1. Our Learning Journey Continues Shelly R. Rider

3. The Practice Standards and Content Standards define what students should understand and be able to do in their study of mathematics. Asking a student to understand something Means asking a teacher to assess whether the student has understood it. But what does Mathematical understanding look like? One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes from. The student who can explain the rule understands the mathematics, and may have a better chance to succeed at a less familiar task such as expanding (a + b + c)(x + y). Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness.

4. The Overarching Habits of Mind of a Productive Mathematical Thinker

5. Quality Instruction Scaffolding Professional Development Process - Talk Moves - Conceptual Learning - Environment [physical & emotional] - Productive Math Discussions - Task Selection - Quality Questioning PLT 2012-2013 PLT 2013-2014

6. Levels of Cognitive Demand High Level Doing Mathematics Procedures with Connections to Concepts, Meaning and Understanding Low Level Memorization Procedures without Connections to Concepts, Meaning and Understanding

7. Hallmarks of “Procedures Without Connections” Tasks Are algorithmic Require limited cognitive effort for completion Have no connection to the concepts or meaning that underlie the procedure being used Are focused on producing correct answers rather than developing mathematical understanding Require no explanations or explanations that focus solely on describing the procedure that was used

8. Procedures without Connection to Concepts, Meaning, or Understanding Convert the fraction to a decimal and percent 3838 3.008.375 = 37.5% 2 4 60.375 56 40

9. Hallmarks of “Procedures with Connections” Tasks Suggested pathways have close connections to underlying concepts (vs. algorithms that are opaque with respect to underlying concepts) Tasks often involve making connections among multiple representations as a way to develop meaning Tasks require some degree of cognitive effort (cannot follow procedures mindlessly) Students must engage with the concepts that underlie the procedures in order to successfully complete the task

10. “Procedures with Connections” Tasks Using a 10 x 10 grid, identify the decimal and percent equivalent of 3/5. EXPECTED RESPONSE Fraction = 3/5 Decimal 60/100 =.60 Percent 60/100 = 60%

11. Hallmarks of “Doing Math” Tasks There is not a predictable, well-rehearsed pathway explicitly suggested Requires students to explore, conjecture, and test Demands that students self monitor and regulated their cognitive processes Requires that students access relevant knowledge and make appropriate use of them Requires considerable cognitive effort and may invoke anxiety on the part of students Requires considerable skill on the part of the teacher to manage well.

12. “Doing Mathematics” Tasks Shade 6 squares in a 4 x 10 rectangle. Using the rectangle, explain how to determine each of the following: a) Percent of area that is shaded b) Decimal part of area that is shaded c) Fractional part of the area that is shaded a)Since there are 10 columns, each column is 10%. So 4 squares = 10%. Two squares would be 5%. So the 6 shaded squares equal 10% plus 5% = 15%. b)One column would be.10 since there are 10 columns. The second column has only 2 squares shaded so that would be one half of.10 which is.05. So the 6 shaded blocks equal.1 plus.05 which equals.15. c)Six shaded squares out of 40 squares is 6/40 which reduces to 3/20. ONE POSSIBLE RESPONSE

13. The Importance of Student Discussion Provides opportunities for students to: Share ideas and clarify understandings Develop convincing arguments regarding why and how things work Develop a language for expressing mathematical ideas Learn to see things for other people’s perspective

14. Quality Instruction Scaffolding Professional Development Process - Talk Moves - Conceptual Learning - Environment [physical & emotional] Grade Level Teachers 2013-2014

15. Classroom Impact Type of Training Knowledge Mastery Skill Acquisition Classroom Application Theory85%15%5-10% PLUS Practice85%80%10-15% PLUS Peer Coaching Study Teams Class Visits 90% 80-90%

17. Peer to Peer Coaching Peer to Peer Coaching is a confidential process through which two or more professional colleagues work together to reflect on current practices.

20. Immediate Next Steps of the CCRS Journey 1)Peer-to-Peer Coaching Process 2)Vertical Math PLT Process

21.  Talk Move Facilitator Notes to guide the PD  Talk Move Participant Packet  Talk Move PowerPoint  Talk Move Video(s)  Talk Move Research Article These resources will be located at http://amsti-usa.wikispaces.com at the close of Monday, August 5 th.http://amsti-usa.wikispaces.com

22. The Journey Ahead Form & Peer-to-Peer Coaching Form

23. PD Structures to Facilitate Learning Teacher Professional Learning Teams PLT Facilitator Coaching Communities PLT Facilitator Side-by-Side Coaching Administrator Professional Learning Teams Peer-to-Peer Coaching

24. Our Learning Journey Continues Shelly R. Rider