Building Math Power: Content-Based Professional Development

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 2 x 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 Effective Mathematics Teacher Pedagogy Best Practices

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”

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