Sarah Howell & Suzanne Meijer Wellington High School

1. Investigating contexts that matter in Statistics Sarah Howell & Suzanne Meijer Wellington High School

2. Overview • Why does the choice of context matter in Statistics? • Intro to How far until it stops? statistical inference resource • Activity 1: What factors influence stopping distance? • Activity 2: Analysis – what do you see and what does it mean? • Writing conclusion – connecting with the context • Why road safety education?

3. Why does our choice of context matter? • “In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically” (NZC) • Student engagement • Activate prior knowledge “Contexts motivate, illustrate potential application, provide a source of opportunity for mathematical reasoning and thinking, and anchor students understanding” (Anthony & Walshaw, 2007)

4. Why does our choice of context matter? • Promoting other values from the curriculum: key competencies, citizenship • Can give students who don’t usually participate a voice in the Maths classroom “...opportunities to explore authentic applications that arise out of real-life contexts can have a significant and sustained impact on student knowledge, attitude, self-esteem, independence, and confidence.” (Alton-Lee, 2003)

5. NZ Transport Agency statistical inference resources • How far until it stops? • Driven to distraction!

6. How far until it stops? Students: • investigate stopping distances of vehicles under different conditions • are provided with an interactive online resourceto provide background context about the 2-second and 4-second following distance rules

7. Intended outcomes for students • Carry out a statistical analysis using the PPDAC statistical enquiry cycle…..…..in a meaningful context. • Create meaning for themselves about stopping distances from raw data and connect this to the 2-second and 4-second rules. • Develop in all areas of the key competencies, with a particular emphasis on using language, symbols and text and participating and contributing. • Develop social competencies as young drivers who contribute to their own safety and the safety of others.

8. How far until it stops? - the context

9. How far until it stops? - the context Total stopping distance Reaction distance • Braking • distance • + • = Linear relationship Quadratic relationship ie 2 x speed = 2 x distance ie 2 x speed = 4 x distance

10. How far until it stops? - the context Total stopping distance Reaction distance • Braking • distance • + • = This context is rich with a number of further factors that need to be appreciated and considered for their potential influence on stopping distances

11. How far until it stops? - the context Total stopping distance Reaction distance • Braking • distance • + • = Think: What factors influences stopping distances? Pair: Discuss with the person next to you Share: Feedback to the group

12. Contextual factors of influence Total stopping distance Reaction distance • Braking • distance • + • = Speed of car Attention Motor skills ie speed of foot to brake • awareness • distraction • noise levels • who else in car • visibility etc….. Familiarity with the vehicle

13. Contextual factors of influence Total stopping distance Reaction distance • Braking • distance • + • = Vehicle features Speed of car Road surface • condition of tyres • brakes – new, worn, ABS • new or late model • weight, balance, suspension….etc • chip • asphalt • gravel • grass • downhill, flat, uphill Weatheregwet or dry

14. Dataset – disclaimer! • Fictional dataset • But… it was created after research. Averages are consistent with what would be expected for road conditions and speed. • Reaction distances based on ‘typical’ reaction times and a linear relationship with speed. • Braking distances obey the quadratic relationship • Tidy, usable data without ‘distractions’

15. How far until it stops? Problem For example: In the NZ Vehicle and Road Safety Study, is the median total stopping distance of vehicles (metres) travelling at 50 km/h greater than the median total stopping distance of vehicles (metres) travelling at 40 km/h? Students: • connect it to the purpose of understanding the 2-second rule • draw on the background resources provided to understand the context • make a justified hypothesis

16. Analysis activity Looking at a set of graphs and summary statistics: • What are the interesting statistical features of the distributions? • How can you link these to the context?

17. Bimodal Right-skew Spread (IQR)

18. Bimodal Uniform/rectangular

19. Similar distributions Right-skew Right-skew Similar medians

20. Conclusion – developing contextual meaning As part of their conclusion the students discussed the context of their investigation and answered questions such as: • What evidence supports the conclusion? • How does the analysis and conclusion provide insight into the 2-second and/or 4-second rules? • Why would your friends who are learning to drive be interested in these results? • Which organisations or other groups of people might be interested in these results, and why? • What other questions has this investigation generated? • What are the implications of the groups for your investigation?

21. What the students come up with – intended outcomes: Students: • developed their own meaning about vehicle stopping distances at different speeds and for different road conditions • linked their findings to the 2-second and 4-second rules • found out just how much of a difference 10 km/h makes to stopping distances • identified factors affecting stopping distances • pooled their separate analyses to discuss the collective meaning of what they have found

22. What the students come up with – unintended outcomes: Students linked their findings to their world in ways that we didn’t anticipate: • discussing the lowering of the speed limit specific to their home suburb of Miramar • discussing the effect modified cars with lowered suspension had on braking distances

23. Why does the our choice of context matter? • “In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically” (NZC) • Student engagement • Activate prior knowledge • Promoting other values from the curriculum: key competencies, citizenship • Can give students who don’t usually participate a voice in the Maths classroom

24. So why choose road safety as a context? • Relevant to students • Accessible and engaging context • Citizenship • Key competency: Participating and contributing • Help them make sense for themselves about their world • Empower them to make decisions using knowledge • Build social competencies • Potential for cross-curricular themes • Whanaungatanga – Build relationships by showing students that you care about what happens to them outside of the classroom • Because young drivers in NZ are over-represented in death and serious injury crashes

25. Resources • NCEA Level 2 Inference resources available from NZTA’s Education Portal in Term 4 2019. • Fully adaptable resources include: • Student practice tasks for How far until it stops? and Driven to distraction! • Assessment schedule with examples of the types of responses which can be expected. • Datasets • Teacher guide with teaching activities to support the report writing process. • More resources to come!

26. NZTA’s Education Portal

27. Driven to distraction! • Context: driver distraction and driver fatigue • Students can use online tools to experience the variables for themselves • Reaction times: Sheep (requires Flash) or Human benchmark • Typing test • Information on the context includes infographics and interactive online modules designed for young drivers:

28. Feedback or questions? • Contact us: • Sarah Howell sarah.howell@whs.school.nz or @Sarah_StatsAko on Twitter • Suzanne Meijer suzanne.meijer@whs.school.nz • Senior Education Advisor (NZ Transport Agency’s Education Portal) • At the NZTA booth at this conference • @NZTAEducation on Twitter • Contact form on the Education Portal www.education.govt.nz “Primary use of context is …..to provide a learning situation that is experientially real for the students and which can be used as a starting point for advancing understanding” (Gravemeijer, 1997)

29. References Alton-Lee, A. (2003). Quality teaching for diverse students in schooling: Best evidence synthesis. Wellington: Ministry of Education. Anthony, G & Walshaw, M. (2007) Effective Pedagogy in Mathematics/Pāngarau: Best Evidence Synthesis Iteration [BES]. Ministry of Education: Wellington.  Gravemeijer, K. (1997).Mediating between concrete and abstract, In T. Nunes & P. Bryant (Eds.). Learning and teaching mathematics: An international perspective (pp. 315-333). London: Psychology Press.