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Beyond the Common Core Grades K-5

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Focus your curriculum to heighten student achievement. Learn 10 high-leverage team actions for grades K–5 mathematics instruction and assessment. Discover the actions your team should take before a unit of instruction begins, as well as the actions and formative assessments that should occur during instruction. Examine how to most effectively reflect on assessment results, and prepare for the next unit of instruction.

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Introduction

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Introduction

You have high impact on the front lines as you snag children in the river of life.

—Tracy Kidder

Your work as an elementary school mathematics teacher is one of the most important, and at the same time, one of the most difficult jobs to do well in education. Since the release of our 2012 Solution Tree Press series Common Core Mathematics in a PLC at Work™, our authors, reviewers, school leaders, and consultants from the Mathematics at Work™ team have had the opportunity to work with thousands of grades K–5 teachers and teacher teams from across the United States who are just like you: educators trying to urgently and consistently seek deeper and more meaningful solutions to a sustained effort for meeting the challenge of improved student learning. From California to Virginia, Utah to Florida, Oregon to New York, Wisconsin to Texas, and beyond, we have discovered a thirst for implementation of K–12 mathematics programs that will sustain student success over time. A focus on the elementary grades is a significant component of the K–12 effort toward improved student learning.

 

CHAPTER 1

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CHAPTER 1

Before the Unit

Teacher: Know thy impact.

—John Hattie

The ultimate outcome of planning before the unit begins is for you and your team members to gain a clear understanding of the impact of your expectations for student learning and demonstrations of understanding during the unit.

In conjunction with the scope and sequence your district mathematics curriculum provides, your collaborative team prepares a roadmap that describes what students will know and be able to demonstrate at the conclusion of the unit. To create this roadmap, your collaborative team prepares and organizes your work around five before-the-unit-begins high-leverage team actions.

HLTA 1. Making sense of the agreed-on essential learning standards (content and practices) and pacing

HLTA 2. Identifying higher-level-cognitive-demand mathematical tasks

HLTA 3. Developing common assessment instruments

HLTA 4. Developing scoring rubrics and proficiency expectations for the common assessment instruments

 

CHAPTER 2

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CHAPTER 2

During the Unit

The choice of classroom instruction and learning activities to maximize the outcome of surface knowledge and deeper processes is a hallmark of quality teaching.

—Mary Kennedy

Learning is experience. Everything else is just information.

—Albert Einstein

Much of the daily work of your collaborative team occurs during the unit of instruction. This makes sense, as it is during the unit that you place much of your collaborative team effort put forth before the unit into action.

Your team conversations during the unit focus on sharing evidence of student learning, discussing the effectiveness of lessons or activities, and examining the ways in which students may be challenged or need scaffolding to engage mathematically. While discussion about some of the tasks and the end-of-unit assessment planning take place prior to the start of the unit, teachers often plan and revise day-to-day unit lessons during the unit as they gain information regarding students’ needs and successes. What your students do and say while developing understanding of the essential learning standards for the unit provides the data for your teacher team conversations.

 

CHAPTER 3

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CHAPTER 3

After the Unit

You can’t learn without feedback. . . . It’s not teaching that causes learning. It’s the attempts by the learner to perform that cause learning, dependent upon the quality of the feedback and opportunities to use it. A single test of anything is, therefore, an incomplete assessment. We need to know whether the student can use the feedback from the results.

—Grant Wiggins

You have just taught the unit and given your common end-of-unit assessment. Did students reach the proficiency targets for the unit’s essential learning standards? How do you know? How do your students know? More importantly, what are the responsibilities of your collaborative team after the unit ends?

Your after-the-unit-ends high-leverage team actions support steps four and five of the PLC teaching-assessing-learning cycle (see figure 3.1).

Source: Kanold, Kanold, & Larson, 2012.

Figure 3.1: Steps four and five of the PLC teaching-assessing-learning cycle.

 

EPILOGUE

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EPILOGUE

Taking Your Next Steps

So now what? You and your collaborative team have moved through the stages of the PLC teaching-assessing-learning cycle, and should now be ready to start the process again with the next unit. Some of the considerations from this handbook relative to work with your instructional unit include:

• Was the size of the unit manageable within the teaching-assessing-learning cycle?

• How did your team discussion of essential learning standards help you to support student understanding?

• How did the design of the mathematical tasks and assessment instruments work? Were they aligned?

• How did the unit formative assessment plan fit with the end-of-unit assessment?

Figure E.1 (pages 146–147) provides a final summative evaluation your team can use at the beginning or the end of the school year to identify your current progress on each of the high-leverage team actions. Celebrate your strengths and prioritize your areas for continued growth.

 

APPENDIX A

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APPENDIX A

Standards for Mathematical Practice

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).

 

APPENDIX B

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APPENDIX B

Cognitive-Demand-Level Task-Analysis Guide

Source: Smith & Stein, 1998. Copyright 1998, National Council of Teachers of Mathematics. Used with permission.

Table B.1: Cognitive-Demand Levels of Mathematical Tasks

 

APPENDIX C

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APPENDIX C

Sources for Higher-Level-Cognitive-Demand Tasks

Common Core Conversation

www.commoncoreconversation.com/math-resources.html

Common Core Conversation is a collection of more than fifty free website resources for the Common Core State Standards in mathematics and ELA.

EngageNY Mathematics

www.engageny.org/mathematics

The site features curriculum modules from the state of New York that include sample assessment tasks, deep resources, and exemplars for grades preK–12.

Howard County Public School System Secondary Mathematics Common Core

https://secondarymathcommoncore.wikispaces.hcpss.org

This site is a sample wiki for a district K–12 mathematics curriculum.

Illustrative Mathematics

www.illustrativemathematics.org

The main goal of this project is to provide guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience upon implementation of the Common Core State Standards for mathematics.

 

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