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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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Epilogue: Your Mathematics Professional Development Model

Briars, Diane J. Solution Tree Press ePub

EPILOGUE

Your Mathematics Professional Development Model

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 all students are provided with exemplary teaching and learning experiences, and you have access to the supports necessary to guarantee all students the opportunity to develop 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 (page 180).

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Appendix B: Standards for Mathematical Content, Grade 6

Briars, Diane J. Solution Tree Press ePub

APPENDIX B

Standards for Mathematical Content, Grade 6

Source: NGA & CCSSO, 2010a, pp. 39–45. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Used with permission.

In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.

(1)  Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates.

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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 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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