A discussion on the Mathematics Education e-mail discussion list

Dear all,

I am attaching what I am also sending to Paul Ernest as copy which he can then
edit for POME. I have heard from some of you about your copy, talked to others,
and, for some of you, this is the first time that you will have been contacted
about this because:

- other messages come in

- some people have sent me earlier messages.

I can't contact everyone by e-mail because I haven't got addresses - can someone pass this on to Malcolm Swan, John Gillespie, Peter Gill?

The suggestions which I have passed on to Paul for consideration are:

I simply responded to his invitation to collect together

the mails in chronological order.

Best wishes all,

Laurinda Brown

----------------------

Laurinda Brown Laurinda.Brown@bristol.ac.uk

9/11/2000

I've been fascinated by the controversy over values in Maths Ed. An invitation to all the participants: would one of you - with the permission of the others - like to collect it all into a dialogue (chronologically I assume) for me to publish in Philosphy of Maths Ed. Journal next issue - available to everyone via the web (address below). A bit of real issues driven controversy is exciting and valuable and I think it should be shared wider (if you are willing).

Paul Ernest <p.ernest@ex.ac.uk>

2/11/2000

I have just come across two UK publications

"Money counts" by BEAM and the Financial Services authority which claims to be developing financial capability in the primary school linked to the numeracy strategy.

Another is a published by the "4 learning and maths year 20002" (never heard of them myself). This is called "Your family counts".

Both books give classroom resources purporting to develop children's and families numeracy by looking at matters financial.

Nothing in these books seems to be developing in children the real values of money - i.e. the issues of disadvantage, poverty, social injustice, usury, etc. etc.

I am interested in thinking about whether some of us could put something together (e.g. "Money Talks" or "It's only being really rich that matters") that consists of activities, examples etc. that raise the critical aspects and uses of mathematics. There might of course be a wealth (sic) of resources out there of which I am unfamiliar, but it strikes me as potentially useful to consider giving teachers some tasks that raises real social questions about the way in which poverty is both unevenly distributed, how poverty is spread, how it costs the poor more to live than it costs the rich and all that stuff.

Is anyone interested, or does anyone have ideas??

Peter Gates

2/11/2000

Anyone who chooses to work with financial institutions or government organisations takes on some important limitations. On the other hand, the possibilities for getting wide distribution of socialist, revolutionary or even liberal texts are limited, and as we know teachers attempting to unsettle the dominant discourse of the maths classroom usually have to resort to their own, or informal, networked materials.

We would entirely support Peter's proposal for the further development of such
materials, and remind readers of this list that it is not the case, as David
Pugalee puts it, that 'mathematics, in general, has not raised the types of
social issues that could be a 'wealth' of conscious raising activities'. Aside
from anything else, our knowledge of 'disadvantage, poverty, social injustice,
usury, etc. etc.', as Peter put it, is often

expressed in terms of mathematical discourses. Indeed, 'mathematics, in general'
is unclear ... Maths education? All classes, all teachers, all age groups, all
countries, all languages?

A key difficulty for teachers at least in the UK trying to centre curricula and pedagogy on issues of social justice is the dominance of official discourses. These limit the possibilities for people attempting to work inside those dominant discourses, including those writing maths books for school use.

Two of us were involved in producing one of the books Peter refers to - "Money
Counts" from BEAM and the Financial Services Agency. The introduction to
this book certainly refers to issues of poverty and social injustice - albeit
couched in the language of social inclusion. Activities include the Cost of
Living which is set in the context of Jaqueline

Wilson's Bed and Breakfast Star - about a homeless family living in hostel accomodation;
Internet Books which raises issues about credit cards and young people's debt;
Gifts, a comparison of different amounts of money (including the National Health
Service budget); Phone a Friend which explores issues around advertising and
confusion marketing; or What will you buy / Special Offers which explore the
different meanings of value (not just monetary).

All these activities were a result of compromises and were certainly toned down. For example, one activity that was edited out was:

Discuss who you might lend money to and for what benefit to yourself

£10 with a return of £15 from an arms manufacturer

£10 with return of £11 from a clockwork radio maker

£10 with no return from a medical emergency appeal.

We think that books like this need to be set against the plethora of materials that are produced by banks - little more than propaganda and free advertising targeted at getting young people to consume their products. It's all very well to produce radical curriculum materials but these are likely to be used by the teachers who would do this anyway.

Finally, it is important to recognise that these activities are aimed at 5 to 11 year olds. Whilst young children's thinking can be very sophisticated, their experience of financial, political and social issues is necessarily limited.

Tamara Bibby, Jeremy Hodgen, Alison Tomlin

3/11/2000

During my years of secondary school teaching I often attempted to introduce
values into mathematics lessons. I found that when I was explicit in this and
directly presented my views (I am a product of the 1960s student New Left) the
students generally listened politely, nodded agreement and then went on with
their mathematical tasks. It was obvious that I had little impact. By accident
one day I found a much better approach. Using data given me by a local mine
manager I had developed a large problem in which

students were to balance the production of 5 mine sites producing multiple minerals
to match predicted customer demand for metals. There was a 'perfect' solution
to the problem that involved increasing production at some sites and decreasing
it at others. One of my students, having personally experienced in his family
the uncertainty arising when local mines shifted production targets, noted that
our equations did not address the issue of employee dislocation. Their interests
had no place in the problem solution. A lively debate re the uses of mathematics
and the need to interject values positions into problem solving followed.

Since this event I have attempted to construct problems that potentially have
a values component, but wait for the issue to arise from the class. Most often
it does and I have seen some very intense debates follow. I have also found
that I do not need to interject to counter extreme positions or spurious arguments.
All the teacher needs to do is to ensure

that the tone of the debate remains reasonable and that the floor is open to
all. In this case students themselves rise to address positions that I would
like to see challenged.

Geoff Roulet

3/11/2000

No course which we teach is ever value neutral. There is a reasonable case to be made that some of what we teach in mathematics supports values which are not in the best interests of our society. But this is only a reasonable case, not a divine message set in tablets of stone. It is therefore important that, in attempting to correct what we may see as an imbalance/inappropriateness in values, we do not do those very things which we are seeking to oppose.

One of the characteristics of librarians which has always impressed me is their commitment to assisting readers to finding out information without asking any questions about the use to which the information will be put. I would argue that mathematics teachers have a similar calling: to provide students with the power of being able to think mathematically and to show them what tools are available within the discipline.

These are dangerous words to write. I know and accept at least some of the arguments for the importance of context, relevance, and the need for social critiquing, though no doubt by now some of my readers will have decided otherwise. But I would still put before Peter Gates and his collaborators what I see as the primary need of ensuring that students learn good mathematics in a way which will enable them to use this mathematics as seems best to them. I have no doubt that some of them will use it in ways to which many (probably most) of us are very much opposed. But this will happen regardless of how much we try to blend social correctness with mathematics teaching.

Personally, I put my long-term confidence in openness, and my fear is that Peter Gates' proposal is a step in the opposite direction. I should be delighted to find out that this is not so.

John Truran

3/11/2000

John raises some important issues here, but let me ask a question.

Assume you were the father of two small girls. Assume also that you were a librarian. Assume someone came in and asked for books somehow related paedophilia. Assume also that a little girl of about 8 had just been murdered by, it is claimed, a paedophile in your area.

Question. What do you do? Just not ask questions? I bet!!

Another question, you are in Germany in 1938 … I will let you finish the analogue.

Personally I find the analogue of the librarian frightening and unhelpful. But it does open up clear blue water between me and you John.

I am personally not in this business because I have some divine desire to teach
maths. I am fundamentally a socialist, that is what drives me and it is paramount
to me. It comes before and is much more fundamental than my teaching. I teach
however as a socialist.

Whose 'good' mathematics, John? The mathematics that killed so many Japanese
in 1945? The mathematics that causes children from ethnic minority groups to
be so disadvantaged in my country as well as yours? The mathematics that alienates
so many girls. OOooo you make me angry!

Mathematics is neither good nor bad - it is people who are.

I am not prepared to stop values being central simple because some don't hold
my values. What I will do is argue my values to show how superior they are than
others. If I win that battle -great. If I loose then I have to rethink or to
keep on battling.

For me (and possibly "my collaborators" that sounds rather chilling John - I wish you hadn't said that it's rather patronising) the Primary need is not "that children learn good mathematics". That is just plan naivete.

OK. Have I changed your mind? No, I thought not. BUT at least I am being open with my values. That surely must give you confidence in me.

Peter Gates

4/11/2000

Carrying on with Peter Gates and John Truran's discussion:

Does E = mc^2 have implicit values?

I wonder if there might not be a confusion between the values which we bring to reading such a statement (including our judgements of historical events in which this played a part), and the values which were implicit in the culture (macro and micro) in which the formula was developed?

If my conjecture that there are differences in these has any validity, then perhaps the statement that E=mc^2 has implicit values is either confusing or amalgamating these two (and perhaps others, such as the values implicit in participating in an e-discussion on this issue). It makes more sense to me to look at the values of people than treating artefacts as containing or holding the values of people who have produced or employed them.

To be really extreme, I find it hard to blame paper and pens for having been used to sign death warrants, no matter how against the actions I might be. I certainly do not refuse to use paper and pencil because of this history.

Now, teaching is done by people to people and so there are implicit and explicit values involved. But it does not follow, for me, that the content of what is being taught is itself value-laden.

Or have I missed the point?

John Mason

6/11/2000

The odd thing about John Truran's message is that it seems to be saying (his disclaimer notwithstanding) that our teaching should not suggest to students that mathematics is 'about' anything. That, I believe, is one of the reasons that so many talented minds from certain demographic groups demonstrate minimal interest in mathematics. If you see a need to change something, to make a difference, to make things better for people, and you have not seen the applicability of mathematics to much of anything, then you probably won't focus much intellectual effort in the direction of mathematics. We need a wide range of intellectually engaging context. Economic issues are very appropriate. And if students get hot about an issue that is the context of their mathematics learning, we will have turned a major corner in mathematics education.

Rosalie A. Dance

6/11/2000

Rosalie Dance has suggested that I seem to be saying that "our teaching should not suggest to students that mathematics is 'about' anything" and that such an approach is a great turn-off for many students.

This is almost certainly a very good point, as is her comment that "we need a wide range of intellectually engaging contexts".

I have been trying not to be too absolute in my statements just because points like these are also relevant. My specific concern in commenting on "Money Counts" was that it could easily become ideologically driven, rather than mathematically driven, and not provide that "intellectually engaging context" which I believe is important. I was also concerned to provide a balance to the current bias away from pure mathematics, even though pure mathematics can also provide an intellectually engaging context.

I was certainly producing a conservative response because I am conscious in
my own country of how good mathematics (dare I say accurate mathematics) is
so often disregarded by teachers (at all levels) and by administrators/politicians.
Perhaps the question I have been feeling towards is really one about whether
mathematics knowledge really does make a difference in this world (at least
at the level of ordinary people) and

how it is possible to demonstrate this to students.

This is not very well put, but I would be very interested to read case studies of where sound mathematical arguments were actually listened to by people who initially had different agendas from the answers.

John Truran

6/11/2000

It's great to see a discussion developing about what we can do to create materials that can be used to open up discussion between teachers and children about financial priorities in society. I think an important part of this would be to talk about the international financial systems; the IMF and World Bank, global currency speculation. futures markets; McDonalds paying children a pittance to make toys for their happy meal boxes and the like.

Recently an intiative was taken to create an international network of maths educators under the name "People Count". This was aimed at "educating the world about the IMF and Worldbank" to link up with recent protests in Prague.

This has generated a lot of interest particularly in Latin America. About 70 people have subscribed to the People Count mail list. In the end difficulties of time and translation meant that this didn't get much further than a statement of intention.

Such an international development probably needs to be more firmly based on the development of the sort of materials that Peter suggests in particular countries first.

I have begun to prepare some materials on the way that votes are bought in
these international financial institutions. It's literally one dollar one vote,
and we know who has the most dollars. The lack of democracy is compounded by
the way in poor countries are forced to group together into voting constituencies
which lead to former British colonies that are poor like the Carribean islands
ending up being represented on the board of

directors by rich ex-British colonies like Canada.

I'd be willing to work one some materials about this and other issues connected to globabisation, debt and poverty.

And what about the mathematics of climate change?

Mark Boylan

8/11/2000

I did of course know the arguments about paedophiles, 1938, and librarians, and I'm sure Peter Gates knows the principle that hard cases make bad laws.

What I have trouble understanding, however, is why Peter is angry with me for
suggesting that mathematics can be "good". Of course, the criteria
we use to judge goodness in mathematics are different from those we use to judge
goodness in people or goodness in how people use mathematics. It seems to me
that they are more intrinsic in the case of mathematics, more self-referent,
less concerned with their effects on others. But I'm very open to suggestions
on this. But I would say that one test I would apply

to any argument put forward is to replace "mathematics" by "music"
to see if the case were still a strong one.

I was aware that Peter was a socialist, and that's not a problem for me. It is good that we are able to fight for our values systems, and I try to do my bit too, though not as strongly or as often as Peter. But while conceding that each teacher's values systems will impinge to some extent on his or her teaching (and I am certainly conscious of some of the ways in which mine do) I also see it as responsibility of a mathematics teacher to make the mathematics central. Peter, as I read him, sees the balance as quite different. I wonder what the consequences of our respective positions are for the good of mathematics teaching as a whole.

I'm sorry if I've offended by using the word "collaborators". It
was not meant to offend. It was merely e-mail-ese for want of a readily available
better word, and I still can't think of one which doesn't have undesirable overtones
for what I want to convey. Help is welcome.

John Truran

9/11/2000

John Truran wrote:

'I was certainly producing a conservative response because I am conscious in my own country of how good mathematics (dare I say accurate mathematics) is so often disregarded by teachers (at all levels) and by administrators/politicians. Perhaps the question I have been feeling towards is really one about whether mathematics knowledge really does make a difference in this world (at least at the level of ordinary people) and how it is possible to demonstrate this to students. This is not very well put, but I would be very interested to read case studies of where sound mathematical arguments were actually listened to by people who initially had different agendas from the answers.'

From Laurinda Brown:

If students are not engaged by the mathematics that they do whether 'value for money' or within the mathematics itself then mathematics certainly will not make a difference in the world of the students and thence not in the wider world. I see myself as a mathematician and teacher as well as a person/human being and mathematics makes the most difference in my own world because of my engagement with it, which also allows me to be numerate in the sense of being aware of how mathematics is used and using it in the way talked about in the book 'Innumeracy'.

I suppose what I try to do in classrooms is to work with students so that they are listened to as they discuss mathematically (and this means their strong arguments in response to questions like 'why?' 'how?' 'what makes a difference?' 'what happens if?' etc and that they learn the power of their thinking mathematically so that they can achieve something they couldn't do without it. David Wheeler's challenge of all children experiencing 'mathematising at least once in their lives so they know what they are choosing away from in deciding not to study mathematics' has certainly coloured my thinking. The lecture in which this was said was entitled 'Humanising mathematics education' and as he talked it started to snow gently - all in all an inspiring event - a long time ago - but I believe that students will not necessarily experience this power of mathematics internally for themselves through someone else's political agenda. This does not mean that I rule that possibility out. Mathematics makes a difference at the level of ordinary people when it makes a difference at the level of the students. This is the challenge I work with.

Laurinda Brown

9/11/2000

I would like to make the following points on the debate around 'Money Counts' in response to John Truran and Laurinda Brown.

I believe that the mathematics curriculum is already ideologically driven both in terms of the content of the curriculum and the way that it is commonly taught. Our choices about what to teach, in what way and how to teach are always choices of value. I think that Peter Gates declaration of his political position as a socialist is both honest and makes transparent his purposes in trying to influence the mathematics curriculum. Personally. I find it hard to put labels on myself nowadays but for me a central concern is empowering students to understand the ecological, economic and social forces that mean our current ways of living in the rich nations are unsustainable. When people do not say where they are coming form politically I get mistrustful.

Too often mathematics education is seen as neutral in terms of value. So we
teach children about large numbers, put standard form in the text books and
curriculum but often this is done in neutral contexts and through repetitive
exercises that are very boring. There are an implicit values in doing this -
mathematics as alien and pointless to the vast majority of students. How about
allowing our students to explore their relationship to

the world through number. To realise how incredibly big they are in relation
to the number of cells in their bodies and how incredibly small they are in
relation to the abundance of life on our planet. How about exploring the relative
size of wealth people own in the world. If Bill Gates' height was proportional
to his height how much bigger would he be than people in the local community
or a child sleeping on the streets in Sao Paulo?

Of course many teachers are already doing this sort of work. I remember how
a class of low attaining, disaffected working class students I taught came alive
when we discussed how much the Director of Direct Line Insurance and engaged
with the intellectual challenge of working our just how many years their low
paid mothers and fathers needed to work to earn the equivalent of one days pay.
"I'm gonna go home and tell my Da' about

this" one said. This may have been the first time he had wanted to talk
to his father about what he did at school.

I am sympathetic to Laurinda's remarks. Not least because I feel strongly that when students have the experience of 'dreaming' mathematical worlds into existence for themselves it can help to give the confidence to try to create similar qualities of beauty, wonder, suprise, order, chaos, rhythm and pattern in other areas of their lives.

But given the fact that the Financial Services Industry wants to influence what is taught in schools surely the main issue is do we want to provide an alternative perspective which at least gives the possibility of students making their own minds up. If we don't then the only voice that will be heard is the corporate voice.

Mark Boylan

10/11/2000

Hold on a minute. This discussion started from Peter's comments on the BEAM
book 'Money Counts' aimed at primary, but there's also related curriculum advice
at www.dfee.gov.uk/circulars/fcg/index.htm.

Now these materials may be flawed and they may be the result of various compromises
- but I don't accept that they represent only the corporate voice. Certainly
as someone involved in the writing, several of us fought hard to include wider
social, political and

economic issues. And, yes, enabling children to challenge the hidden inequities
in our society is important, but we do also need to enable them to develop skills
to live with the financial system we've got. It seems to me important that young
people know when and whether they're being ripped off!

Jeremy Hodgen

10/11/2000

May I bring up a different, partly technical, issue? The mathematics and problem solving styles used in finance/accountancy are rather different to the sort of thing we do up to GCSE, e.g. as far as I can tell fractions are not used at all (everything is turned into decimals). On the other hand who uses non decimal fractions in real life anyway?

I know this as a maths educator married to a tax accountant. On one of the occasions that we came close to divorce we were arguing whether to pay tax on the stake when backing a horse or to pay it on the winnings. We produced opposite conclusions from what turned out to be completely valid but very different mathematical arguments.

At that time I was teaching at a school close by Newbury Racecourse and I found that betting on horses was seen by my pupils as a perfectly normal thing to do and gave me an excellent context for teaching probablitiy but try as I might I could not get them into discussion of the pros and cons of gambling. It was seen as the local industry and thus a Good Thing.

Peter Gill

16/11/2000

As well as emphasising what is wrong with the way money and wealth is used
and distributed, we should also be positive and suggest activities which promote
the sharing of wealth. Rather than simply criticising 'how can you maximise
profit?" questions, we should also promote "how can I raise/ give
away money in a manner that maximises

the benefit to others"? I find that when kids realise there are things
wrong with the world (and its not hard to get most kids angry about injustice)
they want to do something about it … and we can surely find ways of harnessing
social consciences in local, positive

ways? Many schools do such things, though perhaps not in their maths lessons.
This sounds like a 'real problem solving' task that cuts across school curriculum
issues and should best be tackled by several departments working together.

Malcolm Swan

6/11/2000

For easily accessible material suitable for KS4 pupils, see the Century Maths series from Stanley Thornes. 'Handling Data Y10/11 Core' book has some data on '50 Cities of the World'. It contains data such as living space, infant mortality rates etc. Can be used to illustrate Global Education, Citizenship etc as specified in NC 2000.

Paul Marshall

7/11/2000

' And what about the mathematics of climate change?'

For teachers who are looking for materials to use in their classrooms:

John D Collins' (1995) book Maths Matters: Example of Mathematics in the Environment, published by WWF, UK has some excellent examples of how maths can be used to understand what is happening in the environment.

Areas of interest covered are:

Carbon dioxide: Using mathematics to understand the greenhouse effect

Chapter Two: Investigating Population Issues through Mathematics: Ethiopia

Chapter Three: Using mathematics to understand what is happening to the

world's largest veggies - the elephants

Chapter Four: Our Disappearing Countryside

Chapter Five: The Peregrine Falcon -Master of the Skies

Chapter Six: Oil Slicks pollute our seas

The book is designed to be used by students in key stages 3 and 4. Teachers' Notes are provided.

Swee Fong Ng

9/11/2000

I have been asked by one individual for more information on this book - it is full of the sort of challenges Mark talks about and I found that I could use a lot of the ideas which did motivate the students I work with as well as being a good read. Thought I'd send it to the list in response to Mark's thoughts - the important thing is finding something in our own lives and teaching that actually works which is one reason Mark's story is so strong - it worked for him - what works in a middle-class heartland might be different and for a different person. Thanks all for the discussion. Laurinda

Innumeracy - mathematical illiteracy and its consequences - John Allen Paulos
ISBN 0 14 01.2255 9 - Penguin books for us, 1988. Try Amazon - there are now
later books but this first one has some really arresting problems which I have
used with students as appropriate - e.g. how fast does your hair grow - in km/per/hr.
Estimate how much blood there is in the world and give a visual representation
of it. Nice chapter on

Statistics, Trade-offs and Society. It's also a book which some students get
a lot out of reading themselves. Quite a motivator. Hope this is of some use,

Laurinda Brown

16/11/2000

I too think that the equity issues of money in the world are little known in
schools and elsewhere but very important to include. I would like to help in
some way. 4 probably well known starters:

- No doubt you saw the recent ATM article in MT172 by Jonathan Makernan - Not
for the classroom

- There are development education centres around the country - we have one here
in Nottingham called MUNDI - they could help

- Am I right that the New Internationalist still has centre spreads which are
very useful sources of data.

- The voluntary sector aid agencies like OXFAM, Cafod, Christian Aid etc also
have statistics. In addition they have young person centred People Maths activities
for youth groups etc which are effective.

John Gillespie

16/11/2000

There is a real opportunity to address these issues through the implementation
of Citizenship into the National Curriculum. Mathematics can certainly play
an important part in involving children in thinking about these issues in a
constructive way and the Dfee are looking for resources which will support teachers
who want to do this and disseminating them through the National Grid for Learning,
a website which will support

Citizenship will be launched next year. In the meantime there is a small Citizenship
area developing on the Virtual Teacher Centre at

http://vtc.ngfl.gov.uk/

If anyone has materials that they would like to share, please use the Contributory
Database at http://contribute.ngfl.gov.uk/

David Wright

16/11/2000

There is Marilyn Frankentstein's 'Relearning mathematics' which has this sort of stuff, though aimed primarily at adult learners.

You may also have seen the article 'Not for the classroom' by Jon MacKernon in a recent Mathematics Teaching which contains some provocative statistical sources - though we might want to challenge the assumption that these are *not* for the classroom.

Candia Morgan

16/11/2000

A site that may be of interest in this context is:

http://equity4.clmer.csulb.edu/netshare/gdeklerk/ConnectingMathto/

Ian Stevenson

20/11/2000

The BEAM materials do aggrandise money to the extent of producing BIG mega-coins. I generally have a lot of time for BEAM products and the points Peter mentions: 'the issues of disadvantage, poverty, social injustice, usury, etc. etc.' are more on Peter's agenda than on BEAM's agenda. I hope he will take it up. (But see Tamara Bibby's e-mail.)

The other item from "4 learning and maths year 20002" (never (never heard of them myself) has an obvious typo.

It comes from Maths Year 2000 and Channel 4 Learning and is called "Your Family Counts" - part of the MY2000 Family Numeracy Campaign. Peter suggests it has a financial emphasis, which is not entirely correct. To judge for yourself order a free copy (or ten - several millions have been produced!). For details visit www.mathsyear2000.org

I hope Peter's proposal gets developed - indeed earlier on this year I did arrange funding from Maths Year 2000 for a project aimed at social issues of mathematics, and was sorry it was never taken up. (Other funding possibilities still exist.)

John Bibby (no relation to Tamara Bibby)

Addresses:

tamara.bibby@kcl.ac.uk

Mark S. Boylan, m.s.boylan@shu.ac.uk

School of Education, Sheffield Hallam University, College House, Sheffield S10
2BP

Tel 0114 2254398

Laurinda Brown,

Laurinda.Brown@bristol.ac.uk

Rosalie A. Dance, rdance@uvi.edu

Division of Science and Mathematics, University of the Virgin Islands, St. Thomas,

VI 00802 phone 340-693-1253 fax 340-693-1245

Peter.Gates@nottingham.ac.uk

Peter Gill

School of Education, King's College London, Franklin-Wilkins Building, Waterloo
Road

Tel: +44 (0)20 7 848 3188 London SE1 8WA

Fax: +44 (0)20 7 848 3182 United Kingdom

http://www.kcl.ac.uk/education

John Gillespie (Peter would have his e-address)

School of Education, University of Nottingham, Jubilee Campus, Wollaton Road,
Nottingham NG8 1BB. (0)115 951 4988 Fax 0115 951 4475

jeremy.hodgen@kcl.ac.uk

Paul Marshall, PRMLMU@aol.com

John Mason j.h.mason@open.ac.uk

Candia Morgan, temscrm@ioe.ac.uk

Geoffrey Roulet, rouletg@educ.queensu.ca

Coordinator, Centre for Mathematics, Science, and Technology Education

Faculty of Education, Queen's University, Kingston, ON, K7L 3N6

Phone: 613-533-6000 ext. 74935 (Work External)

74935 (Work Internal)

613-531-3348 (Home)

Fax: 613-533-6584

Swee Fong Ng, sfng@nie.edu.sg

National Institute of Education, Mathematics and Mathematics Education Academic
Group, 469 Bukit Timah Road, Singapore 259756 Telephone number: (65) 460-5900

Fax: (65)-4698952

Dr Ian Stevenson, I.Stevenson@ioe.ac.uk

Mathematical Sciences Group, Institute of Education , 20 Bedford Way, London
WC1H OAL http://www.ioe.ac.uk/ms/

Tel: +44 (020) 7612 6676, Office:+44 (020) 7612 6651/4, Mobile: 07779 657094,

Fax: +44 (020) 7612 6686

Malcolm Swan

School of Education, Jubilee Campus, Nottingham NG8 1BB

Tel +44 (0) 115 951 4412

alison.tomlin@kcl.ac.uk

John Truran, truranjk@camtech.net.au

PO Box 157, Goodwood, South Australia 5034

+618 8373 0490 ph

David Wright,

Education Officer, Curriculum and Institutional Development, Becta

British Educational Communications and Technology Agency