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Probability and Statistics Theme. MAA PREP Workshop July 10 th 2003 Maria G. Fung. NCTM Probability and Statistics Highlights. Collect, organize, and display data Use appropriate statistical methods to analyze data Develop inferences and predictions that are based on data

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Probability and Statistics Theme

MAA PREP Workshop

July 10th 2003

Maria G. Fung

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NCTM Probability and Statistics Highlights

  • Collect, organize, and display data

  • Use appropriate statistical methods to analyze data

  • Develop inferences and predictions that are based on data

  • Understand and apply basic concepts of probability

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Probability and Statistics at WOU

  • Foundational Probability and Statistics

    • Statistics Collecting and Graphing Data Describing and Analyzing Data Sampling, Predictions, and Simulation

    • Probability

      Single-Stage Experiments Multistage Experiments

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Advanced Probability and Statistics for K-8 Teachers

  • Explores the above topics in more depth

  • Includes a lab component using Fathom

  • Centers about activities that model probability and statistics instruction in the K-8 classroom

  • Allows students to consider real data

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Checkerboard Games Activities

  • Introduction to or illustration of experimental probability

  • Predictions made and recorded

  • Discussion of results

  • Student-suggested limitations:

    • small sample

    • “fair”? dice

    • time constraints

  • Simulation in Fathom

  • Connections to other topics: binomial distributions, normal curve, Pascal’s triangle

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The Good, the Bad, and the Ugly

  • Modeled after a Sergio Leone’s Western

  • Duel continued until one is left un-hit

  • Shooting continued in the order Ugly-Good-Bad after a hit

  • Whole class discussion of Ugly’s best strategy

  • Simulation strategies considered

  • Geometric series analysis not necessary

  • Area probability models shown

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Design You Own

  • Work on creating an activity or lesson plans centered around probability theory

  • Use the provided materials in your Resource Notebooks or any ideas of your own

  • Make a poster or a presentation of your work to be shared with the group

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Fathom Activities

  • Rowers’ Weights: exercise on looking at data and median/mean resistance

  • Women Senators: categorical variables and their graphical interpretations

  • Televisions and Life Expectancy: correlation is not the same as causality; least square line

  • Boy and Girl Births: binomial distribution simulation

  • Coin Ages: Sampling and a lead into the Central Limit Theorem

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Design or Adapt a Fathom Activity

  • Use the files on your disk or create your own data with Fathom

  • Write a lab exercise or activity or exploration

  • Share your work with the group

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Statistics Assessment

  • Statistics Labs (√-, √, √+)

  • Statistics Journals (e.g. reflections on “How to Lie with Statistics”, reports on NCTM Materials)

  • Statistics Homework (using POW’s format)

  • Exams (with an emphasis on conceptual understanding and not computations)

  • Final Project