What happens to What happens to all that maths?all that maths?

Peter K DunnPeter K Dunn

Department of Mathematics and Department of Mathematics and ComputingComputing

University of Southern QueenslandUniversity of Southern Queensland

IntroductionIntroduction

““MMathematics pervades so many aspectsathematics pervades so many aspectsof daily life that a sound knowledge is of daily life that a sound knowledge is

essential for informed citizenshipessential for informed citizenship” ” (Senior Mathematics A Syllabus)(Senior Mathematics A Syllabus)

So why is participation in advanced So why is participation in advanced mathematics classes declining?mathematics classes declining?

Do students not see mathematics as Do students not see mathematics as useful?useful?

StatisticsStatistics

““The best thing about being a The best thing about being a statistician statistician

is that you get to play inis that you get to play in everyone’s backyard.” (Tukey) everyone’s backyard.” (Tukey)

Perhaps the most useful topic in Perhaps the most useful topic in mathematics is statistics mathematics is statistics —— and yet and yet it is a very small part of it.it is a very small part of it.

School maths/stats is used for School maths/stats is used for real real research.research.

Statistics Statistics isis useful useful

““To isolate mathematics from the To isolate mathematics from the practical demands of the sciences is to practical demands of the sciences is to invite the sterility of a cow shut away invite the sterility of a cow shut away

from the bulls”from the bulls”

(Chebyshev)(Chebyshev)

Stats makes maths relevant: real data, Stats makes maths relevant: real data, examplesexamples

Statistics leads to jobs!Statistics leads to jobs!

Statistics in biologyStatistics in biology

USQ’s internationally recognised USQ’s internationally recognised Muscular Research Laboratory has Muscular Research Laboratory has received over $1M to study Duchene received over $1M to study Duchene Muscular DystrophyMuscular Dystrophy

Statistics used to analyse Statistics used to analyse preliminary results from micepreliminary results from mice

Ca response curve a measure of Ca response curve a measure of muscle strengthmuscle strength

Statistics in agricultureStatistics in agriculture

Compare two GPS methods for Compare two GPS methods for accuracy when spraying cropsaccuracy when spraying crops

Make five runs up and down Make five runs up and down paddock (five “swaths”) and paddock (five “swaths”) and compare GPS resultscompare GPS results

Statistics in engineering Statistics in engineering (cont)(cont)

GIS used to detect weeds for GIS used to detect weeds for potential treatment and eradicationpotential treatment and eradication

Consider the weed Consider the weed Pond ApplePond Apple…… Interest is in knowing where it may Interest is in knowing where it may

appearappear

Statistics in engineering Statistics in engineering (cont)(cont)

Comparing GPS and traditional Comparing GPS and traditional methods of tractor navigation during methods of tractor navigation during sprayingspraying

Queensland Cotton has employed Queensland Cotton has employed USQ statisticians to improve USQ statisticians to improve international competitiveness international competitiveness (commercial-in-confidence)(commercial-in-confidence)

Different irrigation methods have Different irrigation methods have been compared (PRD and RDI)been compared (PRD and RDI)

Visit to Queensland Visit to Queensland Cotton’s gin near DalbyCotton’s gin near Dalby

Statistics in climate Statistics in climate sciencescience

Statistics used for modelling rainfall Statistics used for modelling rainfall (and other climatic variables)(and other climatic variables)

For prediction and computer For prediction and computer simulationsimulation

More difficult than it appearsMore difficult than it appears

Statistics in educationStatistics in education

Teaching aural skills is difficult from Teaching aural skills is difficult from thousands of kilometres away!thousands of kilometres away!

A USQ researcher investigating A USQ researcher investigating different teaching methods to see different teaching methods to see what works bestwhat works best

Mostly using simple tablesMostly using simple tables

Statistics in aviationStatistics in aviation

Private pilot deaths in Australia from Private pilot deaths in Australia from 1992 to 1999 were studied.1992 to 1999 were studied.

The effect of age was of interestThe effect of age was of interest

Statistics in health Statistics in health researchresearch

USQ statisticians involved in many health USQ statisticians involved in many health studies:studies: Nurses surveyed about workplace concernsNurses surveyed about workplace concerns New mothers surveyed about perceptions of New mothers surveyed about perceptions of

breast-feedingbreast-feeding Asthma treatment in Aboriginal communitiesAsthma treatment in Aboriginal communities

Health statistics is a huge area of Health statistics is a huge area of research that often uses simple statisticsresearch that often uses simple statistics

Was the planned change and reasons for the change openly and frequently communicated?

Section Yes No Total Administration 7 8 15Critical care 7 13 20Family health 24 14 38Medical 15 9 24Surgical 6 8 14

Mental health 1 8 9Total 60 60 120

Advanced researchAdvanced research

Of course, not all research is based Of course, not all research is based on secondary school mathematicson secondary school mathematics

But much research is based But much research is based mathematically and statistically on mathematically and statistically on basic conceptsbasic concepts

Other researchOther research

Improving statistical methods for Improving statistical methods for analysing dataanalysing data

Modelling traffic flowModelling traffic flow Modelling wind erosionModelling wind erosion Modelling the flow of air and fluid Modelling the flow of air and fluid

around objectsaround objects Modelling rainfall (and other data) Modelling rainfall (and other data)

that is continuous with exact zerothat is continuous with exact zero

Mathematics at schoolMathematics at school

To To knowknow mathematics is useful, mathematics is useful, students must students must seesee it as useful it as useful

Students must see mathematics and Students must see mathematics and statistics in actionstatistics in action

Can do so by using Can do so by using real datareal data and and seeing seeing real applicationsreal applications

Mathematics is usefulMathematics is useful

Jordan (1994): Students interviewed Jordan (1994): Students interviewed people using mathematics in their jobpeople using mathematics in their job

Junior and Senior Syllabi explicitly Junior and Senior Syllabi explicitly mention students collecting and mention students collecting and analysing their own dataanalysing their own data

Numerous sources of real data apart Numerous sources of real data apart from data students collectfrom data students collect

Enter Qld Statistics Poster Enter Qld Statistics Poster Competition!Competition!

Qld Statistics Poster Qld Statistics Poster CompComp

Open to Years 8 and 9 (teams of 2 or Open to Years 8 and 9 (teams of 2 or 3)3)

Great prizes (computer for school; Great prizes (computer for school; each individual won $150 worth of gift each individual won $150 worth of gift vouchers)vouchers)

Addresses SLE in SyllabusAddresses SLE in Syllabus During National Science WeekDuring National Science Week See See http://http://

www.sci.usq.edu.au/statswebwww.sci.usq.edu.au/statsweb//

Statistics Competition Statistics Competition ProjectsProjects

Does the colour of jelly beans affect Does the colour of jelly beans affect taste?taste?

Can people really distinguish different Can people really distinguish different brands of cola?brands of cola?

Do ants prefer meat or jam sandwichesDo ants prefer meat or jam sandwiches What does Coca-Cola dissolve?What does Coca-Cola dissolve? A study of when buses run lateA study of when buses run late A catapult experimentA catapult experiment

Sources of real data: The Sources of real data: The webweb

Australasian Data and Story Library: Australasian Data and Story Library: http://http://www.statsci.org/data/index.htmlwww.statsci.org/data/index.html

ABS: ABS: http://http://www.abs.gov.auwww.abs.gov.au// Data and Story Library: Data and Story Library: http://http://

lib.stat.cmu.edulib.stat.cmu.edu/DASL//DASL/ Chance: Chance: http://http://www.dartmouth.eduwww.dartmouth.edu/~chance//~chance/ Teaching resources: Teaching resources:

http://www.statsci.org/teaching.htmlhttp://www.statsci.org/teaching.html Datasets for Statistical Analysis:Datasets for Statistical Analysis:

http://http://www.sci.usq.edu.au/staff/dunn/Datasets/index.htmlwww.sci.usq.edu.au/staff/dunn/Datasets/index.html

Sources of real data: Sources of real data: BooksBooks

The best book: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 Jobs for maths/stats graduatesgraduates

““There is currently a very marked shortageThere is currently a very marked shortageof professional statisticians across a of professional statisticians across a

range of disciplines in Australia. range of disciplines in Australia. ““The hottest areas are The hottest areas are

biostatistics/bioinformatics biostatistics/bioinformatics and financial modelling…and financial modelling…

““Advertisements for biostatisticians Advertisements for biostatisticians are going unfilled for a long time.are going unfilled for a long time.

““The methodology division of the The methodology division of the (Australian) Bureau of Statistics (Australian) Bureau of Statistics

reports that the output of honours graduates reports that the output of honours graduates in statistics is no longer sufficient in statistics is no longer sufficient

to fill its annual recruitment needs.to fill its annual recruitment needs.

Jobs for maths/stats Jobs for maths/stats graduatesgraduates

““The need for statisticians is more The need for statisticians is more recognized thanrecognized than

even before in Australia even before in Australia and there are far more employmentand there are far more employment

opportunities than ever before. opportunities than ever before. ““There are several jobs for every honours There are several jobs for every honours

graduategraduatethat Australia is producing. that Australia is producing.

““It is very difficult to understand why the It is very difficult to understand why the number of graduate statisticians number of graduate statisticians

being produced by Australian universities being produced by Australian universities is decreasing rather than increasing.” is decreasing rather than increasing.”

(Smyth)(Smyth)

BioinformaticsBioinformatics

A new disciplineA new discipline A hybrid of statistics, computing and A hybrid of statistics, computing and

biologybiology Time Time magazine April 2002: “The coming magazine April 2002: “The coming

job boom”:job boom”: An estimated 20000 An estimated 20000 unfilled unfilled jobs in the US in jobs in the US in

bioinformatics by 2005bioinformatics by 2005 A number of Australian universities have A number of Australian universities have

bioinformatics degrees (including USQ)bioinformatics degrees (including USQ)

Other names for Other names for statisticiansstatisticians

Psychometrician;Psychometrician; Biometrician;Biometrician; Biostatistician;Biostatistician; Econometrician;Econometrician; Bioinformaticians;Bioinformaticians; Statistical physicist;Statistical physicist; Financial modellerFinancial modeller

Stats Society publicity Stats Society publicity campaigncampaign

You probably wouldn't trust your life You probably wouldn't trust your life to an untrained doctor, to an untrained doctor,

or your teeth to an untrained dentist.or your teeth to an untrained dentist.You probably wouldn't trust your money You probably wouldn't trust your money

to an unqualified accountant. to an unqualified accountant. Yet every day we rely on policies affecting Yet every day we rely on policies affecting

ourourhealth, prosperity and security that are health, prosperity and security that are

foundedfoundedon unprofessional use of statistics. on unprofessional use of statistics.

(SSA, p3).(SSA, p3).

One example: Challenger One example: Challenger disasterdisaster

Challenger space shuttle disaster of Challenger space shuttle disaster of January 1986January 1986

Launch forecast temperature: 31ºF (–Launch forecast temperature: 31ºF (–0.6ºC)0.6ºC)

Previous coldest launch: 53Previous coldest launch: 53ºF (12ºC)ºF (12ºC) Was it too cold for a successful Was it too cold for a successful

launch?launch? NASA engineers thought not based on NASA engineers thought not based on

the evidence:the evidence:

Challenger (cont)Challenger (cont)

Later, statisticians pointed out that Later, statisticians pointed out that the data was inadequatethe data was inadequate

The correct data on which to make a The correct data on which to make a decision was:decision was:

Jobs in statisticsJobs in statistics Statistics jobs in Australia and New Statistics jobs in Australia and New

Zealand: Zealand: http://http://www.statsci.org/jobs/index.htmlwww.statsci.org/jobs/index.html

Listed 250+ jobs for statisticians in 2002.Listed 250+ jobs for statisticians in 2002. Doesn’t list graduate programs, teaching.Doesn’t list graduate programs, teaching. Graduate Programs: Graduate Programs:

http://www.austms.org.au/Jobs/Graduate_programs.htmlhttp://www.austms.org.au/Jobs/Graduate_programs.html Jobs for mathematicians here and Jobs for mathematicians here and

overseas: overseas: http://http://www.austms.org.au/Jobs/Job_listings.htmlwww.austms.org.au/Jobs/Job_listings.html

175 maths graduates in Australia (2001), 175 maths graduates in Australia (2001), only only some some with statistics.with statistics.

Thomas reportsThomas reports

Jan Thomas reported on state of Jan Thomas reported on state of mathematics in Australia (2000 and mathematics in Australia (2000 and 2002):2002): Decline in students studying advanced Decline in students studying advanced

mathematicsmathematics Acute shortage of mathematics teachersAcute shortage of mathematics teachers Acute shortage of mathematics lecturersAcute shortage of mathematics lecturers

Education Queensland has Education Queensland has no incentives no incentives to attract mathematics teachers (I to attract mathematics teachers (I asked)asked)

ConclusionsConclusions Mathematics and statistics Mathematics and statistics isis useful useful Students must see it in action to Students must see it in action to

appreciate thisappreciate this Can use examples of real researchCan use examples of real research Can use real data, or generate real dataCan use real data, or generate real data Enter Qld Statistics Poster CompetitionEnter Qld Statistics Poster Competition Plenty of jobs for statistics graduatesPlenty of jobs for statistics graduates Statistics a small part of school Statistics a small part of school

mathematicsmathematics EQ needs to put incentives in place EQ needs to put incentives in place nownow