King’s PGCE Maths

Constructing a statistics project

Chris Olley

Reading

Graham, A. (2005)

Developing thinking in Statistics,

London: Paul Chapman Ch 2, 3, 6 ,7

Brainstorm (10 mins)

• In your group write down (in the top 2/3 of your page) all of the things you need to include in studying Statistics in a maths GCSE.

• In the bottom third of your page, add additional items needed for A level.

Statistics

• Without data, all you are is just another

person with an opinion. Unknown

• Data is a lot like humans: It is born. Matures. Gets married to other data, divorced. Gets old. One thing that it doesn't do is die. It has to be killed. Arthur Miller

• There are three kinds of lies: lies, damn lies, and statistics. Benjamin Disraeli

Processing and Representing Data

Interpreting and Discussing Results

• Collecting Data

The Data Handling Cycle

Specifying the Problem and Planning

This is … Mathematical Modelling

Statistical AnalysisWhich analyses are open to you?

• Centrality and dispersion• Mean, mode, median• Range, IQR, standard deviation• Box and whisker

• Correlation and regression• Correlation coefficient• Coefficients of linear regression• Scatter plot

The Project1. Hypothesis (amenable to

analysis)2. Indicator → Measure3. Data: bias, sample size,

sampling4. Analysis: using statistics

to support the acceptance or rejection of the hypothesis

5. Report: charts and graphs to assist the presentation

6. Critique

Map (15 mins)Construct one of two maps showing the mathematical elements for statistics (based on GCSE maths requirements)

– Statistical analysis with one variable statistics

– Statistical analysis with two variable statistics

Project (1-var): Fitness

Hypothesis: in this group … the women are fitter than the men.

1. Hypothesis (amenable to analysis)

2. Indicator → Measure3. Data: bias, sample size,

sampling4. Analysis: using statistics to

support the acceptance or rejection of the hypothesis

5. Report: charts and graphs to assist the presentation

6. Critique

Project (2-var): Shoes and Feet

Hypothesis: there is a functional relationship between shoe size and handspan.

1. Hypothesis (amenable to analysis)

2. Indicator → Measure3. Data: bias, sample size,

sampling4. Analysis: using statistics to

support the acceptance or rejection of the hypothesis

5. Report: charts and graphs to assist the presentation

6. Critique

Narrative (15 mins)

In your group:• Sketch out the story you will tell in a

teaching sequence on (either one-variable or two variable) statistics.

• Create a sequence plan table of your map for teaching purposes (narrative) with lesson titles (approx. 6 lessons)

• Each group member prepare detailed lesson objectives.

Orientation

• Cognitive Conflict– Mean, median or mode?– Range, IQR or SD?

• The ‘Our Class’ project …• A summary statistic is representative

(human charts, medians, …)• Which data set could be represented by

this (mean and range, median and IQR, …)

Orientation: Activity (45 mins)

In two subgroups per table:

1. Devise the classroom activities to orient students to the objectives for one lesson in your plan.

2. Sketch out the materials needed to support it.

3. Share your activities with the other half of your group and choose one (set) to share with the whole group.