Overview Share practice from mini-problems Introduction to base ten blocks Practice modeling subtraction Analyzing student errors Wrap up

Mathematical Proficiency for All Students Conceptual understanding - comprehension of mathematical concepts, operations, and relations Procedural fluency - skill in carrying out procedures flexibly, accurately, efficiently, and appropriately Strategic competence - ability to formulate, represent, and solve mathematical problems Adaptive reasoning - capacity for logical thought, reflection, explanation, and justification Productive disposition - habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy Kilpatrick, J., J. Swafford, and B. Findell. (2001). Adding It Up: How Children Learn Mathematics. Washington, DC: National Academy Press.

The Course Matrix: Principled Practice Guiding Principles Domains of Practice Attending to the integrity of the mathematics Committing to the learning and achievement of all students Establishing and managing a productive learning environment Learning from and systematically improving practice Leading a whole class discussion about mathematics Representing mathematical ideas Assessing students’ knowledge, skill, and dispositions Planning mathematics lessons

Sharing Practice What happened in your discussion? What went well? What didn’t go as well? What was most challenging and how did you handle it? How did the problem you used provide students with opportunities to discuss and reason about important mathematical ideas or solution methods? Were there mathematical ideas or skills that were part of this problem that you had not realized? What were some productive moves you used and/or challenges you faced with regard to the following: Creating a productive environment in which students were able to share and listen to each other Supporting all students to engage with the problem and achieve your instructional goal Keeping the work focused on important aspects of the mathematics

Grade Level Groups #1: Jillian, Kristin, Leah #2: Nehal, Lizzy, Lauren #3: Talia, Candace, Kurtis #4: Jackie, Caroline, Liz #5: Pam, Hannah, Katy #6: Catherine, Amy, Molly #7: Kiely, Carly, Lesley #8: Casey, Lisandra, Marissa #9: Winnie, Misty, Caitlin, Cheryl

Learning From and Improving Practice Based on your experience teaching a mini-problem, make additions to our discussion planning framework: Are there sections you would add? Are there points you would add to any of the sections to capture other considerations that are important to make when planning a discussion? Are there existing points or sections you could clarify based on your experience with planning and leading the discussion?

Why did we do this today? Completing a “cycle of practice” Developing your skills at leading a discussion Learning from practice and committing to improvements based on what you learn Learning to talk about your own practice and provide feedback to others

Initial Cycle of Learning About Practice Enacting improved practice Determining productive direction for future practice Considering and preparing for practice Enacting practice Consolidating things learned from practice Exposure to practice

Modeling the Standard Subtraction Algorithm The “modeler”: Select a multi-digit subtraction problem with regrouping. Tell your group whether you will be using a take-away or comparison interpretation of subtraction. Model the subtraction -- talk through each step and carefully map between the materials and the written form. The “critics”: Use the modeling checklist to make notes about the performance. Provide comments and suggestions based on your observations. If your group finishes early, each person should try a new problem using the other interpretation of subtraction.

Analyzing Common Student Errors How might a student have gotten each incorrect answer? What might each error tell you about a student’s understanding of place value? What questions would you want to ask each student to probe his or her thinking?

Wrap Up Assignments Please leave notebooks Comment cards Carefully read student thinking interview assignment. Select student with your CT and email this information to me. Readings (reflective and proactive) Write a reflection about what you have learned and plan to try from your work on the mini-problem Please leave notebooks Comment cards

Initial Cycle of Learning About Practice (TGuide version) Enacting improved practice (engaging purposefully in a more complete/nuanced teaching practice and/or in a setting that more closely embodies an authentic teaching context while collecting artifacts to support professional learning and improvement) Determining productive direction for future practice (planning improved course(s) of action for use in subsequent teaching) Enacting practice (engaging purposefully in a setting that embodies key dimensions of authentic teaching contexts & collecting artifacts to support learning from practice) Consolidating learnings from practice (collaborative and self-reflection on practice utilizing experience, purpose, considerations, and principles) Considering and preparing for practice (building background knowledge about purposes, considerations, and principles, as well as specific options for practice; planning core elements of practice in a supported context) Exposure to practice (hearing about, remembering, or noticing practices in a domain of teaching)