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Created On: 19 October 2013 11:06 AM
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 19 October 2013 11:06 AM
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jencam

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Has anybody here had experience with the SMP modern maths curriculum of the 1960s and 70s? Was it a daft concept or was it a good idea that was implemented prematurely before there was much of a real world demand for it?
 19 October 2013 11:39 AM
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kengreen

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sorry Jen can,

but you have lost me. What exactly is/was SMP mathematics?

I don't doubt for one moment that I was around in the 1960's , but I do not have any bells ringing!

Ken Green
 19 October 2013 12:33 PM
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jarathoon

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This system was taught up until the mid 80's in some schools and helped put a whole generation off mathematics, by trying to dive into abstraction too early.

Set theory is important, in regards to logic and computation, but teaching it too early in too abstract a fashion is a mistake.

As I have said before I think mathematics should really be taught to most people as Arithmetic and Heuristics. In terms of Heuristics see "Problem-Solving Through Problems" Loren C. Larson

Heuristic techniques are divided into the following categories in this book
1. Search for a Pattern
2. Draw a Figure
3. Formulate an Equivalent Problem
4. Modify the Problem
5. Choose Effective Notation
6. Exploit Symmetry
7. Divide into Cases
8. Work Backward
9. Argue by Contradiction
10. Pursue Parity
11. Consider Extreme Cases
12. Generalise

I would also add to this "analogy", which has been extremely important for the historical development of mathematics, as it has in science. It is also vital that we understand more about the role of mathematical analogy within the mathematical teaching process itself I think.

Teaching mathematics this way naturally allows computational techniques and mathematical software aids to be introduced as asides without teaching about them formally and abstractly - that can be left to university level courses in engineering and mathematics.

Even though this is a graduate level textbook you could easily write an interesting and thought provoking textbook on similar lines for GCSE and A Level courses.

James Arathoon


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James Arathoon
 19 October 2013 12:42 PM
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jarathoon

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One mathematical area outside of this structure would perhaps be a module on "Probability and Statisics" which could be taught a separate module in the sixth form. This way studsents interested in the biological and social sciences could take this module on its own to complement their other A level studies.

James Arathoon

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James Arathoon
 19 October 2013 01:10 PM
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jencam

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Statistics and probability are part of the KS2 maths curriculum taught in primary schools.
 19 October 2013 03:38 PM
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jarathoon

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Yes I remember the debate I had with a couple of civil servants on how the fuel poverty figures were now to be calculated and described for public consumption. They used the meaningless term "typical" because they said that people wouldn't understand the terms mean, mode or median, even though this was part of the national curriculum for primary school education. Such is the current level of trust the government has in our education system. [I am guilty of using the word typical on occasion, for a vague situation I haven't thought about much. However this should be the excuse in literature emanating from peer reviewed academics and government]

But I wasn't talking about this level of statistics.

The sort of statistics that you need to understand at A level involve probability and statistical distributions, where calculating one statisical number and comparing it with another, without making sure that the underlying statistical distributions haven't changed substantially, can be very misleading indeed.

For example, statistical analysis of expected lifetime depends on child mortality rates as well when people die of old age, illness, accident or war in later life.

If you try to compare life expectancy in historical times, for which we only have archaeological evidence, with today's figures, then it is necessary to make allowances for how distributions are effected by cultural differences between then and now (who is and who is not cremated and other effects that might cause the original actual distribution to be different from the measured) and physical time related differences, e.g. child skeletons decay away more quickly than adult skeletons and may be under represented in the archaeological record.

Old data may not be directly comparable with modern figures because of distribution differences; hypothesis testing, and the statistical modelling that goes along with it, may be required to generate the two means, or the two modes or the two medians than can be directly compared.

We should also recognise that Darwin's theory of evolution is a statistical theory, the first theory based on statistical laws in fact. In fact when Darwin introduced his theory people most people didn't really understand the concept of statistical law properly; academics and comentators often used the word "law" at that time without knowing they had to distinguish between the terms "statistical law" and "causal law".

Actually a lot of statistical "laws" aren't actually timeless or fixed laws at all; the underlying data in many cases gradually shifts and slowly alters what are often described as laws over time.

If you want to understand Darwin's theory of Evolution you have to learn about statistical distributions of populations and how they are altered by animal culture [how animals interact with other animals of the same species, is not as constant as some naturalists like to pretend] and environmental factors [temperature, temperature swings, predators, disease and species competing for the same resources]. This information feeds into any controls on which animals get to reproduce, how many offspring they have and which of their offspring get to survive, with the same cycle, but slightly different this time, occurring for the next generation.

I personally think that biology and geography specialists at A level could benefit from could benefit from learning more statistics at that stage. A higher level of statistical knowledge, than being able to talk about and calculate, the mean, mode or median, in simplistic and naïve terms.

The next battle after this would be to get mathematical knowledge of those who study political science or history and politics because they aspire to run the country. I expect the country will be bankrupt before I win that battle.

James Arathoon


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James Arathoon
 19 October 2013 04:06 PM
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kengreen

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Hmmm.

While I will concede that statistics can be usefully employed I think that their study should, by compulsion, carry a government health warning. Certainly it should not be taught under the age of (let us say) 18 years - it's best to learn how to lay foundations before you start erecting structures?

I view your post James is a plea for science for science's sake. Far better to use the time exploring the techniques of Euclid.

Ken Green
 19 October 2013 11:47 PM
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ectophile

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Originally posted by: jencam

Has anybody here had experience with the SMP modern maths curriculum of the 1960s and 70s? Was it a daft concept or was it a good idea that was implemented prematurely before there was much of a real world demand for it?


I did SMP maths O-level in 1980, then maths and further maths A-level in 1982. It didn't seem to do me any harm - I carried on to university and got a good degree.

The trouble is, never having done any other maths curriculum, I don't have anything to compare it with.

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S P Barker BSc PhD MIET
 20 October 2013 01:25 AM
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jarathoon

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ectophile,

The possibilities are:

a) you went to a school where maths was taught well. People who complain about the syllabus just happened to go to schools where it was taught badly.
b) the teaching profession reduced the pass rates just to make it look like everything was ok, when it wasn't.
c) there was no problem with new maths and everyone was just imagining it.
d) you are a naturally gifted mathematician and which ever way you were taught it wouldn't have made much difference.


I must admit my experiences were not necesarily typical. I studied the New Maths syllabus for my 'O' Level in maths and then additional maths and passed them in 1982/1983. Up to this point I didn't think there was a problem as I knew nothing else. However when I moved to a different school to study A level maths using a different syllabus, I really struggled, and felt cheated by my previous education. That experience dented my confidence in respect to maths for several years after, but as I am not a naturally gifted mathematician, but have had to develop my skills over the years attrition style, this may have happened which ever way I learnt.

On the wikipedia page

http://en.wikipedia.org/wiki/New_Math

there are some criticisms of the american new maths programme; they seem fair comment in regards to my british experience as well.

According to this page, in 1973, Morris Kline published his critical book "Why Johnny Can't Add: the Failure of the New Math" , which I never knew about and haven't read.

James Arathoon

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James Arathoon
 20 October 2013 10:53 AM
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jencam

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SMP modern maths was taught in some schools from the mid 1960s through to the late 1980s. In those years there wasn't a National Curriculum so schools were free to set their own curricula and buy whatever books they wanted. My own secondary school opted for a traditional maths O Level with questions about algebra, trigonometry, and geometry on the exam papers, but there was also a modern maths O Level tied in with the SMP course. I believe there was also an SMP A Level with a very different content from a traditional maths A Level. The introduction of the National Curriculum and GCSEs in 1988 effectively put an end to the teaching of modern maths in schools as it did not fit in with the reforms. In recent years it has been revived at A Level with the D papers but only a minority of students take them.

Originally posted by: jarathoon
The next battle after this would be to get mathematical knowledge of those who study political science or history and politics because they aspire to run the country. I expect the country will be bankrupt before I win that battle.


Don't worry. My background is politics and economics and my son is mathematician. A few years ago he was teaching me about differential equations that are used in economic modelling to describe dynamic situations.
 20 October 2013 03:41 PM
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jarathoon

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Originally posted by: jencam

Don't worry. My background is politics and economics and my son is mathematician. A few years ago he was teaching me about differential equations that are used in economic modelling to describe dynamic situations.


I am worried, your not running the government.

All to have to realise that recessions have been coming every 6 to 20 years or so for the last few decades...

Mid-1970's
Early 1980's
Early 1990's
Dot Com bust in 2000 (Didn't effect the housing market or consumer much)
Banking Crisis 2008

If we didn't load ourselves with such large levels of debt they wouldn't happen so frequently. Debt makes society dynamic and fast growing, but also unstable in the face of set backs. The differental equation aspect, with much longer time constants, than normally occur in science and engineering.

So given our debt levels are worse than before, we can expect our next serious recession somewhere between 2015 and 2020. 6, 10, 9 and 8 year time intervals between the historic recessions listed. Are we prepared for the next one? Are we preparing contingencies to cope with it? Or are we instigating policies to make it worse? (Through things like the lend to buy scheme)

Waiting for a recession is a bit like waiting for an earthquake; we have to wait a while for the financial stresses to build up again, but no one can predict in advance the exact moment at which it will occur.

Once housing and energy costs together increase above a specific percentage of average household income (I call it the recession trigger ratio because it was roughly the same figure for the 1991 recession and the 2008 recession, but it will probably be different for the next recession).

This particular recession "trigger" ratio will most likely be exceeded once interest rates have started to go up again. The longer we dine on low interest rates the worse the shock of interest rises may be.

The same thing happens to government. Once the debt repayments are higher than a certain fixed percentage of total income, and tax raising options are blocked, then the phone calls to the IMF begin. This normally happens when the interest rates they have to pay on their debt stat rising.

The massive ballooning of UK government debt currently happening will make the next recession in the UK much more uncertain and disruptive for government funded institutions than probably all the previous recessions listed put together. Are we prepared for it? Are we preparing contingencies to cope with it?

No, the government is instigating policies that will make it worse...

James Arathoon

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James Arathoon
 21 October 2013 01:19 AM
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kengreen

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OK,

I hope at least one of the experts posted above understands what the hell it's all about because I'm dashed if I do.

Please, I repeat, please - will someone take their heads out of the clouds and tell me just what is SMP maths?

Ken Green
 21 October 2013 07:45 AM
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rogerbryant

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Hello Ken,

SMP (School Mathmatics Project) was developed in the 1970s (I think by Oxford or Cambridge Uni) as a more thought provoking way of teaching maths. It is (was?) a similar concept to the Nuffield science curiculum.
As with any fixed curiculum it will suit some people better than others and as it required making the students think it was probably more dependant on teacher quality than teaching by rote.

Jencam,

Like Ectophile it seemed to suit me. I got good grades, an engineering degree and what I think is a good job where I still use some maths.

Best regards

Roger
 21 October 2013 12:03 PM
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jarathoon

Posts: 1041
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Originally posted by: kengreen

Please, I repeat, please - will someone take their heads out of the clouds and tell me just what is SMP maths?

Ken Green


I've searched through the mathematical gazette indexes and come up with this list of articles on modern mathematics. You can view one or two for free by registering on myJSTOR

A. W. Bell and W. O. Storer, Modern mathematics in training colleges and university departments of education, 346, Dec 1963, Article

F. J. Budden, Modern mathematics and music ,204,Oct 1967,Article
W. H. Cockroft and F. W. Land, The principles of teaching modern mathematics, 307, Dec1963, Article
Allen F. Edwards On the articles 'Mathematics for the Million' and 'Modern Mathematics in the 5th Forms', 273, Oct 1963, Letter
Margaret Hayman, Courses on 'Modern Mathematics', 306, Oct 1965, Letter
M. H. A. Newman, Modern mathematics and the school curriculum, 288, Dec 1961, Article
A. P. Rollett, A history of the teaching of modern mathematics in England, 299, Dec 1963, Article
G. S. Smithers, Modern mathematics in fifth forms, 9, Feb 1963, Article
F. Smithies, What is modern mathematics?, 278, Dec 1963, Article
W. J. Thompson, Modern Mathematics' at 11+, 97, Feb 1964, Letter
Robin J. Wilson An experiment in the teaching of "modern mathematics" in schools, 22, Feb 1965, Article
A. K. Austin, Using Modern Mathematics, 379, December 1970, Note(C) 233

And lastly without an author

The unnaccepatble face of modern mathematics, 61, June 1975, Editorial

And then silence...

Ken I gave you the link to the Wikipedia page.

http://en.wikipedia.org/wiki/New_Math

I have also found

' "MODERN MATH" AND ITS CRITICS.', W.W.Sawyer

http://www.marco-learningsyste...yer/electricians.html

I think the problem lay with the way large numbers of children were taught including me.

In my particular area I went to the lowest ranked school in my area, because of my fathers religious affiliations. It was probably the worst Catholic School in the country at the time in terms of academic standards at the time and now is a housing estate as the reward for its achievements.

I got my 10 O levels in the lowest ranked school in my area, mostly as a result of self study, so from that point of view alone I am far from typical; the new or modern maths curriculum was not one that sat easy with poor teachers or newly qualified supply teachers or with self study for that matter.

To me looking back it was maths without any real world problems to ground it. In metaphorical terms its a bit like teaching youngsters how to use a garden spade by taking them to an art gallery to observe and theorise about it in the best pristine abstract form and the brightest most clear light, but without giving any context or training in where and how it can be actually be used in practice. Thus it becomes very forgettable, and does not build up properly in a mind such as mine.

James Arathoon

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James Arathoon
 21 October 2013 01:18 PM
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ectophile

Posts: 544
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Originally posted by: rogerbryant

Hello Ken,



SMP (School Mathmatics Project) was developed in the 1970s (I think by Oxford or Cambridge Uni) as a more thought provoking way of teaching maths. It is (was?) a similar concept to the Nuffield science curiculum.

As with any fixed curiculum it will suit some people better than others and as it required making the students think it was probably more dependant on teacher quality than teaching by rote.



Jencam,



Like Ectophile it seemed to suit me. I got good grades, an engineering degree and what I think is a good job where I still use some maths.



Best regards



Roger


It looks like the schools I went to were quite trendy, because I also did Nuffield chemistry.

I never was any good at rote learning, and still don't know my times tables. There were times in exams where I would have to work out a formula from first principles because I couldn't remember it.

I'd rather understand how things relate to each other, and visualise things in my head, rather than just memorising lists of formulae.

-------------------------
S P Barker BSc PhD MIET
 21 October 2013 02:21 PM
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jarathoon

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ectophile, roger,

I studied the nuffield physics couse at A level, but not nuffield chemisty.

The nuffield science courses were indeed thought provoking, however the teaching philosophy behind the nuffield courses, is completely and utterly different to the teaching philosophy behind new/modern maths! I can't see possibly how you can confuse and conflate the two.

"[New Maths] is (was?) a similar concept to the Nuffield science curiculum.".

No look at the the evidence. It wasn't.

James Arathoon



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James Arathoon
 21 October 2013 03:37 PM
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jarathoon

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Draft National Curriculum programmes of study for KS4 [GCSE level] English, maths and science is here

"Aims

The National Curriculum for mathematics aims to ensure that all pupils:
- become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils have conceptual understanding and are able to recall and apply their knowledge rapidly and accurately to problems
- reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
- can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

The programmes of study are organised in a distinct sequence and structured into separate domains. Pupils should make connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge to science and other subjects."


These aims are clear and compatible with how mathematics is used in science and engineering, so I welcome there introduction; if certain mathematically talented young people are sufficiently motivated to supplement this approach with some extra-curricular work in the direction of formal and abstract mathematical approaches, then I would welcome that, if that is what gets them up in the morning; just don't inflict that approach on the whole population as was done with the new / modern mathematics project in the 60's 70's and 80's.

In

http://faculty.education.illin...paradigm/breakell.pdf

John Breakell writes

"The principal aim of the SMP was to develop a modern course applicable to everyday life. A key element in its success, from the point of view of teachers, lay in its completeness."

I would have said...

The principal aim of the SMP was to develop a modern course that was completely inapplicable to everyday life. The key element in its failure, from the point of view of students, lay in its striving for mathematical rigour and completeness.

You don't have to know that abstract set theory underlies the currently accepted theory of numbers, to learn mathematics at school.

James Arathoon


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James Arathoon
 21 October 2013 04:19 PM
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jarathoon

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I am not an expert in the philosophy of mathematics, but the argument we are having reflects that there are two great historical traditions (almost like genetic strains) to be observed amoungst the great mathematicians: those who stress the formal in striving for new knowledge and learning and those who stress the intuitive in striving for new knowledge and learning :

The two books I own on mathematical philosophy underline this basic separation in different ways (there may be better ones I don't know I am not an expert in the field):

The Philosophy of Mathematics (An Introductory Essay) by Stephan Korner
and
The Mathematician's Mind (The pychology of invention in the Mathematical Field) by Jacques Hadamard

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James Arathoon
 21 October 2013 05:03 PM
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kengreen

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Ah,

At last some (sort of) answers.

The fact that the "new" mathematics emanated from a university answers most of my queries; professors who either live in the clouds or who collects fees for research on behalf of industry are the least qualified to teach.

Someone posted that he has never mastered his times tables - then how the devil does he ever carry out the process of division?you can't do it using log tables because that requires the ability to add or subtract - also a sub division of tables? The quickest way, of course, is by twelve-inch slide rule but that requires the ability to get a rough answer (by mental arithmetic) and so set the decimal point - which also can be done at speed using the multiplication tables?

Sir Keith Joseph, as Minister for education, publicly declared against tables on the grounds that everyone today had an electronic calculator. But then of course it is normal for politicians to shoot themselves at ground level?

Put simply, there is no substitute for hard work at the beginning of one's education although I admit that the overwhelming desire on the part of "new" educationists is to save the little dears from being exposed to hard work?I believe that anyone entering the teaching profession should be issued with a high-grade mirror.

I heartily disagree with James in his championing of "the philosophy of mathematics" - such a subject was never addressed by a true mathematician. They are people who, out of nothing but curiosity, pursue interesting ideas - I put forward the work of Heaviside who, while unable to prove his thesis, nevertheless had the conviction to press on with and prove his case by practice.

I have no desire nor intention to be rude, but there is a saying that "those who can, do; those that can't, teach." To that I add :"the rest go into politics!"

Ken Green

Edited: 21 October 2013 at 11:02 PM by kengreen
 21 October 2013 06:12 PM
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jarathoon

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Originally posted by: kengreen

They are people who, out of nothing but curiosity, pursue interesting ideas - I put forward the work of Heaviside who, while unable to prove his thesis, nevertheless had the conviction to press on with and prove his case by practice.



Like the famous Heaviside quote:

"The following story is true. There was a little boy, and his father said, "Do try to be like other people. Don't frown." And he tried and tried, but could not. So his father beat him with a strap; and then he was eaten up by lions.

Reader, if young, take warning by his sad life and death. For though it may be an honour to be different from other people, if Carlyle's dictum about the 30 million be still true, yet other people do not like it. So, if you are different, you had better hide it, and pretend to be solemn and wooden-headed. Until you make your fortune. For most wooden-headed people worship money; and, really, I do not see what else they can do. In particular, if you are going to write a book, remember the wooden-headed. So be rigorous; that will cover a multitude of sins. And do not frown."


Electromagnetic Theory (1912), Volume III; p.1; "The Electrician" Pub. Co., London.

Heaviside was a self-taught intuitive mathematician who advocated mathematical rigour when writing books.

James Arathoon

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James Arathoon
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