Maths Education

What is mathseducation for?a journey into the unknown : 

What is mathseducation for?a journey into the unknown Professor Martin Westwell

What is mathseducation for?a journey into the unknown : 

What is mathseducation for?a journey into the unknown To prepare young people for a (socially and economically) prosperous future in a world increasingly influenced by science and technology.

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“The future”

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change after Kurzweil 2005 “The singularity is near” Mass use of technology

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Predicting the future At current rates of progress (number of technological inventions) we can expect: over the next 25 years - 100 years worth of progress over the next 100 years - 20,000 years worth of progress after Kurzweil 2005 “The singularity is near”

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Predicting the future We are preparing our students for jobs that don’t exist, using technologies that have not been invented, to solve problems that we haven’t even considered yet.” Richard Riley, US Secretary of Education (1999)

What is mathseducation for?a journey into the unknown : 

What is mathseducation for?a journey into the unknown Maths for higher education “maths for all” - numeracy?

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Impact of information technology Question rich Answer poor Question poor Answer rich In mathematics, the art of asking questions is more valuable than solving problems. Georg Cantor 1845- 1918

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downloading essays from the internet "could not be controlled" "The availability of the internet is a powerful aid to learning but carries a new generation of risks of plagiarism." QCA chief executive, Ken Boston (November 2005) information  knowledge

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Developing skills Hybrid laparoscopy training system (video & real)21 residents, 12 attending, 15 men, 18 women Past game play (>3hr/week)37% fewer errors (P<0.02) 27% faster (P<0.03) High scoring gamers (top tertile)47% fewer error (P<0.001) 39% faster (P<0.001) Relative weight analysis0.3% years of training 2% sex 2% cases performed 10% video game experience 31% video game skill Rosse et al 2007, Archives of Surgery

What is mathseducation for?a journey into the unknown : 

What is mathseducation for?a journey into the unknown “Creativity is the global education challenge” Ralph Tabberer, UK Director General of Schools

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Age 22 32 42 52 62 72 82 92 Weinberg & Jones, National Bureau of Economic Research, Working Paper 11799, Revised - October 2007 “ordinary science”

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Age 22 32 42 52 62 72 82 92 “ordinary science” Weinberg & Jones, National Bureau of Economic Research, Working Paper 11799, Revised - October 2007 “revolutions”

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Jules Henri Poincaré A collection of facts is not science any more than a pile of bricks is a house. William Bragg The important thing in science is not so much to obtain new facts as to discover new ways of thinking about them.

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von Karolyi et al, Brain and Language (2003) 85 427–431

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von Karolyi et al, Brain and Language (2003) 85 427–431

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von Karolyi et al, Brain and Language (2003) 85 427–431

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von Karolyi et al, Brain and Language (2003) 85 427–431

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von Karolyi et al, Brain and Language (2003) 85 427–431

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von Karolyi et al, Brain and Language (2003) 85 427–431

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von Karolyi et al, Brain and Language (2003) 85 427–431

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von Karolyi et al, Brain and Language (2003) 85 427–431

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von Karolyi et al, Brain and Language (2003) 85 427–431

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possible impossible impossible Dyslexics - 1.7 seconds von Karolyi et al, Brain and Language (2003) 85 427–431 possible possible impossible impossible None dyslexics - 2.9 seconds possible

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Precocious IQ higher than chronological average Rapid information processing require less repetition sometimes slower at classroom answers Top-down understanding big-picture, abstract want to know lots of stuff Creative inter-subject connections Intelligent, gifted, talented

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O’Boyle et al 2005 Cognitive Brain Research 25:583

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O’Boyle et al 2005 Cognitive Brain Research 25:583

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Limitation through categorisation IQ tests & planting doubt Learning styles, boys/girls, left brain/right brain Value of education, literacy, etc Dad/mum couldn’t do that either Students’ theories of intelligence

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Making maths meaningful individual's experience individual’s values career pathways abstract concepts - metaphor family experience & values informal experience cutting edge use success in maths relevance to others lifestyle choices

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“Modern education is experiencing unprecedented levels of change, and has been for some time. Futurelab report (2006) “Teachers Learning with Digital Technologies” Change in education may now be thought of as a constant condition rather than an event.”

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Dealing with uncertainty Risk Making decisions under varying levels of probability Ambiguity Making decisions with unknown probabilities or unknown outcomes 10 10 ? ? Technology – dad’s and their phones! Emotional content – anxiety can stop us from learning What goes on in the brain? different regions – different behaviours – role of emotion So what? Our natural response to ambiguity can inhibit innovation & leadership Huettel et al 2006, Neuron

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Dealing with uncertainty “People often prefer the known over the unknown, sometimes sacrificing potential rewards for the sake of surety” “Overcoming impulsive preferences for certainty [may be required] to exploit uncertain but potentially [beneficial] options” Risk Making decisions under varying levels of probability Ambiguity Making decisions with unknown probabilities or unknown outcomes Huettel et al 2006, Neuron 70% parents believe they are in a good position to advise their children on career education choices

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Teachers innovate anyway (given space) Adapting to new circumstances, environments, “education climates,” “education revolutions” Developing professional skills Empowerment for professionals Embedded innovation: creativity + application Modeling behaviours for learners Personalisation & seizing learning opportunities “Knowledge economy” See www.futurelab.org.uk/projects/teachers_as_innovators Teachers as innovators Maths & its context changes - the “meaning” changes

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teaching & learning science of learning cutting edge maths addressing diversity technology: opportunities & risks assessment How to achieve what maths education is for? cultural value

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specialised proficiency multi-disciplinary teams communication Reducing ambiguity to risk Pegg, J., Lynch, T., & Panizzon, D. (2007) Exceptional Outcomes in Mathematics Education

What is mathseducation for?a journey into the unknown : 

What is mathseducation for?a journey into the unknown martin.westwell@flinders.edu.au