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Teaching Strategies to Make Statistics Concepts Meaningful

Teaching Strategies to Make Statistics Concepts Meaningful. Georgia Mathematics Conference October 18, 2012 Dianna Spence Gregg Velatini North Georgia College & State University This work supported by grants NSF DUE-0633264 and NSF DUE-1021584. What’s In Store. Sample Learning Tasks

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Teaching Strategies to Make Statistics Concepts Meaningful

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  1. Teaching Strategies to Make Statistics Concepts Meaningful Georgia Mathematics Conference October 18, 2012 Dianna Spence Gregg Velatini North Georgia College & State University This work supported by grants NSF DUE-0633264 and NSF DUE-1021584

  2. What’s In Store • Sample Learning Tasks • ExplorationsExperiencing Statistics Concepts • ProjectsSynthesizing and Applying • Simulations:Establishing Reasoning behind Statistical Inference • CCGPS • Understand and evaluate random processes underlying statistical experiments • Make inferences and justify conclusions from sample surveys, experiments, and observational studies

  3. Explorations: Sampling • “Teacher” request: Please hold questions or ask them privately • Population: All words in the Gettysburg Address • Task: Obtain a representative sample from this population Gettysburg Address

  4. Random Numbers (TI-83/84 Family) • Suggestions • Compare student values for first random number • Press <ENTER> arbitrary number of times to randomize BEFORE starting sample • What about repeats? • Same random number? • Same word?

  5. Typical Student Data BEFORE AFTER 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5

  6. Explorations: Comparing Data • Scenarios • Height • Memorizing letters • Key Ideas • Variable • Observation vs. Experiment • Treatment • Random Assignment • Blind Treatment

  7. Projects Student tasks • Identify research questions • Define suitable variables, including how to quantify and measure variables • Submit project proposal and obtain approval • Collect data • Design unbiased data collection method • Address sampling issues • Analyze and interpret data • Write a report on methods and results • Present research and findings to class

  8. Available Resources • Student Guide • Instructor Guide • Technology Guide • Appendices • A – E: for students and instructors • T1 – T3: for instructors • Available online: http://faculty.northgeorgia.edu/DJSpence/NSF/materials.html

  9. Sources of Data: 3 Categories • Administer surveys • Student constructs a surveyand has people fill it out • Find data on the Internet • Physically go out and record data • e.g., measure items, time eventswith a stopwatch, look at prices, look at nutrition labels

  10. Surveys

  11. Surveys What’s wrong with these? • What religion are you? (circle one) Methodist Baptist Catholic Muslim Jewish • On a scale of 1 to 10, how stressed are you?

  12. Surveys A construct to measure stress Please mark each statement that is true about you. __If I could stop worrying so much, I could accomplish a lot more. __Currently, I have a high level of stress. __In this point in my life I often feel like I am overwhelmed. __I have a lot to do, but I just feel like I can’t get ahead or even sometimes keep up. __I often worry that things won’t turn out like they should. __I have so much going on right now, sometimes I just feel like I want to scream. Score “1” for each checked box. Range is 0 to 6, with higher numbers indicating higher levels of stress.

  13. Surveys Some considerations: • Consider using scales/constructs • e.g., Appendices B,C • Maintain confidentiality • Use anonymous surveys for sensitive data

  14. Internet Data SourcesI. Government/Community • Census Bureau: http://www.census.gov/ • Bureau of Justice Statistics: http://bjs.ojp.usdoj.gov/index.cfm?ty=daa • City Data Site: http://www.city-data.com/ • State and county statistics sites • State and national Dept.’s of Education • County tax assessment records

  15. Internet Data SourcesII. Restaurants: Nutrition Info • Applebees Nutrition Guide • Arby's Nutrition Guide • Burger King Nutrition Guide • IHOP Nutrition Guide • KFC Nutrition Guide • Longhorn Nutrition Guide • McDonald's Nutrition Guide • Olive Garden Nutrition Guide • Ruby Tuesday's Nutrition Guide • Subway Nutrition Guide • Taco Bell Nutrition Guide • GoogleYOUR favorite place to eat!

  16. Internet Data SourcesIII. Sports Data • Sports Statistics Data Resources (Gateway) http://www.amstat.org/sections/SIS/Sports Data Resources/ • General Sports Reference Sitewww.sports-reference.com • NFL Historical Stats: http://www.nfl.com/history • Individual team sites

  17. Internet Data SourcesIV. Retail/Consumer (General) • Cost/Prices • e.g., Kelley Blue Book: http://www.kbb.com/ • Consumer Report ratings .http://www.consumerreports.org/cro/index.htm • Product Specifications • e.g., size measurements,time/speed measurements,MPG for cars

  18. Sample Student Projects(See Appendix D) • Matched Pairs t-Test: • 2-tailed: Ha predicting that on average, students’ rating of Coke and Pepsi would be different. • t statistic =2.62 • P value= 0.0116 (2-tailed) • Conclusion: Evidence that on average, students rated the two drinks differently (Coke was rated higher) Participant Coke Pepsi #1 8 9 #2 7 5 . . .

  19. Sample Student Projects • t-Test for 2 independent samples: • 1-tailed: Ha predicting that on average fruit drinks have higher sugar content per ounce than fruit juices • t statistic = -0.14 • P value= 0.5555 • Conclusion: Sample data did not support Ha. No evidence that on average,fruit drinks have more sugar than fruit juices.

  20. Sample Student Projects • t-Test for 2 independent samples: • 1-tailed: Ha predicting that in local state parks, oak trees have greater circumference than pine trees on average • t statistic = 4.78 • P value= 7.91 x 10 –6 • Conclusion: Strong evidence that in local state parks oak trees are bigger than pine trees on average. • Lurking variable identifiedand discussed: age of trees (and possible reasons that oak trees were older)

  21. Sample Student Projects • Matched Pairs t-Test: • 1-tailed: Ha predicting on average, Wal-Mart prices would be lower than Target prices for identical items • t statistic =.4429 • P value= 0.3294 • Conclusion: Mean price difference not significant; insufficient evidence that Wal-Mart prices are lower. Item WalMart Target 64-oz. Mott’s Juice 2.79 2.89 12-oz LeSeur Peas 1.19 1.08 . . .

  22. Sample Student Projects

  23. Sample Student Projects

  24. Sample Student Projects

  25. Sample Student Projects

  26. Assessment • Weight of projects • Scoring rubrics • Advantages – consistency, manageability, communication of expectations • See Appendix T3 • Team member grades • Accountability of individual members

  27. Simulations • Activities courtesy of materials by Rossman & Chance; see Rossman, Introducing Concepts of Statistical Inference • Scenario #1:Babies’ reactions to mean and nice toyshttp://statweb.calpoly.edu/bchance/applets/BinomDist3/BinomDist.html

  28. Simulations • Activities courtesy of materials by Rossman & Chance; see Rossman, Introducing Concepts of Statistical Inference • Scenario #2:Dolphin therapy for depressionhttp://www.rossmanchance.com/applets/Dolphins/Dolphins.html

  29. Discussion / Q&A

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