1. Materials Beliefs Cut-up beliefs Answer key Adjusting support tool Tasks activity Martha’s carpeting problem (on ppt) Fencing problem (labels) 3-5 tasks (6-8 tasks) Levels of cognitive demand Answer key Factors affecting copies

2. Supporting Implementation of Mathematics Standards RSD Principals October 22 and 23, 2014 Sue Larson Nora Ramirez

3. Outcomes Become familiar with a tool to adjust support by self assessing mathematics instruction at a school site Increased ability to affect teachers’ beliefs regarding the teaching and learning of mathematics Raise awareness of how mathematical tasks differ with respect to their levels of cognitive demand Increased understanding of an administrator’s role in supporting teachers as they implement math standards Consider expectations of teachers as they implement problem solving (related to the October 31 RSD Professional Development Day)

4. A Data Collection Tool Adjusting Professional Support

5. Outcome Become familiar with a tool to adjust support by self assessing mathematics instruction at a school site

6. Beliefs about Teaching and Learning Mathematics Pass out slips of paper in each group Sort beliefs as either productive and unproductive beliefs with each person taking a turn to read and determine if the belief is productive or not. The group then reaches consensus on each decision. Check answers. Principles to Actions: Ensuring Mathematical Success for All, NCTM 2014

7. Beliefs about Teaching and Learning Mathematics Count off 1-6. Get into numbered group taking the list of Productive and Unproductive Beliefs with you. How might you coach a teacher to address this unproductive belief? Principles to Actions: Ensuring Mathematical Success for All, NCTM 2014

8. Reflection What unproductive beliefs do you find more prevalent in your school? What moves might you make to begin to overcome these unproductive beliefs?

9. Beliefs about Teaching and Learning Outcome Increased ability to affect teachers’ beliefs regarding the teaching and learning of mathematics

10. Mathematical Tasks

11. Oct 31 Professional Development Outcomes To reinforce the foundations of teaching and learning mathematics by enhancing teachers’ ability to: – Use problem solving as a vehicle to teach in a balanced approach – Select/modify/create tasks with high levels of thinking

12. Agenda Activate Prior Knowledge Problem Solving Introduction Tasks and Mathematical Practices Problem Solving #1 Tools for Problem Solving Problem Solving #2 Balanced Approach Stations

13. Independent Work Begin to solve these two problems individually. Record your work in your packet. Martha’s Carpeting Fencing

14. Martha’s Carpeting Task Martha is recarpeting her bedroom, which is 15 feet long and 10 feet wide. How many square feet of carpeting will she need to purchase? Martha’s Carpeting Task Martha is recarpeting her bedroom, which is 15 feet long and 10 feet wide. How many square feet of carpeting will she need to purchase? Fencing Task Ms. Brown’s class will raise rabbits for their spring science fair. They have 24 feet of fencing with which to build a rectangular rabbit pen to keep the rabbits. 1.If Ms. Brown’s students want their rabbits to have as much room as possible, how long would each of the sides of the pen be? 2.How long would each of the sides of the pen be if they had only 16 feet of fencing? 3.How would you go abut determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it. Fencing Task Ms. Brown’s class will raise rabbits for their spring science fair. They have 24 feet of fencing with which to build a rectangular rabbit pen to keep the rabbits. 1.If Ms. Brown’s students want their rabbits to have as much room as possible, how long would each of the sides of the pen be? 2.How long would each of the sides of the pen be if they had only 16 feet of fencing? 3.How would you go abut determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it.

15. Partner Work Continue to work on the two problems with your partner. Martha’s Carpeting Fencing

16. Presentations.

17. Group Discussion How are Martha’s Carpeting Task and the Fencing Task the same and how are they different? Do the differences matter? Consider your own experience in solving the tasks, the “mathematical possibilities” of the tasks, and/or the complexity of the tasks.

18. Math & Science Collaborative “There is no decision that teachers make that has a greater impact on students’ opportunities to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages students in studying mathematics.” Lappan and Briars, 1995 Analyzing Mathematical Tasks

19. DIGGING INTO TASKS - Categorizing - Characterizing

20. Categorizing Tasks Sort Tasks A – P into two categories [high-level and low-level] Develop a list of criteria that describe the tasks in each category

21. Categorizing Tasks LowHigh A, D, E, G, L, OB, C, F, H, I, J, K, M, N, P

22. Math & Science Collaborative Discussion What are the characteristics of the tasks you categorized as “low” level? What are the characteristics of the tasks you categorized as “high” level?

23. Math & Science Collaborative Discussion Are all high-level tasks the same? Is there an important difference between Tasks J and B? Are all procedural tasks the same? Is there an important difference between Tasks I and O?

25. Categorizing Tasks, Part Two Further sort the mathematical tasks into four categories: – Memorization tasks – Procedural tasks without connections – Procedural tasks with connections – Doing mathematics tasks

26. Reflection & Share What information can we add to our initial brainstorm: – What are characteristics of high levels of mathematical thinking and reasoning?

27. Math & Science Collaborative Categorizing Tasks “If we want students to develop the capacity to think, reason, and problem solve then we need to start with high- level, cognitively complex tasks.” Stein & Lane, 1996

28. 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

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

30. Factors Associated with the Decline of High-Level Demands 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)

31. Factors Associated with the Maintenance of High-Level Demands 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)

32. Reflect and share What do you now understand about the levels of demands of tasks?

33. Problem Solving Select task considering – Level of cognitive demand – The mathematics students will apply and learn – The accessibility of the task to students Anticipate student responses – Possible student misconceptions – Different strategies and tools students might use – Language that indicates understanding Adapted from Principles to Actions

34. Problem Solving Teacher presents problem, facilitates the KFA process and does not model or suggest a solution process. Teacher has tools available for student use. Students work individually, then in pairs/groups while the teacher – Monitors, – asks guiding questions that promote the SMP, – assesses students’ understanding, and – chooses students to present and sequence of presentations. Teacher facilitates discourse requiring students to explain, defend, ask questions, clarify, model with equations, use representations and appropriate tools, use precise language, make connections, etc. Teacher facilitates a class summary and an individual reflection. Adapted from Principles to Actions

35. Supporting Teachers What is your role in supporting teachers as they implement problem solving? Think about what you can do to help teachers implement problem solving how you might help them learn what problem solving looks like and sounds like how you will scaffold their learning and implementation What might you tell your teachers that you expect to see in their classrooms? Think about how often you expect to see problem solving the type of problems teachers use how you might help them persevere what student engagement might look like acceptance and acknowledgment of the learning process

36. Outcomes Become familiar with a tool to adjust support by self assessing mathematics instruction at a school site Increased ability to affect teachers’ beliefs regarding the teaching and learning of mathematics Raise awareness of how mathematical tasks differ with respect to their levels of cognitive demand Increased understanding of an administrator’s role in supporting teachers as they implement math standards and specifically problem solving Consider expectations of teachers as they implement problem solving (related to the October 31 RSD Professional Development Day)

37. Evaluation, Feedback and Input Complete the project’s evaluation form Complete the + / Δ form.