Teaching is a real life job and there is a desperate need for them!

That's why my suggestion might work. I am suggesting we use experienced teachers, possibly from fields other than science or mathematics, to take on this professional learning. These guys already have the teaching and classroom management its just a matter of learning some new material and techniques. Secondary teachers working outside their fields do this a lot. At least this would be a formal process where quality could be more even.

Adrian, do you believe this may be the case for science too? I am looking into this for my PhD.

I think you are correct in blaming the marketing departments in universities for some of this misinformation.

For example; I was told that companies are 'screaming for Photonics graduates' (which, luckily I was interested in anyway). As it turns out there are perhaps a hand full of jobs being advertised each year and most are short term contract positions in universities.

That said, I think more people should have mathematics training, as it improves their critical thinking and logic. Which can only make them better in what ever area they work in.

What we really have a shortage of are mathematically literate people. Not mathematicians.

If maths was so good at improving critical thinking we wouldn't have ridiculous uncritical stories like this one getting published!! Why not interview the head PR manager at Coke and ask if people should consume more soft drink? If the main (only?) destination open to maths graduates is teaching maths so as to produce more maths graduates who can go into teaching, then the folly of the entire exercise should be plain for all to see.
Maths is important, but it has been hyped out of all proportion and is actively making millions of people (read students and primary teachers) miserable every year. What we really have a shortage of is critical thinking. Not mathematicians or mathematically literate people.

That is a very cynical and, frankly, ignorant view. Rather than go into why I simply suggest you read the book Innumeracy (http://www.amazon.com/Innumeracy-Mathematical-Illiteracy-Its-Consequences/dp/0809058405) it articulates the point far better than I could.

Well I'm not sure which of us is better illustrating ignorance Sean - one of the hallmarks of understanding an idea is being able to explain it. Rather than handballing your criticism, which of my points is so clearly in error?

Fine

"If maths was so good at improving critical thinking we wouldn't have ridiculous uncritical stories like this one getting published!!"

The validity of this claim is based on your personal opinion that the article is ridiculous. Your personal opinion is not sufficient to rebuke my claim that mathematics improves critical thinking.

I anticipate that you will counter this with asking me to validate my original claim that mathematics improves critical thinking. Well I don't need to because this has been done by others. For example:
An Introduction to Critical Thinking - SD Schafersman 1991
Courses and Instruction Affecting Critical Thinking - Lisa Tsui 1990

I also note that you only took issue with my critical thinking claim and not the logic. I argue that logic is essentially the foundation of critical thinking. Therefore, if you don't take issue with my claim of mathematic improving logic then you necessary cannot take issue with mathematics improving critical thinking.

"If the main (only?) destination open to maths graduates is teaching maths so as to produce more maths graduates who can go into teaching"

It is my opinion that this claim is patently false. It’s your claim so the burden of proof lies with you. However, a quick search on Seek.com using the key word 'Mathematics' produced the following results:
Information & Communication Technology (67)
Government & Defence (56)
Education & Training (51)

So, less than 30% of the jobs being advertised were for education.

"Maths is important, but it has been hyped out of all proportion and is actively making millions of people (read students and primary teachers) miserable every year."

Hyped out of all proportion is utter hyperbole.

Mathematics is not actively doing anything as it is not a free agent.

Your statement about making millions of students and teachers miserable actually highlights the reason we need more mathematical literacy. Students in the primary years have very little reason to be miserable about mathematics. The majority of their attitudes at this level are shaped by their role models. These are typically negative.
Just the other day I had a teacher joking with me at an open night that she didn't understand the maths resources that were laid out on a table for us to look at.
How the hell is that funny?!
She is going to be teaching my child this year!
Sadly it is the norm for people to think maths is hard and is just this thing that nerds need to know about but not 'normal people'. Attitudes like this rub off on kids so that by the time they actually hit more challenging mathematics they are ruined and have all sorts of mental blocks that prevent them from succeeding. It is therefore no surprise that some are made to feel miserable by the experience of learning and then teaching mathematics.

“What we really have a shortage of is critical thinking. Not mathematicians or mathematically literate people.”

I don’t disagree with the first sentence. However, there is clearly a shortage of mathematicians. Did the article over state this? Perhaps. I do take issue with the last part namely that there is not a shortage of mathematically literate people.

The numbers of examples that disprove this assertion are endless.

*Checkout staff that can’t handle change unless it is worked out for them by the register.

*The way the media and governments manipulate people with figures and statistics.

*I know personally of several people in sever debt and most of this can be attributed to their mathematical illiteracy. Like buying more than they need because they get a special deal for buying two at once.
Or making only the minimum payment on a credit card thinking this to be ok when at that rate of payment it will literally take a lifetime to repay.

*Or, as a previous article on the conversation pointed out, people’s general inability to assess risk (http://theconversation.edu.au/danger-youre-at-serious-risk-of-no-sorry-its-all-relative-12218)

I hope I have demonstrated sufficiently my understanding.

That's more like it Sean! It's not much of a "Conversation" if you just direct people to books you like.
"The validity of this claim is based on your personal opinion that the article is ridiculous. Your personal opinion is not sufficient to rebuke my claim that mathematics improves critical thinking."

You seem to have (illogically?) latched onto only a partial quote Sean. I didn't describe the article as simply 'ridiculous', I said it was a "ridiculous uncritical stor[y]". The point of my quip was that the article does not provide a critical analysis of the current situation, it merely presents one view unsubstantiated by credible evidence. You have provided something more like evidence for Roslyn's view than she did - and at least from this decade!! Even a numb skull like me knows it is ridiculously uncritical to purport to provide any kind of current economic analysis about the world based on pre-GFC data.
So I suggest that if someone promoting mathematics on the basis of its ability to improve critical thinking thinks that this is not an example of uncritical thinking, then they should think again ;-)
More generally, maths education isn't designed to be critical, it is designed to produce people who can replicate correct techniques and arrive at correct answers. This is almost anti-critical.

My comment about maths graduates becoming maths teachers to produce more maths graduates was a reference to the numerous other comments here suggesting teaching is a viable alternative for those maths majors who can't find work as if that somehow solves the broader problem. It wasn't intended to be a serious workforce analysis. However, that doesn't mean that your conclusions are correct. Know that I am delighted to make your argument stronger albeit at your own expense, because unfortunately (ironically?) your maths is wrong. Seek.com currently spits out 453 jobs for a search based on 'mathematics' of which 66 are tagged as Education & Training - a mere 15% of advertised 'mathematics' jobs. But let's not dwell here on an argument I wasn't really making.

I'll pretend you were being funny rather than puerile re: maths not being a free agent.

I may also have to pretend your next piece of logic was meant in jest too:
"a) Students in the primary years have very little reason to be miserable about mathematics. b) The majority of their attitudes at this level are shaped by their role models. c) These are typically negative."
Perhaps if your read it in the sequence b) c) a) you will see how you have contradicted yourself.
I wont go on about how upsetting it is that my car has no reason to stop running even though it hasn't got any fuel in it. I also wont go on about how you continued to make my point with your comment on your child's teacher.

And then we come to some common ground :-) And while I might take issue with your phrasing about numbers of examples being infinite, I agree that there is much to be troubled with in the broader community re: functional numeracy. HOWEVER, I believe that the maths curriculum is so bloated with useless content that we fail to teach kids stuff that they will actually use and benefit from. I want my kids to know when politicians are trying to baffle them with statistical bullshit, I want them to know how to handle their finances and invest sensibly, but I really don't give a ring tailed possum turd whether they can anti-differentiate. All this other guff switches of teachers, what to say of kids, and turns maths into an ordeal to be endured for many - if not most.

Yes Sean, I think you've demonstrated your understanding sufficiently [ although it would be unkind of me to say otherwise :-) ]

To refine my point re: critical thinking; I was coming from the perspective that the logic implicit in mathematics is the underpinning of critical thinking. I recognise that critical thinking is a higher order process and involves more than just logic. But without logic there is no critical thinking, period.

I share your feelings about the quality of mathematics training and agree it could, no should, be done better. My feelings come from a more general place where mathematics training, when done properly, provides students with the fundamental cognitive tools to function in a modern world.

The seek number I quoted were literally cut and pasted I don't know what else to say about that.

Yeah, I was pretty much trying to be funny.

I don't think I contradicted myself with statements a, b, and c. What I was saying is that in terms of the maths they are learning (identifying shapes, simple arithmetic etc.) there is nothing to really be miserable about. The misery is passed onto them by their role models. This is sad and only makes things more difficult.

This is similar to recent findings that suggest that (unsurprisingly) females are equally competent at mathematics as males; however they generally have more difficulty engaging with the topic largely because of antiquated social attitudes towards them and their perceived abilities.

I have been tutoring and teaching maths and physics for almost 10 years now and I have learnt that one of the most common blocks people have that prevent them from reaching their potential is the idea that 'this is hard'. This becomes a self-fulfilling prophesy. I have had excellent results with scores of students by removing this attitude.

Now, I agree with you strongly in terms what mathematics is suitable for various people. Certainly not everyone needs to know how to integrate (anti-differentiate). However, and this is a big however, there are actually many people who do need to know how to do this and similar things and they are being actively steered away from it by teachers (primarily) and the structure of the education system. For example; two of the three universities in South Australia do not require that students take the highest level of maths in year 12 to get into science or engineering. Why, well it's a marketing game they are playing to the detriment of the education they offer. I constantly have to tell my students, you cannot avoid that maths. You will do it eventually. If you don't do it at high school then you do it at uni and ultimately that is taking up space in a degree that could be used for something more advanced.

On the flip side, it is currently possible to finish high school without taking any mathematics courses in years 11 and 12. How? Well with subjects like Nutrition being categorised as quantitative and being put on equal ground with basic maths subjects. These subjects include no calculus but plenty of financial and statistical topics.

We have an education system that apparently values being able to work out how many calories there are in a meal (hint; read the labels) on the same level as calculating how much interest can be saved by paying you home loan off fortnightly rather than monthly. This is why I lament the current state of mathematical instruction in this country.
All I really want to see is mathematics being treated as an essential skill. While recognising that there are people with different requirements there should still be a base requirement. I also want people to get over the idea that maths is boring and not fun and all the other silly dogmatic thinking that accompanies the subject. Maths can be difficult but that doesn’t make it a waste of time. Indeed, it is the difficult things that are often the best use of our time and our amazing brains.

So perhaps we have found enough common ground to agree that this article could have been a better exemplar of critical thinking...
I agree with much more of what you say here - although I am not so concerned about maths not being compulsory in the final years. Only 0.5% of the workforce use higher order maths, so it seems unnecessary to 'train' 100% as if they are all going to become part of this 0.5%. After all, if brain surgeons manage to acquire their most important skills post-school, then so can all the STEM folk.
I am inclined to believe that it is this kind of wrong headed emphasis on maths that actively works against producing a more functionally numerate (broadly conceived) populace. Schools persisted with Latin for decades before finally realising that it was doing more harm than good - it turns out people can become fluent English users without it...

Brain surgeons acquire more and more skills post-school after more and more years of practice but to gain a practice in brain surgery I am pretty sure that brain surgeons need to have some competency in mathematics and logics.
I think a background in mathematics benefits a person's work. His/her work can be carried out more properly and quicker.
Children who know mathematics learn to use the hand-held calculators quicker and can tell if results on the LED display are wrong when some bits are dead eg 2x9 =18, not 16 as displayed; or square root of 2 is 1.414 instead of 1.111 as displayed.
Training 100% of the workforce to read and write Queen's English or higher order maths is every educator's dream. Of course, it is an impossible task. We are finding ways to bring the average level of competency in maths of the whole population to a higher level, but the main obstacle is we don't have enough mathematicians or competent maths teachers to start and perform this task properly. This is similar to the task of a poor country wanting to bring the standard of living of its people to above the poverty line and it needs more investors, more innovative entrepreneurs, more industrialists. However, to have enough innovative entrepreneurs or industrialists a good level of mathematical education for its people will be a great deal of help as shown in more industrialized countries. This may be the reason why many countries give more weight to mathematical teaching and assessment in their educational system.

I think we are largely in agreement Ngoc, so I wont waste time quibbling over minor differences. Where I do strongly disagree, however, is the notion that maths education is some kind of panacea to all of the world's problems. This is just more of the hype typically attributed to maths and it is utterly unjustified. Arguably the biggest role maths plays in society is as a screening device - a thinly disguised attempt at a meritocratic IQ test. With this function being diluted by maths not being compulsory through to Year 12 anymore is making those who liked the system, or like the prestige formerly attached to maths, are starting to squeal. And let's be realistic, the Industrial Revolution brought about probably the greatest changes (advances?) to society seen in the last few centuries, and there was no mass mathematics education going on at the time. The great maths experiment has already happened, and if the arguments about maths being so fundamental to innovation and economic development were true then we wouldn't be where we are today.

"..there was no mass mathematics education going on at the time (of the industrial revolution).." Perhaps at that time the maths level of the populace is sophisticated enough so government at the time devoted more time, money and effort on encouraging technologists, industrialists, scientists in their invention, innovation and results of their effort culminate in the industrial revolution.

If maths education did not make any inroads into teaching people Boolean algebra then I doubt we could have witnessed army of software engineers around the world being able to spend time on coding bit by bit byte by byte to write computer programs producing graphics and fanciful animated things in games for us young and old to enjoy nowadays, not to mention many other useful application programs which can simplify many difficult daily tasks in life such as industrial drafting, designs etc.

I have to agree to disagree with you: The hype typically attributed to maths is utterly justified and urgently needed for a better future of Australia's maths education and consequently for the advancement of Australian science and technology (which is lagging behind many developing countries). Government needs policies measures to promotes maths education in Australia unless it is contented with letting our respectable level of living condition continue to depend on sale revenue from exports of natural resources and agricultural products hence continue to rely on: (i) our natural resource endowment which will be exhausted and/or competed by resources elsewhere or by man-made alternatives; (ii) climatic conditions which are influenced heavily by the anthropogenic greenhouse effect; and (iii) export prices which are determined by forces in the world market. All these factors are well outside the effective control of our government since Australia is still and will remain a small economic political military power in this world.

There's a lot there that is pretty speculative Ngoc, and I suspect you'd struggle to find many who would describe things the way you have. I'm also pretty confident that there aren't many software engineers who can perform Boolean algebra - they don't have to, just as designers don't have to be software engineers to use CAD software. Not everyone needs Boolean algebra to be productive members of society, or even to work in the IT industry. One of the problems of hype is that people stop believing it once they see it to be false - this may be a factor in why so many people are climate change deniers, for instance. If they spent years being made to feel stupid by maths, being told they'd never amount to anything without it, and then discover that they actually have done fine without it, then maybe they can't trust all those "experts" after all? See how a little speculation can go a long way? :-)

Cases mentioned in my previous post refer to the case of "vanguard" scientists and innovators who can bring a country to the next level of science and technology and industrialization, especially the digital and telecommunication revolution. Nowadays IT or computer programmers are just pickers of the fruits of the hard work of those "vanguard" scientists, it is just like children who bypass the time table or slide rule with hand held calculators being able to do from simple arithmetic operations to fanciful trigonometric, log...functions without the need to know that the instruments in their hand are based on Boolean algebra and binary number. How many drivers know how their car with all the gadgets work? but all the engineers who design them must know how to apply maths in their engineering studies to come up with such innovative beautiful product.

At the moment, as far as I can see, the world is moving into new hitechs such as nanotech, biotech, greentech. Top maths advisers are worrying about the shortage of mathematicians for Australia to meet the challenges of those coming global technological revolution. Are you?

No. The vanguard is a tiny fraction of the tiny fraction who use higher order maths. These people will always pursue maths regardless of how little or much they get exposed to in school. Brain surgeons get trivial exposure to their specialisation in school yet somehow me manage to churn them out, and the next great breakthrough/advancements will not be born in classrooms either. Genius does not come from doing maths in school - in fact some say schooling excels at quashing brilliance... I would argue that kids are better left with a positive experience of maths so that they might want to pursue more later, than to be fed toxic levels of tedious irrelevant bumph year after year that puts them off for life.

Genius, whether in higher order maths or otherwise, have ideas that create technical changes influencing life of billions of people, creating millions jobs. But we are not talking about genius, we are just worrying about the Average Level of Maths Competency of normal people being insufficient to get the economic and business benefits of those technical changes.

I think this is a very good idea. Generally people, organisations and/or societies measure those things that are important to them.

I think it's a terrible idea. How about those courses that think maths is relevant pre-requisite make maths a pre-requisite? Oh wait, they already do that. Why would you want to tinker with such a blunt tool as the ATAR? If I'm passionate about drama and want to pursue theatre studies, why should I be forced to do maths just to compete to get into the course of my dreams? Maths IS NOT beneficial to EVERYONE. Millions of people are living perfectly fulfilling lives without any maths qualifications and having blissfully forgotten whatever useless maths was shoved down their throat at school. Start recognising that education is just another marketplace of ideas, and if your ideas aren't catching on, chances are you have a crap product - or a very niche one.