The Teaching of Mathematics – a Rant
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My Experience of Maths as a Child
When I was a child at school, I learned my maths from teachers with a wide range of understanding of the subject. I was fortunate in that one of my teachers in kindergarten taught it extremely effectively.
As my schooling went on, my understanding of maths continued to develop. I still use this as a basis for much of my own work today.
There was a theme that ran through all of my teachers’ delivery: “All the answers in mathematics are known.”, and as a student I was expected to learn them.
Other Sciences in the News
Ever since I can remember, there have been reports in the popular media about progress in the sciences, but that reports of progress in mathematics were distinctly lacking. Recent examples in the sciences include developments in astronomy and information technology. As an impressionable child, the message that I learned was that while the physical sciences was an area of active research (in all its different fields), nothing was happening in mathematics. This, of course, was a completely false impression.
My Own Experiences as a Teacher of Maths
It was my pleasure to work with a youth-at-risk student who had both the desire and capacity to learn mathematics. This was up to Year 10 level. At the end of the course I asked him if he thought that all the answers to all the problems in mathematics were solved, and he answered with an emphatic yes. When I told him that there were myriad as yet unsolved problems in mathematics, he was incredulous.
At the same time I also tutored a year 9 student with her mathematics. From the nature of the feedback from her Mathematics teacher, and also looking retrospectively at my own feedback to her, I expect that she also would come to the notion that all the problems in mathematics were solved. She was not a strong enough student to cope with the alternative notion, so I forebore to mention it.
And So to University
Well, I went to university to read mathematics, and the result was a disaster. Okay, I may not have been bright enough to make the grade, but I am convinced that the culture shock from “all the answers are known” to “here we address unsolved problems” did not help, and I strongly suspect that I am not alone.
A More General Malaise
Mathematics is an enabling tool with which to do science. No year goes by but I hear of university science lecturers bemoaning the lack of mathematical understanding in the year’s undergraduate intake. By way of example, young people go into environmental science courses without appreciating that they need a very good grasp of statistics, and then find themselves in a remedial maths course just to catch up.
Just to make matters worse, the Training Packages used in Australia no longer identify mathematics as an explicit employability skill. The message is clear: numeracy is not seen as being important. I am no longer surprised by shop assisants who are totally thrown when I hand over $20.30 for an item costing $15.30: I am now just saddened. Mind you, this dropping of mathematics from the list of employability skills comes as a result of research done in Australia into the needs of Australia’s employers. I wonder how employers will cope with an even less numerate workforce in the medium-term future.
What Needs to be Done?
The message needs to be put out to the whole of the Australian primary and secondary educational establishment that mathematics is important. We are handicapping ourselves economically as a nation by remaining as innumerate as we are. We are also failing to properly prepare those who go onto university degree courses in whatever science subject: this does nothing for the future development of the country.
And on a personal note, I think that it is high time that Year 12 teachers in mathematics should better prepare those students who a going on to study mathematics at university: there are lots of challenges for the students to take on!
Where on Earth did Australian industry get the idea that they don’t need numerate employees? So that said employees don’t realise they’re being stiffed on their pay cheques? And how could the guvm’nt follow sheeplike to such a daft conclusion? Whatever happened to the notion that maths is actually USEFUL? I mean real mathematics, not just arithmetic. Things like algorithms for data encryption, data compression, pattern recognition, signal detection, signal prediction and tracking, etc. How do they think a grocery store bar code scanner works? By magic?? Sigh… I suppose one just gives up on the idea of competing in a high-tech world.
In almost every job, arithmetic is useful. The lack of arithmetic skill in the Australian workforce is as lamentable as it is true. As a consequence it costs me perhaps 60 seconds at the checkout as a questionably bright but unquestionably uneducated employee has to manually sum 10 lots of an item I wish to purchase. This has an undoubted cost to the Australian economy; a cost Australia is evidently extremely willing to bear. So much for arithmetic.
Mathematics, as applied by those who design algorithms for data encryption, data compression, pattern recognition, signal detection, signal prediction, tracking and grocery store bar code scanning, is as beyond the career grocery store checkout operator as brick paving is to Steven Hawking. The world is a better place for the mathematical complexities of, say, digital medical imaging as it is for well laid, trip-free and blind-friendly brick paving.
Deliver both arithmetic and mathematics to all. And in an effective way. Then look for the deficiencies, and address them. What of the present state of the mathematical approach to risk management and actuarial science, given existing global financial circumstances?
We DO have bar code scanners, weather forecasts and MRI machines. We also have conservationists and environmentalists working synergistically with brick paving companies.
As a medical science lecturer and radiographer I contend that life is better now than it’s ever been. Latin, the language of anatomy and medicine, is dead in Australian medical undergraduates. Yet I would rather trust my life to the partially numerate and latinophobic specialists of today than the fully numerate and latinoliterate doctors of yesterday. Let those who will do mathematics.
> Yet I would rather trust my life to the partially numerate and
> latinophobic specialists of today than the fully numerate and
> latinoliterate doctors of yesterday.
Of course.
> Let those who will do mathematics.
Impossible if mathematics is not being taught. That’s the point. To be sure, only a few will find the discipline attractive. But we need those few, and we need them operating at the full capacity of their mathematical potential.
> We DO have bar code scanners, weather forecasts and MRI machines.
I recall a cartoon: one caveman says glumly to the other caveman “Og discovered fire and Thorak invented the wheel. There’s nothing left for us to do.” What do we NOT now have because some untutored genius hasn’t unlocked a key mathematical result?
> What of the present state of the mathematical approach to
> risk management and actuarial science, given existing global
> financial circumstances?
Actually, remarkably good. The present crisis has been predicted for some time, and one or two institutions who paid attention to the models instead of the emotionally driven market hype are doing splendidly. For example a modest bank in the US Southwest called Wells Fargo which has no bad debt and was recently able to purchase a former financial powerhouse called Wachovia for a song. They’re laughing all the way to the, ah, bank…
In the mean time, let’s drink a toast to skilled brick layers!