SACE Stage 1 Mathematics STATISTICS

1. SACE Stage 1 MathematicsSTATISTICS 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: • Userandom sampling,if a sampling is involved. • Userandomisation 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: • http://www.anu.edu.au/nceph/surfstat/surfstat-home/surfstat.html • http://davidmlane.com/hyperstat/index.html

30. Resources • A site which uses the problem solving approach to teach statistics. It has modules which can be downloaded, although not easily. • http://www.stats.gla.ac.uk/steps/glossary/index.html

31. Resources • This site is a good interactive site for normal calculations: • http://psych.colorado.edu/~mcclella/java/zcalc.html • 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 . http://www.bio.ri.ccf.org/docs/ASA/stn.html 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.