Reconceptualising ‘Statistics’ in Class Or Sex, Drugs and Alcohol in Mathematics Jim Ridgway SMART Centre School of Education University of Durham, UK
Dec 18, 2015
Reconceptualising ‘Statistics’ in Class
Or Sex, Drugs and Alcohol in Mathematics
Jim Ridgway
SMART Centre
School of EducationUniversity of Durham, UK
Jim Ridgway Durham
OECD Global Project
Beyond GDP – Measuring the Progress of Societies
What do citizens value?What do communities want for the future?Can we use existing measures or create new
ones to measure social progress?
Jim Ridgway Durham
Public Education
“ produce a broader, shared, public understanding of changing conditions, while highlighting the areas of significant change or inadequate knowledge”
Istanbul Declaration
Jim Ridgway Durham
Web 2.0 – Information Explosion
• Search engines• Government and NGO websites• Communication tools
– youtube for video, clipmarks to assemble webpages• Interactive documents • Discussion forums on data
– Many eyes, swivel• Wikis – on reasoning with evidence
– Interactive demonstrations, self test and diagnostics• Mash-ups
– E.g. INTERSOS google maps plus data on [war, water, mobility…] from 3G phones
• Information and misinformation explosion– Astroturfing, wikiscanner
Jim Ridgway Durham
Challenges
Every interesting problem in health, crime, poverty, environment, education, personal well being…
Jim Ridgway Durham
Challenges
Every interesting problem in health, crime, poverty, environment, education, personal well being…
is multivariate
Jim Ridgway Durham
Challenges
Every interesting problem in health, crime, poverty, environment, education, personal well being…
is multivariate
has non-linear relationships
Jim Ridgway Durham
Challenges
Every interesting problem in health, crime, poverty, environment, education, personal well being…
is multivariate
has non-linear relationships
has confounding variables
Jim Ridgway Durham
Challenges
Every interesting problem in health, crime, poverty, environment, education, personal well being…
is multivariate
has non-linear relationships
has confounding variables
So we might have some problems developing ‘public understanding’
Jim Ridgway Durham
Statistics and School Statistics
• 21st Century Statistics – data and problem driven– modelling targeted towards particular problem areas
(e.g. biometrics, demography, econometrics)– creating models to fit interesting problems NOT fitting
interesting problems into standard models» from (da Silva 2006)
Jim Ridgway Durham
Reasoning from Evidence - % of Exam points National Exams (Statistics) 2004
ExamBoard
Exam 1 Exam 2 Exam 3 Exam 4
AQA 25 20 25 23
OCR 24 29 29 14
CCEA 12 33
Edexcel 27 25 33
WJEC 3 28 21
OCR 25 31 28 22
Jim Ridgway Durham
English High-stakes Assessments in Statistics
• Most points are allocated for computational and procedural skill
• Few points are allocated for conceptual understanding or interpretation
• There was NO example where students considered more than 2 variables
• Given 2 variables, ALL relations were linear
Jim Ridgway Durham
The English Statistics Curriculum..
• Focuses on mastery of technique• Analyses toy data via standard (1920s) methods• Makes little use of computers• Is quite unlike ‘real’ statistical practice
• So our most interested and able students see statistics as difficult, dull, and rather useless
Jim Ridgway Durham
Public Education
“ produce a broader, shared, public understanding of changing conditions, while highlighting the areas of significant change or inadequate knowledge”
Istanbul Declaration
Jim Ridgway Durham
From Problem to Policy
• Problem definition• Problem exploration
– Data• What is relevant?
• What is available?
• Is it reliable?
• What does it show?
• Modelling– Theorising
• Informal
• Formal
• Policy formulation, implementation, revision
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Exploring Data
• Sexually transmitted diseases
• Drug use
• Heart disease
• NZ wages
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Heuristics
• Critique the quality and source of the data
• Describe and explore phenomena before you try to explain things
• Separate analysis and interpretation – especially in observational data
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Heuristics
• Focus on effect size not significance level• Check that the effect size is a lot bigger than the
likely error of measurement• Identify variables that have the strongest effects• Look at absolute levels – are they big enough to
be worth worrying about?• look for the ‘dog that didn’t bark’ – were there
things you expected to see, but didn’t?
Jim Ridgway Durham
Heuristics
• Explore the effects over different values of each variable – look for different functional relationships over different values of a variable (if it is cold, nothing happens…then as it gets warmer…)
• Look for non-linear relationships• Look for interactions, and think about ‘data surfaces’• Disaggregate the data, and see if the patterns of
relationships stay the same as in the aggregated data• Think about possible confounding variables outside the
variables being analysed
Jim Ridgway Durham
From Problem to Policy
• Problem definition• Problem exploration
– Data• What is relevant?
• What is available?
• Is it reliable?
• What does it show?
• Modelling– Theorising
• Informal
• Formal
• Policy formulation, implementation, revision
Jim Ridgway Durham
Ambitions for adults – e.g. uses for national surveys
• Full report – allow access to raw data• Press release• Mash-up
– Open for comments, with expert commentary– Linked to Wikipollution/ Wikiwhatever
• Press release with embedded interactive display– Podcast– free applets that can be plugged into media websites
• BBC website 20m hits/month
Jim Ridgway Durham
Our ambitions for students
They should :
• View data as integral part of dealing with any situation
• Be able to view data reporting critically
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What can educators do? - An Alcohol Mashup
Multivariate display on alcohol use by young people, and newspaper articles
• Student group activity: either– Critique a media account– Write their own article– Create a presentation
• Analyse responses– Informal discussions between researchers– Researchers write formative feedback– Create and apply an analytic framework
Jim Ridgway Durham
Study
3 hours explore interfaces play with mashup create ‘product’
School School Type Ages
(years) Student Products
A Selective, girls 13 6 B Selective, girls 14 29 C Comprehensive, co-ed 15 16 D Private, co-ed 13,14,15 39
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Summary
• 83/90 reports made use of data • 54/90 reports used data accurately to critique or create
text media• 13/90 responses discussed 2 way interactions
• 61/90 responses showed evidence of manipulating our displays– 14 of the 61 showed evidence of moving the position of variables
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Summary
• 19/90 responses explicitly reported trends clearly and accurately
• A further 10/90 reported trends explicitly with some success
• A further 38/90 responses interpreted graph points accurately– Often these used the start and end of a time period for
comparison, but without explicitly referring to behaviour over the time period
• A further 16 had some success in this
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Summary
Literary
• Only 4/90 reports were rated poor across – Style and– Sense of audience and
– Structure and logical coherence
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Summary
Sourcing own data
• 19/90 FOUND NEW data– This was not asked for or expected!
– 15/19 data were directly relevant– 4/19 data were partially relevant (e.g. US data)
• Only 4 of the 19 cited the source of their data
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Informal Teacher Feedback
• Mostly high levels of pupil engagement
• Genuine group work in many cases – to complete the task effectively in the time required people to take on different aspects
• Rich task integrating mathematical skills with other ‘soft skills’ valued by employers
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In terms of PPDAC
• Problem definition and understanding• Planning• Data gathering• Analysis• Conclusions and communication
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In terms of Key Competencies
• Thinking – making sense of information• Using language, symbols and texts• Managing self• Relating to others• Participating and discussing
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Promoting Sense-making Based on Evidence
• Define and describe attainment– What skills are critical for dealing with mis/information– Are there hierarchies of knowledge?– What heuristics are useful?– To what extent do students already have these skills?
• Identify student (and teacher) misconceptions– What should the diagnostic actions be?
• Recognise and reward good performance– Find clear examples of good/OK/inadequate student work– What form of feedback is effective in improving learning?– How do we operationalise qualitative judgements?
Jim Ridgway Durham
Conclusions
• We DO need to promote uncommon common sense• Innovative curricula need innovative activities,
pedagogies and assessments• Pupils CAN reason with MV data
• We have a lot of work to do!
Jim Ridgway Durham
Data references
• STI data produced by the Health Protection Agency– http://www.hpa.org.uk
• Alcohol data in Drug use, smoking and drinking among young people in England in 2005.– http://www.ic.nhs.uk/datasets
Jim Ridgway Durham
Multiple scales on vertical axis
School life expectancy (years)
Adolescent fertility rate (%)
Adult unemployment (‘000s)