Our Learning Journey Continues Shelly R. Rider

The Overarching Habits of Mind of a Productive Mathematical Thinker

Are you looking in the mirror or out the window? Pausing Paraphrasing Probing for specificity Putting ideas on the table Paying attention to self and others Presuming positive intentions Promoting a Spirit of Inquiry Seven Norms of Collaboration DuFour, Richard, et. al. Learning by Doing. Bloomington: Solution Tree, (p. 104)

What can we do differently in our leadership skills in order to 1) have powerful conversations with our PLT members and 2) grow in our capacity to lead the implementation of the CCRS, through the application of best practices?

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

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%

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

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

Procedures without Connection to Concepts, Meaning, or Understanding Convert the fraction to a decimal and percent = 37.5%

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

“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%

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.

“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

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

Our Learning Journey Continues Shelly R. Rider