Year 3: Day 2

1. On a post-it note, respond to the following question in a complete sentence:What is one central theme of the TTLP article? Year 3: Day 2

2. What’s golden? Year 3: Day 2

3. Agenda • Introductions and Norms • Morning Jumpstart: What’s my rule? • Reflecting on the TTLP • Activity – Dots and the spreading virus • Lesson Reflection: Reflecting on SMCs and SMPs • Lesson Study lesson planning • Lunch • Launch after Lunch: What’s my rule? • Activity – Dynagraphs with Desmos • Lesson Reflection: Reflecting on SMCs and SMPs • Daily Evaluation

4. Evolving Norms for this PD • We will be ready for class and use our class time effectively. • We will keep our focus on learning and use technology for personal reasons during breaks. • We will be respectful of each other’s time and space and work efficiently. • We will actively participate by (a) listening to each other, (b) giving others our attention, (c) not speaking when someone else is talking, and (d) regularly sharing our ideas in class. • If we disagree with someone or are unclear, we will ask a question about his or her idea and describe why we disagree or are confused. • We will ask questions when we do not understand something. We will comment on others’ ideas rather than the person.

5. Evolving Norms for this PD • We will take advantage of opportunities to share ideas and gather feedback through presentations. • We will encourage one another to share ideas. • We will show our appreciation to one another for their ideas. • If we disagree with someone or are unclear about their ideas related to mathematics content and pedagogy, we will ask a question about his or her idea and describe why we disagree or are confused. • We will ask questions when we do not understand something about mathematics content and pedagogy. • We will comment on others’ ideas about mathematics content and pedagogy rather than the person.

6. Evolving Norms for this PD • We will always look for another approach to solve problems. • We will use pictures, graphs, tables, symbols, numbers, manipulatives, and/or words to assist us while doing mathematics. • We will persist with every problem and examine it from multiple perspectives. • We will be mathematically precise whenever possible. • We will explain and justify our ideas in a way that everyone can understand. • We will engage in rough-draft talk and encourage others to do so as well.

7. Activity: Dynagraphs • Desmos is a free online software that supports mathematics lessons aimed at grades 6-20. • Today’s activities could also be performed in Geogebra; however, we aim to follow a set of lessons and explore features of Desmos.

8. Morning Jumpstart: What’s my rule?

9. Viruses (aka Growing Dots)

10. Viruses aka Growing Dots • This task has three parts. We will pause after each part to reflect on how it connects to EE content and the SMPs. • Growing Dots 1 • Examining a video for evidence of algebraic thinking • Growing Dots Extension 1

11. Reflecting on SMCs and SMPs • Share across your table with different SMPs and SMCs addressed by today’s activities. • Be purposeful indicating what specific behaviors or habits led you to conclude that you engaged in a specific SMP. • Similarly, what did the instructor(s) do to encourage/foster/facilitate that SMP? • In what ways could we UDL this lesson? • UDL = Universal Design for Learning. We will explore this more deeply later today.

12. Lesson Study: Goals • Overarching goal: • To collaborate in ways that help us improve our mathematics teaching and learning and reflect upon those actions. • Immediate goals: • Each group will design, enact, reflect upon, and improve one mathematics lesson per semester. This lesson will be taught twice during one day by the same instructor. • This is a learning process for everyone: the instructional team, you, and your lesson study group. Be patient, flexible, and open to trying something new.

13. Lesson Study Planning • Work in lesson study teams to plan a lesson for our September 13 session. • Think about: • What Expressions and Equations (EE) content standards will be the focus? • What SMPs will be the focus of the lesson? • What TTLP questions will you focus on? Your group members should agree on 2-3 questions from each part that you will address in this lesson. • How will students be assessed? (This doesn’t have to be formal!)

14. Lesson Study: Expectations • Expectations: • Lessons should provide outlets for co-teaching and offer rich learning opportunities for ALL learners. • The focal task should be a problem, not an exercise that is immediately solved with a previously learned strategy. The problem ought to be complex, open, and have realistic elements. The goal is to promote problem solving, not efficiency with a known procedure. You have approximately 45 minutes for your lesson. • Ideas for promoting mathematical student-teacher and student-student discourse should be evident in the lesson. Questions prompting mathematical discussions, including eliciting misconceptions, must be present. • Students should be doing mathematics beyond calculating and executing a known (previously learned) procedure.

15. Lesson Study: Action Plan • Frame your lesson using the research question in mind: “How does this lesson support students’ content learning through engagement in the mathematical practices?“ • Your lesson study group should agree on at least two questions from each part that you will addressed in this lesson. Note: Your final lesson must be uploaded to the website (or sent to Jessica (jbelche@bgsu.edu) by 11:59pm on Friday, September 9.

16. Lunch

17. Launch after Lunch What’s my rule? (Using dynagraphs)

18. Brief Reading • Usiskin (1999) shares a few comments about notions of expressions and equations. Read these two pages and reflect on the following questions. Be prepared to justify your responses with evidence from the text AND teaching experiences. • What are the five types of expressions? • What are the five ways variables might appear in expressions? • How do you use “variable” in your mathematics teaching? • Why do learners struggle with the notion of variable?

19. Activity: Dynagraphs • Desmos is a free online software that supports mathematics lessons aimed at grades 6-20. • Today’s activities could also be performed in Geogebra; however, we aim to follow a set of lessons and explore features of Desmos.

20. Activity: Dynagraphs • Please go online and enter the following link into your web browser: http://student.desmos.com • When prompted, enter class code: 84gp • When finished, return to http://student.desmos.com and enter class code: DVYF • When finished, return to http://student.desmos.com and enter class code: 5NAJ • You should work independently, conferring in pairs as needed.

21. Reflecting on SMCs and SMPs • Share across your table with different SMPs and SMCs addressed by today’s activities. • Be purposeful indicating what specific behaviors or habits led you to conclude that you engaged in a specific SMP. • Similarly, what did the instructor(s) do to encourage/foster/facilitate that SMP?

22. Take Care • Please complete the exit ticket. • What is something that you liked about today (to keep up)? • What is something that you learned from today? • You may leave personal items in the room (e.g., books, calculators, and notebooks). • Please help us keep the room in order by throwing away any trash and tidying your area. • Bring snacks, drinks, and/or other food to share! • See you tomorrow and travel safely!