1. Professional Development Focused on Children’s Algebraic Reasoning in Elementary School Research Article Discussion led by Gwenanne Salkind & David Van Vleet

2. Background Authors Jacobs, Franke, Carpenter, Levi, Battey Algebra Algebra is the gatekeeper Transition from arithmetic to algebra Algebraic reasoning Professional Development Little evidence of the effects of PD

3. Purpose To investigate the effects of using algebraic reasoning as the centerpiece of professional development for teachers in Grades 1-5 in an urban, low-performing school district

4. The Authors describe: Their conceptualization of algebraic reasoning Their approach to professional development

5. Relational Thinking “Relational thinking represents a fundamental shift from an arithmetic focus (calculating answers) to an algebraic focus (examining relations)” (p. 260). What do the authors mean by this? What is relational thinking?

6. Relational Thinking Understanding the Equal Sign 7 + 5 =  + 6 Using Number Relations to Simplify Calculations (9 x 57) + 57 =  Generalizations 0 + b = b

7. Professional Development What was the researchers’ approach to professional development? What were the goals of the professional development? What were the researchers’ beliefs about effective professional development? What was the structure of the professional development?

8. Professional Development Sustained, ongoing Connected to teachers’ work with their students Focused on student thinking Explored the mathematics Created classroom tools (index cards) Counter-storytelling On-site support

9. Measures What measures did the researchers use to evaluate the professional development?

10. Measures Student Measures Written mathematics tests Relational-thinking interviews Teacher Measures Survey of students’ experience with with algebraic-reasoning tasks Written mathematics tests Interviews to assess teachers’ knowledge of student thinking

11. What were the findings? Teacher Measures Survey of students’ experience with algebraic-reasoning tasks Written mathematics tests Interviews to assess teachers’ knowledge of student thinking

12. What were the findings? Student Measures Written mathematics tests –Equality subtest –Targeted-computation subtest –Solving-equations subtest –Generalizations subtest Relational-thinking interviews

13. Findings What findings make sense to you? What findings surprised you?

14. Reflections What does this study contribute to the research on teaching and learning mathematics? What ideas can you take from this study as you plan your own research?

15. Reference Jacobs, V. R., Franke, M. L., Carpenter, T. P., Levi, L., & Battey, D. (2007). Professional development focused on children’s algebraic reasoning in elementary school. Journal for Research in Mathematics Education, 38(3), 258-288.