Moving on with Statistics

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Moving on with Statistics

• How to engage students with the subject post 16
• Mark Kent,
• Head of Mathematics and Computing/ICT Faculty
• The Sixth Form College Solihull
• sallysallymark_at_kent25.freeserve.co.uk

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My experience in Statistics Education

• Worked in Sixth Form Colleges for nearly 20
  years, teaching A Level and International
  Baccalaureate Mathematics and Statistics.
• MSc with Sheffield Hallam University in Applied
  Statistics with Stats Education in 1997
• Led the Maths Department at Cadbury College
  Birmingham for 7 years developed A level
  Statistics course growth to around 150 students
• Set up and led the first Specialist Maths Sixth
  Form College project a Maths/Stats outreach to
  Birmingham secondary students.
• Joined The Sixth Form College Solihull in January
  2006 as Head of the Maths and Computing/ICT
  Faculty

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Statistics a Popular Option Post 16

• AQA Statistics A level a practical Statistics
  course for students with a minimum of a grade C
  at GCSE suitable for Intermediates!!
• Hundreds of students take the course at Cadbury
  and Solihull about 75 with Intermediate B and
  C grades at GCSE.
• Pass rates at A level close to 100 over a seven
  year period. AS pass rates around 80.
• Student questionnaire responses and AS to A2
  progression indicate both enthusiasm for the
  subject and often pleasant surprise with grades
  obtained!

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Statistics isnt Mathematics!

• Students who often struggle with Pure Mathematics
  can do very well at Applied Statistics.
• It requires a different approach/mindset.

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Statistics is the missing link!

• A large number of other AS/A2 subjects use
  Statistics all the time e.g. Psychology, Biology,
  Geography, Economics.
• Many careers involve use of statistical
  techniques.

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A philosophy of Statistics Education

• It should be in context.
• Its delivery should begin with practical
  activity, adding a theoretical structure later,
  or simultaneously.
• Use technology, but start with something concrete
  stats education research indicates this is the
  best approach.
• Avoid using abstract, artificial data.
• Fit your activities to the interests of the
  students post 16 this is food, money, mobile
  phones etc.
• Make maximum use of statistical experiments.
• Dont worry about things going wrong they often
  do but the students dont mind!!

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The philosophy in practice

• Plan to incorporate a practical example into
  every topic area taught on the work-scheme.
• Practicals need not take the whole lesson 10
  minutes is often enough.
• Avoid the urge to rush the teaching of a topic
  without concrete examples its a false economy.

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The importance of the first lesson

• Do something memorable e.g. a smokers fitness
  experiment

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Mars Bars and Memory a good first lesson at AS
level

• Record how many random digits out of 10 students
  can remember at lesson start.
• Students consume a mini mars bar and the memory
  test is repeated every 5-10 minutes.
• Results recorded and represented on box plots.
  Memory peaks around 20 minutes after consumption.

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Results of Mars Experiment
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Examples of Practicals in a teenage context

• Mobile Phones
• Start with a question are students
  ambidextrous?
• What does that mean and how can we test it
  student responses.
• Make use of simple equipment could use rulers,
  calculators, but best is a mobile phone all
  students possess one!
• Students time each other in pairs to text (not
  send) the word college with left and right
  hands separately.
• Analysis depends on level could use comparative
  box plots, hypothesis test on differences (t
  test). Can also look at spread of data and
  breakdown into gender etc.

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Chocolate

• Does Chocolate increase ability to concentrate?
• A variation on the Mars Bars experiment.
• Compare before and after (15 minutes approx.)
  consumption scores in remembering 10 random
  numbers.
• Use AUTOGRAPH and Binomial Distribution a sign
  test.

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Scandal

• Modelling a Poisson Distribution
• Distribute newspapers around the room all have
  same brand of paper (Daily Mail, Guardian etc.)
• Ask to record the number of scandals in the first
  five pages.
• Data is messy what is a scandal?
• Could also count number of pictures, number of
  feelgood/happy stories.
• Find mean and variance on calculators from class
  data usually very close to each other. Fit a
  Poisson model usually very good fit (dont
  worry if it isnt)

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What about the dry topics?

• Make them as practical as possible
• Limit exposition at board
• Use e.g. card-matching activities to get students
  practicing without realising
• Avoid endless repetition of textbook exercises
  use selectively.
• Mini whiteboards useful in testing understanding.
• Variety essential.

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Use of Technology

• Technology is a vital tool in doing
  statistics. Its use in the classroom can be
  extremely helpful
• AUTOGRAPH useful for recording, graphing,
  analysing data collected.
• MINITAB a more powerful tool. Diagrams and
  analytical tools superior to AUTOGRAPH and EXCEL.
• EXCEL spreadsheets can be useful in a variety
  of ways e.g. in simulations.
• Graphics calculators many statistical functions
  and graphing tools. Something all can get their
  hands on.
• http//www.mathsnet.net/ an excellent free
  website (for A Level) that has hundreds of
  applets and examples on Statistics and
  Mathematics for insertion into lessons.
• Avoid over-use of technology.
• Try and use a concrete, practical example of
  something with students first.

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Monty Hall Demo on mathsnet.net
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Statistics in the Real World

• Try and plan at least one trip a year which
  illustrates work covered in classroom e.g. visit
  to Cadburys factory to see quality control in
  action.
• Get a statistician to come in and talk about
  their work.
• Even better, stage a Statistics Conference at
  school/college one at Cadbury College for last
  two years (Mobile Phones, Heart Disease).
• Make it cross curricular (involve Biologists,
  social scientists) and work together with other
  institutions (other schools, the RSS, Plymouth
  University etc.)

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A Trip to the Grave!

• Find the nearest large church graveyard and
  divide the land into areas e.g. older graves,
  recent, child/family burials (if distinct areas
  in yard).
• Assign groups of students to each area.
• Students start at a random point and use dice and
  coins to decide movement (left, right, forward or
  back then number of paces)
• Record details on nearest grave age at death,
  gender, occupation (if there), size of headstone,
  date buried etc.
• Pool data on return and use as a basis of class
  and project work.

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Dicey Statistics!

• Give each child a die and explain that you are
  interested in finding out the most likely number
  of throws up to and including the first six ask
  them to guess this first.
• Carry out the experiment once and tally results.
  Repeat for greater sample size.
• Students are usually surprised by the result.
• Many peoples instincts about probability are
  based on false ideas.

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Dice Experiment Theory

• A Geometric Distribution
• Let X the number of throws up to and including
  the first six
• X G (1/6)
• P(X 1) 1/6
• P(X 2) 1/6 5/6
• P(X 3) 1/6 (5/6) (5/6) etc.
• Mean 1/(1/6) 6

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X 1 or 2 are the most likely scores
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A final practical example works with year 7
upwards

• Poverty
• Distribute squares of CDM bar around class do
  it unevenly.
• Obtain class reaction unfair?
• Calculate mean arrange it to be 2 if possible.
• Discussion on averages to ensue which is best
  one.
• Give say 6 squares of chocolate to the boy/girl
  with most mean increases! Link to Aid to
  developing countries and question of corruption.
• Students decide how to redistribute squares so
  median is 2 and then mode is 2.

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Dont be afraid to experiment!

• The course will be a success if you
• Build in practical activities into work-schemes
  in EACH topic and encourage staff to try new
  ideas.
• Observe each other teaching be supportive.
  Team-teaching can also help.
• Continue to produce a bank of low and hi-tech
  activities (card-matching, dominoes, data-sets on
  MINITAB and AUTOGRAPH etc.) and incorporate into
  your work-schemes.
• This will take time (a two year project)
  involve the whole department, use Standards Unit
  materials and templates to help.
• Plan variety into individual lessons and the
  organisation of each term.
• Have at least one field trip/visit per year
• Embed practical application/context into each
  topic how is it used in the real world?
• Allow for the use of different student learning
  styles.
• Have regular reviews after each topic and build
  in at least 4 weeks of revision before each set
  of exams if possible.
• Show enthusiasm for the subject!

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In Closing ..

• Statistics is a fascinating subject pre and post
  16.
• Students really enjoy using it to deal with
  real-world problems.
• Intermediate C grade students up to A students
  can do VERY well on an A Level Statistics course
  (AQA only truly applied course available, but MEI
  now has AS only course).
• There is a desperate need world-wide for
  statisticians, and excellent career prospects for
  those who study it in higher education.
• It is a really rewarding subject to teach.