I agree with some recent suggestions that the UK's approach to maths teaching and maths education should be modified.
There are big problems with mathematics, and maths teaching. My view is that 25% of the population could perhaps have really good understanding of maths, with a further 25-50% having moderate understanding, and some people will just never get it at all.
Our current education system seems, on the face of it, to try a one size fits all approach. OK - I know it doesn't quite, but up to GCSE level it's not great.
Some students who can cope with Maths to GCSE, then try to go on to A-Level find that they've almost run in to a brick wall.
Many teachers are themselves not particularly good at maths - or may hold a view that maths doesn't matter. I'm not particularly referring to maths teachers, though some of these may not be excellent at maths. If a child hears from (say) the English or history teacher that "I was never very good at maths, but I've done OK ..." or something like that, then a message is sent out that maths is not important. The same teacher may nevertheless, if a good teacher, express enthusiasm for his or her own subject.
It is also possible that some very good mathematicians may not be very good teachers, but that does not imply that very good mathematicians are necessarily not good teachers. There are likely to be some who are both good mathematicians and good teachers. These are people who we should employ in our schools.
There are problems with maths education. Some students can't cope with the abstract nature of it. Some can't put it into context - "why is maths important?", "why is it important to me?", "why is it interesting?", "what's it used for?" etc. Some students may be very happy working with abstractions, yet others want to work on real world problems. Knowing that many of the greatest mathematicians were also scientists might help students. Newton developed some aspects of calculus perhaps because of a desire to understand gravity and planetary motions. Gauss was also an astronomer. Einstein developed some aspects of tensor calculus, but is most famous as a physicist. These were people who had problems to solve, and mathematics helped them.
Many of the devices and tools we now use on a daily basis could not have come into being without some understanding of mathematics. Electronics and electrical circuits have been designed using maths. Digital radio and TV relies on coding methods and modulation methods, some of which were developed by mathematicians. Reed-Solomon error correction used for CDs, DVDs and in digital broadcasting was originally proposed as an exercise in coding based on group theory. It is unlikely that OFDM (Orthogonal Frequency Division Multiplexing) could have been developed to the extent that it is without input from mathematicians. Computers might have developed much less rapidly without the help of George Boole (Boolean Algebra) and Alan Turing and von Neumann - all mathematicians.
Regarding employment, mathematicians and engineers are still amongst some of the highest paid professionals. The downside of this is that good mathematicians are likely to obtain employment in occupations other than teaching.
Where the UK's treatment of mathematics in schools seems to fail is that it does not enthuse children who are able enough and push them to attainable goals. One argument might be that we only need perhaps the top 5% of our population to understand enough mathematics, so it's OK to teach it to only a moderate level for everyone else. There might also be an assumption that the brightest and most able kids will do it anyway, so why bother.
Labelling is also a problem. Mathematics contains many branches - algebra, calculus, logic, geometry, trigonometry etc. It is perfectly possible for a child to like logic and dislike geometry, but statements which lump everything about maths together are not helpful - "maths is boring ...". Obviously the same is true for other subjects. The subject called History contains Roman and Greek history, as well as English history around 1500-1700, and also European history in the 20th Century. It is likely that students will prefer some periods to others. Similarly some students of English may not like Shakespeare, but may enjoy poetry, or novels, or 20th Century American literature.
There is no point in trying to teach mathematics to children who really have little aptitude or enthusiasm, but there is still a significant proportion of the UK's children who could both learn mathematics to a high standard, and also be enthusiastic about it.
I welcome Carol Vorderman's suggestion that the UK should adopt new attitudes to mathematics teaching, though I feel that splitting teaching into only two groups won't solve the problem. It should, however, not be acceptable for a teacher in a non-maths subject to discourage students by the kind of statement mentioned earlier. We need a much more enthusiastic and comprehensive approach to maths teaching, in which able maths teachers are matched to appropriate student groups, and don't simply provide drill and practice sessions in numbers, fractions, simultaneous equations, differential systems etc., but put the subject into context for those who wish to appreciate it.
There are big problems with mathematics, and maths teaching. My view is that 25% of the population could perhaps have really good understanding of maths, with a further 25-50% having moderate understanding, and some people will just never get it at all.
Our current education system seems, on the face of it, to try a one size fits all approach. OK - I know it doesn't quite, but up to GCSE level it's not great.
Some students who can cope with Maths to GCSE, then try to go on to A-Level find that they've almost run in to a brick wall.
Many teachers are themselves not particularly good at maths - or may hold a view that maths doesn't matter. I'm not particularly referring to maths teachers, though some of these may not be excellent at maths. If a child hears from (say) the English or history teacher that "I was never very good at maths, but I've done OK ..." or something like that, then a message is sent out that maths is not important. The same teacher may nevertheless, if a good teacher, express enthusiasm for his or her own subject.
It is also possible that some very good mathematicians may not be very good teachers, but that does not imply that very good mathematicians are necessarily not good teachers. There are likely to be some who are both good mathematicians and good teachers. These are people who we should employ in our schools.
There are problems with maths education. Some students can't cope with the abstract nature of it. Some can't put it into context - "why is maths important?", "why is it important to me?", "why is it interesting?", "what's it used for?" etc. Some students may be very happy working with abstractions, yet others want to work on real world problems. Knowing that many of the greatest mathematicians were also scientists might help students. Newton developed some aspects of calculus perhaps because of a desire to understand gravity and planetary motions. Gauss was also an astronomer. Einstein developed some aspects of tensor calculus, but is most famous as a physicist. These were people who had problems to solve, and mathematics helped them.
Many of the devices and tools we now use on a daily basis could not have come into being without some understanding of mathematics. Electronics and electrical circuits have been designed using maths. Digital radio and TV relies on coding methods and modulation methods, some of which were developed by mathematicians. Reed-Solomon error correction used for CDs, DVDs and in digital broadcasting was originally proposed as an exercise in coding based on group theory. It is unlikely that OFDM (Orthogonal Frequency Division Multiplexing) could have been developed to the extent that it is without input from mathematicians. Computers might have developed much less rapidly without the help of George Boole (Boolean Algebra) and Alan Turing and von Neumann - all mathematicians.
Regarding employment, mathematicians and engineers are still amongst some of the highest paid professionals. The downside of this is that good mathematicians are likely to obtain employment in occupations other than teaching.
Where the UK's treatment of mathematics in schools seems to fail is that it does not enthuse children who are able enough and push them to attainable goals. One argument might be that we only need perhaps the top 5% of our population to understand enough mathematics, so it's OK to teach it to only a moderate level for everyone else. There might also be an assumption that the brightest and most able kids will do it anyway, so why bother.
Labelling is also a problem. Mathematics contains many branches - algebra, calculus, logic, geometry, trigonometry etc. It is perfectly possible for a child to like logic and dislike geometry, but statements which lump everything about maths together are not helpful - "maths is boring ...". Obviously the same is true for other subjects. The subject called History contains Roman and Greek history, as well as English history around 1500-1700, and also European history in the 20th Century. It is likely that students will prefer some periods to others. Similarly some students of English may not like Shakespeare, but may enjoy poetry, or novels, or 20th Century American literature.
There is no point in trying to teach mathematics to children who really have little aptitude or enthusiasm, but there is still a significant proportion of the UK's children who could both learn mathematics to a high standard, and also be enthusiastic about it.
I welcome Carol Vorderman's suggestion that the UK should adopt new attitudes to mathematics teaching, though I feel that splitting teaching into only two groups won't solve the problem. It should, however, not be acceptable for a teacher in a non-maths subject to discourage students by the kind of statement mentioned earlier. We need a much more enthusiastic and comprehensive approach to maths teaching, in which able maths teachers are matched to appropriate student groups, and don't simply provide drill and practice sessions in numbers, fractions, simultaneous equations, differential systems etc., but put the subject into context for those who wish to appreciate it.
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