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Common Core Mathematics in a PLC at Workâ„¢, Leader's Guide

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This leader companion to the grade-level teacher guides illustrates how to sustain successful implementation of the Common Core State Standards for mathematics. Discover what students should learn and how they should learn it. Comprehensive research-affirmed analysis tools and strategies will help collaborative teams develop and assess student demonstrations of deep conceptual understanding and procedural fluency.

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Chapter 1 Leading High-Performing Collaborative Teams for Mathematics

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The Common Core State Standards provide a consistent, clear understanding of what students are expected to learn, so that teachers and parents know what they need to do to help them learn. The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers. With American students fully prepared for the future, our communities will be best positioned to compete successfully in the global economy.

—NGA & CCSSO

The mission of the K–12 CCSS for mathematics is ambitious yet attainable. Thus, it will require your strong leadership for the right kind of professional development—professional development that leads to effective and consistently implemented instructional and assessment practices. To successfully and equitably implement these expectations, the teachers you lead must be engaged in an ongoing process of professional development and learning. Among your primary leadership responsibilities are to monitor, pressure, and support the successful implementation of the CCSS for mathematics—at your level of leadership and influence within the school organization.

 

Chapter 2 Leading the Implementation of the Common Core Standards for Mathematical Practice

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Reasoning and sense making must become a part of the fabric of the mathematics classroom. Not only are they important goals themselves, but they are the foundation for true mathematical competence. Incorporating isolated experiences with reasoning and sense making will not suffice. Teachers must consistently support and encourage students’ progress toward more sophisticated levels of reasoning.

—NCTM

Mathematics education in the United States has a long history of confidence in standards and curriculum programs as the primary means to improve student achievement (Larson, 2009). However, reliance on standards and materials to improve student achievement has not resulted in dramatic improvements in student learning, and more importantly, it has not resulted in a narrowing of existing achievement gaps (Loveless, 2012). If CCSS implementation is to be more than a superficial gesture in your school or district—more than a content standards mapping—and is instead to result in real improvements in student learning and to close the achievement gap, then implementation efforts need to be more about instruction—how teachers approach student learning of the content standards. As Wiliam (2011) contends, “Pedagogy trumps curriculum. Or more precisely, pedagogy is curriculum, because what matters is how things are taught, rather than what is taught” (p. 13).

 

Chapter 3 Leading the Implementation of the Common Core Mathematics Content

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The Standards for Mathematical Content are a balanced combination of procedure and understanding. Expectations that begin with the word “understand” are often especially good opportunities to connect the practices to the content. . . . In this respect, those content standards which set an expectation of understanding are potential “points of intersection” between the Standards for Mathematical Content and the Standards for Mathematical Practice.

—NGA & CCSSO

In this chapter, you will examine the content, language, organization, and expectations of the CCSS for your K–12 mathematics curriculum. This chapter helps you to better understand the content expectations described in the grade-level books for this series and helps you monitor your collaborative teams’ ability to deliver on and implement the expectations of the CCSS for your mathematics program.

This chapter also describes your role in facilitating the implementation of a mathematics curriculum that meets the vision and the expectations of the CCSS content standards. Depending on your background (or comfort level) and interest in mathematics, it can be difficult to articulate your exact expectations for a high-quality mathematics program that mirrors and reflects the expectations of the CCSS for mathematics. However, your leadership can and should monitor the existence of a clearly articulated mathematics curriculum that is aligned with the standards.

 

Chapter 4 Leading the Implementation of the Teaching- Assessing-Learning Cycle

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An assessment functions formatively to the extent that evidence about student achievement is elicited, interpreted, and used by teachers, learners, or their peers to make decisions about the next steps in instruction that are likely to be better, or better founded, than the decisions they would have made in absence of that evidence.

—Dylan Wiliam

The focus of this chapter is to illustrate the appropriate use of ongoing student assessment as part of an interactive, cyclical, and systemic collaborative team formative process on a unit-by-unit basis. You can support your collaborative teams by using this chapter as the engine that will drive your systematic development for student attainment of the Common Core mathematics content and instruction described in chapters 2 and 3.

When led well, ongoing unit-by-unit mathematics assessments—whether in class, during the lesson checks or end-of-unit assessment instruments, like tests, quizzes, or projects—serve as a feedback bridge within the teaching-assessing-learning cycle. The cycle requires your teams to identify core learning targets or standards for the unit, create cognitively demanding common mathematics tasks that reflect the learning targets, create in-class formative assessments of those targets, and design common assessment instruments to be used during and at the end of a unit of instruction.

 

Chapter 5 Leading the Implementation of Required Response to Intervention

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Ultimately there are two kinds of schools: learning enriched schools and learning impoverished schools. I have yet to see a school where the learning curves . . . of the adults were steep upward and those of the students were not. Teachers and students go hand and hand as learners . . . or they don’t go at all

—Roland Barth

As the curriculum is written, the unit learning targets are set, and the assessments are in place, teachers’ current instructional processes need to meet the needs of each student in their courses. As you read the Common Core State Standards for mathematics for the first time, you might think about the students in each class, school site, or district and wonder, “Will they be able to respond positively to the expected complexity for each grade level? Can teachers develop the CCSS Mathematical Practices in each student? How will each student be able to succeed with rich and meaningful mathematical tasks? Are there different learning opportunities for different groups of students, depending on their mathematics ability or diversity? How can teachers generate equitable learning experiences so that each student is prepared to meet the demands of the Common Core mathematics as described in this book?” The key to answering these questions is the essential work of the collaborative teams you lead. To create an equitable mathematics program, teachers and school leaders alike must ensure current structures for teaching and learning will generate greater access, equity, and opportunity to learn for each student in each grade level or course.

 

Epilogue Your Mathematics Professional Development Model

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Implementing the Common Core State Standards for mathematics presents you with both new challenges and new opportunities. The unprecedented adoption of a common set of mathematics standards by nearly every state provides the opportunity for U.S. educators to press the reset button on mathematics education (Larson, 2011). Collectively, you and your colleagues have the opportunity to rededicate yourselves to ensuring that all students are provided with exemplary teaching and learning experiences, with access to the supports necessary to guarantee an opportunity for improved mathematical proficiency.

The CCSS college and career aspirations and vision for teaching, learning, and assessing students usher in an opportunity for unprecedented implementation of research-informed practices in your school or district’s mathematics program. In order to meet the expectations of the five fundamental paradigm shifts described in this book, you will want to assess your current practice and reality as a school against the roadmap to implementation described in figure E.1.

 

Appendix A Standards for Mathematical Practice

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Source: NGA & CCSSO, 2010, pp. 6–8. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Used with permission.

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. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

 

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