Developing Mathematical Practices for Geometry, Algebra II and Beyond

1. Developing Mathematical Practices for Geometry, Algebra II and Beyond Developed by Education Development Center, Inc. with support from the Massachusetts Department of Elementary and Secondary Education

2. Course Goals • Understand the Standards for Mathematical Practice • See how the practices contribute to increasing the sophistication of students’mathematical exploration and problem-solving • Learn how the practices bring coherence to the high school mathematics program • Consider instructional strategies that support students’ development of the Standards for Mathematical Practice

3. Why Focus on the Eight Standards for Mathematical Practice ? “These Standards are not intended to be new names for old ways of doing business. They are a call to take the next step. It is time for states to work together to build on lessons learned from two decades of standards based reforms.” -2011 Massachusetts Curriculum Framework for Mathematics (page 4) -Common Core State Standards for Mathematics (page 5)

4. These Practices Define the “Next Step!” in Math Education • “The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years.” Page 17, 2011 Massachusetts Curriculum Framework for Mathematics

5. Who should sign up for this course? • Grades 9-12 mathematics teachers • Special education teachers working in grades 9-12 mathematics classrooms • Secondary mathematics coaches • Cross-district or cross-grade teams are encouraged

6. The Participant Experience

7. Learn about the Eight Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

8. The Mathematics: • Focus on mathematics beyond Algebra 1 • Make connections across the high school course of study

9. Participant Experience • Do mathematics together to identify their own (and colleagues’) use of the Mathematical Practices • Learn to appreciate multiple approaches to mathematical problem-solving

10. Participant Experience, continued • Consider how to treat other areas of the curriculum in ways that highlight both specific content and the Standards for Mathematical Practice

11. Follow-up Sessions • Presentation of final projects • Discussion of student work

12. Participant Take-Aways Tools: Strategies: • Big Ideas of the Standards for Mathematical Practice • “Ask yourself…” questions to recognize the Mathematical Practice • “Lessons in Action” lesson planning template • Guess-Check-Generalize • Chunking • Point Tester Lesson Plans: • For lessons they’ve created, as well as • Ideas from lessons generated by colleagues

13. Guess-Check-Generalize Guess and Check

14. Chunking 49x2 + 35x + 6 49x2 + 35x + 6 = (7x)2 + 5(7x) + 6 = ♣2 + 5♣ + 6 = (♣ + 3)(♣ + 2) = (7x + 3)(7x + 2)

15. Course Logistics • 45 hours: equivalent to 6 full day sessions (8:00-4:00) plus classroom experimentation • Five full days in Summer, plus 2 half-day follow-up sessions during the school year. • 3 graduate credits (for a fee) or 67.5 PDPs Summer Sessions 1-5 Fall S6 Fall S7

16. Teacher Impact • Understanding of what the Standards for Mathematical Practice are, and how they can be used to unify the high school mathematics curriculum. • The capacity to identify the use of the Mathematical Practices in student work. • An appreciation of, and a commitment to teaching via the type of “low threshold, high ceiling tasks” that prompt the use and development of mathematical habits of mind.