1. Building Math Power: Content-Based Professional Development Integrating Mathematics and Pedagogy to Maximize Teacher Effectiveness Kimberly Rimbey, NBCT, M.Ed. Peggy Akin, author

2. Why are we here? True stories… 5th Grade Class… 4 + 8 = 1 + 11 1st Grade Teacher… 6th Grade Teacher…

3. So why are we here? Concurrent content & pedagogy development Tools for teachers as learners: –Provide/develop classroom activities –Use pedagogy-rich mathematics curriculum –Model best practices and good pedagogy for the adults as learners Writing mathematical ideas Discourse Cooperative learning

4. Outcomes for Session What mathematics content do elementary teachers need? (discuss) What pedagogy and best practices skills do elementary teachers need? (discuss) If we know both of these… How can professional development be designed to develop both content and pedagogy? (look at one model)

5. Relevant Research According to D. Ball (2005), teachers need Common content knowledge (WHAT & HOW) Specialized content knowledge (WHY) Knowledge of content and students (PEDAGOGY) Knowledge of teaching and curriculum (PEDAGOGY & BEST PRACTICES)

6. Relevant Research According to D. Ball (2003), what mathematical problems arise in teaching? Analyzing errors Giving and evaluating explanations Appraising unexpected claims, solutions, methods

7. Unexpected Method 1 2 2x 2 = 4

8. Relevant Research According to D. Ball (2003), what mathematical problems arise in teaching? Analyzing errors Giving and evaluating explanations Appraising unexpected claims, solutions, methods Choosing and using representations Investigating correspondences among representations and solutions

9. Solutions & Representations 2 x 5 = 10 11 x 11111 = 1111111111

10. Relevant Research According to D. Ball (2003), what mathematical problems arise in teaching? Analyzing errors Giving and evaluating explanations Appraising unexpected claims, solutions, methods Choosing and using representations Investigating correspondences among representations and solutions Choosing and using definitions Interpreting and responding to students’ ideas

11. Relevant Research D. Ball, 2003

12. Common vs. Specific Knowledge Subtraction with Regrouping… Common Knowledge - HOW to subtract (usually understood as an algorithm using “borrowing”) Specific Knowledge - the concept behind the subtraction - understanding the WHY’s as well as alternative algorithms

13. Active Participation Time… What are some common misperceptions among elementary teachers (think about both common & specific knowledge)? –Number Sense –Operations –Patterns, Algebra, & Functions –Geometry & Measurement –Process Standards (CPR’s) Think of 1 and write down Round Robin - share at table

14. Getting to the heart of content Go beyond fun activities Go beyond elementary content Look at middle/high school curriculums Teach the general content with an easy- to-see path to the specific content I planned to write my own curriculum…

15. I wanted something that… Tempers bad feelings about high school/college mathematics experiences Builds on prior knowledge Deals with sound mathematics Focuses on the big ideas of mathematics Is activity based Has best practices built in Develops critical and creative thinking Develops understanding through guided discovery Teaches to the whole [child]

16. Then I found

17. Planning for the Course Generate Lists Content (strands, concepts, PO’s) Best Practices/Pedagogy Strategies Content Lessons Grade-Level Lessons Classroom Materials

19. Best Practices (Marzano) What teaching techniques must be implemented? Work & study habits Big ideas & essential questions Identifying similarities and differences Reinforcing effort & providing recognition Homework & Practice Nonlinguistic representations Setting objectives & providing feedback Cues, questions & advanced organizers

20. Good Pedagogy Strategies What should teachers be able to do? Develop vocabulary Analyze errors Use cooperative roles & structures Implement good questioning strategies Encourage writing across the curriculum Represent ideas (manipulatives, pictures, symbols) Relate to real life

21. Putting the Pieces Together Content Pedagogy Best Practices Effective Mathematics Teacher

22. Case Study…Functions 24 second and third grade teachers Beforehand - –1 could define a function –1 could relate a function to graphic representations –0 could identify a real-life situation that could be represented by a functional relationship Afterward - –24 “light bulbs” went off when introduced to the “function machine” and how it related to equations –23 gasps when the function table was graphed on a coordinate grid

23. Tools Pedagogy-Rich Mathematics Curriculum –Building Math Power by Peg Akin Provide/develop classroom activities –Video –On-Level Lessons –Teaching Student-Centered Mathematics by John Van De Walle

24. Tools (cont.) Model Pedagogy & Best Practices for teachers as learners (during delivery of content & activities) Used cooperative structures –Round Robin sharing during “pre-test” –Assigned roles & structure for reading –Groups were looser when doing content work - asked quicker participants to hold comments Representing ideas Incorporating structured discourse Developing vocabulary Using technology (video clip)

25. Active Participation Time… Take a look at the 4th paper in the BMP handout (second 17) Take a look at the 3rd paper from the back (25)

26. Video & Lesson Teachers need to SEE this in action –Live is best (as with “Lesson Study” format) –Video is sufficient Functions Video Sample lessons modeled and extended with teachers

27. Active Participation Time… View first 3 min. of “The Function Machine” lesson (first page after outline) Try out the “Object Functions” lesson Biggest “aha” of the day… “Graphing Functions” lesson from the t-tables (geometry PO)

28. Student Work

29. “Graphing Functions” InsectsWings 12 24 36 48 510

30. Evidence of Success In order to determine your effectiveness Teacher pre-post tests (content) Surveys before and after (pedagogy, best practices, & attitudes) Anecdotal records (reflective as learners & as teachers) Student assessments ***Difficulty - determining exactly what impacted student learning unless using a control group

31. Outcomes for Session What mathematics content do elementary teachers need? (discuss) What pedagogy and best practices skills do elementary teachers need? (discuss) If we know both of these… How can professional development be designed to develop both content and pedagogy? (look at one model)

32. In Closing… Tools –Use pedagogy-rich content materials –Provide or allow time to develop classroom activities –Model best practices –Let them SEE it in action One more story…kindergarten teacher…

33. Contacts Kimberly Rimbey, Creative Learning Specialists mathspec@cox.net www.geocities.com/kimrimbey/index.html 623-261-2199 Peg Akin, Building Math Power pegakin@mindspring.com www.buildingmathpower.com 623-8455-6923