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Tag Archives: mathematics

 “A specially commissioned Irish Times poll in 2014 revealed most people had no idea the bulk of government spending went on social welfare payments, including pensions, and public service pay. Most people believed politicians’ pay accounted for more spending than either of these items.” – http://www.irishtimes.com/opinion/stephen-collins-ireland-not-immune-to-virus-that-spawned-donald-trump-s-success-1.2747037

The media, according to the author of the article, Stephen Collins, must take some responsibility for this ignorance. He’s wrong. For once the media cannot be responsible. Ignorance – no, let’s be blunt, monumental stupidity – on this scale wasn’t caused by media. The survey result suggests a spectacular and basic failure in the Irish education system.

Regularly a citizen hears it said or reported in the media something along the lines of, “If politicians weren’t paid so much, there’d be plenty of money for …” Average intelligence and slight education should prompt reaction, “Hang on, that can’t be true!”

Right, let’s admit intelligence for all. That means turning attention to education. It is unacceptable that the majority of respondents in a properly conducted survey are incapable of participation in a basic public controversy. That such mass incompetence has been found should prompt a rush to research in order to find the root of the failure.

Ok, let’s not over-react. It was one survey and its purpose was not to measure educational attainment, but it does accord with my experience as a lecturer, a consumer of media and a citizen who engages in casual conversation at bus stops.

Apart altogether from the concern that a significant number of citizens cannot participate in a public controversy, there should also be concern among those who view education as training for work. That is to say, there is little point in fussing over the proportion of students taking higher level maths in the Leaving Certificate or the general maths needs of industry, when it would seem that perhaps the majority have no grasp of numbers and quantity.

Returning to the degree of blame for public ignorance which journalists should bear, it may be that they are as much victims of a failure to educate as the citizens whose views they report. Consider the possibility that many journalists think it makes sense when someone says, “If politicians weren’t paid so much, there’d be plenty of money for …”

The list of things which well-meaning people have suggested should be added to the school curriculum is endless. Karlin Lillington, a very good tech. journalist, has argued in The Irish Times Business and Technology supplement (March 28th 2013) that coding be taught at school.* The thesis is that since many companies have started with the lone, self-taught coder, having a mass of people able to code would prompt business start-ups and would make many young people ready to take up employment in the tech. sector.

On the face of it, it seems an attractive idea but – and surprisingly from someone like Karlin Lillington – it is strangely outdated and out of touch with the reality of work today.

Two of the central planks supporting the argument are very weak. Firstly, while it is very likely that those who started and built a business on their inventive coding were at it from age 14 or younger, that observation has a familiar ring because it is made regularly about all manner of industry. Media regularly carry anecdotes about business people being enterprising from a very early age and these reports are often linked to a demand that business and enterprise appear on the school curriculum.

Secondly, there is nothing to indicate that anything like the majority of jobs in the tech. sector call for coding skills. A cursory examination of the recruitment sections on the websites of the large tech. companies reveals an interesting research project. Some of these companies recruit some coders, some recruit none. All, however, require competence in operating the new technology and in the ways of working that the technology has created. Indeed it might be argued that the belief that coding skills should be universal rests on a simple misunderstanding around the term “tech. industries”.**

Aside from the basics of the argument, Karlin may be getting too close to the technology and paying insufficient attention to its effects. “Today’s children,” she says, “will graduate into an overwhelmingly digital world, where daily life is immersed in code.” That’s simply untrue and misunderstands mass use of digital devices and media. Most young people don’t understand the word “digital” and think it means “modern” or even “cool”. Their life is not immersed in code; they are unaware of the code running their devices. Their playful indifference to matters technological, coupled with ease of use, may even obscure something that flies in the face of the thoughtless consensus that “the kids are great with the computers!” At the heart of the error is the observation that children and young people generally use computer devices almost constantly. They seem to be very comfortable with them and they learn to use new devices and apps quickly. To complete the myth there’s an endless supply of old duffers prepared to feed the stereotype that is the older person, unable to adapt and acquire the skills to operate these new gadgets. The truth is that technology always develops from specialist to mass or domestic use. In the 1970s a basic video recorder was analogue, huge, expensive, confined to TV companies and required a skilled operator. Similarly, there was a time – and it is a long time ago now – when expertise was needed to do anything on a computer. Nowadays little or no skill is required for many uses.

Those young people who appear so computer savvy for the most part are doing little that is creative or clever.*** It is true that being inventive and developing new apps etc. requires skill but that kind of activity is rare. The difficulty is that not only do the majority of young people make little creative or intellectual use of the technology but they generally lack the skills to go beyond social media and games or even to maximise the potential. Imagine years ago if someone had admired a young person for being able to operate a television set! Well, admiring a young person for being constantly and comfortably on-line is almost as daft. It is also patronising.

There is a final theme in Karlin’s piece. It seems reasonable to suggest that coding skills would teach people how to think. There certainly is a need to teach young people to analyse, criticise, organise, solve problems and present their findings/arguments. However, teaching coding skills with this end in mind would be very restrictive and conservative. It would be a poor substitute for logic or philosophy more generally.

There needs to be a hard look at the easy assumptions that lead to demands for more and more training as opposed to education in schools. It was always the case that schooling needed to be general. Schools needed to produce people who could make their way in the world as both citizens and as workers. What technology has done is to emphasise this need. Put aside for now the making of decent, socialised people and of citizens prepared and able to participate in a republic. Those looking to serve the “jobs market” by reforming the education of children need to look more closely at the jobs.

It is absolutely certain that science and engineering specialists are required but there are two other things which are equally certain and they have been created by the technology at the heart of this discussion. Firstly, it is certain that aside from the most menial of jobs, there is now no employment in the developed world for the unskilled and uneducated. Secondly, outside of technical skills the world of work today calls for the generalist, someone who is adept with information, someone who can research, argue and present. These of course rest on literacy, numeracy and a great deal of general knowledge.**** In the short to medium term there is a demand for a second and third language.

There really is no place in the office (or at home or abroad linked to the office) for someone unable to speak and to write fluently and well, for someone unable to research independently, for someone without general knowledge and for someone with no grasp of mathematics, science and technology.

When thinking about the reform of education, it is a mistake to fall back on the centuries old division between humanities and science. It is a mistake too to emphasise training over education. These are not mistakes purely in terms of concerns that teaching should lead to the enjoyment of a full life. These are now mistakes in terms of serving industry.*****

If Karlin were to look around the office at the Irish Times and see what is actually being done and who does it best, and then travel to the tech. companies around Dublin, look again and perhaps sit in on a few routine meetings, she would see that teaching skills – other than literacy and numeracy – to children is a very outdated notion.

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* http://www.irishtimes.com/business/sectors/technology/net-results-digital-economy-begins-with-teaching-kids-coding-1.1340843
** https://colummccaffery.wordpress.com/2013/02/11/could-inaccurate-use-of-the-term-tech-sector-be-misguiding-education-policy/
*** https://colummccaffery.wordpress.com/2012/09/05/republican-citizens-on-facebook-need-to-choose-their-friends-deliberately/
**** https://colummccaffery.wordpress.com/2010/09/27/the-smart-economy-and-technologys-democratic-vector/
***** https://colummccaffery.wordpress.com/2010/05/26/increased-emphasis-on-vocational-education-is-a-pretty-bad-idea-now/

National Certificate of Competence for Workers in the Media and Food Industries 2013

Mathematics paper one: Basic burger mixing

Please read the paper.
Please answer all five questions.
You may use a calculator, a computer connected to the web or both. You may phone to consult a friend.

Q 1. A burger is made from a mixture of Irish beef and an imported filler material. The burger contains 29% horse meat. If the filler is not 100% horsemeat, what is the maximum Irish beef content of the burger?

Q 2. Burgers are made from a mixture of Irish beef and an imported filler material. If there is one kilo of Irish beef, what weight of filler material must be added in order to ensure that the burgers comprise 29% imported filler material?

Q 3. Burgers are made from a mixture of Irish beef and horsemeat. If there is one kilo of Irish beef, what weight of horsemeat must be added in order to ensure that the burgers comprise 29% horsemeat?

Q 4. Burgers are made from a mixture of Irish beef and an imported filler material. If one kilo of burger mix contains 71% Irish beef and 29% horsemeat, what proportion (percentage) of the filler material is horsemeat?

Q 5. “In mathematics and in the manufacture of burgers quantity is the property of magnitude involving comparability with other magnitudes.” Explain. (Your answer should make reference to the distinction between trace elements and ingredients.)

Good luck with that!

It is intriguing that the presence of tiny amounts of horse DNA in beef burgers and the presence of 29% of horse in one beef burger continues to be covered by media as one story. It may be a profoundly depressing suggestion but it is possible that the reason for the conflation is an alarmingly poor grasp of basic mathematics.

Industry explanations for the presence of horse DNA go something like this: “We use pure Irish beef but we add some filler which we buy in from the continent and it is possible that this may have somehow been contaminated by horsemeat.”

Clearly if this explanation is applied to the 29% finding, it is complete bollocks. 29% is pushing on for one third horsemeat.

Let’s slap the beef down in front of us. It’s 100% Irish beef but in order to make it stick together and/or to reduce cost, we increase its volume by adding 50% imported filler. It is now roughly 60% Irish beef and 30% imported filler.

Assuming that the truth has been told about the Irish beef content, there is only one way that there could be 29% horsemeat in the burgers: the filler must have been almost 100% horsemeat! Pure horsemeat, not traces of horse DNA!

Yes, the figures above were made up but they are not fantastic. The point is that the story about traces of horse DNA is not the same story as the 29% horsemeat content. That it is treated as such feeds a fear either that journalists can’t grasp the numbers or that they can but they believe that citizens cannot.
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I’ve mentioned poor basic maths before:
https://colummccaffery.wordpress.com/2010/09/27/the-smart-economy-and-technologys-democratic-vector/
https://colummccaffery.wordpress.com/2010/05/26/increased-emphasis-on-vocational-education-is-a-pretty-bad-idea-now/

There is a need for a shower of realism over many who talk of Ireland’s educated workforce and the need to bend education to serve the knowledge/smart/information economy/society. I fear that the level of education is pretty poor in precisely the areas that emerging society demands. I fear too that those who talk most of the knowledge/smart/information economy/society have reflected least on what it means.

The backward workforce

Too many of my students have poor literacy skills. This is a common topic of conversation among university lecturers. So too is the lack of general knowledge among students. It is far less common to have such conversations about the poor command of pretty basic math, science and technology. I don’t want to clutter this piece with examples but an archetype might write “shouldof”, think that the USSR still exists, be unable to manipulate percentages, have no grasp of statistics and consider basic science a no-go area for all but the expert. Such a person betokens neither an educated workforce nor a competent citizenry.  

Not so smart policy

No one in their right mind would argue that that the kind of society and economy determined by increased application of technology – especially IT – does not require experts or does not require quite a few experts in these fields. However, no one who has looked at the effect and the likely future effect of these same technologies on society and the workplace would place too great an emphasis on the creation of an excessively large numbers of experts. For a long, long time technology has had a democratic vector: it demands proportionately greater numbers of effective, creative users than experts in the field itself.  The danger in the current pre-occupation with science education is that it might be successful and produce two categories of frustration: a glut of experts with no career prospects and a mass of people without the skills to prosper or create prosperity. A considered, realistic education policy will try to ensure that mass education will deliver citizens and workers who are competent to contribute in our time.

The smart worker or even the smart citizen

The world of work – or at least that part of it that pays reasonably well – that has emerged over, say, the past 30 years demands that people be articulate, literate, numerate and informed. (I should add “secure” but this would open up another argument.) These are the preconditions for flexibility, creativity and innovation. There is absolutely no point in talking about a smart society or economy unless the mass of people are pretty smart.

http://www.prospectmagazine.co.uk/2010/09/university-challenge/

http://www.prospectmagazine.co.uk/2010/09/unloved-british-universities/

I was posting over at Ferdinand von Prondzynski’s blog   ( http://universitydiary.wordpress.com/) when I thought that I should make the point on my own blog. Ferdinand was saying in support of changing university education that, “we simply cannot run a university system that now admits a large percentage of the population as if we were running small elite institutions. The elite students of former times generally had very un-specific expectations of their education. For them it was all part of assuming the knowledge and the style of privilege, not about undergoing specific vocational training.” I disagreed. Of course increased numbers and different times mean change but the whole purpose of increased access is to make higher learning available to all who can benefit. Moreover, that’s what the world of work now requires.

More vocational training rather than education is the demand of people – including students – who fail to appreciate what has happened to work and yet are aware that too many graduates complete their education lacking important skills.

The “information society” has consequences for university education. As a term, it is often reduced to meaningless guff but it should not be dismissed by thoughtful people. In careless use it becomes fused with “knowledge society” and provides a justification for a pretty daft approach to education: an increased emphasis on mere training for the majority and an increase in the number of PhDs. I don’t want to talk right now about the latter but training in preference to education is precisely what, let’s call it, industry doesn’t need right now.

Anyone who has given serious thought to the concept of an “information society” either from a political or a business perspective realises pretty quickly that such a society depends not merely on skilled people but on educated, thinking, and – yes – innovative people. In short, the humanities graduate’s time has come! (I recall commenting during a discussion with a group of lecturers that innovation is what separates a 2.1 from a 2.2.)

There are however “employability” problems with some graduates and the problems have nothing to do with the traditional university approach to learning. Too many students lack the skills necessary to making the best use of their education. Too many are not fully literate, cannot cope with the mathematics essential to a full life today, have no real understanding of technology or economics, have poor general knowledge and cannot present themselves or their work in public. These are mere skills and could never figure in a university education. However, it should not be possible to achieve the status of graduate without these skills. They are essential and they should be mastered while in primary and secondary school. Most lecturers are aware of the literacy and the general knowledge problem. Many may be aware that perhaps the majority of students are poor communicators and that work today demands effective participation at meetings and making presentations. Some lecturers may not have noticed the mathematics problem. What do I mean by this? Here are a few examples that I’ve come across. Students frequently have no grasp of the magnitude of numbers. They would find the creation of mathematical expressions for, say, a spreadsheet very difficult. The concept of random distribution would be new to them. I won’t labour this on into basic science, technology and economics. The point is that today effective citizenship – never mind a job – requires these skills. While someone without them should not be at university, most certainly a graduate must have them.

A university is not the place for teaching skills. However, until such time as the rest of the educational system addresses the problem, universities in order to maintain standards and credibility should test for them. There can be no question of awarding grades, let alone making it part of the degree programme. This is about finding competence; it is pass or fail. I realize that suggesting such tests – and I’m not talking about labour intensive exams. – seems impractical or extreme for institutes of higher learning but I can’t come up with another short term remedy.