George Ekol University of Witwatersrand, South Africa.

1. Perspectives on foundation statistics: Some examples from prospective secondary mathematics teachers. George Ekol University of Witwatersrand, South Africa.

2. UGANDA (E. Africa) • Rep. of SOUTH AFRICA

3. Need for well founded evidence Stigler (1999)- Putting statistics on the table.

4. Statistics on the table (Stigler,1999).

5. Statistics Education

6. Background_ Stat. education Foundations of statistical thinking: (Wild & Pfannkuch,1999; delMas & Liu, 2005; delMas, Garfield, & Ooms, 2005; Batanero, Burrill, & Reading, 2011; GAISE, 2005, 2016; Moore, 2010). • Variability; • Reasoning involving statistical graphs; • Integrating statistical and contextual knowledge;

7. Background … • Representing data to enable a clear understanding of the underlying concepts (Wild & Pfannkuch,1999). • Need for data for supporting claims (Wild& Pfannkuch,1999; Stigler, 1999).

8. Statistics on the table (Stigler,1999).

9. Purpose of the study • Identify which elements of the foundations statistical thinking are prevalent in pre-service teachers’ comments about statistics after an introductory statistics semester course. • Suggest some implications for statistics education

10. Research Questions 1. Which elements of the foundations of statistical thinking are more likely to emerge from pre-service secondary mathematics teachers’ statements about statistics, before and after teaching statistics during school practice? 2. What are the implications for pre-service secondary statistics teacher education?

11. Theoretical bases • Understanding of, and appreciation for, variability as a core component of statistical thinking (Burrill, 2019 (IASE Workshop), Cobb, 1992; Moore,1998; Garfield & Ben-Zvi, 2008; GAISE, 2005,2016). • Statistical thinking in empirical inquiry (Wild & Pfannkuch, 1999). • Attitude towards statistics (Schau et al.1995). • Levels of conceptual understanding of statistics (del Mas, Garfield, Ooms & Chance, 2007).

12. Methodology Study design:Qualitative (Case study) Core logic: Contextualization- (understanding data from a different theoretical perspective.)

13. Methodology.. Data source: Secondary qualitative data from Fitzmaurice et al. (2014). Secondary data are analyzed based on the foundations of statistical thinking framework ( Wild & Pfannkuch, 1999) and some elements of (GAISE, 2005;2016).

14. Data source Secondary qualitative data from Fitzmaurice et al. (2014). • n=9 (6M,3F); (5 finalists, 4 second yr.; BSc. (Math., Phy. Sc. degree)). • All had completed one semester course in introductory statistics). • Report data from 6 (2F,4 M)

15. Data Analysis

16. Observations from data analysis • Trans-numeration: representing data to enable clear understanding of statistical concepts-(5) • Reasoning with graphs-(3) • Integrating statistical contextual knowl’ge- (2) • Need for data -(1) • Consideration of variability -(1) (Research question 1)

17. Example1:Trans-num’(Sec. sch. exp.) “…statistics needs to be taught well…it is important to have a really good foundation […] like everything with maths, if you don’t understand the basics you can’t develop […] you can’t’ build on it.” [Second yr. male 3]

18. Example 2: Reasoning with graphs (teacher knowl’dge) “…actually knowing what the figures mean when you see them. And stuff like standard deviation as well […] like seeing a figure […] whatever 1.3 and saying that’s leaving it off.Yeah, maybe there is a grey area there where people don’t really know, including myself, what these things actually mean.” [Second yr. male]

19. Example 3: Consideration of var. (Reason for perceived diff’ty of stat. ) “You could think you were right for the whole question and then it could end up that you weren’t at all. So we learned the other topic more […] at least we will know if we were right or wrong” [Second yr. male 4] ------ (i) Solve for x: log3 243=32x+1 (ii) Briefly describe what standarddeviation means.

20. Example 4: Trans-num.(contribution of sch. practice) “…out of the [subjects] I have taught, statistics has been the one I’ve liked most…. I don’t know. I just liked it because it is a lot more engaging … and you don’t have to follow the book …It’s is easier to teach statistics -the students can relate to it….It is something that’s valuable both in life and when you move on.” [4th yr. female].

21. Position Main argument of this paper (with the support of secondary data from Fitzmaurice et. al, 2014) is that: Pre-service secondary mathematics (statistics) teachers can change their perceptions of difficulty of statistics, if they are encouraged by their respective educators and mentors; and are enabled to practice teaching statistics, as they teach mathematics.

22. Implication for Stat. teacher education. • Encourage pre-service teachers to teach statistics, as well as mathematics topics during school practice if teaching statistics is optional in their teacher education program. • Honours projects in statistics-specific topics. • Statistics teaching and leaning at the school level is not going to improve soon, unless stat/maths. teachers are deliberately trained to teach statistics.

23. Thank you. Email: george.ekol@wits.ac.za