Is all this fuss around numeracy really warranted? I met a trainer in a government department who had to put his staff through a Level 2 numeracy test. He was surprised to find that many failed - as he regards them as good at their jobs.The claim is that 13.5 million people are 'stressed out' by their poor numeracy. But when did you last hear anyone tell you that they're 'totally stressed about my algebra skills'. The second claim is that 15.1 million have poor numeracy skills (equivalent of G or below at GCSE). This made me think.
Is it right that the standard here is the Maths GCSE. I have known lots of happy, successful people who handle money and numbers and bets who have no GCSE in Maths.
Numbers
While I accept that much of the 'number' content in the national Curriculum is sound, even here, knowing about prime numbers, square and cube roots etc seems remotely useful.
Shape and space
OK, working out the area of a rectangle I get - we all have to buy carpets and paint etc. But trigonometry? The volume of a sphere? Vectors? Transformations? It's mostly useless, except for a small minority of people.
Handling data
Some of this is useful but not all. Have you ever seen a stem or leaf table? Simple probability is fine - but calculating mutually exclusive events? It's over-engineered.
Algebra
This is where it all goes wrong. Here's a quote from Roger Schank who looked into the dodgy history of why algebra became so embedded in curricula, "I'm a math major and a computer science professor, and algebra has never come up in my life, maybe it has in yours." I'd argue that little or nothing in algebra is useful for the vast majority of people in work. In fact it is so conceptually difficult and of such little practical use that most of us who master it forget it soon after we've passed the exam. When was the last time you used a simultaneous linear or quadratic equation?
Algebra is bad for our kids
Even worse, could algebra be damaging our kids approach t maths? I suspect that algebra is the single most damaging cause of poor numeracy. As soon as kids face this useless challenge they are turned off the subject. It kills any interest in maths stone dead. They instinctively kow that it's useless knowledge.
What counts can't always be counted
In truth we need a simple standard in the 'real world' application of maths that is free from the Maths GCSE. Simple mastery of arithemetic, calculating areas, percentages and reading graphs would do. We need to produce adults who love to learn, not adults who avoid all learning because it reminds them of the horrors of school and algebra.
14 comments:
Donald, perhaps we could use some of the time gained by throwing algebra and trigonometry overboard for a bit of probability and statistics. Those are skills I employ every day.
I've taught entry level university math for years and quickly came to the conclusion that one of the primary problems with mathematics education is mathematicians. Unfortunately the same thing is true for physics and physicists.
The damage we do to people by demanding mastery of irrelevant "knowledge" and skills is enormous. The lucky ones recover (or learn to ignore) the damage to their self-esteem. Those that are not so fortunate see their gpa's take a serious hit because of the math course they're required to take or, in the worst case, have to leave their chosen field of study because they didn't get the grade required in the mandatory (and demonstrably irrelevant) math course.
As fate would have it I'm just starting to teach a math prep course for carpentry students next week and I'm, quite frankly, struggling with how to present the material the program entrance exam includes.
Present on this exam, for example, are questions which require some knowledge of mutually exclusive events in statisitics! In carpentry? I'd suggest time and effort would be far better directed towards ensuring the probability that anything falls down is 0.
Interestingly the fine folk at cognitive daily have been blogging about maths and learning. Take a look:
http://scienceblogs.com/cognitivedaily/2007/10/children_learn_and_retain_math.php
I agree wit hJay that a little stats is useful, but nowhere near as useful for the majority of people as learning a little programming, which is close to algebra in its use of variables and formulae but enables students to do really amazing things.
Interesting point Clive. Raises the question about leaving simple algebra for IT coding courses, as opposed to mainstream GCSE Maths.
It's this embedded 'real world' approach to maths that seems to be both useful and necessary.
Running a simulated shop with a till, giving out change, ordering stock, giving discounts, paying interest on loands etc seems to be a better way of doing basic number theory than the present dry approach.
...and I would like to add that I've been able to create a very happy adult life for myself that does not involve fractions!
:-)
Not sure about this "down" on algebra. If you want to use Excel's built in functions you need to know enough algebra to be able to make sense of them. I've no idea whether this is GCSE level or "below".
Donald -
I need to respectfully disagree with your post. I think algebra is of great importance - it is, however, taught poorly, which also leads to the problem.
As a sales trainer, I use algebra constantly - solving for resizing photos, creating examples for case studies and the like.
While some math teaching (in the US) has been improved, there is still very little focusing on practical applications. Usually it's a few "word problems" tacked on at the end. And as a former physics teacher, my students used to say : "I HATE word problems!" to which I'd respond that life is word problems.
Many people use algebra and simply don't realize it. A mechanic for example needs to know gear ratios to get the right gear size. Solving this is algebra - but the mechanic - who is so intimate in his work - doesn't realize it is algebra. He simply makes the calculation without the association.
Your assertions on math instructors is correct: very few bring the topic alive. Instructors need to do a better job of tying theory to life, something that academia has done poorly for centuries or millenia.
This whole dialog seems to be along the lines of removing difficult subjects so that students who are unable or unwilling to master abstract concepts can continue to have a sense of success. Such a concept could only arise in a country like the US... still sitting on our erstwhile laurels and thinking we're empire builders, rather than empires in full throttle decline in a race toward the bottom)
I predict it will only get worse as the top of the educational field gets clogged with ambitious semi literates.
Empires are built on algebra?
I'm a bit late on this one, but...
Maths is considered useful because it provides universal solutions (‘same problems, same formulas’ in the sense of Richard Feynman)
Maths is about connections and these connections have an inner logic.
If you slice the subject by some notion of ‘utility’ or ‘usefulness’ what you valued has been destroyed, and students will spot the lack of coherence and reject it (Keyskills, anyone?)
So if you say dump algebra and replace it with statistics, my thesis is that you will end up teaching algebra anyway so they can use the statistics...
loved your post Donald- have felt for a long time as teacher of university statistics that teaching most mathematics in school is tantamount to child abuse.
It is done because those who are going to go on to use it need to be taken through as much content as possible. It is too hard to work out who might be good at maths so the best approach is to push all kids through as far as possible. That means that 99% of kids end up having wasted probably a year of their time in school learning stuff they will never use so the 1% who will need it, get it.
It is so wasteful, especially since the focus on making future technologists, engineers, actuaries etc means that the time that could be spent on making sure all kids pick up basic mathematics competencies they need in life ("home" geometry, how compound interest works, balance sheets, progressive taxation, probability, understanding basic stats in newspapers, how to interpret graphs, how statistics can be used to lie etc) don't get covered. Sure they are there in the curriculum somewhere but swamped by what will be esoterica for almost all of them once they leave school.
As I said, I think it is state-sanctioned child abuse to torture so many kids for so long on pointless content just to be able to select and groom a tiny elite. We should be able to do better these days than keep thrashing our kids with a Victorian educational model. We should think about the oportunity and downstream cost of all that wasted time in schools to identify and train the mathematical athletes who will make a future societal contribution by way of their skills. We should find ways to do both the selecting AND the basic mathematical competencies.
We are running a multi-year SAS-style selection course for future maths athletes under the guise of mass education. As on the commando selection course, there are a great many more who suffer and fail, than get through. Do we still have to do maths in schools like this?
Mathematics education is a prime classic example of the current darwinian educational system that is as profligate with the potential of our children as the SAS selection process is of the energy and enthusiasm of those who do not measure up to elite standards.
The bottom line for me is that when these majority non-maths students get to my class they can't do anything except quake at the thought of more numbers.
What a great success for our education system to keep sending out into the world generations of kids suffering post-traumatic stress disorder instead of universal basic mathematical competence.
Thanks - what a brilliant post. All of this effort and waste just to satisfy a University entrance system. It's the scale of the waste, mental suffering and sense of failure that really comes through. Thanks again.
Don, the problem is with the teachers and the system, not the subject. There are alternative systems like Vedic Maths that could compress the maths curricula into a single page - why are they not used? Do check out http://blog.tatainteractive.com/2006/02/2b_or_not_2b_pr.html for more on this.
Contrary to common belief, we use maths all the time unconsciously; it's the teachers' lack of finesse in bringing this latent knowledge into our consciousness that we really hate. Maths is everywhere….. for instance, even dogs need to solve a differential equation in their heads and calculate the value of x, y & z before they can catch a ball/frisbee thrown at them
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