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

2. 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.

3. 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

4. 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

5. 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

6. 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?

7. 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

8. 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

9. 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.

10. 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?

11. Wrap Up Assignments Please leave notebooks Comment cards
Carefully read student thinking interview assignment. Select student with your CT and 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

12. 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)