University Outreach The impact of computers and the internet on globalising mathematics education Toni Beardon University of Cambridge mmp.maths.org AIMSSEC www.aims.ac.za/aimssec EWM Conference Cambridge Sept. 2007 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 EWM Conference Cambridge Sept. 2007 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 1. 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. 2. 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 teachers” 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 workplace • 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 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 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 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? 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 http://www.internetworldstats.com/stats.htm Updated June 2007 EWM Conference Cambridge Sept. 2007 The Digital Divide Internet penetration- percentage of population • • • • • • • • Sweden USA Hong Kong UK China South Africa India Sierra Leone 75.6% (highest in Europe) 69.7% 68.2% (highest in Asia) 62.3% 12.3% 10.3% 3.7% 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 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 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/ 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 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 http://www.aims.ac.za/askaims http://nrich.maths.org/discus 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 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 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 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 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 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 http://thesaurus.maths.org EWM Conference Cambridge Sept. 2007 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 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 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 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 Em’power’ed Salinon Differs Why 24? Keep You Distance Basket Case Vecten Subject content Quadratic & cubic equations Complex numbers Complex Numbers Quaternions Fields 3D Geometry Trigonometry 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? Em’power’ed Find the smallest natural numbers a, b and c such that a 2 2 b 3 3 c 5 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 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 Thank you AIMSSEC - Muizenberg South Africa MMP - Cambridge England Toni Beardon [email protected] 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 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 EWM Conference Cambridge Sept. 2007

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# The Motivate Project - Faculty of Mathematics