1. M ATHEMATICS E DUCATION L EADERSHIP T RAINING : “ MEASUREMENT & S TATISTICS : 6-8” Carmen Wilson, Ashe County HS carmen.Wilson@ashe.k12.nc.us June 22-26, 2015

2. “S ELECTING & C REATING M ATHEMATICAL T ASKS ”

3. In 1972, 48 male bank supervisors were each given the same personnel file and asked to judge whether the person should be promoted to a branch manager…The files were identical except that half of them showed that the file was that of a female and half showed that the file was that of a male. Of the 24 “male” files, 21 were recommended for promotion. Of the 24 “female” files, 14 were recommended for promotion. (B. Rosen & T.Jerdee (1974). “Influence of sex role stereotypes on personnel decisions”, Journal of Applied Psychology;59:9-14.)

4. What is Random?

5. Jelly Blubbers!

6. 3 second glance:

7. Pick 10: NumberDiameter (mm)

8. 3 second glance: Pick 10:

9. Simple Random Sample of 10: NumberDiameter (mm)

10. 3 second glance: Pick 10: SRS of 10:

11. Yesterday, we discussed measurement bias. Today, we see that there can also Be sampling bias. Let’s watch a clip from the past… (Moore, D. Decisions Through Data (1993). COMAP)

12. Types of Samples: Convenience Sample Voluntary Response Sample Systematic Random Sample Simple Random Sample Stratified Random Sample Cluster Sample Multi-Stage Sample

13. Can you identify any possible sources for bias here? A marketing research company was asked to Determine how much money teenagers Spend on recorded music. The company Randomly selected 80 malls around the Country. A field researcher stood in a Central location in the mall and asked Passers-by who appeared to be teens to fill Out a questionnaire. Based on 2050 Completed questionnaires, the company Reported the average amount spent to be $255 per teen per year.

14. Jelly Blubbers is like the Random Rectangles activity…

15. Heads or Tails?

16. Some Simulation Sites: http://www.shodor.org/interactivate/activities/Coin / https://www.random.org/coins/ http://mathforum.org/mathtools/cell/m4,6.14,ALL,A LL/ http://www.shodor.org/interactivate/activities/Coin / https://www.random.org/coins/ http://mathforum.org/mathtools/cell/m4,6.14,ALL,A LL/

17. Mystery Dice: What’s in the Bag?

18. How do we calculate theoretical probabilities ?

19. Experiment 4 from Probability Activities by Key Curriculum Press:

20. A more challenging problem… (from AP Statistics 2009B Free Response #2, College Board)

21. A RE YOU STILL THINKING ABOUT WHETHER THOSE WOMEN WERE VICTIMS OF DISCRIMINATION ?

22. In 1972, 48 male bank supervisors were each given the same personnel file and asked to judge whether the person should be promoted to a branch manager…The files were identical except that half of them showed that the file was that of a female and half showed that the file was that of a male. Of the 24 “male” files, 21 were recommended for promotion. Of the 24 “female” files, 14 were recommended for promotion. (B. Rosen & T.Jerdee (1974). “Influence of sex role stereotypes on personnel decisions”, Journal of Applied Psychology;59:9-14.)

23. Let’s keep playing… How about a game of Greedy Pig? RoundPoints 1 2 3 4 5 TOTAL

24. Chuck-A-Luck A player chooses a number from 1 to 6. Three dice are rolled. If the player’s number appears… 3 times – win $3 2 times – win $2 1 time – win $1 0 times – lose $1

25. What could you EXPECT to happen if you played Chuck-A-Luck MANY TIMES? Justify your answer.

26. Some “classic” counting problems: The Birthday problem…

27. Playing the Lottery… Pick 6/49

28. In 1972, 48 male bank supervisors were each given the same personnel file and asked to judge whether the person should be promoted to a branch manager…The files were identical except that half of them showed that the file was that of a female and half showed that the file was that of a male. Of the 24 “male” files, 21 were recommended for promotion. Of the 24 “female” files, 14 were recommended for promotion. (B. Rosen & T.Jerdee (1974). “Influence of sex role stereotypes on personnel decisions”, Journal of Applied Psychology;59:9-14.)

29. Student Misconceptions…

30. “Both Answers Make Sense!” Lockwood, E. (2014) Mathematics Teacher. Vol. 108, No. 4, 297-299.

31. For a more in-depth explanation: http://combinatorialthinking.com/ http://combinatorialthinking.com/

32. Time for Reflection…

33. Classwork/Homework EXIT Ticket For Tonight: Read “Orchestrating Discussions” For Friday: Prepare to Share

34. Bibliography for Tuesday: Burrill, G., Franklin, C., Godbold, L., Young, L. (2003). Random Rectangles. Navigating through Data Analysis in Grades 9-12. Reston: NCTM. Crites, T. & St. Laurent, R. (2015). Putting Essential Understanding of Statistics into Practice in Grades 9-12. Reston: NCTM. Foley, G. (2009). QUANT (Quantifying Uncertainty & Analyzing Numerical Trends. Columbus: Ohio Resource Center. Lockwood, E. (2014) Mathematics Teacher. Vol. 108, No. 4, 297-299.

35. Lovell, R. (1993). Probability Activities For Problem Solving & Skills Reinforcement. Berkely: Key Curriculum Press. Moore, D. (1993). Decisions Through Data. DVD. COMAP. Moore, D. (2005). “Jelly Blubbers Activity”. Statistics, Concepts and Controversies, 4 th Edition. New York: W. H. Freeman. Scheaffer, R. (1996). Activity Based Statistics. New York: Springer-Verlag.

36. Smith, M., Hughes, E., Engle, R. & Stein M. “Orches- trating Discussions”. (2009). Mathematics Teaching in the Middle School, Vol. 14, No. 9, 548-556. Smith, M. & Stein, M. “Selecting and Creating Mathematical Tasks: From Research to Practice”. (1998). Mathematics Teaching in the Middle School, Vol. 3, No. 5, 344-349.