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History of mathematics resources for KS3 and
KS4 |
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School: St Edmund’s
Catholic School, Kent |
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Fellow: Snezana Lawrence |
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Email: snezana_l@hotmail.com |
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Website: www.mathsisgoodforyou.com |
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The aims of the project: |
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The main aim of my project is a development
of a base of knowledge and resources by concentrating
particularly on introducing the historical
context into the study of mathematics at Key
Stages 3 and 4. |
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The aim of the project is not to deal with
the historical aspect of mathematical sciences
in an anecdotal way, but to instead seek to
reinvigorate the creative search for mathematical
truth through giving the tools and examples
from the history of mathematics. I was hoping
that this approach would inspire young mathematicians
to whom the project is dedicated, to recognise
the creative nature of mathematical enquiry
and to gain an insight into the various techniques
of research, analysis and synthesis of mathematical
thought through the study of the subject’s
history. |
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Outline of the plan: |
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My plan was to complete a web site during
the fellowship year, although I did not have
the strict deadline for having the web site
fully operational and ‘live’ on
the web. At the first meeting in June when
I spoke to my mentors we agreed that some
targets have to be set, and that by the forthcoming,
January meeting, I would have the structure
of the web site with some initial information
and worksheets available. I hope (technology
permitting) that this will be met. After the
presentation and the consultation with my
mentor, the web site will be put on the Internet.
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My further plan is to have the full web
site running by the end of the school year
for both KS3 and KS4. The enclosed list shows
in more detail the plan of completion of the
web site. |
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There will still be lots to do over the
coming year(s) in terms of making this a lasting
resource for both teachers and students at
this level. I hope that at the end of this
year I will be able to put a proposal to a
publisher for a book which will be based on
the resources from the web site. |
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Changes made and what is gained |
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As I have piloted the project in my school,
I have throughout the year tried numerous
lesson plans and the most successful ones
will be available through the web site. This
was very valuable experience as I could see
first hand what kind of effort was worthwhile
and would meet with approval both from pupils
and/or teachers. I found for example, that
putting too much detail in the schemes of
work was not very helpful. I then tried giving
simple instructions incorporated within the
worksheets for main lesson or for a lesson
starter. This proved to have much better impact
and could be immediately used. This realisation
had a major impact on my work and I hope that
this will come through the final ‘product’
in terms of usability. |
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I came across the problem of not having
reliable technology to provide the environment
for my project. This meant that some of the
resources that I was piloting and had put
onto the server for other teachers to use
throughout my school was not used often. I
tried putting the resources on a CD and this
had mixed blessings – the structure
of the web site was still not clear at this
point, so the resources were just ‘piled
up’ and some of my colleagues didn’t
use them because of this problem. It became
obvious to me that two criteria would have
to be satisfied for my project to succeed: |
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the structure of the courses
would have to be crystal clear for people
to see how to use the resources and
what part of the curriculum they could
relate the worksheets to |
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the web site would have to be accessible
not only through the network but on
individual machines and through printed
material (hence my desire to publish
a book at the end of the project). |
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During 2004 I developed a school web site
for maths and ict departments, where I posted
many worksheets and study guides that I developed
during the previous two years. I found that
my pupils used this very often (especially
the study guides as they could be downloaded),
because they knew where they were, how to
use these resources, and what they could use
them for. I used this experience to incorporate
some of the knowledge gained into designing
my new website. I also took into account some
suggestions by my pupils on the structure
and accessibility of the web site. I found
this to be very valuable experience, and an
exercise which helped me revitalize my web-building
skills. |
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When I started the project, I first plotted
the National Curriculum against the topics
from the history of mathematics. I then tried
some topics as I went through the year teaching
at both KS3 and KS4 levels. I found that quite
a few topics could be studied at both KS3
and KS4 but with a different level of attention
to detail and producing worksheets which catered
for different levels of difficulty. I also
found that some parts of the NC were more
interesting than others from the point of
view of the history of mathematics, and tried
to make a list of priorities which is now
my guiding light in completing the web site.
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The amount of work that I have been putting
into the project has been quite substantial.
I have spent almost every holiday and at least
several hours per week working on the worksheets,
thinking of lesson starters linked to the
history of mathematics, and making the structure
of the web site clear and consistent. This
work, however, gave me enormous pleasure and
I have definitely enriched the experience
of my pupils in mathematics, as most of them
now speak freely and matter-of-factly about
certain historical details with confidence
and pride. |
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Some personal reflections |
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The changes that I made were all positive
– I had to develop my work through practice,
and by facing some challenges with technology
realised where potential difficulties would
lie with others actually trying to use the
finished resource. |
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The only surprise I had was looking recently
through the many copies of drafts of devising
the web site structure. At times I could hear
myself saying “whatever was I thinking
when I did this” as I went through pages
and pages of repetitious lists. I am however,
now very happy with the structure and have
been able to apply the main concept to each
part of the web site. I have compiled a list
of topics, which have been linked to the National
Curriculum (loosely at the moment, but I plan
to actually give hyperlinked references to
that at the end of the project) and these
are also given in years from Y7 to Y11 so
that one can either go to the main topics
list and decide to work on one topic at all
levels of difficulty or go to the courses
list and work on different topics throughout
that year. |
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What next |
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I plan to put the web site live after the
January meeting, with indication what is coming
and when to the website in the future. |
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The major work will be putting
the worksheets together and formatting them
into a downloadable files and then ‘attaching’
them to the main pages of the site. |
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In terms of my students working through
this site I plan to take note of all practices
and make these also available as a guide to
those teachers who would like to read through
my experiences and possibly develop their
schemes of work on similar bases. |
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In terms of my students working through
this site I plan to take note of all practices
and make these also available as a guide to
those teachers who would like to read through
my experiences and possibly develop their
schemes of work on similar bases. |
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This project brought
an international dimension to mathematics
through teaching and learning about
its history |
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The practice behind the project is
partly to also initiate and enhance
an understanding of different cultural
approaches and encourage comparison
between these |
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Through worksheets and pages the project
employs an interdisciplinary approach,
in particular in relation to visual
and literary arts (1) |
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The project encourages the study of
‘old masters’ through both
facts about mathematicians and their
discoveries (offering a safe environment
for self-discovery and self-identification
in the context of the history of mathematics) |
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Rather than trivialising the subject,
learning about mathematics’ history
allows children to realise the potential
and importance of mathematics and not
only its most practical uses in the
context, for example, related to calculation
of tax or credit interest. This helped
my pupils begin to nurture an intellectual
fascination with mathematical concepts
– I have already managed to attract
pupils from all abilities range to join
a mathematical tutor group based on
these principles. |
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Simplest examples would be studying
Escher’s art and Lewis Carroll’s
(aka Charles Dodgson) children’s
literature. |
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I have now realised that it will take me
almost as much effort to publicise the site
and to make it really useful as it did to
make it. Therefore I cannot say with certainty
whether this will be possible to be achieved
this school year as I aim to finish the site
by the end of it, and would presumably need
to wait until the next September to start
letting people know about the site. |
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TOPICS DEADLINES |
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Yellow - has been
completed, but may need putting intro correct
format |
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Pink – a web
page will be available, worksheets to follow
by end of Easter holidays |
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Red – both a web
page and worksheets to be made by July 2005
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INTRODUCTION TO MATHS |
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Y7 & 8 |
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Introductory and
end of term gems - what is mathematics, origin
of mathematics,
uniqueness of mathematics, mathematics - the
science and art of patterns. |
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Y9 |
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What did some of
the most famous people think of mathematics?
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Y10 & 11 |
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Erdösese - a language
of mathematics |
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NUMBER |
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Y7 |
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Odd and
even, prime, perfect, amicable, figurate numbers
Superstitions and beliefs about numbers
First symbols for numbers, different cultures
Egyptian mathematics
- Rhind papyrus, fractions, multiplication
through duplation
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Y8 |
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Greek
and Roman numeration
Abundant,
deficient, amicable, perfect numbers
Eratosthenes sieve and some properties of
prime numbers
Pythagorean
brotherhood and their number beliefs
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Y9 |
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Base
arithmetic - binary, operations with, other
bases
Binary - Boole and his algebra - link
to c4 logic
Primeness - Goldbach's conjecture |
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Y10 & 11 |
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Irrational
numbers and whey they are so. Proof that is
irrational
On decimals and fractions introduce the idea
of infinity - infinitely small; Zeno's paradoxes
Unit fractions
and the Eye of Horus
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NUMBER OPERATIONS (all years) |
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So you think you can
number basic mathematical operations?
Mathematical symbols - try some maths without
using them Napier's rods |
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GEOMETRY |
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Y7 |
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Greek
mathematics = geometry
Descartes coordinate system |
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Y8 |
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History
of representational techniques
Perspective - short history
Regular polyhedra and Plato
Beautiful proportions - maths and art; square
roots of 2, 3, and 5 and where can they be
found |
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Y9 |
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Circle
geometry
The quest for pye
Mathematics
and art - the work of Esher and mathematics
behind it. Drawing Esher tessellations
Beautiful proportions - maths and art; square
roots of 2, 3, and 5 and where can they be
found Construction of the Golden Mean
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Y10 & 11 |
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Euclid,
further story, non-Euclidean geometry
Hagia Sophia and
the dome; other domes
Euclidean
and non-Euclidean parallel lines
Archimedes'
formulae for calculating the volume of a sphere
and a cylinder
Coordinate system in descriptive geometry,
few examples and the history
Graph Theory - Königsbeg bridges
Four colour theorem
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TRIGONOMETRY (all courses apart
from Year 7) |
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Pythagoras'
theorem - calculations, problems, and constructions
Pythagoras and his brotherhood |
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ALGEBRA |
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Y7 |
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History
of the name
Substitution
through Egyptian and Mayan mathematics
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Y8 |
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History
of the name with greater explanation
Substitution
into formualae from the Rhind Papyrus and
its description |
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Y9 |
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Indices
and standard form - laws, negative indices,
fractional indices |
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Y10 & 11 |
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Fermat’s
Last Theorem and its link with Pythagoras’
theorem
Diophantine
equations and the link with Euclidean algorithm
Number
and number patterns and sequences –
Fibonacci’s sequence. recognise, construct,
find formula for linear and quadratic sequence,
create sequence
Graphs
– coordinates, plotting, equations,
solutions of simultaneous equations
Descartes and his coordinate system |
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DATA COLLECTION AND REPRESENTATION
(all years) |
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Pictograms
from prehistoric and Egyptian times |
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LOGIC (all years) |
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Paradox
– Epiminides’ Paradox |
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Y10 & 11 |
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Binary
– Boole and his algebra |
