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Chapter 3: Implementing the Common Core Mathematics Content in Your Curriculum

Briars, Diane J. Solution Tree Press ePub

CHAPTER 3

Implementing the Common Core Mathematics Content in Your Curriculum

The standards are meant to be a blueprint for math instruction that is more focused and coherent. The focus and coherence in this blueprint are largely in the way the standards progress from each other, coordinate with each other and most importantly cluster together into coherent bodies of knowledge. … Maintaining these progressions in the implementation of the standards will be important for helping all students learn mathematics at a higher level. … Fragmenting the Standards into individual standards, or individual bits of standards, erases all these relationships and produces a sum of parts that is decidedly less than the whole.

—Daro, McCallum, & Zimba

Chapter 2 addressed one of the two types of Common Core standards—the Standards for Mathematical Practice—and illustrated instructional practices that promote students’ proficiency in these practices. This chapter analyzes the second type of standard—the Standards for Mathematical Content. As you read this chapter, keep in mind that the Standards for Mathematical Practice and the Standards for Mathematical Content together form the Common Core State Standards. Mathematical proficiency is defined both by the content and skills that students need to know and be able to use and the mathematical habits of mind they have acquired.

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Chapter 4: Implementing the Teaching-Assessing-Learning Cycle

Briars, Diane J. Solution Tree Press ePub

CHAPTER 4

Implementing the Teaching-Assessing-Learning Cycle

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 and your collaborative team can use this chapter as the engine that will drive your systematic development and support for the student attainment of the Common Core mathematics content expectations as 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 team 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.

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Chapter 5: Implementing Required Response to Intervention

Briars, Diane J. Solution Tree Press ePub

CHAPTER 5

Implementing Required Response to Intervention

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 in hand as learners … or they don’t go at all.

—Roland Barth

As the curriculum is written, the learning targets are set, and your assessments are in place, your instructional processes need to meet the needs of each student in the courses you teach. As you read the grades 6–8 Common Core mathematics for the first time, what went through your mind? Were you thinking about the students in your class, your school, or part of your district and wondering, “Will they be able to respond positively to the expected complexity in each grade level?” Did you reflect on how you would be able to develop the CCSS Mathematical Practices in each student? How will each student be able to succeed with rich and rigorous mathematical tasks? Are there different learning opportunities for different groups of students, depending on their mathematics ability or diversity? How can you 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 part of the essential work of your collaborative team. To create an equitable mathematics program, you and your colleagues must ensure current structures for teaching and learning will generate greater access and opportunity to learn for each student.

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Chapter 2: Implementing the Common Core Standards for Mathematical Practice

Briars, Diane J. Solution Tree Press ePub

CHAPTER 2

Implementing the Common Core Standards for Mathematical Practice

The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction.

—NGA & CCSSO

The CCSS for mathematics include standards for student proficiency in mathematical practice as well as content standards for developing student understanding. According to the CCSS, “The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students” (NGA & CCSSO, 2010a, p. 6). The ultimate goal is to equip your middle school students with expertise that will help them be successful in doing and using mathematics not only in grades 6–8 but in their high school, college, and career work, as well as their personal life. College instructors of entry-level college courses across disciplines rated the Standards for Mathematical Practice of higher value for students to master in order to succeed in their courses than any of the content standard domains. This was true for college instructors in each of the fields of mathematics, language, science, and social science (Conley, Drummond, de Gonzalez, Rooseboom, & Stout, 2011).

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Appendix A: Standards for Mathematical Practice

Briars, Diane J. Solution Tree Press ePub

APPENDIX A

Standards for Mathematical Practice

Source: NGA & CCSSO, 2010a, 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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