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 Understand and apply basic concepts of probability

Probability and Statistics at WOU Foundational Probability and Statistics Statistics Collecting and Graphing Data Describing and Analyzing Data Sampling, Predictions, and Simulation Statistics Collecting and Graphing Data Describing and Analyzing Data Sampling, Predictions, and Simulation Probability Probability Single-Stage Experiments Multistage Experiments

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

Checkerboard Games Activities Introduction to or illustration of experimental probability Predictions made and recorded Discussion of results Student-suggested limitations: small sample small sample “fair”? dice “fair”? dice time constraints time constraints Simulation in Fathom Connections to other topics: binomial distributions, normal curve, Pascal’s triangle

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

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

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

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

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