What happens to all that maths? Peter K Dunn Department of Mathematics and Computing University of Southern Queensland
Introduction “Mathematics pervades so many aspectsof daily life that a sound knowledge is essential for informed citizenship” (Senior Mathematics A Syllabus) • So why is participation in advanced mathematics classes declining? • Do students not see mathematics as useful?
Statistics “The best thing about being a statistician is that you get to play in everyone’s backyard.” (Tukey) • Perhaps the most useful topic in mathematics is statistics — and yet it is a very small part of it. • School maths/stats is used for real research.
Statistics is useful “To isolate mathematics from the practical demands of the sciences is to invite the sterility of a cow shut away from the bulls” (Chebyshev) • Stats makes maths relevant: real data, examples • Statistics leads to jobs!
Statistics in biology • USQ’s internationally recognised Muscular Research Laboratory has received over $1M to study Duchene Muscular Dystrophy • Statistics used to analyse preliminary results from mice • Ca response curve a measure of muscle strength
Statistics in agriculture • Compare two GPS methods for accuracy when spraying crops • Make five runs up and down paddock (five “swaths”) and compare GPS results
Statistics in engineering (cont) • GIS used to detect weeds for potential treatment and eradication • Consider the weed Pond Apple… • Interest is in knowing where it may appear
Statistics in engineering (cont) • Comparing GPS and traditional methods of tractor navigation during spraying • Queensland Cotton has employed USQ statisticians to improve international competitiveness (commercial-in-confidence) • Different irrigation methods have been compared (PRD and RDI)
Statistics in climate science • Statistics used for modelling rainfall (and other climatic variables) • For prediction and computer simulation • More difficult than it appears
Statistics in education • Teaching aural skills is difficult from thousands of kilometres away! • A USQ researcher investigating different teaching methods to see what works best • Mostly using simple tables
Statistics in aviation • Private pilot deaths in Australia from 1992 to 1999 were studied. • The effect of age was of interest
Statistics in health research • USQ statisticians involved in many health studies: • Nurses surveyed about workplace concerns • New mothers surveyed about perceptions of breast-feeding • Asthma treatment in Aboriginal communities • Health statistics is a huge area of research that often uses simple statistics
Was the planned change and reasons for the change openly and frequently communicated? SectionYes No Total Administration 7 8 15 Critical care 7 13 20 Family health 24 14 38 Medical 15 9 24 Surgical 6 8 14 Mental health 1 8 9 Total 60 60 120
Advanced research • Of course, not all research is based on secondary school mathematics • But much research is based mathematically and statistically on basic concepts
Other research • Improving statistical methods for analysing data • Modelling traffic flow • Modelling wind erosion • Modelling the flow of air and fluid around objects • Modelling rainfall (and other data) that is continuous with exact zero
Mathematics at school • To know mathematics is useful, students must see it as useful • Students must see mathematics and statistics in action • Can do so by using real data and seeing real applications
Mathematics is useful • Jordan (1994): Students interviewed people using mathematics in their job • Junior and Senior Syllabi explicitly mention students collecting and analysing their own data • Numerous sources of real data apart from data students collect • Enter Qld Statistics Poster Competition!
Qld Statistics Poster Comp • Open to Years 8 and 9 (teams of 2 or 3) • Great prizes (computer for school; each individual won $150 worth of gift vouchers) • Addresses SLE in Syllabus • During National Science Week • See http://www.sci.usq.edu.au/statsweb/
Statistics Competition Projects • Does the colour of jelly beans affect taste? • Can people really distinguish different brands of cola? • Do ants prefer meat or jam sandwiches • What does Coca-Cola dissolve? • A study of when buses run late • A catapult experiment
Sources of real data: The web • Australasian Data and Story Library: http://www.statsci.org/data/index.html • ABS: http://www.abs.gov.au/ • Data and Story Library: http://lib.stat.cmu.edu/DASL/ • Chance: http://www.dartmouth.edu/~chance/ • Teaching resources: http://www.statsci.org/teaching.html • Datasets for Statistical Analysis:http://www.sci.usq.edu.au/staff/dunn/Datasets/index.html
Sources of real data: Books • The best book: Hand, Daly, Lunn, McConway & Ostrowski (1994). A Handbook of Small Data Sets. London: Chapman and Hall • 510 small, real, indexed data sets
Jobs for maths/stats graduates “There is currently a very marked shortageof professional statisticians across a range of disciplines in Australia. “The hottest areas are biostatistics/bioinformatics and financial modelling… “Advertisements for biostatisticians are going unfilled for a long time. “The methodology division of the (Australian) Bureau of Statistics reports that the output of honours graduates in statistics is no longer sufficient to fill its annual recruitment needs.
Jobs for maths/stats graduates “The need for statisticians is more recognized thaneven before in Australia and there are far more employmentopportunities than ever before. “There are several jobs for every honours graduatethat Australia is producing. “It is very difficult to understand why the number of graduate statisticians being produced by Australian universities is decreasing rather than increasing.” (Smyth)
Bioinformatics • A new discipline • A hybrid of statistics, computing and biology • Time magazine April 2002: “The coming job boom”: • An estimated 20000 unfilled jobs in the US in bioinformatics by 2005 • A number of Australian universities have bioinformatics degrees (including USQ)
Other names for statisticians • Psychometrician; • Biometrician; • Biostatistician; • Econometrician; • Bioinformaticians; • Statistical physicist; • Financial modeller
Stats Society publicity campaign You probably wouldn't trust your life to an untrained doctor, or your teeth to an untrained dentist. You probably wouldn't trust your money to an unqualified accountant. Yet every day we rely on policies affecting ourhealth, prosperity and security that are foundedon unprofessional use of statistics. (SSA, p3).
One example: Challenger disaster • Challenger space shuttle disaster of January 1986 • Launch forecast temperature: 31ºF (–0.6ºC) • Previous coldest launch: 53ºF (12ºC) • Was it too cold for a successful launch? • NASA engineers thought not based on the evidence:
Challenger (cont) • Later, statisticians pointed out that the data was inadequate • The correct data on which to make a decision was:
Jobs in statistics • Statistics jobs in Australia and New Zealand: http://www.statsci.org/jobs/index.html • Listed 250+ jobs for statisticians in 2002. • Doesn’t list graduate programs, teaching. • Graduate Programs: http://www.austms.org.au/Jobs/Graduate_programs.html • Jobs for mathematicians here and overseas: http://www.austms.org.au/Jobs/Job_listings.html • 175 maths graduates in Australia (2001), only some with statistics.
Thomas reports • Jan Thomas reported on state of mathematics in Australia (2000 and 2002): • Decline in students studying advanced mathematics • Acute shortage of mathematics teachers • Acute shortage of mathematics lecturers • Education Queensland has no incentives to attract mathematics teachers (I asked)
Conclusions • Mathematics and statistics is useful • Students must see it in action to appreciate this • Can use examples of real research • Can use real data, or generate real data • Enter Qld Statistics Poster Competition • Plenty of jobs for statistics graduates • Statistics a small part of school mathematics • EQ needs to put incentives in place now