1. Chromatic Mathematics! Using Color to Create Meaningful Links Between Representations NWMC 2014 Mini-Course Krista Strand University of Oregon Portland State University

2. Introductions

3. Motivation for this mini-course

4. I believe that math is most powerful when it is grounded in sense-making.

5. Motivation for this mini-course I believe that math is most powerful when it is grounded in sense-making. Using colors in a mathematically meaningful way is something I encourage my students to use.

6. Motivation for this mini-course I believe that math is most powerful when it is grounded in sense-making. Using colors in a mathematically meaningful way is something I encourage my students to use. Last year, one student really ran with it!

7. Plan for the Morning 9:00 [introductions, etc.] 9:15 Introduction & looking at examples 9:45 Digging into the math: colorful creations of our own [Break 10:30-10:45] 11:30 Sharing ideas for applying this to Grades 3-6 classrooms

8. Plan for the morning

9. I: Examples and introduction to the overall idea

10. Plan for the morning I: Examples and introduction to the overall idea II: Digging into the math: colorful creations of our own

11. Plan for the morning I: Examples and introduction to the overall idea II: Digging into the math: colorful creations of our own III: Considering ideas for bringing this into the classroom

12. An example

13. Think Time: What do you notice when comparing the black & white version to the color version? Write down your ideas.

14. An example Think Time: What do you notice when comparing the black & white version to the color version? Write down your ideas. Partner Sharing: What did you notice?

15. What is a representation?

16. A way of expressing a mathematical idea or strategy.

17. What is a representation? Mathematical Symbols (2 + 3 = 5) Mathematical Symbols (2 + 3 = 5) Drawings or Pictures A way of expressing a mathematical idea or strategy. Diagram Number Line Words (spoken or written)

18. Linking representations Mathematical Symbols (2 + 3 = 5) Mathematical Symbols (2 + 3 = 5) Drawings or Pictures Diagram Number Line Words (spoken or written) Lesh, Cramer, Doerr, Post, & Zawojewski, 2003

19. Linking representations Linking representations consists of “…explicitness about how two or more representations are related (e.g, pointing to specific areas of correspondence)” Learning Mathematics for Teaching, 2011

20. How?

21. Pointing and talking

22. How? Pointing and talking Drawing circles and/or arrows

23. How? Pointing and talking Drawing circles and/or arrows Using colors

24. How? Pointing and talking Drawing circles and/or arrows Using colors Possible advantages: More visually “permanent” than pointing/talking Possibly less cluttered than circles/arrows Specific points of correspondence are quickly identifiable.

25. More examples

26. Let’s do some mathematical coloring of our own

27. Incorporating this into our teaching?

28. Instruction as Interaction Teacher Students Mathematical Content Cohen, Raudenbush & Ball (2003)

29. Incorporating this into our teaching? Teacher Students Mathematical Content Use color in teacher explanations to the whole class Use color in the Teacher’s Guide to remember important mathematical connections “Coloring” prompts on written tasks Encouraging meaningful color in students’ posters Highlighting connections on students’ work that is on the board or a poster. Formative Assessment

30. Thank you for coming! Krista Strand kstrand@uoregon.edu