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Evaluating Statements about Probability
Before the
  • Assessment Task: Are They Correct? (15 minutes)
    • Set this task, in class or for homework, a few days before the formative assessment lesson. This will give you an opportunity to assess the work. You will then be able to find out the kinds of difficulties students have with it. You will then be able to target your help more effectively in the follow-up lesson.

      • Give out the assessment task, Are They Correct?.
      • Briefly introduce the task and help the class to understand each problem.
        • Read through each statement, and make sure you understand it.
        • Try to answer each question as carefully as you can.
        • Show all your work so that I can understand your reasoning.

      It is important that, as far as possible, students are allowed to answer the questions without your assistance.

      Students should not worry too much if they cannot understand or do everything, because in the next lesson they will engage in a similar task, which should help them. Explain to students that by the end of the next lesson, they should expect to answer questions such as these confidently. This is their goal.

  • Assessing Students' Responses
    • Collect students' responses to the task. Make some notes on what their work reveals about their current levels of understanding and their different problem solving approaches.

      We suggest that you do not score students' work. The research shows that this will be counterproductive, as it will encourage students to compare their scores, and will distract their attention from what they can do to improve their mathematics.

      Instead, help students to make further progress by summarizing their difficulties as a series of questions. Some suggestions for these are given on the next page. These have been drawn from common difficulties observed in trials of this unit.

      We suggest that you write a list of your own questions, based on your students' work, using the ideas that follow. You may choose to write questions on each student’s work. If you do not have time to do this, select a few questions that will be of help to the majority of students. These can be written on the board at the end of the lesson.

      Common Issues: Suggested Questions and Prompts:

      Q1. Student assumes that both outcomes are equally likely.

      • What factors affect whether it will rain tomorrow?
      • What does a probability of 0.5 mean?

      Q2. Student assumes that later random events "compensate" for earlier ones.

      • For example: The student argues that if there are already four boys in the family, the next is likely to be a girl.
      • What is the probability that the baby will be a girl?
      • Does the fact that there are already four boys in the family affect the sex of the next child?

      Q3. Student relies on their own experience.

      • For example: The student states they have never thrown four sixes in a row.
      • Is it more difficult to throw a six than a two?
      • Is it more difficult to throw a six, then another six or a two, then a three?
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