Tools for Teachers: Enhancing Instructional Frameworks in Mathematics

1. NCDPI District Leaders Professional Development Session Standards Revision & Updated Resources

2. Agenda Overview of Tools Project - 20 minutes Instructional Framework -1 hour 50 minutes Resources & Wiki - 2 hours, 10 minutes PD Modules - 20 minutes Team Planning Time - 30 minutes Additional resources and questions - 15 minutes

3. Where Would You Like to Be? The Mountains The Beach The Lake The City

4. Tools for Teachers - Project Purpose

5. Project Organization and Management Management Team and Executive Committee Kelly DeLong Richmond County – Fiscal Partner Kay Pitchford UNC Pembroke - Lead IHE Partner Katie Mawhinney Appalachian State Mathematics Connections Wendy Rich Asheboro City Schools K-5 Coordination Jeane Joyner Meredith College Logistics Lead Writers/Developers Dawne Coker - Kindergarten Tery Gunter – 2nd Grade Drew Polly – UNC Charlotte Units and Tasks Felisia Gulledge/ Martha Butler – 1st Grade Leanne Daughtry – 3rd Grade Ana Floyd – 4th Grade Marta Garcia – 5th Grade

6. Grade Level Writing Teams

7. Pilot Locations

8. Resources Available • Teacher Resources: • Instructional Frameworks, Lessons, Games, Formative Assessment Tasks, Number Talk Resources, Content Briefs, & Video Clips • Parent/Family Resources: • Letters, Games, Tips & Video Clips • Professional Development Resources • PLC and/or school-level professional development

9. Instructional Framework Overview

10. Our Current Climate... How do you decide the order that content will be taught in your grade level? How do you decide how much time you will spend teaching content in your grade level?

11. Building Instructional Frameworks Effectively Step 1 - Coherence - What standards in a grade level “go together” mathematically? (instructional clusters) Step 2 - Sequence - In what order should the clusters be placed? Step 3 - Timing- About how long will each cluster take to teach? Step 4 - Rationales and Considerations- How do we capture our reasoning and current research in writing notes to support teachers in using the framework?

12. Multiple Partners Working Together Through multi-tiered partnerships, the Instructional Frameworkwas co-designed to create a suggested statewide pacing guide that can be a professional learning tool that increases: • A shared common vision of high-quality mathematics instruction • Sense-making of new standards • Use of research in instructional decision making • Social networking among researchers, administrators, and teachers

13. CollaborativeK-8 Instructional Frameworks

14. Instructional Framework Development

15. Using Instructional Frameworks Effectively Standardizing curriculum materials can undermine teachers’ ability to facilitate learning. • Dictated pacing with expectations for strict adherence to quarterly, weekly, daily schedules doesn’t allow for meeting individual student needs or interests. • Pacing guides contribute to teachers’ feeling of needing to “cover everything” before a corresponding quarterly benchmark or end-of-year assessment. • Teachers under time pressure often adapt by dropping the conceptual-based, student-led activities in favor of more teacher directed activities. Teachers of low-performing and minority students are more likely to drop cognitively demanding activities than other teachers. (Bauml, 2015; David, 2008)

16. Using Instructional Frameworks Effectively Curriculum materials can supportteachers’ ability to facilitate learning. • Pacing guides help teachers learn the curriculum and make decisions about how to sequence the content. • Pacing guides serve as a cue about the amount of emphasis a particular concept should receive based on the time allotted. • Pacing guides can serve as a way to organize resources and materials (“my nine-week binder”). • Pacing guides and other curricular materials can in themselves serve as professional development. (Bauml, 2015; David, 2008)

17. Using Instructional Frameworks Effectively • Emphasize curriculum guidance, not prescriptive pacing • Focus on central ideas with links to exemplary curriculum materials, lessons, and instructional strategies • Adjust frequently based on feedback from teachers • Allow for flexibility and unpredictability based on differences in teachers, students, and contexts • Address development of student reasoning and how to build upon it (progressions) (David, 2008)

18. District Considerations • Use of the Instructional Framework is a choice • Resources can be accessed in two places: • NC2ML: http://www.nc2ml.org • Tools for Teachers: http://tools4ncteachers.com • The NC Math Check-ins will be aligned to the Instructional Framework

19. NC K-5 Instructional Frameworks • What do you notice? • What do you wonder? www.nc2ml.org

20. Fourth Grade Instructional Framework

21. Instructional Framework Components • ClusterName • Duration • Content Standards • Supporting Standards • Mathematical Practices

22. Instructional Framework Components • What is the mathematics?

23. Instructional Framework Components • Important considerations?

24. Exploring the Frameworks • Select a partner and explore the framework for one grade. • Use the scavenger hunt handout to guide your exploration. • Be prepared to share your findings with tablemates. • What commonalities are you noticing?

25. Establishing Community: Cluster 1 Drop Everything And Math 1-100 Problem • Imagine that all of the integers from 1 to 100 are written on the board. 1 2 3 4 5… 98 99 100 • Erase any two numbers that appear on the board. • In place of the two erased numbers, write the number that represents the sum plus the product of those two numbers. • Repeat this operation until only a single number remains. • What are some possible values for the remaining number? Example of a possible first iteration: 1 2 3 4 5… 98 99 100 (1 + 2) + (1 x 2) = 5 1 2 3 4 5… 98 99 100 5 3 4 5… 98 99 100

26. Cluster 1: Building a Math Community Cluster 1 provides time for teachers to set up their classrooms and establish their mathematical communities. This includes: • Developing classroom norms for communication • Developing math routines • Setting various expectations for the structure of the math block • Modeling and practicing expectations for mathematical discourse • Introducing the mathematical practices • Developing positive attitudes and mindsets towards mathematics and problem solving Representing and interpreting data is the content used to develop the classroom culture at the fourth grade level.

27. Break Time

28. Let’s Follow A Concept Throughout the Course of a Year In the Framework • Break into 3 groups - assign each group 3 clusters • Read your clusters, note where multiplication (or multiplicative thinking) is within each. • Record your findings on chart paper. • Share. • How does the concept build throughout the year?

29. Toolkit Overview

30. Teacher Toolkit • Student-Centered Lessons • Formative Instructional and Assessment Tasks • Student Work Samples • Parent/Family Materials • Professional Development Modules • Revised NCSCOS for Mathematics • Unpacking Documents • Instructional Framework • Instructional Videos

31. Lesson Preview

32. Toolkit Lessons Types of Lessons Practice & Games Core Instruction

33. Math Instruction What would you expect to see if you were observing a student-centered mathematics lesson? • What would the teacher be doing? • What would students be doing?

34. Shifting to Student-Centered Instruction

35. NC State Fair: Line of Fortune • If there are 50 places for the students to choose to stand in line, where can the students stand to be sure to get 3 prizes? • Where can the students stand to be sure to get 4 prizes? • Where should you stand if you want to get all 5 prizes? • Which places should you avoid? How do you know to avoid the spots?

36. Engage in a Student-Centered Lesson • Preview the lesson • Note the Launch, Explore, and Discuss phases of the lesson • How is this lesson different from a “traditional” math lesson?

37. Lunch Time

38. Launch, Explore, Discuss Lesson Framework Look at this article…. Questions to Consider with Colleagues Question 1: (Launch) Question 2: (Explore) Question 3: (Discuss)

39. Lesson Format: Launch, Explore, Discuss Launch Explore Discuss The purpose of the launch is for the teacher to: • help students understand the context of the problem • issue a mathematical challenge to the students • “hook” students on the concept, context, or task • elicit prior understanding and misconceptions

40. Characteristics of Effective Launches • Relate the content, story, or task to students’ lives • Create challenges for students • Revisit and connect ideas from prior math experiences • Vary from day to day • Expectations for work and collaboration are clear • Clearly focused

41. Lesson Format: Launch, Explore, Discuss Launch Explore Discuss During the Explore phase of the lesson - • Students are actively engaged in mathematics, solving the problem using strategies that make sense to them • Teacher is active • Circulating, monitoring and observing students as they solve the problem • Asking questions to encourage thought, redirect and/or extend learning, and better understand students’ strategies • Selecting which students will share and in what order • Providing support when necessary

42. Lesson Format: Launch, Explore, Discuss Launch Explore Discuss During the Discuss phase of the lesson - • Selected students explain their solutions and processes to the group • Whole class views and discussions solutions • Strategies are compared, summarized, and discussed • Teacher asks questions to guide students to make connections between strategies, representations, and content

43. 5 Practices for Orchestrating Discussions • Anticipating • Monitoring • Selecting • Sequencing • Connecting

44. Models of Instruction I We You You We I

45. Parent/Family Materials

46. Parent/Family Letters for Clusters

47. Parent/Family Letters for Clusters

48. Parent/Family Letters for Clusters

49. Assessment Preview

50. Formative Instructional & Assessment Tasks Solve the following task: