The Teaching of Mathematics – a Rant
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!