1. Toni Beardon University of Cambridge mmp.maths.org
22 March, 2017
University Outreach The impact of computers and the internet on globalising mathematics education
Toni Beardon
University of Cambridge
mmp.maths.org
EWM Conference Cambridge Sept. 2007

2. EWM Conference Cambridge Sept. 2007
22 March, 2017
Content of talk
Introduction
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
Videoconferencing
Multilingual thesaurus
Problem posing and problem solving as a shared activity
EWM Conference Cambridge Sept. 2007

3. EWM Conference Cambridge Sept. 2007
22 March, 2017
EWM Conference Cambridge Sept. 2007

4. Two inter-related programmes AIMS and AIMSSEC
22 March, 2017
Two inter-related programmes AIMS and AIMSSEC
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 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

5. EWM Conference Cambridge Sept. 2007
22 March, 2017
AIMSSEC Now and Future
EWM Conference Cambridge Sept. 2007

6. Legacy of Apartheid in SA Education
22 March, 2017
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.”
Verwoerd 1953
EWM Conference Cambridge Sept. 2007

7. EWM Conference Cambridge Sept. 2007
22 March, 2017
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 teachers” The South African Government National Strategy for Mathematics Science and Technology
EWM Conference Cambridge Sept. 2007

8. The backlogs from so many years of apartheid education
22 March, 2017
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

9. Information Communication Technology
22 March, 2017
Advances in
Information Communication Technology
EWM Conference Cambridge Sept. 2007

10. Global school and university campus
22 March, 2017
Global school and university campus
No age, gender, social or racial barriers
How can we best use new technology to
promote public understanding of mathematics
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

11. Speed of penetration of ICT and expectations of change
22 March, 2017
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 Mosaic Netscape IE
WWW now has 1,173 million users, after 16 years
Computers and globalisation have transformed the workplace
Students today face a new era with demands for new skills
Is educational change keeping pace?
EWM Conference Cambridge Sept. 2007

12. Can ICT bridge the educational gap?
22 March, 2017
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

13. Impact of ICT on students
22 March, 2017
Impact of ICT on students
Students have increasing daily access to a range of technologies:
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

14. Where does learning happen?
22 March, 2017
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 technology
improved understanding of issues by patients
recording and playback of angiograms
body scanning, pregnancy scanning
EWM Conference Cambridge Sept. 2007

15. In the developed world has ‘education’ failed to deliver?
22 March, 2017
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.
e.g
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 today?
EWM Conference Cambridge Sept. 2007

16. and access to education worldwide
22 March, 2017
Statistics on access to the internet
and access to education worldwide
EWM Conference Cambridge Sept. 2007

17. EWM Conference Cambridge Sept. 2007
22 March, 2017
Internet Usage – The Big Picture Updated June 2007
EWM Conference Cambridge Sept. 2007

18. The Digital Divide Internet penetration- percentage of population
22 March, 2017
The Digital Divide Internet penetration- percentage of population
Sweden % (highest in Europe)
USA %
Hong Kong % (highest in Asia)
UK %
China %
South Africa 10.3%
India %
Sierra Leone 0.2% (lowest in Africa)
EWM Conference Cambridge Sept. 2007

19. Access to Higher Education
22 March, 2017
Access to Higher Education
Average for 30 OECD countries
is 47% of 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 world
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

20. Can educators use ICT to close the gaps in educational opportunities?
                               
22 March, 2017
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 education
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

21. EWM Conference Cambridge Sept. 2007
22 March, 2017
Some examples of collaborative learning and web-based technologies
EWM Conference Cambridge Sept. 2007

22. Peer Assisted Learning
22 March, 2017
Peer Assisted Learning
Science Technology
Informatics & Mathematics
Undergraduate Links between
University & Schools 1987
askNRICH
Ask-a-Mathematician service
Online Discussion Forum 1997
askAIMS
Ask-a-Mathematician service
from the African Institute for
Mathematical Sciences in
Muizenberg South Africa 2003
EWM Conference Cambridge Sept. 2007

23. Carl’s Question to askNRICH
22 March, 2017
Carl’s Question to askNRICH
Carl pm 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 real:
x2 +2x sin θ +3cos2 θ = (1)
Now show that the roots of the equation:
x2 + (5cos2θ +1)x + 9cos4 θ = (2)
are the squares of the roots of equation (1)
See askedNRICH
EWM Conference Cambridge Sept. 2007

24. The response from askNRICH
22 March, 2017
The response from askNRICH
James pm 3 June Gives first response, advising on how to proceed
Carl 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 method
Carl 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

25. EWM Conference Cambridge Sept. 2007
22 March, 2017
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 explanation.
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

26. EWM Conference Cambridge Sept. 2007
22 March, 2017
EWM Conference Cambridge Sept. 2007

27. The Motivate Project motivate.maths.org
22 March, 2017
The Motivate Project motivate.maths.org
provides maths and science videoconference lessons linking schools in UK, India, Pakistan, Singapore South Africa
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

28. EWM Conference Cambridge Sept. 2007
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T of V
EWM Conference Cambridge Sept. 2007

29. Space Science Example of a Year Long Programme
22 March, 2017
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

30. Global-campus e-learning for school students
22 March, 2017
Global-campus 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

31. Problem Solving A Gateway to Research
22 March, 2017
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

32. EWM Conference Cambridge Sept. 2007
22 March, 2017
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.
Subject content
Root Tracker Quadratic & cubic equations Complex numbers
2 and 4 Dimensional Numbers Complex Numbers Quaternions Fields
Flight Path D Geometry Trigonometry
Epidemic Modelling Statistics Analysing data
Diophantine n-tuples Number Theory
Em’power’ed Indices Equatons
Salinon Ratio Circles Area
Differs Dynamical Systems
Why 24? Prime numbers Factors
Keep You Distance Triangles Quadrilaterals Polygons
Basket Case Arithmetic Sums and products
Vecten Geometry Recurrence relations
EWM Conference Cambridge Sept. 2007

33. EWM Conference Cambridge Sept. 2007
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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?
Em’power’ed
Find the smallest natural numbers a, b and c such that
Salinon
Compare the shaded area (made up of semi-circles)
with the area of the circle on AB as diameter.
EWM Conference Cambridge Sept. 2007

34. A selection of problems from the NRICH website: Mathematical Skills
22 March, 2017
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
Em’power’ed Using algebra
Salinon Proving Aesthetics
Differs Investigating Spotting patterns Making and proving conjectures
Why 24? Proving
Keep You Distance Working systematically
Basket Case Using trial and improvement
Vecten Making and proving conjectures
EWM Conference Cambridge Sept. 2007

35. Thank you Toni Beardon lab11@cam.ac.uk
22 March, 2017
Thank you
AIMSSEC - Muizenberg South Africa MMP - Cambridge England
Toni Beardon
EWM Conference Cambridge Sept. 2007

36. EWM Conference Cambridge Sept. 2007
22 March, 2017
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 mathematics.
£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