History of Mathematics in and for the Curriculum
Notes and References (Part 1)
1. Websites
a. Organisations and sources
These are the most reliable sources for general information. The BSHM site contains
links to other sites which are also good and reliable, and which contain more
specialised information. The MacTutor site is the best for Biographies and
summaries of Historical Topics. The HPM website provides international links and
notices of research topics, projects, publications and other useful items. MathDL
LOCI contains accounts of classroom practice and other items of interest.
Generally the links to other sites from these sites are reliable and often contain much
more information on the history of different subjects.
British Society for the History of Mathematics (BSHM) exists to promote research
into the history of mathematics and its use at all levels of mathematics education.
The Society's Bulletin is published by Taylor and Francis, and carries a wide range of
articles and reviews of interest to the history of mathematics and mathematics
education communities.
This link provides information about how to join the Society; this site also contains
information about the Society and its history, its current activities, and various
resources on the history of mathematics.
http://www.dcs.warwick.ac.uk/bshm/
There is now a BSHM Education site:
http://www.bshmeducation.org/education.html
MacTutor History of Mathematics Archive
http://www-history.mcs.st-and.ac.uk/history/
The most reliable source for biographies and discoveries of mathematicians, accounts
of civilisations and cultural aspects, particular topics and many other items.
History and Pedagogy (HPM) is the International Study Group on the Relations
between History and Pedagogy of Mathematics affiliated to ICMI. Researchers in
mathematics education, teachers, curriculum developers, mathematicians, and many
historians of mathematics are members of the group. Amongst other things, HPM
organises satellite meetings of the ICME conference. The site contains HPM
Newsletters, notices of HPM meetings, and links to other sites of interest.
http://www.clab.edc.uoc.gr/hpm/
Mathematical Sciences Digital Library (MathDL) is sponsored by the Mathematical
Association of America.
http://convergence.mathdl.org/jsp/index.jsp
It has an on-line publication called LOCI with a subsection called CONVERGENCE
a collection of resources for teaching mathematics using its history.
http://convergence.mathdl.org/mathDL/23/
© Leo Rogers.
Revised June 2009
Leo.Rogers@education.ox.ac.uk
Oxford University
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History of Mathematics in and for the Curriculum
b. Specialised sites.
There are many, and it depends on interests and how specialised you want to get. I
offer only two as examples.
EUCLID This is David Joyce’s site at Clark University - everything you ever wanted
to know about Euclid’s Elements with Java animations of the theorems.
http://aleph0.clarku.edu/~djoyce/java/elements/toc.html
ARCHIMEDES PALIMPSEST PROJECT
Fascinating, exciting and ‘bang up to date’! Follow the history of the document, its
recovery and the process of preparing it for examination.
The subject of this website is a manuscript of extraordinary importance to the history
of science, the Archimedes Palimpsest. This thirteenth century prayer book contains
erased texts that were written several centuries earlier still. These erased texts include
two treatises by Archimedes that can be found nowhere else, The Method and
Stomachion.
Listen to the video clip of Reviel Netz, the foremost world expert on the interpretation
of Greek mathematical manuscripts, and share his excitement about the discovery of
Archimedes’ original writing not seen for more than a thousand years!
http://www.archimedespalimpsest.org/
c. Nearer to Home
NRICH
These articles are mostly for KS3, KS4, KS5 and some A Level.
Leo Rogers’ history ‘episodes’.
I have added what I am calling ‘Pedagogical Notes’ to each of these.
From a Random World to Rational Universe
http://nrich.maths.org/public/viewer.php?obj_id=6120
Randomness and Brownian Motion
http://nrich.maths.org/public/viewer.php?obj_id=6127
History of Time Measurement
http://nrich.maths.org/public/viewer.php?obj_id=6070
History of Negative Numbers
http://nrich.maths.org/public/viewer.php?obj_id=5961
Proof - Brief Historical Survry
http://nrich.maths.org/public/viewer.php?obj_id=5996
The Four Colour Theorem
http://nrich.maths.org/public/viewer.php?obj_id=6291
Geometry from Practice to Abstraction
http://nrich.maths.org/public/viewer.php?obj_id=6352
A History of Algebra - Part 1 Visualisation
© Leo Rogers.
Revised June 2009
Leo.Rogers@education.ox.ac.uk
Oxford University
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History of Mathematics in and for the Curriculum
http://nrich.maths.org/public/viewer.php?obj_id=6485
Algebra Part 2 - Representation
http://nrich.maths.org/public/viewer.php?obj_id=6546
Some selected topics by other people:
The Ishango Bone
http://nrich.maths.org/public/viewer.php?obj_id=6013
Understanding Hypotheses
http://nrich.maths.org/public/viewer.php?obj_id=6178
Women in Maths
http://nrich.maths.org/public/viewer.php?obj_id=5748
Negative Numbers
http://nrich.maths.org/public/viewer.php?obj_id=5747
The Victorian Classroom
http://nrich.maths.org/public/viewer.php?obj_id=5892
History of Astronomy
http://nrich.maths.org/public/viewer.php?obj_id=2567
History of Time and Measurement
http://nrich.maths.org/public/viewer.php?obj_id=6070&part=notes
Babylonian Numbers
http://nrich.maths.org/public/viewer.php?obj_id=6001
If you go to the ‘Search NRICH’ box at the top of the main page and put in ‘History’
you will find 77 matches (or more by now) giving a wide range of topics, and 58
articles all classified by Key Stage.
MOTIVATE
This is the Video Conference site for schools set up by the Millennium Mathematics
project and run by Cambridge University.
http://motivate.maths.org/
Click on ‘Mathematics’ under Conference Programmes to find the list of video
conferences and you will find Babylonian Mathematics (for 11-13 yr olds) at:
http://motivate.maths.org/conferences/conference.php?conf_id=175
Eleanor Robson is one of the world’s foremost experts in Babylonian Mathematics
and a member of BSHM.
Here you can download Eleanor Robson’s PowerPoint presentation, copies of the
project work and pages on numbers and fractions. (and for 8 - 10 yr olds) at:
http://motivate.maths.org/conferences/conference.php?conf_id=153
Ella Kaye presented her evaluation of this project at BSRLM on 15 November 2008
Maths is Good for You
This site is run by Snezana Lawrence at Simon Langton School in Canterbury.
http://www.mathsisgoodforyou.com/
This site is growing and has a number of good ideas and historical materials for use in
schools.
Snezana is the Education Officer for the BSHM and has set up a History Community
on the NCETM website. She is responsible for the Education area on the BSHM
website
© Leo Rogers.
Revised June 2009
Leo.Rogers@education.ox.ac.uk
Oxford University
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History of Mathematics in and for the Curriculum
2. Golden Rules for studying the history of mathematics
If you already have some research experience, then this next list may seem obvious,
but if you look at ‘histories’ of mathematics you will find that they all have their
faults - some more than others.
a) Chronology versus History.
Chronology is useful, but is not history. A time-ordered list of events is just the ‘raw
material’ from which we start. The history begins when we fill in the ‘gaps’, and
that’s where it gets really interesting.
b) Credulity.
Historical and mathematical material contains many errors. Some of it is repeating
traditional beliefs without foundation, others from carelessness, ignorance, prejudice
or chauvinism. Do not believe anything automatically. Check against other sources.
c) Priorititis.
The claim that “X did something first” is usually meaningless. There are ambiguities
about what the ‘something’ is, and what is meant by ‘doing’ it. There are plenty of
examples where we can find precursors to an idea. Nothing appears ‘out of the blue’,
and there are often discoveries that have happened virtually simultaneously and
independently of each other.
d) The Solomon Syndrome
Historians have often judged mathematics of the past as ‘right’ or ‘wrong’ by their
own standards. Typical examples are where an author blames a historical figure for an
‘incorrect proof’ without understanding exactly what it was that the person was trying
to ‘prove’. Other common errors have blamed past mathematicians for not having the
‘correct concept’ of something which we take for granted today.
e) Speculation.
If you can’t show why, how or what happened, don’t invent a reason. If you feel a
need to say something, make sure the reader/listener knows you don’t know and that
you are making a suggestion or giving a plausible reason.
f) The Matthew Synrdome.
Matthew’s Gospel says that ‘to those who have much, more shall be given’. The
importance of well-known figures is often exaggerated because their work is more
likely to have been preserved and investigated. Beware of the ‘halo effect’. Euler was
not responsible for the whole of 18th century mathematics, as some might lead you to
believe, and there is controversy over Cauchy’s role as the reviewer (and possible
plagariser) of the work of Bolzano and Galois.
g) Plagiarism.
We need to be clear about our sources and reference everything. With the use of the
internet, it is even more difficult to spot students’ use of un-referenced material.
Wikipedia and similar places are not reliable, and while they might be used by some
© Leo Rogers.
Revised June 2009
Leo.Rogers@education.ox.ac.uk
Oxford University
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History of Mathematics in and for the Curriculum
to gain information, must be checked against reliable printed sources (usually from
reputable journals). Learning to use Google Scholar is an art in itself.
(These rules are adapted from Ken May’s Bibliography and Research Manual of the
History of Mathematics, Toronto 1973)
3. Books.
There are many books on the history of mathematics around now, and it is sometimes
difficult to find the best available. In general anything published before about 1970
does not reflect the new attitudes to historical research, nor the awareness of the
contributions of non-European cultures. All general histories of mathematics have
gaps and often you will have to go to more specialized texts to find what you want.
At this moment I am suggesting only Five Principal General Reference Books.
Others are not useless - we can learn from all of them, but keep in mind the list of
caveats above. I have put Amazon prices if you want to buy - but look in your library
first.
1. The best standard general History of Mathematics at the moment is:
Katz, V. (1998) A History of Mathematics: An Introduction.
Harlow, England and Reading Massechusets
Addison Wesley
This book includes mention of the important contributions of the indigenous cultures
of other parts of the world, and of the important contributions of the Chinese, Indian,
Mesopotamian and Egyptian civilizations. It brings us up to date with selected issues
in 20th century mathematics. Amazon from £27. Get the full version not the short one.
2. A comprehensive source on all kinds of aspects of using historical material in
schools and universities is:
Fauvel, J. and van Maanen J. (2000)
History in Mathematics Education: The ICMI Study.
Dordrecht, Boston, London.
Kluwer
This contains pretty well all that was known about using history of in the mathematics
classroom, from curriculum surveys, national approaches, political influence,
philosophical and multicultural issues to research perspectives and examples of the
use of original sources. I suggest you get hold of this if you can. Your library may
have a copy - or get it on inter-library loan and photocopy the bits you want. You can
get a used one from Amazon for about £40.
Unfortunately this book is expensive, even though there is a paperback edition. It was
intended for teachers, but few teachers have seen it. The problem is that Kluwer is
well-known for being expensive, but unfortunately they won the publishing contract
from ICMI for a whole series of mathematics education ‘studies’ which are all very
expensive. The International Commission for Mathematics Instruction (ICMI) is the
organizing body that supports mathematics teaching and research.
3. The latest Source Book of information on the latest research on Ancient Cultures.
Katz, V. (ed) ( 2007)
The Mathematics of Egypt, Mesopotamia, China, India and Islam: A Sourcebook.
Four internationally renowned authors write on their own subjects of expertise.
This is the real background for the ‘elementary’ mathematics taught in school:
© Leo Rogers.
Revised June 2009
Leo.Rogers@education.ox.ac.uk
Oxford University
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History of Mathematics in and for the Curriculum
Arithmetic, practical geometry, proto-algebra and trigonometry. Amazon about £40.
Princeton.
Princeton University Press
4. A brand new and very different History of Mathematics
Robson, E. and Stedall, J. (eds.) (2008)
The Oxford Handbook Of the History of Mathematics.
Oxford , OUP
Naturally, this book has to be selective, but it is arranged in ‘themes’ rather than in
chronological eras. This is a completely different approach to writing the history of
mathematics.
Geographies and Cultures: Global, Regional and Local.
People and Practices: Lives, Practices and Presentations.
Interactions and Interpretations: Intellectual, Mathematical and Historical.
It deals with mathematics arising from cultural practices as well as the technical
aspects of contemporary mathematics taught in schools and colleges.
Together they deal with the mathematics of 5000 years, but without privileging the
past three centuries, and an impressive range of periods and places with many points
of cross-reference between chapters. The key mathematical cultures of North
America, Europe, the Middle East, India, and China are all represented here as well as
areas that are not often treated in mainstream history of mathematics, such as Russia,
the Balkans, Vietnam, and South America.
5.An important source book for any one who is interested in the development of the
mathematics at levels usually found in a university undergraduate course is:
Stedall, J, (2008) Mathematics Emerging. Oxford, O.U.P.
This book contains the resources, translations and commentaries of original
mathematical works that were assembled and used for the Oxford University course
on the History of Mathematics.
Eighteen chapters span the usual topics in Calculation, The beginnings of the
Calculus, Number Theory, Probability, Functions, Continuity, Algebra, Complex
Analysis, and Foundations of Mathematics. Each of the sections contains samples of
original texts, together with translations and valuable commentaries.
© Leo Rogers.
Revised June 2009
Leo.Rogers@education.ox.ac.uk
Oxford University
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