University Outreach
The impact of computers
and the internet
on globalising mathematics education
Toni Beardon
University of Cambridge
EWM Conference Cambridge Sept. 2007
Content of talk
Outreach from universities to promote mathematics around the world
Advances in ICT - consequent changes in society and work
Need for different skills and effects on education
The Digital Divide
Some statistics about access to education worldwide
How can we use ICT to narrow the gap in educational opportunities?
Examples of collaborative learning and web-based technologies
Experiments in using ICT for academic collaboration at all levels
PAL - Peer Assisted Learning
Interactive web-publishing
Multilingual thesaurus
Problem posing and problem solving as a shared activity
EWM Conference Cambridge Sept. 2007
EWM Conference Cambridge Sept. 2007
Two inter-related programmes
Both projects based in Muizenberg, serving Africa
Partnership between Universities:
The Western Cape, Stellenbosch, Cape Town, Cambridge, Oxford, Paris-Sud-XI
AIMS – residential institute, one year masters level mathematics course
• 50 students – started September 2003 - students from across Africa.
• Teaching philosophy: enquiry based learning, discussion and problem
solving in a collegiate atmosphere …
• AMINET – similar institutes being set up in Uganda, Ghana and other
African countries.
AIMSSEC - interactive school mathematics programme
• Strong local management and roots (but drawing on MMP/NRICH)
• Professional development courses for teachers
• Motivate videoconference masterclasses linking schools around the world
• askAIMS - African online mathematical forum
• Learning resources distributed on CDs with links to SA school curriculum
• Distance learning and online community
EWM Conference Cambridge Sept. 2007
AIMSSEC Now and Future
EWM Conference Cambridge Sept. 2007
Legacy of Apartheid in SA Education
“My department's policy is that Bantu
education should stand with both feet in
the reserves and have its roots in the spirit
and being of Bantu society... There is no
place for [the Bantu] in the European
community above the level of certain forms
of labour... What is the use of teaching the
Bantu child mathematics when it cannot use
it in practice? That is quite absurd.
Education must train in accordance with
their opportunities in life, according to the
sphere in which they live.”
EWM Conference Cambridge Sept. 2007
Verwoerd 1953
Shortage of teachers with
mathematics and science qualifications
a serious problem in UK and USA as well as in developing world
“The shortage of competent teachers
results in less qualified and
inadequately prepared teachers
assuming teaching roles. The negative
consequence hereof manifests as a
vicious cycle of low quality teaching,
poor learner performance, and a
constant undersupply of quality
The South African Government National
Strategy for Mathematics Science and
Technology 2005-2009
EWM Conference Cambridge Sept. 2007
The backlogs from so many years of
apartheid education
• Illiteracy rates are high, 30% of adults over 15 years old
(6-8 million adults) are not functionally literate
• Percentage of population over 20 years old with high school
or higher qualification: 65% of whites, 40% of Indians, 17%
of the coloured population and 14% of blacks
• Teachers in rural & township schools are poorly trained
• South African learners achieve poor results in international
comparisons behind other African countries. In The Trends
in International Mathematics and Science Study (TIMMS
2003), SA learners scored 264 points for mathematics and
244 for science compared to international averages of 467
and 474.
EWM Conference Cambridge Sept. 2007
Advances in
Information Communication Technology
EWM Conference Cambridge Sept. 2007
Global school and university campus
No age, gender, social or racial barriers
How can we best use new technology to
1. promote public understanding of mathematics
2. improve the quality of mathematics education
• at school level – to raise standards of university intake
• at undergraduate level for full and part time students
• at research level for academic collaboration
EWM Conference Cambridge Sept. 2007
Speed of penetration of ICT
and expectations of change
• TV reached 50 million users worldwide in 38 years
• WWW reached 50 million in 4 years
Tim Berners-Lee 1991 libwww CERN
1993 Mosaic
1994 Netscape
1995 IE
• WWW now has 1,173 million users, after 16 years
• Computers and globalisation have transformed the
• Students today face a new era with demands for
new skills
• Is educational change keeping pace?
EWM Conference Cambridge Sept. 2007
Can ICT bridge the educational gap?
The internet and communication technology
is of equal importance in society to
the invention of the printing press
Increased public access to information and increased educational opportunities
Investment in ICT infrastructure
Has there been the expected widespread
change in educational practice and
educational standards?
EWM Conference Cambridge Sept. 2007
Impact of ICT on students
• Students have increasing daily access to a range of
• cellphones, personal organisers, cameras, calculators, gps
• TV, videos, music, computer games
• internet to find information, communicate, purchase, play
• Most of this access is outside formal learning environment
• Learning is often through play
• Learning style inherently non-linear, experiential
• Reference to instruction manual is last resort
• Association and creativity are crucial strategies
EWM Conference Cambridge Sept. 2007
Where does learning happen?
• Schools and universities not the only arena for education
• Modern society requires lifelong learning
• ICT contributes in other areas to the overall level of
education in society
eg. Health
• greater access for patients to information via
• improved understanding of issues by patients
• recording and playback of angiograms
• body scanning, pregnancy scanning
EWM Conference Cambridge Sept. 2007
In the developed world
has ‘education’ failed to deliver?
What is expected?
What improvements in academic performance should arise from
access to ICT?
Technology has changed the role of people in the workplace and in society.
We have easy and free access to information sources.
Independent learning skills and skills in finding, analysing, understanding and communicating
knowledge score over more traditional ways of learning and over learning by rote.
How do we judge success in education?
Are the assessment standards of the last century appropriate
EWM Conference Cambridge Sept. 2007
Statistics on access to the internet
and access to education worldwide
EWM Conference Cambridge Sept. 2007
Internet Usage – The Big Picture
Updated June 2007
EWM Conference Cambridge Sept. 2007
The Digital Divide
Internet penetration- percentage of population
Hong Kong
South Africa
Sierra Leone
75.6% (highest in Europe)
68.2% (highest in Asia)
0.2% (lowest in Africa)
EWM Conference Cambridge Sept. 2007
Access to Higher Education
• Average for 30 OECD countries
is 47% of 18-30 age group
New Zealand 76%
Finland 71%
UK 45%
USA 43%
• E-learning and distance learning extend access
and opportunities
• Changes in student demography in developed
increase in proportion of age cohort in higher education
student fees, student debt
majority of students in employment while studying
EWM Conference Cambridge Sept. 2007
Can educators use ICT to close the
gaps in educational opportunities?
…. not a level playing field
The internet is a cheap way to distribute learning resources and provide adult
Government and local education authority networks distribute learning
resources and enable sharing of ideas – including downloads and caches.
Bandwidth costs favour the developed world
Across Digital Divide, CD’s are a cheap substitute for internet
Satellite links spread connectivity to rural areas
Simputer and solarpc
Free Software -
The Digital Divide Network –
EWM Conference Cambridge Sept. 2007
Some examples of collaborative learning
and web-based technologies
EWM Conference Cambridge Sept. 2007
Peer Assisted Learning
Science Technology
Informatics & Mathematics
Undergraduate Links between
University & Schools 1987
Ask-a-Mathematician service
Online Discussion Forum 1997
Ask-a-Mathematician service
from the African Institute for
Mathematical Sciences in
Muizenberg South Africa 2003
EWM Conference Cambridge Sept. 2007
Carl’s Question to askNRICH
Carl. 12.27pm 3 June:
Hi, With less than 4 days to go before my A level maths
exams, I really should be able to do this, and so I'm quite
annoyed at myself. Please could someone help?
Find, in terms of π, the complete set of values of θ in the
interval: 0 ≤ θ ≤ 2 π for which the roots of equation (1) are
x2 +2x sin θ +3cos2 θ = 0
Now show that the roots of the equation:
x2 + (5cos2θ +1)x + 9cos4 θ = 0
are the squares of the roots of equation (1)
See askedNRICH
EWM Conference Cambridge Sept. 2007
The response from askNRICH
James. 2.00 pm 3 June Gives first response, advising on how
to proceed
Carl 12.16 am 4 June Hi James, I'm going to try it myself
now, I'll post a message to let you know how I got on. I
think I'll be able to solve it now.
9 more messages with discussion of the concepts and
Carl 12.18 pm 5 June That makes it very clear, thanks very
much. It must have taken you a while. If you're doing uni
exams, good luck to you too!
…. See Onward & Upward on askNRICH
EWM Conference Cambridge Sept. 2007
Please Explain
By Woon Khang Tang, age 17, to askNRICH
Thank you!!! Even though I don't really understand at first
glance, but I'll print it out and read it again until I understand.
I'm sure I'll understand, and a million thanks for your detail
I'm really desperate after I've gone through dozens of books
and my teacher didn't explain why.
I was really surprised when I asked my friends and they told me
just memorize the formula. As long as you know how to apply the
formula, it's ok. I really hate to memorize formulas without
understanding and proving them. Without understanding the
formula, when I apply the formula, it's like you can find the
right answer easily, but you don't know what the heck are you
doing, and that's really really stupid!!!
EWM Conference Cambridge Sept. 2007
EWM Conference Cambridge Sept. 2007
The Motivate Project
• provides maths and science videoconference lessons
linking schools in UK, India, Pakistan, Singapore South
• school teachers learn along with their students
• enriches the mathematical/scientific experience of
school students of all ages
• gives students opportunities to:
• learn from an expert
• go beyond the curriculum
• work collaboratively with their class-mates
• do their own independent research
• communicate with other students across the world
• present their work to an authentic audience
EWM Conference Cambridge Sept. 2007
EWM Conference Cambridge Sept. 2007
Space Science
Example of a Year Long Programme
• 6 VCs in the year – work on
the solar system, our galaxy, the universe
• 2 London and 2 South African schools
• VCs led by Dr Lisa Jardine-Wright, from
the Institute of Astronomy in Cambridge
and the Greenwich Observatory
A short clip:
EWM Conference Cambridge Sept. 2007
e-learning for school students
“NRICH has helped spread the idea that
maths can be something the world can do
together. It has increased awareness
that there is maths going on everywhere.
We have fun doing these problems.”
(Secondary teacher, NRICH Evaluation 1997/98)
EWM Conference Cambridge Sept. 2007
Problem Solving
A Gateway to Research
Moving forward from teaching and learning
about mathematics
to include more teaching and learning
how to do mathematics
how to communicate mathematics
EWM Conference Cambridge Sept. 2007
We’ll look at a selection of problems from the NRICH website and think about
how they might be useful in developing mathematical understanding and skills.
Root Tracker
2 and 4 Dimensional Numbers
Flight Path
Epidemic Modelling
Diophantine n-tuples
Why 24?
Keep You Distance
Basket Case
Subject content
Quadratic & cubic equations Complex numbers
Complex Numbers Quaternions Fields
3D Geometry
Statistics Analysing data
Number Theory
Indices Equatons
Ratio Circles Area
Dynamical Systems
Prime numbers Factors
Triangles Quadrilaterals Polygons
Arithmetic Sums and products
Geometry Recurrence relations
EWM Conference Cambridge Sept. 2007
Basket Case
Find four amounts of money which added or multiplied together both give £7.11
Keep Your Distance
Draw 4 points so that there are only 2 different distances between any of them
Why 24?
Take any prime number, square it, subtract 1, divide by 24. What happens? Why?
Find the smallest natural numbers a, b and c such that a 2  2 b 3  3 c 5
Compare the shaded area (made up of semi-circles)
with the area of the circle on AB as diameter.
EWM Conference Cambridge Sept. 2007
A selection of problems from the NRICH website:
Mathematical Skills
Root Tracker
Visualising Conjecturing Proving
2 and 4 Dimensional Numbers Using isomorphism Independent learning
Linking concepts Appreciating history
Flight Path
Modeling physical situations
Epidemic Modelling
Modeling real life Setting parameters,
Analysing data
Diophantine n-tuples
Proving Appreciating history
Cutting edge research
Using algebra
Proving Aesthetics
Investigating Spotting patterns
Making and proving conjectures
Why 24?
Keep You Distance
Working systematically
Basket Case
Using trial and improvement
Making and proving conjectures
EWM Conference Cambridge Sept. 2007
Thank you
AIMSSEC - Muizenberg South Africa
MMP - Cambridge England
Toni Beardon
EWM Conference Cambridge Sept. 2007
AIMSSEC needs funds to continue its work
in South Africa and every little helps:
£2.50 pays for a learner in SA to take part in a video-conference
masterclass linking SA & UK schools. This pays for the bus to take the
learners to the Science Centre in Cape Town and for all the expenses
connected with the video-link. Usually 120 South African children take
part in each video-conference.
£10 pays for a resource pack of learning materials for teaching
£300 pays all expenses for a teacher for a 10 day residential professional
development course followed by 3 months distance learning. This includes
travel, tuition, accommodation, food, stationery and a package of teaching
and learning materials to take back to school.
£15,000 is the total cost of a 10-day residential course for 50 teachers
followed by 3 months distance learning.
The AIMSSEC account is administered by the University of Stellenbosch.
For details of how to make a donation through the Stellenbosch Foundation
Charitable Trust see:
Please send a covering letter saying that the donation is to AIMSSEC and
what you would like the money to be used for. Cheques should be made
payable to: Stellenbosch Foundation -AIMSSEC Cost Centre R268
EWM Conference Cambridge Sept. 2007

The Motivate Project - Faculty of Mathematics