Selecting an activity
As we did in Week 1, we are going to finish this week by asking you to plan, teach and report back on a teaching activity, this time involving conditional probability.
You can start with the ‘Dog ate my homework’ activity as we have described it - it is a tried and tested approach that we have used successfully in a wide range of classrooms. If you have an alternative activity that you are keen to try, then we would like to hear about that as well.
Before you plan your lesson, it is worth thinking about how the material that we have presented here can be applied to other settings. We emphasised the importance of some key questions, which are essentially these:
- What is the probability that a guilty person is accused?
- What is the probability that an accused person is guilty?
This kind of question arises in a range of interesting real-life situations. Consider this scenario:
A particular medical condition is known to affect one in 1000 of the general population. A new test has been developed to screen for the condition.
- The test always gives a positive or negative result.
- The test will correctly give a positive result for 99% of people who have the condition
- The test will give an incorrect positive result for 2% of people who do not have the condition
This scenario has exactly the same mathematical structure as ‘The dog ate my homework’. Some key questions are:
- What is the probability that a person with the condition receives a positive test result?
- What is the probability that a person who receives a positive test result actually has the condition?
- What is the probability that a person who receives a negative test result actually has the condition?
The answers are interesting - we already know that the probability of someone with the condition receiving a positive result is 99%, but less obviously:
- The probability that someone with a positive result actually has the condition is less than 5%
- The chances that someone who is given the all-clear turns out to actually have the condition, are about 1 in 100 000.
Tempting though it is, we would offer the following words of caution before exploring this alternative scenario.
- Firstly, any medical scenario obviously needs to be handled with sensitivity - our ‘Dog ate my homework’ setting is deliberately light-hearted, and should not lead to any difficulties.
- In terms of practicalities, ‘The dog ate my homework’ has been carefully planned so that the data collection exercise will give usable results. Testing for rare medical conditions is difficult or impossible to model using the system of spinners and cubes that we have described!
For these reasons, we suggest starting with a more controlled (if somewhat artificial) scenario like ‘The dog ate my homework’. More realistic scenarios involving rarer events can be tackled in more advanced work, perhaps using a spreadsheet model to generate data.
In the next step, you will have the opportunity to tell us about a lesson you plan and teach using some of this week’s ideas.
- What are the main ideas that you are keen to try?