Real and Relevant Problem Solving

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Real and Relevant Problem Solving. Doreen Connor Neville Davies John Marriott Royal Statistical Society for Statistical Education Nottingham Trent University. The New National Curriculum. Key Stage 4 The handling data cycle

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Real and Relevant Problem Solving

Doreen Connor

Neville Davies

John Marriott

Royal Statistical Society for Statistical Education

Nottingham Trent University

The New National Curriculum

Key Stage 4

• The handling data cycle
• Presentation and analysis of large sets of grouped and ungrouped data, including box plots and histograms, lines of best fit and their interpretation
• Measures of central tendency and spread
• Experimental and theoretical probabilities of single and combined events

Key Stage 3

• The handling data cycle
• Presentation and analysis of grouped and ungrouped data, including time series and lines of best fit
• Measures of central tendency and spread
• Experimental and theoretical probabilities, including those based on equally likely outcomes
Real and Relevant

National Curriculum

• Using Statistics to explain and predict
• Emphasis on practical applications
• Common sense approach
• Linking to work in areas other than Maths
Real and Relevant ?

Year 7 e.g. from the National Numeracy Strategy

I can catch either a Direct bus or a Transit bus to go home.

For my last five journeys on each bus, this is how long I had to wait:

Direct Bus 10 min 8 min 5 min 9 min 8 min

Transit Bus 16 min 1 min 2 min 15 min 1 min

Calculate the mean and the range for the waiting time for each bus. Using the mean and the range, decide which bus it would be more sensible to catch.

Explain why.

Real and Relevant
• “Statistics is the art and science of learning from data!” ~Franklin and Agresti 2007
• Statistical literacy is key
• Statistics is not black and white
Real Life Data

What do the numbers mean?

NHS head for a budget deficit of nearly £1billion.

Is that a big number?

This represents 1% of the NHS budget which has an error margin of 2%

The NHS spends £1600 per person -1% - £16

(The cost of 1 visit to a GP =£18)

“ The Tiger that Isn’t”

Michael Blastland & Andrew Dilnot (2007)

Real Life Data

What do the numbers mean?

All Teenagers?

How has drink regularly been defined?

How was the actual question they were asked phased?

How many people were asked and what age where they?

What situation were they asked the question in?

4 in every 10 of teenagers drink regularly!

“ The Tiger that Isn’t”

Michael Blastland & Andrew Dilnot (2007)

Real Life Data

What do the numbers mean?

How Many?

“ The Tiger that Isn’t”

Michael Blastland & Andrew Dilnot (2007)

Real Life Data

GATSO

What do the numbers mean?

Regression to the Mean

Real Life Data

What do averages mean?

Average 2.3 children?

“It says that most families have two older children and say one under the age of five”

“The .3 is a child that is growing up to be an older child. So that, like, the kid is 3 now, once it turns 10, it will get to 1, so they will have 3 children sort of thing”

“Well, a mum might have 2 children, and she might be pregnant”

What do you think?

3

Real Life Data

www.CensusAtSchool.ntu.ac.uk

Started in the UK in 2000

The classroom, pupils and teacher comprise the ‘census’ unit.

Collects data from & about children – stored in an international database.

Returns data in raw form along with teaching and learning resources.

Real Life Data

International Portal

Real Life Data

United Kingdom

Real Life Data

Completing the questionnaire

Real Life Data

Using real data

So what is wrong with this?

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Phase 4 data 2003/4

16775 children

Police

Press

Television

Political parties

Big companies

Religious Institutions

Government

United Nations

Big Companies

Police

Press

Television

Religious institutions

Government

United Nations

Political Parties

Real Life Data

www.ExperimentsAtSchool.ntu.ac.uk

Real Life Data

www.ExperimentsAtSchool.ntu.ac.uk

Real Life Data

Simulations and sampling

Our New Dynamic Datatool

To enable each learner to investigate and interrogate the data

Coming soon :-

The Datatool

Two Questions
• How can we encourage mathematics teachers to make their statistics/data handling lessons more real and relevant for children?
• How can we spread the word about the freely available resources out there to help them to use the PSA rather than teach techniques in isolation which is boring and irrelevant for both the teachers and pupils?
Real Life Data

Teaching Data Handling and Probability

• Teachers are the people who need to bring statistical literacy to learners to prepare them to enter society
• Do we challenge people’s idiosyncratic and partial understanding?
• Some places for more reading….
Real Life Data

Teaching Data Handling

• Keep it fun
• Keep it real
• Keep it at their level