1. What about the P in the PPDAC cycle? Pip Arnold The University of Auckland

2. Statistical investigation cycle Has at its heart a starting point based on a problem. Four or five phases. –Wild & Pfannkuch, 1999 –Graham, 2006 –Franklin & Garfield, 2006

3. Wild & Pfannkuch, 1999

4. First year Pre- and post-test responses Ten-lesson teaching unit Collaboration between teacher and researcher Year 10 students Teaching experiment (Bakker, 2004)

5. Initial findings Students unable to show what they knew because their question was unsuitable, ie it could not be answered by the data given. Bigger problem when teacher didn’t identify that the question was not able to be answered with the data given.

6. Asking questions My theory is that there is question posing and question asking. Question posing results in a question being formally structured, whereas question asking is a continual spontaneous interrogative process.

7. Question posing (two types) Question posing arises as a result of having a problem that needs to be addressed using a statistical investigation. Investigative question –The question being asked of the data Survey question –The question asked to get the data

8. Literature Review Some authors specify the purpose –Pfannkuch & Horring, 2005; Burgess, 2007; Rubick, 2000; Graham, 2006 Lack of clarity from some authors –Russell, 2006; Hancock, Kaput & Goldsmith 1992 Confusion from some authors –Whitin, 2006; Konold & Higgins, 2002, 2003; Lehrer & Romberg, 1996

9. Confusion example Konold and Higgins (2003) in their review of statistics education research devote some of their discussion to the forming of a statistical question. They report on the challenge for students and teachers of taking a general question and then transforming this into a question that can be answered with data, that is, a statistical question. Clearly they are discussing the investigative question. However, later on in their discussion there is a slight confusion as to which of the two purposes they are referring to, investigative or survey.

10. Confusion example “ Elementary school students can learn a lot about data as they grapple with issues that arise in formulating statistical questions, especially when they anticipate conducting surveys with the questions they design. By thinking about how they would answer a proposed question, students quickly discover not only the range of different responses but also that multiple interpretations of a question are possible and the wording of the question matters. ” Konold & Higgins (2003, p.195)

11. Question asking (two types) The interrogative questions – questions that are asked as checks within the cycle (the problem, the plan, the data (given data sets), the analysis, the conclusion); The analysis questions that are asked about the statistics, graphs and tables to develop a description of and an inference about what is noticed (the analysis).

15. Types of investigative questions Summary –A description of the data, usually a single data set Comparison –Comparing two (or more) sets of data across a common variable Relationship –Interrelationship between two paired variables Pfannkuch & Horring, 2005; Graham, 2006

16. Ideas to include Typicalness and data as an aggregate rather than individual cases (Konold & Higgins, 2002, 2003; Bakker & Gravemeijer, 2004).

17. What next Categorised summary and comparison questions based on the results of the pre- and post-tests of the first cycle.

18. Summary Questions

20. Comparison Questions

22. Findings Students better at posing comparison questions Modelling important Posing questions at the heart Asking questions integral (Friel, Curcio, & Bright, 2001)

23. Questioning the question What was the original question that was used to collect the data (survey question)? What type of data is being used? What graph or display of the data will be made? What hypothesis can be made about the data? Is the question interesting?

24. Questioning the question Who would be interested in the answers to this question? Is there enough data available to answer the question (issues around sample size)? What background information is available about the data (how it was collected, who it was collected from, when it was collected etc.)? Is the variable of interest in the dataset? Is the investigative question “ right ” ?

25. Second year Pre- and post-test responses Student interviews 14 lesson teaching unit Collaboration between teacher and researcher Year 10 students studying Year 11 Maths Teaching experiment (Bakker, 2004)

26. Some work for you 2008 questions posed Using the summary and comparison tables provided allocate a category to each of the questions posed.

27. Issues that came up For the group

28. Issues that came up What is the population? –Yr 11, NZ, 2007, C@S database Average/typical/range do these all mean the same? a, the, nothing (a boy, the boys, boys) –Sample/population –Individual/aggregate What is typical?

29. Ideas to mull over IndividualAggregate SampleWho is the tallest? Typical height of the boys PopulationHeight of a typical boy Typical height of boys…

30. Ideas to mull over 2 No qualifier GenderAgeYear 11 No qualifier NZ C@S 2007

31. Students

32. BoysGirls

33. Students BoysGirls <15yrs 15yrs 16yrs >16yrs

34. Students BoysGirls <15yrs 15yrs 16yrs >16yrs Yr 11

35. Students BoysGirls <15yrs 15yrs 16yrs >16yrs Yr 11 NZ

36. Students BoysGirls <15yrs 15yrs 16yrs >16yrs Yr 11 NZ C@S

37. Students BoysGirls <15yrs 15yrs 16yrs >16yrs Yr 11 NZ C@S 2007

38. Students BoysGirls <15yrs 15yrs 16yrs >16yrs Yr 11 Year 11 NZ C@S 2007

39. What makes a good question can be answered with the data –Sample size, variable(s) available population of interest is clear –a, the, nothing sample v target population Indvidual v aggregate variable(s) of interest is/are clear intent (summary, comparison, relationship) is clear –What is typical? is clear one that we are interested in the answer

40. Where to from here RESEARCH QUESTION Do students draw better conclusions if they can pose a suitable investigative question that they understand?