That is not a mathematical argument as there is no

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That is not a mathematical argument. As there is no good evidence, it can’t be accepted in court. Once you have modeled this process for students, give them responsibility for deciding whether there is an evidential base for each claim and challenge. Is that a mathematical argument? Is there good evidence for what [Shelley] has just said? Does the evidence support her conclusion? Once students have worked through the four pieces of evidence, ask them to come to a collective decision about the verdict. Do you find the factory owner guilty or not guilty? If there is disagreement, take arguments from both sides. You may find you cannot reach a collective decision. In that case, suggest students send the defendant for a retrial. Whole-class discussion: summing up (5 minutes) Point out that an important message of this lesson is that it is easy to ‘get it wrong’ when interpreting statistics, especially in complicated real-world situations. In reality, most of the ‘evidence’ in this lesson is too vague to draw any firm scientific conclusions. A lot of questions are left unanswered. How, exactly, were the wildlife surveys conducted? Why did the second survey look at so many more fish than the first? How do you ‘count the number of invertebrates’ at a site? The dam has reduced the flow of the river by 80%. Even without the pollution, is it possible that this could affect the wildlife or the popularity of the Riverside Center? Can you see any other problems with the data collection? / with the statistics that have been calculated? If you think it is appropriate to the class, you could mention that if they study statistics further they will learn how to calculate significance : the likelihood that a difference in two results is not just ‘the luck of the draw’. Most serious scientific studies will do this, but you do not often find it in news reports! Follow-up lesson: Unhappy Campers (15 minutes) Give each student a copy of the Unhappy Campers task. Explain that this task uses very similar math to the lessons on river pollution, but in a new context. Help students to read through the task sheet and use questions to help them understand the context: What is a wind turbine? What are they used for? What do decibels measure? How loud is 50 decibels? 30 decibels? [0 decibels is the threshold for human hearing. A whisper in a quiet library is about 25 decibels. Normal conversation at about five feet is around 60 decibels.] Ask students to work on their own on the assessment task, bearing in mind what they have learned during the previous lesson. I want you to work on this task, using those same ideas about a fair, mathematical critique. Remember not to believe all the arguments someone gives you using statistics.
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Teacher guide Interpreting Data: Muddying the Waters T-8 After the assessment, you may find it useful to ask students to compare their responses to the first and second assessment tasks, so they can see the progress they have made.
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