1. Scottsboro City 6-8 Math September 3, 2015 JEANNE SIMPSON LESHELL SMITH AMSTI MATH SPECIALISTS

2. Welcome Name School Classes you teach Share a classroom success and challenge from last year. 2

3. He who dares to teach must never cease to learn. John Cotton Dana

4. Agenda  Aspire Data  Implementing the Standards for Mathematical Practice  Number Talks  Vertical Planning

5. acos2010.wikispaces.com

6. http://actaspire.avocet.pearson.com/ actaspire/home

7. Reporting Categories All questions are either measuring  Grade Level Progress – mathematical topics new to the grade  Foundation – topics learned in previous grades Some questions are also categorized as  Modeling – questions that assess understanding of mathematical models and their creation, interpretation, evaluation, and improvement  Justification and Explanation – giving reasons for why things work as they do, where students create a mathematical argument to justify (constructed response)

8. Points by category and grade.

13. Interpreting the Standards for Mathematical Practice Session 1

14. edc.org Introduction to the Course: Survey What We Know about the SMP Consider how you would complete the following sentences: Something I know about the Common Core Standards for Mathematical Practice is… Something I want to learn about the Common Core Standards for Mathematical Practice is... Interpreting the SMP Course – Session 114

15. mathpractices.edc.org

16. edc.org Introduction to the Course: Preview the Course Why are the Standards for Mathematical Practice, and the habits of thinking they describe, important? Interpreting the SMP Course – Session 116

17. edc.org Introduction to the Course: Preview the Course Course Goals: Increase awareness of the Common Core Standards for Mathematical Practice (SMP) Develop understanding of the SMP connected to the Standards for Mathematical Content Cultivate capacity to identify the SMP in student thinking Develop ability to plan how to use instructional tasks in order to encourage student engagement in the SMP Interpreting the SMP Course – Session 117

18. edc.org Introduction to the Course: Preview the Course Common Core State Standards for Mathematics Adopted by 43 states, District of Columbia, 4 territories, & Dept. of Defense Ed. Activity National Governors Association Center for Best Practices, Council of Chief State School Officers – www.corestandards.orgwww.corestandards.org Grade level content standards for K-8 and High School: – “Standards define what students should understand and be able to do.” “Clusters summarize groups of related standards.” “Domains are larger groups of related standards.” Standards for Mathematical Practice: – “…describe varieties of expertise that mathematics educators at all levels should seek to develop in their students ” – “…describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years.” Interpreting the SMP Course – Session 118

19. edc.org Introduction to the Course: Preview the Course Common Core Standards for Mathematical Practice 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. (See handout with descriptions of each.) Interpreting the SMP Course – Session 119

20. edc.org Introduction to the Course: Preview the Course Course Structure (see Course Overview handout): Ten two-hour sessions – Sessions 1-2: Introduction – Sessions 3-6: Focus on Algebra & Functions Contexts – Sessions 7-9: Focus on Geometry Contexts – Session 10: Conclusion & Consideration of Statistics Contexts All eight SMP highlighted over time – not every standard in every session nor a single standard per session. Interpreting the SMP Course – Session 120

21. edc.org Introduction to the Course: Preview the Course Core Activities of Course: Doing and Discussing Mathematics (All Sessions except Session 4) – Exploring Mathematics Tasks as mathematical learners – Discussing use of Standards for Mathematical Practice (SMP) Examining “Student Dialogues” (All Sessions except Session 4) – Student Dialogues that offer examples of the SMP in student thinking – Discuss questions focused on SMP, mathematics, and classroom practice Planning Classroom Lessons (Sessions 3, 4, and 8) – Using tasks from Course (Session 3) or from your Curricula (Sessions 4 & 8) Analyzing Student Work From Your Students (Sessions 4, 5, and 9) – Using tasks from Course (Session 4) or from your Curricula (Sessions 5 & 9) Interpreting the SMP Course – Session 121

22. edc.org Introduction to the Course: Preview the Course Planning lessons and collecting student work for analysis: After Session 3 use task from Sessions 1 or 3 with students – Content for both tasks is in the domains of Operations & Algebraic Thinking and Expressions & Equations – Session 1 task content: factors, multiples, relatively prime numbers – Session 3 task content: numerical expressions After Session 4 use task from your own curriculum or of your choosing that highlights algebra, functions, number content After Session 8 use task from your own curriculum or of your choosing (could be from course) that highlights geometry content Interpreting the SMP Course – Session 122

23. edc.org Introduction to the Course: Preview the Course Interpreting the SMP Course – Session 123 Session 1 Goals: Increase awareness of the Standards for Mathematical Practice (SMP). Develop understanding of the SMP and their connection to the Standards for Mathematical Content. Session 1 Checkpoints: After engaging in this session, you should be able to… State open questions or confusions about the SMP that should be addressed during the course. Explore and discuss mathematics and mathematical thinking with your colleagues in the group. Identify examples of one or more SMP in your own or a colleague’s approach to a mathematics task. Describe MP 1 (Make sense of problems and persevere in solving them) and MP 3 (Construct viable arguments and critique the reasoning of others) Identify examples of MP 3 in a Student Dialogue and provide justification for the examples.

24. edc.org Introduction to the Course: Preview the Course Interpreting the SMP Course – Session 124 Session 1 Agenda: Introduction to the Course  Survey What We Know about the SMP  Preview the Course Mathematics Task Exploration  Solve Mathematics Task  Share Strategies SMP Exploration  Discuss in Small Groups  Share-Out and Summarize Student Dialogue Exploration  Introduce Student Dialogues  Read Student Dialogue  Discuss Teacher Reflection Questions Session 1 Mathematics Task and Student Dialogue: Integer Combinations— Postage Stamps

25. edc.org Mathematics Task Exploration: Solve Mathematics Task In other PD experiences working on mathematics tasks, what made those experiences productive? Individual work on task. – Track the twists and turns in your thinking. Small group work on task. Interpreting the SMP Course – Session 125

26. edc.org Mathematics Task Exploration: Share Strategies – Part I Share and discuss: How did you start out thinking about the task? How did your thinking change, and what prompted that change? What conclusions, hypotheses, and questions have you generated about possible and impossible postage amounts? Interpreting the SMP Course – Session 126

27. edc.org Mathematics Task Exploration: Share Strategies – Part II Share and discuss: Examples of thinking from your own or your colleagues’ work on the task that illustrate the Standards for Mathematical Practice. Interpreting the SMP Course – Session 127

28. edc.org Standards for Mathematical Practice Exploration: Discuss in Small Groups Read the Standards for Mathematical Practice (SMP) handout. Re-read the descriptions of MP 1 and MP 3, highlighting key words and phrases. In small groups: – Discuss meaning of MP 1 and of MP 3. – Create summary descriptions of MP 1 and of MP 3. 2-3 sentences. May include examples. Write on large paper to share with rest of group. Interpreting the SMP Course – Session 228

29. edc.org Standards for Mathematical Practice Exploration: Share-Out & Summarize Share and discuss summaries in whole group for: MP 1: Make sense of problems and persevere in solving them. MP 3: Construct viable arguments and critique the reasoning of others. Interpreting the SMP Course – Session 129

30. edc.org Student Dialogue Exploration: Introduce Student Dialogues – Part I Dialogue between three fictitious middle grades or high school characters (either Sam, Dana, and Anita, or Chris, Lee, and Matei) working on a mathematics task The dialogues are intended to: – Clarify the meaning of particular SMP by showing what student discourse could be – Illustrate key ideas about the Standards for Mathematical Practice (SMP) in context using specific mathematical content – Serve as an artifact to promote discussion among educators about the SMP, about mathematics, and about issues of teaching practice. Interpreting the SMP Course – Session 130

31. edc.org Student Dialogue Exploration: Introduce Student Dialogues – Part II Given the intention to illustrate the meaning and key ideas of the SMP: – Plausible student thinking, but the discourse may not always sound realistic. – The student characters are “caricatures,” intended to illustrate particular types of thinking and discussion. – A teacher voice is intentionally not included. – Discussion of whether or how a teacher might intervene, or of how to promote similar thinking with your own students, are productive avenues for discussion. Interpreting the SMP Course – Session 131

32. edc.org Student Dialogue Exploration: Read Student Dialogue Read the Student Dialogue out loud. Read the Student Dialogue individually – focus on mathematical thinking used by the students. Interpreting the SMP Course – Session 132

33. edc.org Student Dialogue Exploration: Discuss Teacher Reflection Questions Small groups: Discuss Questions #1-4 on the Teacher Reflection Questions handout. – Refer to the Standards for Mathematical Practice handout. – Be specific about what evidence you see in the dialogue. – Time permitting: Discuss any or all of Questions #5-6. Whole group: Discuss Question #2. Resource for later: Mathematical Overview Interpreting the SMP Course – Session 133

34. edc.org Homework Review Homework before Session 2: – Read the Introduction to the Standards for Mathematical Practice handout. – (Optional) Review the Mathematical Overview handout (information about today’s math task and student dialogue). Interpreting the SMP Course – Session 134

35. edc.org Number Talks Interpreting the SMP Course – Session 135

36. NUMBER TALKS Helping children build mental math and computation strategies!

37. Number Songs How well do you listen?

38. KEY COMPONENTS Classroom environment and community Classroom discussions The teacher’s role The role of mental math Purposeful computation problems

39. PREPARING FOR NUMBER TALKS Select a designated location that allows you to maintain close proximity to your students for informal observations and interactions. Provide appropriate wait time for the majority of the students to access the problem. Accept, respect, and consider all answers. Encourage student communication throughout the number talk.

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45. DISCUSSION Contact Info: jeanne.simpson@uah.edujeanne.simpson@uah.edu leshell.smith@uah.edu

46. edc.org Planning Time Choose a standard that you will be teaching soon. Work with the teachers in your grade level to plan a task for this standard using the planning questions. Be prepared to share.

47. edc.org Next Meeting – Friday, November 13 Today I learned…. A question I still have is…. Interpreting the SMP Course – Session 147

48. edc.org Contact Information jeanne.simpson@uah.edu leshell.smith@uah.edu acos2010@wikispaces.com