Toni Beardon University of Cambridge



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University Outreach The impact of computers and the internet on globalising mathematics education

  • Toni Beardon

  • University of Cambridge

  • mmp.maths.org


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




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 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


AIMSSEC Now and Future



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



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 2005-2009



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.



  • Advances in

  • Information Communication Technology



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


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 workplace

  • Students today face a new era with demands for new skills

  • Is educational change keeping pace?



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?



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



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


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. http://www.quickmath.com/ http://mathworld.wolfram.com/

  • http://www-groups.dcs.st-and.ac.uk/~history/

  • 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?



  • Statistics on access to the internet

  • and access to education worldwide



Internet Usage – The Big Picture http://www.internetworldstats.com/stats.htm Updated June 2007



The Digital Divide Internet penetration- percentage of population

  • Sweden 75.6% (highest in Europe)

  • USA 69.7%

  • Hong Kong 68.2% (highest in Asia)

  • UK 62.3%

  • China 12.3%

  • South Africa 10.3%

  • India 3.7%

  • Sierra Leone 0.2% (lowest in Africa)



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 world

      • increase in proportion of age cohort in higher education
      • student fees, student debt
      • majority of students in employment while studying


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 http://www.simputer.org/ and solarpc http://solarpc.com/

  • Free Software - http://www.opensource.org/

  • The Digital Divide Network – http://www.digitaldivide.net/



  • Some examples of collaborative learning and web-based technologies



Peer Assisted Learning

  • askAIMS

  • Ask-a-Mathematician service

  • from the African Institute for

  • Mathematical Sciences in

  • Muizenberg South Africa 2003

  • http://www.aims.ac.za/askaims



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 real:

  • x2 +2x sin θ +3cos2 θ = 0 (1)

  • Now show that the roots of the equation:

  • x2 + (5cos2θ +1)x + 9cos4 θ = 0 (2)

  • are the squares of the roots of equation (1)

  • See askedNRICH



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 method

  • 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



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!!!



http://thesaurus.maths.org



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




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:



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)



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


  • 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 3D 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



  • 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.



  • 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



Thank you



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: http://www0.sun.ac.za/stigting/make_a_donation_give.html

  • 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



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