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Tanks, Planes, and UNICEF

Tanks, Planes, and UNICEF. Math Olympiad 2011 Northwest Missouri State University Neil Hatfield. Reasoning and Sense Making with Data Analysis. Statistical Problem Solving. Formulating a question (questions) that can be addressed with data.

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Tanks, Planes, and UNICEF

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  1. Tanks, Planes, and UNICEF Math Olympiad 2011 Northwest Missouri State University Neil Hatfield Reasoning and Sense Making with Data Analysis

  2. Statistical Problem Solving • Formulating a question (questions) that can be addressed with data. • Designing and employing a plan for data collection. • Analyzing and summarizing that data. • Interpreting the results from the analysis, and answering the question(s) on the basis of the data. • NCTM (2000) and Guidelines for Assessment and Instruction in Statistics Education (2007)

  3. Reasoning and Sense Making • Common Thread: Focus on making sense of and reasoning about the variation in data. • “Why is our data not all the same?” • Data Analysis • Modeling Variability • Connecting Statistics and Probability • Interpreting Designed Statistical Studies

  4. Data Analysis • Gaining insight about a solution to a statistics question by • Collecting Data • Describing Features of the Data • Using Graphical and Tabular Representations • Numerical Summaries

  5. Modeling Variability • Developing probability models to describe the long-run behavior of observations of a random variable. • The design and implementation of a simulation provides transitional steps in the development of reasonable mathematical models for describing the long-run behavior of a random variable.

  6. Connecting Statistics and Probability • By incorporating randomness, probability provides a way to make sense of the variation in the sample. • Sampling distribution of a sample statistic summarizes the long-run behavior of the statistic from repeated random sampling. • Sampling distributions make crucial links among data analysis, probability, and inferential reasoning in statistics.

  7. Connecting Statistics and Probability

  8. Interpreting Designed Statistical Studies • Students should understand that the scope of inference for a study is related to the manner in which the data are collected. • Sampling distributions offer a way to quantify the uncertainty associated with statistical inference. • The reasoning employed in statistical inference is often quite difficult for students • Using a simulation to create a sampling distribution offers an intuitive way to help students develop this reasoning.

  9. Three Activities • Tanks: How Statistics Won World War II • Variation of the famous World War II German Tank Problem. • Planes: Where to Put the Armor? • World War II British Bombers (Operations Research) • UNICEF: What Does It Show? • Deceptive Statistics

  10. TanksHow Statistics Won World War II • Formulating a question or questions: • Done for the students, initially; homework • Designing and Employing a plan for data collection. • Data Analysis—drawing random samples • Analyzing and summarizing the data. • Data Analysis—finding statistics • Modeling Variability—determining variance • Interpreting the results from the analysis. • Connecting Statistics and Probability—randomness, simulation, bias • Interpreting Studies—how to choose a good estimator

  11. PlanesWhere to Put the Armor? • Formulating a question or questions: • Question Analysis—is it really the right question? • Designing and Employing a plan for data collection. • Data Analysis—collecting the right data, biased data • Analyzing and summarizing the data. • Data Analysis—finding statistics • Modeling Variability—determining variance • Interpreting the results from the analysis. • Connecting Statistics and Probability—simulation, biased data • Interpreting Studies—answering the question with the right data

  12. UNICEFWhat Does It Show? • Formulating a question or questions: • Question Analysis—What is the question? • Designing and Employing a plan for data collection. • Data Analysis—Where did they get their data? • Analyzing and summarizing the data. • Data Analysis—What do their summaries really tell us? • Data Analysis—What are graphs really honest? • Interpreting the results from the analysis. • Interpreting Studies—Does the data support what they said?

  13. Purpose • Reasoning and Sense Making • Data Analysis • Get students to think critically about the world around them.

  14. Materials • Like what you’ve seen? • You can download all the materials from my website: • You may also email me at S267115@nwmissouri.edu http://catpages.nwmissouri.edu/s/15/s267115/presentations.html

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