Statistical Literacy Phil Doyle p.doyle@auckland.ac.nz

1. Statistical Literacy Phil Doyle p.doyle@auckland.ac.nz Viney Shandil, Semisi Talakia’atu, Aisea Fifita, Dr Sashi Sharma (University of Waikato)

2. Definitions of statistical literacy • Assessing statistical literacy • Teaching statistical literacy

3. Definitions of statistical literacy

4. According to Gal (2002) there are five interrelated knowledge bases that must be used to exhibit statistical literacy • mathematical knowledge • statistical knowledge • knowledge of the context • literacy skills • critical questions as well as dispositional elements that include • beliefs and attitudes • a critical stance Gal, I. (2002). Adults’ statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70(1) 1-51

5. New Zealand Curriculum Statistical literacy … S3-2 Evaluate the effectiveness of different displays in representing the findings of a statistical investigation or probability activity undertaken by others. S4-2 Evaluate statements made by others about the findings of statistical investigations and probability activities. S5-2 Evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings. S6-2 Evaluate statistical reports in the media by relating the displays, statistics, processes, and probabilities used to the claims made. …

7. Level 3 Statistics Statistical investigation • Conduct investigations using the statistical enquiry cycle: • gathering, sorting, and displaying multivariate category and whole-number data and simple time-series data to answer questions • identifying patterns and trends in context, within and between data sets • communicating findings, using data displays. Statistical literacy • Evaluate the effectiveness of different displays in representing the findings of a statistical investigation or probability activity undertaken by others. Probability • Investigate simple situations that involve elements of chance by comparing experimental results with expectations from models of all the outcomes, acknowledging that samples vary.

9. Level 4 Statistics Statistical investigation • Plan and conduct investigations using the statistical enquiry cycle: • determining appropriate variables and data collection methods • gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationships, and trends • comparing distributions visually • communicating findings, using appropriate displays. Statistical literacy • Evaluate statements made by others about the findings of statistical investigations and probability activities. Probability • Investigate situations that involve elements of chance by comparing experimental distributions with expectations from models of the possible outcomes, acknowledging variation and independence. • Use simple fractions and percentages to describe probabilities.

10. “You get dumber as you get older” The strip graph shows that people aged 20-24 years are the biggest group with a qualification. People aged 85 plus are the biggest group with no qualification. Source: 2001 Census: Education 2001

11. Level 5 Statistics Statistical investigation • Plan and conduct surveys and experiments using the statistical enquiry cycle: • determining appropriate variables and measures • considering sources of variation • gathering and cleaning data • using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets • comparing sample distributions visually, using measures of centre, spread, and proportion • presenting a report of findings. Statistical literacy • Evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings. Probability • Compare and describe the variation between theoretical and experimental distributions in situations that involve elements of chance. • Calculate probabilities, using fractions, percentages, and ratios.

12. Box plot of total income by partner status

13. Level 6 Statistics Statistical investigation • Plan and conduct investigations using the statistical enquiry cycle: - justifying the variables and measures used; - managing sources of variation, including through the use of random sampling; - Identifying and communicating features in context (trends, relationships between variables, and differences within and between distributions), using multiple displays; -making informal inferences about populations from sample data; - justifying findings, using displays and measures. Statistical literacy • Evaluate statistical reports in the media by relating the displays, statistics, processes, and probabilities used, to the claims made. Probability • Investigate situations that involve elements of chance: • comparing discrete theoretical distributions and experimental distributions, appreciating the role of sample size; • calculating probabilities in discrete situations.

15. Assessing statistical literacy

16. A statistical literacy construct - Watson and Callingham What are the progressions? How to assess? Levels of Statistical Literacy (Watson & Callingham, 2003) 1. Idiosyncratic - one-to-one counting, ability to read cell entries. 2. Informal Intuitive - non-statistical beliefs, one-step calculations. 3. Inconsistent - limited appreciation of content and context without justification,qualitative ideas. 4. Consistent Non-critical - straight-forward engagement with context; statistics, simple probabilities and graphs. 5. Critical Questioning engagement; appreciation of variation; qualitative interpretation of chance. 6. Critical Mathematical - questioning critical engagement with context; proportional reasoning; subtle language.

17. Assessing statistical literacy Adapted from Watson & Callingham (2003) Levels of Statistical Literacy Stage 0 – 1 Idiosyncratic and informal – Questions and or statements are not based on the data Stage 2 Consistent Non-critical - Accurate use of statistics, appropriate but non-critical engagement with the problem and/or context of the problem Stage 3 Early critical – Can attend to more than one aspect of the problem and/or context of the problem to show relational thinking Stage 4 Advanced Critical – There is questioning, critical engagement with context; proportional reasoning, deals with subtle language

18. Teaching statistical literacy

19. Statistical literacy has been positioned as an important skill for citizens and a desired outcome of statistics education. However, while the knowledge bases and beliefs and attitudes that underlie statistically literate behavior have been outlined in some detail, it is less clear how to develop them Iddo Gal

20. Statistical literacy According to Gal (2002) there are five interrelated knowledge bases that must be used to exhibit statistical literacy • mathematical knowledge • statistical knowledge • knowledge of the context • literacy skills • critical questions as well as dispositional elements that include • beliefs and attitudes • a critical stance Gal, I. (2002). Adults’ statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70(1) 1-51

22. http: • www.stanscafe.co.uk/

23. Statistical literacy According to Gal (2002) there are five interrelated knowledge bases that must be used to exhibit statistical literacy • mathematical knowledge • statistical knowledge • knowledge of the context • literacy skills • critical questions as well as dispositional elements that include • beliefs and attitudes • a critical stance Gal, I. (2002). Adults’ statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70(1) 1-51

24. The need for good data http://www.stats.govt.nz/ http://www.babynamewizard.com/ http://www.gapminder.org/

28. http://www.oecdbetterlifeindex.org/ • http://www.statschat.org.nz/

29. Statistical literacy According to Gal (2002) there are five interrelated knowledge bases that must be used to exhibit statistical literacy • mathematical knowledge • statistical knowledge • knowledge of the context • literacy skills • critical questions as well as dispositional elements that include • beliefs and attitudes • a critical stance Gal, I. (2002). Adults’ statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70(1) 1-51

31. Hypothesis: It is useful for students to know about Vocabulary Reading for comprehension Showing thinkng

32. Hypothesis: It is useful for students in statistics to know about vocabulary Explicit teaching of subject specific words. Cloze strategies: miss out prepositions- get students to fill in gaps - talk about why they chose those words and how it can change the meaning of the maths.  Barrier games - (look online) receptive and productive language.

33. Hypothesis: It is useful for students to know about text features of statistics reports. Use $100 words idea. Not all words are equal. Which ones are most important? Skim and predict- before you read. The author has arranged the information in a specific way for you to work your way through.

34. Statistical literacy According to Gal (2002) there are five interrelated knowledge bases that must be used to exhibit statistical literacy • mathematical knowledge • statistical knowledge • knowledge of the context • literacy skills • critical questions as well as dispositional elements that include • beliefs and attitudes • a critical stance Gal, I. (2002). Adults’ statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70(1) 1-51

36. Statistical literacy According to Gal (2002) there are five interrelated knowledge bases that must be used to exhibit statistical literacy • mathematical knowledge • statistical knowledge • knowledge of the context • literacy skills • critical questions as well as dispositional elements that include • beliefs and attitudes • a critical stance Gal, I. (2002). Adults’ statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70(1) 1-51

37. Key findings • All students can develop critical thinking skills. • Students can be taught how to question and challenge data. • Context and literacy skills place huge demands on students, but teachers can help develop the skills and dispositions to experience success.

38. Major implications • A need to focus on classroom activities that develop critical thinking skills rather than statistical procedures and skills. • A need to create a classroom climate that positively engages all students and promotes statistical argument and discussion,. • Opportunities for students to work with real data are required. Activities should move from familiar to unfamiliar contexts. • A need to cater for individual needs with teachers able to recognise how to progress students through stages of statistical literacy.