Probability and Statistics

1. Probability and Statistics ECI 695 February 26, 2009 Day 7

2. Week 7 Agenda • Project 1: Turn in tonight • Return Focus Questions 1 • Analysis of “Blue Crab” data • Reading: NCTM Yearbook Chapters 1 and 2 • Math Activity: Stem and Leaf Plots • Reading: The Power of Representation: Graphs and Glyphs • DMI Chapter 5

3. Focus questions chapter 4

4. “Ten best Homeworks” • Homework is self-graded • Ten points per week • Accumulate your best ten • Submit grade at end of course

5. The Blue Crab

6. Eastern Shore Black 2 Blue 8 Green 16 Orange 8 Pink 0 Red 2 Yellow 3 White 12 Portsmouth Black 10 Blue 12 Green 3 Orange 9 Pink 2 Red 7 Yellow 1 White 6 Blue Crab Data: Sample

7. Eastern Shore Black 5 Blue 6 Green 4 Orange 6 Pink 2 Red 5 Yellow 1 White 4 Portsmouth Black 2 Blue 6 Green 8 Orange 4 Pink 1 Red 2 Yellow 2 White 8 Blue Crab Data: Actual

8. Blue Crab Data • Spreadsheet

9. YEARBOOK CHAPTER 1

11. GRAPHING WITH FOUR-YEAR-OLDS Yearbook Chapter 1

12. Emerging Mathematical Abilities • Comprehending one-to-one correspondence • Understanding set membership • Retrieving information • Creating order

13. Goal • Support children’s use of mathematical reasoning as they move from collecting to interpreting data.

14. Professional Development • What are children capable of doing? • How do you talk with young children?

15. Graphing through surveys Advantages: • Familiar activities • Interesting to children • Opportunities for mathematical reasoning • Cross-content areas

16. Harold’s Survey

17. Harold’s Accomplishments • Posed his own question • Demonstrated 1-to-1 correspondence • Displayed several levels of info • Invented symbols • Solved a problem (no answer) • Sought validity • Organized his recordings into groups

18. Intention vs. Convention • “Just because a child’s product may look unconventional on the surface, it does not mean that it lacks intention.”

19. Concerns • Graphs must conform to standard formats • Children must be shown “how” • Lack of confidence in their ability to collect and organize data • Fear of how to talk with children about their ideas

20. Survey by “S.”

21. L: Classroom Centers

22. J: Community Workers

23. YEARBOOK CHAPTER 2

25. WHAT DOES IT MEAN THAT“FIVE HAS A LOT?” Yearbook Chapter 2

26. From the World to Data and Back • Changes over time

27. Mittens

28. 2nd Graders: Pockets

29. Upper Elementary:Summarizing and Comparing • Data as “aggregate” (Konold) • Shape, spread, concentration • Mean and standard deviation; median and quartiles • Median: elementary • Mean: middle school

30. Transitioning • Mode • Clumps • Measures of Central Tendency

31. Clusters (5th graders)

32. Recommendations • Have students develop representations • Meaning of symbols • Compare groups • Look for concentrations • Ask for descriptions of the clumps

33. Math activity:Stem and leaf plots

34. Consider this jump-rope data collected from two school classes. Which class did better overall?

35. Number of Jumps

37. Which class did better? • Eastern Shore: Ms. R • Portsmouth: Mr. S

38. Baseball data

39. Home Run Leaders, 1921-2001

41. Which league is better?

42. Home Run Leaders: Homework • Locate data for the years 2002-2008 • Add these numbers to the stem and leaf plot • Does this affect the comparison between leagues?

43. Home Run Leaders: Homework • Create a joint stem and leaf plot for the years 1983-1995 and 1996-2008 • Combine the American League and National League data for this comparison • How do the “early years” compare with the “later years?”

44. DMI CHAPTER 5

45. DMI CHAPTER 6

46. Math ActivityBox Plots

47. Box plotsinauguration age data

48. What do you think? • How old are presidents and vice presidents at the time of their inauguration?

49. Box plots: Inauguration age data (Does not include 21st century elections)

50. Ages of Presidents