1. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006 OSPI Mathematics  Mathematics is a language and science of patterns  Mathematical content (EALR 1) must be embedded in the mathematical processes (EALRs 2-5)  For all students to learn significant mathematics, content must be taught and assessed in meaningful situations

2. Mathematics Initiative Office of Superintendent of Public Instruction WERA 2006 12-7-2006 Data to Display: Graphs Tell a Story WERA, December 7, 2006 Karen Hall, OSPI Mathematics Initiative Specialist

3. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006 Weather Story

4. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006 Why do we care? A numerate person should be able to  interpret data presented in graphical form  reason with data  evaluate the soundness of conclusions based on data  draw conclusions/support with data.

5. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006 CU02 (Organize, Represent, and Share Information)  (4.2.1, 4.2.2, 4.2.3) PS03 (Data Representation and Interpretation) and Interpretation)  (1.4.5, 1.4.6)

6. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006 Student Weakness- Graphs  Drawing graphs is usually satisfactory. Students have difficulty interpreting information from graph.  Students have difficulty knowing when to use which type of graph.

7. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006 Graphs we will examine  Bar graph  Line graph  Scatter plot  Connected Scatter plot

8. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006 Components of a graph  titles  labels  appropriate and consistent scales  an accurate data display

9. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006 Comparison of Categories Frequency Plots of categorical data:  Bar Graph (categories are attributes or numbers)  Line Graph (categories are time intervals of equal value)

10. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006 Categorical Data: Non-numerical

11. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006 Categorical Data: Equal Time Intervals

12. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006 Categorical Data: Equal Time Intervals

13. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006 Categorical Data: Equal Time Intervals

14. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006 CAUTION: Looks like a scatter plot when months treated as numbers by EXCEL

15. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006 Voting Methods 1980 to 2006

16. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006 Date from Continuous set of Numbers  Scatter plot  Connected Scatter Plot

17. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006

18. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006 Scatter Plot with line of regression www.isteve.com/BabyGap-scatterplot2-WV-fixed.gif

19. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006

20. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006 Connected scatter plot

21. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006

22. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006 Research on “Student thinking about data”  Experts look at data as a collection or aggregate  Students new to the study of data look at data as individual cases or subgroups of individuals. They tend not to see aggregate features. Chapter 13, NCTM Research Companion to Principles and Standards for School Mathematics

23. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006 Look at student work.

24. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006 Improve Student Performance Create opportunities to  Explore meaningful data sets  Use student’s intuitive approach  Explore scale and interval width  Draw conclusion and then support it with data from student’s data set

25. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006 Exploring Data Sets  Understand the context of data  Make a hypothesis about what data might show  Investigate their hypothesis  Choose type of graph to display their data  Make conclusion supported by data  Make conjectures for additional studies

26. Mathematics Initiative Office of Superintendent of Public InstructionWERA12-7-2006Resources  Miller, Jane E, The Chicago Guide to Writing About Numbers, Univ. Chicago Press, 2004  Tufte, Edward R., The VIsual Display of Information, Graphics Press, 2001  Curcio, Frances R., Developing Graph Comprehension, NCTM, 1989  Tinker Plots, Key Curriculum Press