1 SACE Stage 1 Mathematics STATISTICS Session 4 The syllabus, do and don’ts, projects and resources.

2 The Syllabus  Group Exercise: Look closely at the syllabus and see what we have and have not covered in the workshops.

3 Investigations for teaching and learning  A central theme of these workshops has been the use of investigations and activities as a vehicle for the teaching and learning of statistics.  This raises the question of how one obtains appropriate investigations and activities.  There are many resources available, especially on the internet, and a list some potentially useful sites will be provided  BUT…

4 Investigations for teaching and learning  Suitable problems and data can be difficult to find.  You need to be clear at the outset about why you are trying to develop a particular investigation.  Some points to consider follow.

5 What is the purpose?  A data investigation is useful only if it achieves a particular purpose.  For example, the road safety data serves as a vehicle to:  Illustrate the use of histograms  Illustrate the use of descriptive statistics  Illustrate the cycle of investigation by successive refinement of the problem being solved

6 What is the purpose?  The Titanic investigation serves as a vehicle to:  Illustrate the use of tabulation and graphing for categorical data  Illustrate the use of boxplots.  Illustrate the cycle of investigation by successive refinement of the problem.  Together with the road safety data, provide a contrast between the different variable types

7 What is the purpose?  When developing an investigation for a teaching and learning role you should have in mind a specific area of the syllabus that is to be explored.  When you find a good problem/dataset, it is natural and appropriate to use it for whatever you can.  But it must serve a specific purpose in relation to the syllabus.

8 Engaging the students  A data analytic investigation will work best when the students become actively involved in the process.  They must see that there is a real problem to solve and be enthusiastic about its solution  This means that the context must be understandable and of at least some interest  More importantly, the problem must be genuine.

9 Engaging the students  Be wary of investigations where there is high enthusiasm for the subject in general or for some peripheral aspects, but the statistical value of the investigation is next to nil.  For example, the idea of an investigation of “some data from the AFL” may appeal to a large body of students BUT:  There are almost no good problems that we can collect data for and solve in this area.

10 Engaging the students  A second example is a poorly designed “Estimate the proportion of red smarties” type of sampling activity.  It is clearly great fun!  But it will be almost useless for teaching sampling if:  There is no worthwhile problem to solve.  We can’t say whether sampling was random.  We can’t compare estimates to the correct answer.  The fun aspect is a distraction rather than motivator.

11 Role of statistics  The heart of a data analytic investigation must be a problem(s) that requires the use of certain statistical techniques.  Investigations where the statistics are an afterthought or peripheral are unlikely to be effective.  One must discourage students from emotional distractions and ensure they stick to the statistics.

12 Correctness  The statistical methods must be used correctly.  In the road safety example we concentrated on a problem that in itself is not enough to answer the bigger question.  But it was a problem where the methods could be used convincingly and correctly.

13 Correctness  Sometimes potentially interesting problems are unsuitable because the available methods cannot be applied correctly.  For example, environmental data are interesting and worthwhile but almost always require advanced methods.

14 A Check List for Investigations  Is it real, engaging and worthwhile?  Can I get real data associated with the problem?  Does it give access to the knowledge I want the students to learn in a manner that is statistically correct?  How do the Road Accident problem, Titanic problem and the Straw activity shape up?

15 Don’t force the issue  Not everything is best developed through data analytic investigations.  For example, sampling is developed far more effectively through the straw activity rather than “solving a real-life problem”  If an investigation or activity looks too contrived, it is probably not worthwhile.

16 Don’t force the issue  There is still the need for traditional delivery and practice of some of the detailed technical points  But these will be more meaningful and better motivated in the context of previous investigations and activities.

17 Don’t force the issue  For example, in discussing the histogram we need to deal with technical issues relating to bin-width. That is:  How should we choose the number of bins?  Can the choice of bins influence conclusions?  An appropriate time to consider this is after an investigation in which the histogram played a key role in forming conclusions.

18 Student projects  The guidelines for developing investigations for use in the classroom apply to student project work as well.  If possible, the student should choose their own problem and in the course of doing so ensure that …

19 Student projects  It is a real, engaging and worthwhile problem.  They can get real data associated with the problem.  They can apply the knowledge they have learned to solve the problem in a correct manner.

20 Real, engaging and worthwhile  Students should:  Consider their interests.  Consider their family/school network.  Read widely.  Consider ethical issues.  Students should not:  Take on a huge task. (KISS principle)  Acquire data and try to make a problem out of it.

21 Data collection  Often, secondary data is of little use.  The statistical analysis has already been done.  When collecting their own data students should:  Use random sampling, if a sampling is involved.  Use randomisation in any experiments.  Collect sufficient data.  Use family connections or friends as appropriate.

22 Data collection  When collecting their own data students should not:  Badger people in public (in person,by phone or letter).  Collect petrol in glass bottles.  Measure speeds of cars with radars.

23 Applying knowledge  Students, with guidance from the teacher, should ensure they are using their knowledge correctly.  They should not “throw every possible thing they know at the problem”.  If they do they are probably doing something wrong.

24 Applying knowledge  They should be made to feel confident that a simple and relatively short analysis is fine so long as it is correct and heads toward a solution to the problem.  They should be happy that establishing ‘no difference’ is as good as establishing a difference.  They should be aware that they are probably not going to prove any result at year 11 level, but will be able to form a conjecture.

25 Some examples  Does gypsum or sand work better to improve drainage in soil?  Does castration or testicle insertion result in the heavier sheep at sale age?  Which form of advertising works best for Pizza Haven - flyers or magazine advertising?

26 Some examples  Does Mozart’s music improve performance in cognitive tasks?  Are stock-broker chosen portfolios better than randomly chosen folios?  Do Duracell batteries last up to 10 times longer?  Are the reaction times of Year 2 students different from Year 8 students?

27 Some examples  Are the TER scores of students who attended a school for R-12 different from those who entered at Year 8?  See past Quantitative Methods examination for some more ideas.

28 Resources  There are MANY. But like all resources you may need to use a number to get what you want.  Some suggested resources are …

29 Resources  Two on-line texts. The second site has particularly good applets:  home/surfstat.html 

30 Resources  A site which uses the problem solving approach to teach statistics. It has modules which can be downloaded, although not easily. 

31 Resources  This site is a good interactive site for normal calculations:   A text Moore, D.S.(1993) Introduction to the Practice of Statistics, W.H.Freeman, San Francisco.

32 Resources  The site of the Statistics Teacher Network Newsletter. It is a joint production of NCTM and the American Statistical Association and contains articles on resources, class projects and graphing calculators. Numerous other journals are available.  See the syllabus for further references, surf the net and ask your colleagues.