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

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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

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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

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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

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AIMSSEC Now and Future
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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

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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

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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.

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• Advances in
• Information Communication Technology

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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

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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?

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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?

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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

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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

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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?

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• Statistics on access to the internet
• and access to education worldwide

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Internet Usage The Big Picture
http//www.internetworldstats.com/stats.htmUpdate
d June 2007
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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)

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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
  

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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, CDs 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/

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• Some examples of collaborative learning and
  web-based technologies

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Peer Assisted Learning

• Science Technology
• Informatics Mathematics
• Undergraduate Links between
• University Schools 1987
• askNRICH
• Ask-a-Mathematician service
• Online Discussion Forum 1997
• http//nrich.maths.org/discus

• askAIMS
• Ask-a-Mathematician service
• from the African Institute for
• Mathematical Sciences in
• Muizenberg South Africa 2003
• http//www.aims.ac.za/askaims

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Carls 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 p, the complete set of
  values of ? in the interval 0 ? 2 p for
  which the roots of equation (1) are real
• x2 2x sin ? 3cos2 ? 0
  (1)
• Now show that the roots of the equation
• x2 (5cos2? 1)x 9cos4 ? 0
  (2)
• are the squares of the roots of equation (1)
• See askedNRICH

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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

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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!!!

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http//thesaurus.maths.org
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The Motivate Projectmotivate.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

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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

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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)

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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

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• Well 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
• Empowered 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

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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?
• Empowered
• 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.

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• 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
• Empowered 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

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Thank you

• AIMSSEC - Muizenberg South Africa MMP
  - Cambridge England
• Toni Beardon
• lab11_at_cam.ac.uk

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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_giv
  e.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