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Counting Fish

I need a figure for the fish population in a lake, how does it help to catch and mark 40 fish ?

Snow and Cholera

Stage: 4 Challenge Level: Challenge Level:1

Why do this problem :

This problem calls for good application of practical reasoning and is a great simple example of the process of making and testing hypotheses.

Possible approach :

Start by discussing epidemics, or Cholera in particular, using the supporting material. The main task is for students to think about what information, recorded in the text, allowed John Snow to recommend a course of action. Explain that John Snow was a pioneer in medicine in London in the 19th century who thought that diseases such as Cholera were water-borne. As news of this outbreak reached him he went quickly to the Broad Street area of London before too many people had fled so that he could ask questions that would help him form a view about the likely cause of the disease. A key concept to draw out as students discuss the task and the context is that a hypothesis is never completely settled. It is more useful to describe it as a process of increased confidence in our account of the situation.

Key question :

  • What is Cholera ?

  • Which information supports the parish Board of Guardian's decision to make the Broad Street pump unusable by removing the pump handle ?

  • Was the decision certain to be correct ?

Possible extension :

Lion Hunting is a similar context but involves a more complex relationship between incidents and the 'centre' or source.

Possible support :

The problem In the Bag takes students to the heart of hypothesis-making in a very simple way : samples, even a large number of samples, never settle the question beyond all doubt, they do however increase confidence in our belief. It ceases to be a hypothesis when we open the bag and reveal the actual contents.

More supporting information about John Snow and the Cholera epidemics, and the Mathematics of Diseases, can be found by following this link .

And this article gives more background on Understanding Hypotheses.