not there.

Research suggests that people maybe born with a natural number sense. I am convinced that somewhere there is a 'maths' gene and lots of people simply don't have it.

There's nothing wrong with that. People can't excel at everything.

Originally posted by john124
The y=2x+1 was the example I saw teachers in a school on the news showing students on a graphical calculator. I reckon I could teach any 15-16 yr old how to draw the graph of this who are willing to learn this within 5 minutes on a whiteboard, and visually this is better than on a touch screen.

I would love to see you try and teach it in five minutes. Please, if you ever get the opportunity to try it, videotape the lesson for me and let me see it.

Originally posted by john124
Using the graphical calculator just adds unnecessary jargon into their heads at this level, and overcomplicates the situation.

Students are familiar with mobile phones, iPods and an array of other hand-held gadgets. The jargon from a calculator is no more difficult than what students can already master by themselves, without teachers showing them.

reply to post by tezzajw


University Professors are stating that A Level Maths does not even go far enough to allow an easy transition onto degree level Maths. And further Maths is recommended.

I have nothing against teaching A level students the use of graphical calcs, but there is zero reason for these to be part of the A level Maths examination, as that is basically giving away marks.

I don't think you can say because standard calculators are used instead of long multiplication, that this means graphical calcs should be used in exams. The students aren't assessed on multiplication of large numbers, but they are assessed in plotting maths functions. This is a basic component at A level, as learning multiplication tables at a younger age. This stays with you forever.

Employers and Universities are looking for these skills over how to input on a graphics calculator. Yes students have to learn how to interpret results and there's always the garbage-in-garbage-out scenario possibility. But generally a student would learn the input technique over the mathematical technique. I guarantee this would happen, it's not long since I was a student myself at this level, and students would go for the easier route of learning if the opportunity presented itself.

To allow graphical calcs in exams means this mathematical technique is no longer part of the assessment. If we compromise and have a section A and B with one with the graphics calculator, then this just opens the door to allowing a graphics calculator for the whole A level Maths exam, and therefore lowering the standard of skills learnt.

However you put it, the skills of operating a graphics calculator are nowhere near as relevant as students learning it from a book, pen and paper and standard calculator. And the tech savvy youngsters probably don't need to read a manual to use their phone, therefore they can pick up how to use a graphical package in much the same way. The interface is intuitive much in the same way as a calculator. I realised it appears I said otherwise earlier, but sorry that was a mistake and I actually meant that it was more hassle on a graphical calculator only for the very easiest of linear equations, except for the least able of students.

A level Maths assessment should stick to the mathematical principles for the assessment, and not assess data input as anything more than a subsidiary. Are we going to assess year 9 students next on how to input 6*6 on a calculator?

Listen, we don't need to assess the kids on this.... University Professors have put forward how this can be detrimental and dumbing-down to an extent possibly where kids don't even know how to integrate and differentiate basic trig functions.

And my previous comment was a little rushed, and may not have been as clear as this one with more relevant points.

And I am definitely for graphics calculator usage in any classroom where the teacher deems it appropriate as a secondary after teaching the material. Or of course if the student has his/her own. But I am completely against using these as a primary method of teaching as it sets a dangerous precedent, and any use whatsoever during examinations. Any diminuishing of A level maths will just prevent students from attaining the necessary understanding for degree level basics.


[edit on 9-7-2009 by john124]

Employers want people who can solve their problems. I guarantee you that very few people will solve engineering problems using pen and paper. They'll use computers, with CAS algorithms. Graduates, with little exposure to CAS will not be as versatile as those who are competent with them.

The graphics calculators and software packages used by A level students in this new scheme for 2011 pales in comparison to the packages that are used in the workplace.

Universities do offer courses with CAS algorithm packages on engineering courses and other courses. Students will only learn a great deal when at this level using such graphical packages.

An introduction into a basic graphics calculator or online/offline software package is useful, but would not be at all detrimental if the students first used these at university.

They would of course be at a much greater disadvantage not to be able to understand their core modules because of their lack of understanding of basic trigonometry or calculus, due to not needing this for A level because their A level Maths exams didn't even ask them to perform this task.

I think this is likely the positions taken by many University Professors in Maths. I know the lecturers of Engineering courses with less Maths orientated modules would see a slight benefit, but this causes more problems for Physics & Maths courses than the problems it solves in Engineering courses.

And surely this just means A level Maths required in 2 or more different syllabuses depending on the pathway of the student to be taken. Rather than just changing A level Maths to be more favourable to Engineering over Maths courses.

[edit on 9-7-2009 by john124]

Originally posted by john124
I have nothing against teaching A level students the use of graphical calcs, but there is zero reason for these to be part of the A level Maths examination, as that is basically giving away marks.

Then the assessment needs to be looked at and adjusted accordingly. There are many ways to ask questions, where having a CAS calculator provides no advantage.

You seem to skip over the part where I have described how exams can also be technology free. Isn't that good enough to test a student's ability to demonstrate basic processes?

Originally posted by john124
Employers and Universities are looking for these skills over how to input on a graphics calculator.

I disagree. Employers are looking for people who can get the job done, whatever the means.

Originally posted by john124
But generally a student would learn the input technique over the mathematical technique. I guarantee this would happen, it's not long since I was a student myself at this level, and students would go for the easier route of learning if the opportunity presented itself.

How is one way of learning 'easier' than another way of learning? Provided that you have learnt, does it matter how you got there?

Originally posted by john124
To allow graphical calcs in exams means this mathematical technique is no longer part of the assessment.

Completely unfounded opinion and contradictory to research. Allowing CAS calculators in exams means that a different set of skills are being tested. Questions need to be written that are specifically tailored to the technology.

Originally posted by john124
If we compromise and have a section A and B with one with the graphics calculator, then this just opens the door to allowing a graphics calculator for the whole A level Maths exam, and therefore lowering the standard of skills learnt.

Please supply your data to prove this. I know by reading your fearmongering statements that you have not researched this topic and you are trying to pass off your opinion as fact.

Originally posted by john124
However you put it, the skills of operating a graphics calculator are nowhere near as relevant as students learning it from a book, pen and paper and standard calculator.

I disagree. Mathematics is more the richer for embracing technology. Mathematical progress has been richly rewarded with the introduction of computers and CAS software. Wanting students to return to using slide-rules is a backward step. Wanting students to return to using a scientific calculator is a backward step. Wanting students to return to using a graphics calculator is a backwards step. CAS calculators will not go away and they will be an integral part of learning mathematics.

Originally posted by john124
A level Maths assessment should stick to the mathematical principles for the assessment, and not assess data input as anything more than a subsidiary. Are we going to assess year 9 students next on how to input 6*6 on a calculator?

Your example again highlights how little research you have done on this topic.

Originally posted by john124
Listen, we don't need to assess the kids on this.... University Professors have put forward how this can be detrimental and dumbing-down to an extent possibly where kids don't even know how to integrate and differentiate basic trig functions.

Could you please link me?

Originally posted by john124
But I am completely against using these as a primary method of teaching as it sets a dangerous precedent, and any use whatsoever during examinations. Any diminuishing of A level maths will just prevent students from attaining the necessary understanding for degree level basics.

What you think mathematics education should be is not where it is currently going. The CAS calculators will be an integral tool to help learning - when used effectively. Poor use of the CAS calculators will be detrimental, like poor use of any other tool.

reply to post by tezzajw

I disagree. Employers are looking for people who can get the job done, whatever the means.

It's no good if the students can't pass their exams at University to a reasonable level or even at all because they fail to understand the basic Maths concepts.

Look I understand you feel the use of graphics calculators on exam papers requires more dedicated skills in the assessment than IMO.

You could be right, I'm not sure if I can provide any more than an opinion to back up how I feel about it.

You would be better trying to convince these academics if you feel they are not taking advantage of an opportunity, but rather squandering it:

The academics - at least 62 of them as of Thursday afternoon - say that in particular the compulsory algebra and calculus units are "considerably less demanding and cover less content than A-level".

[edit on 10-7-2009 by john124]

[edit on 10-7-2009 by john124]