Alabama College- and Career-Ready Standards for Mathematics

1. Thinking Through A Lesson Alabama College- and Career-Ready Standards for Mathematics Quarterly Meeting #3

2. Thinking Through a Lesson: Successfully Implementing High-Level Tasks Session I: Outcomes: • Discuss and examine the thought process of developing a lesson/unit that is standards-based. • Select rich tasks that match student friendly outcomes and provide evidence of student learning.

3. Why Lesson Planning? The effectiveness of a lesson depends significantly on the care with which the lesson plan is prepared. (Brahier, 2000)

4. Why Lesson Planning? Good planning “shoulders much of the burden” of teaching by replacing “on the fly" decision making” during a lesson with careful investigation into the what and how of instruction before the lesson is taught. (Stigler & Hiebert, 1999, p.156)

5. During the planning phase, teachers make decisions that affect instruction dramatically. They decide what to teach, how they are going to teach, how to organize the classroom, what routines to use, and how to adapt instruction for individuals. (Fennema & Franke, 1992, p. 156) Why Lesson Planning?

6. An effective mathematical task is needed to challenge and engage students intellectually.

7. Read an excerpt from the article:

8. What causes high-level cognitive demand tasks to decline?

10. Comparing Two Mathematical Tasks Solve Two Tasks: Martha’s Carpeting Task The Fencing Task

11. How are Martha’s Carpeting Task and the Fencing Task the same and how are they different? Comparing Two Mathematical Tasks

12. Do the differences between the Fencing Task and Martha’s Carpeting Task matter? Why or Why not? Comparing Two Mathematical Tasks

13. Similarities and Differences Similarities Both are “area” problems Both require prior knowledge of area Differences The amount of thinking and reasoning required The number of ways the problem can be solved Way in which the area formula is used The need to generalize The range of ways to enter the problem

14. Does Maintaining Cognitive Demand Matter? YES

16. Linking to Literature/ Research: The QUASAR Project The Mathematical Tasks Framework TASKS as they appear in curricular/ instructional materials TASKS as set up by the teachers TASKS as implemented by students Student Learning Stein, Smith, Henningsen, & Silver, 2000, p. 4

17. Patterns of Set up, Implementation, and Student Learning Task Set Up Task Implementation Student Learning A. High High High B. Low Low Low C. High Low Moderate Stein & Lane, 2012

18. Routinizing problematic aspects of the task • Shifting the emphasis from meaning, concepts, or understanding to the correctness or completeness of the answer • Providing insufficient time to wrestle with the demanding aspects of the task or so much time that students drift into off-task behavior • Engaging in high-level cognitive activities is prevented due to classroom management problems • Selecting a task that is inappropriate for a given group of students • Failing to hold students accountable for high-level products or processes (Stein, Grover & Henningsen, 2012) Factors Associated with the Maintenance and Decline of High-Level Cognitive Demands

19. Scaffolding of student thinking and reasoning • Providing a means by which students can monitor their own progress • Modeling of high-level performance by teacher or capable students • Pressing for justifications, explanations, and/or meaning through questioning, comments, and/or feedback • Selecting tasks that build on students’ prior knowledge • Drawing frequent conceptual connections • Providing sufficient time to explore (Stein, Grover & Henningsen, 2012) Factors Associated with the Maintenance and Decline of High-Level Cognitive Demands

20. Decline Routinizing problematic aspects of the task Shifting the emphasis from meaning, concepts, or understanding to the correctness or completeness of the answer Providing insufficient time to wrestle with the demanding aspects of the task or so much time that students drift into off-task behavior Engaging in high-level cognitive activities is prevented due to classroom management problems Selecting a task that is inappropriate for a given group of students Failing to hold students accountable for high-level products or processes Maintenance Scaffolding of student thinking and reasoning Providing a means by which students can monitor their own progress Modeling of high-level performance by teacher or capable students Pressing for justifications, explanations, and/or meaning through questioning, comments, and/or feedback Selecting tasks that build on students’ prior knowledge Drawing frequent conceptual connections Providing sufficient time to explore Factors Associated with the Maintenance and Decline of High-Level Cognitive Demands

21. “Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.” (Stein, Smith, Henningsen, & Silver, 2011) “The level and kind of thinking in which students engage determines what whey will learn.” (Hiebert et al., 2011)

22. [Common Core State Standards for Mathematics] represent a significant departure from what mathematics is currently taught in most classrooms and how it is taught. Developing teachers’ capacity to enact these new standards in ways that support the intended student learning outcomes will require considerable changes in mathematics instruction in our nation’s classrooms. Such changes are likely to occur only through sustained and focused professional development opportunities for those who teach mathematics. Sztajn, Marrongelle, & Smith, 2011

23. Job-Alike Reflection 3. How can we help teachers improve their capacity to plan (and enact) lessons that support students’ learning? 4. How would you conduct professional development with teachers to see how lesson planning addresses content rigor, task selection, student engagement and math practices, formative assessment, generating student work samples for assessment, and assisting struggling students?

24. Thinking Through a Lesson: Successfully Implementing High-Level Tasks Session 2 Outcomes: • Develop student friendly outcomes that reflect the rigor and depth of content. • Select rich tasks that match student friendly outcomes and provide evidence of student learning. • Model teacher collaboration on identifying resources for implementing CCRS Math Standards.

26. Thinking Through a Lesson Protocol (TTLP) Planning Template

27. Thinking Through a Lesson ProtocolBackwards Planning What will you see or hear that lets you know students are developing understanding of the concepts? What questions will you need to ask to build mathematical understanding? What mathematical concepts will be developed in the implementation of this task? What do you expect your students to do as they engage in the lesson? Share, Discuss, and Analyze Set Up Explore

29. K-2 Sample Task Dan’s older brother Sam collects car stickers for his scrapbook. Sam decides to give Dan some of his stickers. Sam gives Dan 7 stickers. Sam now has 12 stickers. How many stickers did Sam have before giving some to Dan?

30. K-2 Sample Task

31. 18 90 108 81 31 99 + + - + - + = = = = = = 3-5 Sample Task Use the digits 3, 4, 5 and 6 to complete each number sentence. A digit can only be used once in each number sentence.

32. 3-5 Sample Task

33. Grades 6 – 8 Sample Task REPRESENTING AND INTERPRETING PROPORTIONAL RELATIONSHIPS: Computer Games

34. Grades 6 – 8 Sample Task Slippery Slopes: Saving Money

35. Grades 9 – 12 Sample Task

36. Grades 9 – 12 Sample Task

37. What are some of the potential benefits of using the TTLP? • With which components of the lesson planning protocol do you feel especially comfortable? • Which components would you like to focus on more? How can the ideas and tools from this activity support you with that? Reflection

39. Conclusion Not all tasks are created equal -- they should provide a variety of opportunities for students to learn mathematics. High level tasks are the most difficult to carry out in a consistent manner. Engagement in cognitively challenging mathematical tasks leads to the greatest learning gains for students. Professional development is needed to help teachers build the capacity to enact high level tasks in ways that maintain the rigor of the task.

40. Job-Alike Reflection 5. Are there any aspects of your own thinking and/or practice that our work today has caused you to consider or reconsider? Explain. 6. Are there any aspects of your students’ mathematical learning that our work today has caused you to consider or reconsider? Explain. 6a. What would you like more information about?

41. Resources

42. www.mathccc.org

43. Insidemathematics.org

44. Insidemathematics.org

45. map.mathshell.org.uk/materials Mathematics Assessment Project (MAP)

46. 20 ready-to-use Lesson Units for Formative Assessment for high school. cross referenced to CCSS content and practices standards. (Ultimately 20 per grade 7-12) Summative assessments, aimed at “College- and Career-Readiness,” presented in two forms: (1) a Task Collectionwith each task cross-referenced to the CCSS, and (2) a set of Prototype Test Formsshowing how the tasks might be assembled into balanced assessments. Professional development modules Mathematics Assessment Project (MAP) map.mathshell.org.uk/materials

47. MAP Formative Assessment Lessons • Assessment task, individual work (15 min) • Teacher reviews work, creates questions to improve solutions • (Whole group discussion) • Partner or small group task to increase understanding, address misconceptions • Debriefing discussion • Revision of work on original assessment

48. The Illustrative Mathematics Project Hyperlinked CCSS Developing a complete set of tasks for each standard Range of difficulty Simple illustrations of single standards to complex tasks spanning many standards. Provide a process for submitting, discussing, reviewing, and publishing tasks. Launch Team: Phil Daro, William McCallum (chair), Jason Zimba illustrativemathematics.org

49. illuminations.nctm.org/Lessons.aspx

50. mathedleadership.org