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

UK School Statistics is?

Defined by high stakes tests…

So analyse the tests…

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

Albert Einstein

Things should be made as simple as possible…

Jim Ridgway Durham

Albert Einstein

Things should be made as simple as possible…

but not any simpler

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

Exploring Data

• Sexually transmitted diseases

• Drug use

• Heart disease

• NZ wages

Jim Ridgway Durham

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

Jim Ridgway Durham

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

Jim Ridgway Durham

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

Jim Ridgway Durham

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

Jim Ridgway Durham

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

Jim Ridgway Durham

Summary

Literary

• Only 4/90 reports were rated poor across – Style and– Sense of audience and

– Structure and logical coherence

Jim Ridgway Durham

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

Jim Ridgway Durham

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

Jim Ridgway Durham

In terms of PPDAC

• Problem definition and understanding• Planning• Data gathering• Analysis• Conclusions and communication

Jim Ridgway Durham

In terms of Key Competencies

• Thinking – making sense of information• Using language, symbols and texts• Managing self• Relating to others• Participating and discussing

Jim Ridgway Durham

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)

Jim Ridgway Durham

www.dur.ac.uk/smart.centre/freeware

Reconceptualising ‘Statistics’ in Class

Or Sex, Drugs and Alcohol in Mathematics

Jim Ridgway

SMART Centre

School of EducationUniversity of Durham, UK