king’s pgce maths constructing a statistics project chris olley
TRANSCRIPT
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.