1. Session 2 Objective You will synthesize your knowledge of Mathematical Practice Standard 4 Model with Mathematics.

2. Question to Ponder What does Model with Mathematics mean to you? *Self-Reflection *Partner Reflection *Use pink post-it notes to record ideas *Place post-its on grade level posters

3. NCTM Principles to Actions Ensuring Mathematical Success for All ©2014 “In Principles to Actions, NCTM sets forth a set of strongly recommended, research- informed actions for all teachers, coaches, and specialists in mathematics; all school and district administrators; and all educational leaders and policymakers.” (page 4)

4. NCTM Principles to Actions Ensuring Mathematical Success for All ©2014 Guiding Principles for School Mathematics Teaching and Learning Access and Equity Curriculum Tools and Technology Assessment Professionalism

5. NCTM Principles to Actions Ensuring Mathematical Success for All ©2014 Effective Teaching and Learning An excellent mathematics program requires effective teaching that engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically. (page 7)

6. NCTM Principles to Actions Ensuring Mathematical Success for All ©2014 The learning of mathematics has been defined to include the development of five interrelated strands that, together, constitute mathematical proficiency (National Research Council 2001): 1. Conceptual Understanding 2. Procedural Fluency 3. Strategic Competence 4. Adaptive Reasoning 5. Productive Disposition Partner Activity, Reflection, Handout

7. NCTM Principles to Actions Ensuring Mathematical Success for All ©2014 Student learning of mathematics “depends fundamentally on what happens inside the classroom as teachers and learners interact over the curriculum” (Ball and Forzani 2011, p. 17). Ball and other researchers (e.g., Ball et al. 2009; Grossman, Hammerness, and McDonald 2009; Lampert 2010; McDonald, Kazemi, and Kavanagh 2013) argue that the profession of teaching needs to identify and work together toward the implementation of a common set of high-leverage practices that underlie effective teaching. By “high-leverage practices,” they mean “those practices at the heart of the work of teaching that are most likely to affect student learning” (Ball and Forzani 2010, p. 45).

8. NCTM Principles to Actions Ensuring Mathematical Success for All ©2014 Mathematics Teaching Practices Establish mathematics goals to focus learning. Implement tasks that promote reasoning and problem solving. Use and connect mathematical representations. Facilitate meaningful mathematical discourse. Pose purposeful questions. Build procedural fluency from conceptual understanding. Support productive struggle in learning mathematics. Elicit and use evidence of student thinking.

9. NCTM Principles to Actions Ensuring Mathematical Success for All ©2014 Use and connect mathematical representations. Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving. Group activity using protocol adapted from the National School Reform Faculty “Save the Last Word for ME” protocol.

10. “Save the Last Word for ME” 1. Work in grade level groups. Choose a timekeeper (who also participates) who has a watch. 2. Each participant reads the selection, “Use and Connect Mathematical Representations”, highlighting what s/he considers to be (for him or her) the most significant ideas. 3. When the group is ready, a volunteer member identifies the part of the article that s/he found to be most significant and reads it out loud to the group. This person (the presenter ) says nothing about why s/he chose that particular passage. 4. The group should pause for a moment to consider the passage before moving to the next step. 5. The other 2 or 3 participants each have 1 minute to respond to the passage — saying what it makes them think about, what questions it raises for them, etc. 6. The first participant then has 3 minutes to state why s/he chose that part of the article and to respond to— or build on — what s/he heard from his/her colleagues. 7. The same pattern is followed until all members of the group have had a chance to be the presenter and to have “the last word.” 8. Group share-out.

11. Question to Ponder How does the Mathematics Teaching Practice, “Use and Connect Mathematical Representations” support or reinforce Mathematical Practice 4: Model with Mathematics? *Self-Reflection *Partner Reflection *Use yellow post-it notes to record ideas *Place post-its on grade level posters

12. http://commoncore.americaachieves.org Group activity using protocol adapted from the National School Reform Faculty “Jigsaw” protocol. 1.Work in grade level groups. 2.Participants view the video and take notes using assigned focus areas and charts provided. 3.Small group discussion. 4.Group share out. Note-taking charts, handout

13. http://commoncore.americaachieves.org Small Group Discussion Protocol As each person shares his or her notes related to the focus areas, discuss how the teacher’s use of questioning, instructional strategies, the classroom environment, and materials helped to reinforce the Mathematical Practice of Modeling with Mathematics. Also discuss any changes or recommendations you would make to strengthen each focus area in relation to Modeling with Mathematics.

14. Question to Ponder Based on the video jigsaw, what other strategies might you consider when designing a lesson focusing on Math Practice Standard 4? *Self-Reflection *Partner Reflection *Use green post-it notes to record ideas *Place post-its on grade level posters

15. Objective for Session 2: You will synthesize your knowledge of Mathematical Practice Standard 4 Model with mathematics. In your grade level group, synthesize your learning from this session by reviewing and discussing the color-coded post-its on your poster. Be prepared to share your synthesized learning of what Modeling with Mathematics looks like at your grade level and how you will use that new learning in designing a lesson during session 3.