Warm-Up Discuss homework at your table: Building Students’ Understanding: The Equal Sign Resource Inventory (what do you use?) Growth Mindset Focal Student Update 1

Michigan Integrated Mathematics Initiative MI 2 – Day 3 8:00 a.m. - 3:00 p.m. 2

Agenda Warm-up & Address Homework Common Core State Standards Smarter Balanced Assessments Atlas Rubicon Unit Perspective 8 mathematical practices Lessons 6 – 8 Lunch Atlas, Progression, & Turn on math TTLP Article Lesson Planning Tool (with focal student in mind)

Common Core State Standards for Mathematics (CCSSM) “These standards are not intended to be new names for old ways of doing business. They are a call to take the next step.” 4

Goals Deepen understanding of CCSS Content Practice Instruction Assessment (day 5) Explore CCSS Units Atlas Turn on CC Highlight Lessons Consider strategies for increasing accessibility 5

Could these standards really be better? 6 How might my colleagues and I continue to make sense of these standards together? What is changing and what is staying the same? Why do the Standards for Mathematical Practice matter? What is the purpose of the MAISA CCSSI Units? Do the MAISA Units replace my textbook?

Frequently Asked Questions Will this curriculum replace my instructional materials? Are the CCSS the current standards in Michigan? No, these materials are designed to support teachers’ use of their instructional materials. They are intended to be tools to guide instruction and provide contexts for professional learning. Yes, the CCSS are Michigan’s Standards. They were officially adopted by the SBE on June 15,

8 Working Together: Governors and Chief State School Officers

9 Mathematics Standards Standards for Practices Standards for Concepts and Procedures Greater balance of concept and skill development Greater access for all students Major shifts include: Standards for Mathematical Practices Attention toward content as it develops within and across grades levels (trajectories) Teaching with and assessing high demand tasks

Standards for Mathematical Practice “The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important ‘processes and proficiencies’ with longstanding importance in mathematics education.” (CCSS, 2010) 10

Standards for Mathematical Practice 11 William McCallum Standards for Mathematical Practice Tucson, April 2011 Reasoning and explaining Modeling and Using tools Seeing Structure and Generalizing

Common Core State Standards Mathematics Standards for Practice Standards for Concepts and Procedures What implications do you foresee as you consider attending to both types of standards?

Learning Trajectories and the Common Core State Standards “A teacher or test designer seeing exclusively within the grade level will miss the point [of the number line]. Multi-grade progression views of standards can avoid many misuses of standards” (p.43). 13

14 CCSS States and the Balanced Assessment Consortium

Claims for Mathematics Summative Assessment 15 “Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.” Claim 1: Concepts and Procedures, ≈ 40% “Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.” Claim 2: Problem Solving ≈ 20% “Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.” Claim 3: Communicating Reasoning ≈ 20% “Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.” Claim 4: Data Analysis and Modeling ≈ 20%

A Balanced Assessment System These new assessment are scheduled to begin in the spring of 2015!

Released Assessment Items What do the tasks in each color category have in common? 17 What do tasks like these potentially reveal about student understanding? What do the tasks like these potentially mislead about student understanding?

Common Core State Standards Oakland Initiative The goal of the Common Core State Standards Initiative (CCSSI) is to provide support and direction for educators as they move toward full implementation: CCSS are organized into an aligned curriculum of coherent units of study. The resources are particularly designed to highlight needed shifts in content related and pedagogical practices. Unit Template Highlight Lesson Formative Assessment Resources (video, sample student work, rubrics, instructional websites, etc.)

CCSS Mathematics Initiative Oakland 19 NATIONAL State Curriculum Consultants, AMTE, NCTM, NCSM and Smarter Balanced Consortium Joseph Martineau MDE, SBAC Ruth Anne Hodges, OSI MCTM Mathematics and Science Center Network OS Valerie Mills, OS, NCSM  Avondale  Berkley  Birmingham  Bloomfield Hills  Brandon  Clarenceville  Clarkston  Clawson  Farmington  Ferndale  Hazel Park  Holly  Holly Academy  Huron Valley  Lake Orion  Lamphere  Madison  Novi  Oak Park  Oakland Schools  Oxford  Pontiac  Rochester  Royal Oak  South Lyon  Southfield  Walled Lake  Waterford  West Bloomfield COUNTY STATE MAISA

CCSS Initiative Oakland 20 National Projects CCSS Curriculum Mathematics Writing Team OS Mathematics Pilot and Review Teams Curriculum Leadership Team and Mathematics Leadership Team DRAFT Unit of Study Highlight Lesson Formative Assessment Revise Units, Lessons, & Assessments Trial Lessons Collect & select sample student work Classroom Video Organize and facilitate project activities Facilitate communication among teachers & administrators

Three Year Implementation Process Year Full K-12 curriculum for both ELA and Math aligned to CCSS Year One unit of study per grade (K-12) for both ELA and Math Year Four additional units of study per grade (K- 12) for both ELA and Math Proposed process for development of K-12 curriculum aligned to Common Core State Standards for both ELA and Mathematics

Unit Development by Mathematical Trajectory 22 K1st2nd…11th Unit 1 … Unit 2 … Unit 3. Unit 3. Unit 3. …Unit 3.

Key Features of CCSS Curriculum Emphasis on the use of student thinking within instruction and assessment Content and practice standards that call for a balance of conceptual understanding and procedural fluency Incorporation of mathematical explanations Use of multiple representations (Technology) Integration of accessibility strategies (Universal Design for Learning, UDL) Learning opportunities and assessments that include inquiry and exploration Tools to support implementation … 23

Grade Level Unit Components (Atlas) 1. Unit Themes Graphic Focus Questions Intellectual Processes Key Concepts 2. Content Standards Abstract CCSS Standards 3. Instructional Resources Illuminations Children’s Literature Texas Instruments References Applets 4. Professional Resources NCTM Articles Books 24

Orientation to the Unit (Atlas) Refer to one unit of study for examples that articulate the components of the unit template. 1. What opportunities for helping teachers understand the standards as a set of related ideas and teach the mathematics in a way that emphasizes connections between and among mathematical ideas? 2. How might a single unit support teachers in making both content related and pedagogical shifts in practice? 25

Atlas Unit Similarity & Differences Read Units Record your findings 1 person report 26

Lunch We will reconvene at 12:45 p.m. to begin work on the formative assessment. 27

Highlight Lesson Components 1. Model Lesson Themes Graphic Focus Questions Intellectual Processes Key Concepts 2. Model Lesson Content Standards Abstract CCSS Standards Lesson Instructional Resources 3. Sequence of Lesson Activities Selecting and Setting up a Mathematical Task Launch Supporting Students’ Exploration of the Task Sharing and Discussing the Task 28

Highlight Lesson 29

Baseball Lesson Do the Math Discuss the Teacher Resource Materials Available Browse Atlas Lesson Planning Groups 30

Atlas Curriculum Mapping Units, Highlight Lessons, Formative Assessments and other resources available in Atlas by Rubicon 31

32 Units of Study Lesson resources Assessment resources Professional resources Video Sample student work And more

Teachers and Tasks Matter Stein, Grover & Henningsen (1996) Smith & Stein (1998) Stein, Smith, Henningsen & Silver (2000) 33 The Mathematical Tasks Framework Tasks as set up by teachers Tasks as they appear in curricular materials Tasks as enacted by teachers and students Student learning

Thinking Through a Lesson Protocol Smith, M.S., Bill, V., & Hughes, E.K. (2008). Thinking through a lesson: Successfully implementing high- level tasks. Mathematics Teaching in the Middle School, 14,

Lesson Planning & Article Insert 5 minute timer here 35

Adapted from Lesh, R., Post, T., & Behr, M. (1987). Representations and Translations among Representations in Mathematics Learning and Problem Solving. Geometric/ Graphical Verbal (written and oral) Tabular Contextual Symbolic Pictures Oral Language Manipulative Models Real-World Situations Written Symbols Representation Stars 36

CCSS Move Toward Greater Connections & Coherence “When students can connect mathematical ideas, their understanding is deeper and more lasting.” (NCTM, 2000 p.64) “When students understand the interrelatedness of mathematics, they often have many more strategies available to them when solving problems and insights into mathematical relationships.” (Hiebert, 1997) “Through instruction that emphasizes the interrelatedness of mathematical ideas, students not only learn mathematics they also learn about the utility of mathematics.” (NCTM, 2000, p.64) “Toward greater focus and coherence” (CCSS, 2010, p.3) 37

“To help young people learn the more complex and analytical skills they need for the 21 st century, teachers must learn to teach in ways that develop higher-order thinking and performance. Darling-Hammond and Richardson, 2009 To develop the sophisticated teaching required for this mission, education systems must offer more effective professional learning…”

Thinking Through a Lesson Protocol Smith, M.S., Bill, V., & Hughes, E.K. (2008). Thinking through a lesson: Successfully implementing high- level tasks. Mathematics Teaching in the Middle School, 14,

Orientation to the Lesson Orient yourself with the format of a Highlight Lesson. 1. Compare a Unit and the corresponding Highlight Lesson, how are they related and how are they unique? 2. What about this lesson format might support teachers in making both content related and pedagogical shifts in practice. 40

Formative Assessment: A Difference that Can Make a Difference! Black and Wiliam (1998) report, based on their extensive review of research, typical effect sizes of formative assessment experiments are between 0.4 and 0.7. These results are larger than most instructional innovation strategies. “…the evidence is that ways of managing formative assessment that work with the assumptions of "untapped potential" do help all pupils to learn and can give particular help to those who have previously struggled (Black and Wiliam, p. 11).”

Reengagement A Formative Assessment Strategy Reengagement: is a formative assessment strategy by which teachers use information from student work to design a learning opportunity that is an evolution of the original task and is focused on enhancing students’ current understandings; is grounded in the effective and intentional use of student thinking to forward learning; and requires interactions between and among teachers, students, and the content to be learned. 42

Formative Assessment Components 1. Formative Assessment Task 2. Sequence of Assessment Activities Give the Assessment Task Re-engage: Select and Share Representative Solutions Summarize Independent Practice 43

Formative Assessment Task 44

Formative Assessment Reflection Orient yourself with the format of this component and then consider: 1. How do the task and design of the activity compare to your current practice? 2. How might the use of formative assessment tasks such as this support learning for students and for teachers? 45

Curriculum Reflection Consider each of the components in a Unit: Unit Overview Highlight Lesson Formative Assessment In what ways might the MAISA Units, Lessons and Assessments support amore coherent curriculum? What implications for change did today’s activities and discussions prompt for you as you consider your setting? 46

1.Exploring a Complete Unit of Study 2.Curriculum Alignment 3.Teaching & Learning Trajectories across Grades 4.Modified Lesson Study Profession al Learning Models

The CCSS Resources are… not self-enacting raw materials to support teachers as they reorganize their instruction and work to implement the CCSS 48

End of Day Reflections 1.Pick an idea that came up today and that you found particularly interesting. What is your current thinking about this idea? What questions do you still have? 2.What is your reaction to the work we did today? What seems promising and/or challenging at this point? 49

Contact Information Geraldine Devine Dana Gosen Valerie Mills Jim Randall Carrie Zielinski 50

Connections Across Grade Levels: Exploring a Trajectory Review the three units in your grade band and consider how the mathematics progresses over time. 1. What do you notice about the development of the mathematics? 2. How might understanding this mathematical trajectory impact instruction? 51