Building Students’ Deep Understanding through a Common Core-Aligned Unit

Setting the Stage Reflect on planning and pedagogical practices in context of the CCLS instructional shifts in mathematics

Rigorous Tasks as Unit Drivers Evaluate and strengthen the alignment of a unit’s culminating task Evaluate and adjust the rigor of a unit’s culminating task

Planning with the Instructional Shifts in Mind Analyze the coherence of tasks within a unit Study the elements of a Common Core-aligned lesson plan Create or revise a lesson plan for an instructional task

Supporting the Instructional Shifts through Mathematical Talk Participate in a text-based discussion about mathematical talk and analyze a video of

mathematical talk in action

Bringing it all Together Watch video of classroom practice and analyze teacher moves and student

knowledge and skills Determine next steps for unit outline Reflect on own practice in the context of course learnings Create an action plan for building school-wide capacity

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Building Students’ Deep Understanding through a Common Core-Aligned Unit

Session 2: Rigorous Tasks as Unit Drivers

1. Introduction, Logistics, review of Bridge to Practice from Session 1

2. Activity #1: Aligning a Unit’s Culminating Task to the CCLS

3. Introduction to Depth of Knowledge

4. Activity #2: Using Depth of Knowledge to Assess the Rigor of a Sample

Mathematics Task

6. Reflection, Strategies for Sharing, Bridge to Practice, and Feedback Forms

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Reflecting on Bridge To Practice from Session 1

What unit did you choose for this course?

Why did you choose it?

What have you already developed for this unit? (lesson plans, formative assessments, rubrics, etc.)

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ACTIVITY #1

ALIGNING A UNIT’S CULMINATING TASK WITH THE CCLS

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What do you consider to be the important components of a unit plan in math?

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Unit Outline Components

• Overarching Questions: The big inquiries of a unit. These questions reach across and connect content and skill in the unit. Each experience allows students to deepen responses to the overarching questions.

• Primary CC Content Standards addressed in the Unit: What content, skills, and performances will be the major focus for this unit?

• Primary CC Mathematical Practices addressed in the Unit: Which Practices lend themselves to deepening conceptual understanding and fluency in math for this unit?

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Unit Outline Components Sequenced Activities: Activities cohere around the same

content/performances as assessment task. Activities a) allow for CCLS-based work that parallels assessments in smaller chunks; b) are sequenced to prompt retrospective work; and c) provide a model of the kind of writing, skills, and performances required by the culminating assessment.

Instructional Tasks: Provide opportunities for students to a) learn/experience/build their content knowledge b) develop skills embedded in the Math Practices; c) are sequenced to move learners from basic procedural knowledge to higher level thinking about math; and d) mirror the assessment tasks in order to provide support for students to learn the content, habits, and skills they need to successfully and independently complete the unit's culminating task.

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Unit Outline Components

Embedded Assessments: List the ways in which you will assess student learning during and after the instructional task.

Culminating Assessment Task: How can the content, skills, and performances in the unit be combined to elicit student responses that demonstrate a deep understanding of the unit standards?

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Performance Tasks

What comes to mind when you hear the term “performance task?”

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Step 1. Work the task thoroughly.

Step 2. Compare your work with the answer key/rubric and other instructional support materials.

Step 3. Identify the content and performances required.

Step 4. Match the content and performances to the CCLS.

Step 5. Rate the alignment of content.

Step 6. Rate the alignment of performances.

Step 7. Additional considerations.

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SEVEN STEPS FOR ALIGNING MATHEMATICS TASKS TO THE CCLS

Step 5: CCLS Mathematics Content Standards: Content vs. Performance

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CCLS Content Performance

4.NF.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Sample Task Alignment

Grade 2 – Carol’s Numbers

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Common Practice Task:

Carol’s Numbers – Grade 2

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DEBRIEF CAROL’S NUMBERS

• What was your solution?

• What content was required to solve the task?

• What performances were required to solve the task?

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DEBRIEF CAROL’S NUMBERS: SOLUTION AND CONTENT AND PERFORMANCES

• Solution: 1) 7422) 247; Put the smallest number on the left, the next

smallest number in the middle and the largest number last.

3-5) See number line and discuss.

• Content: Place value, three-digit numbers, number line

• Performances: Represent, compare, read and write, understand

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DEBRIEF CAROL’S NUMBERS: ALIGNMENT WITH MATH PRACTICES

MP.1 Make sense of problems and persevere in solving them.

MP.3 Construct viable arguments and critique the reasoning of others.

MP.6 Attend to precision.

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DEBRIEF CAROL’S NUMBERS: ALIGNMENT WITH THE CCLS CONTENT STANDARDS

2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.

2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

2.NBT.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.

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DEBRIEF CAROL’S NUMBERS: ALIGNMENT WITH MATH PRACTICES

MP.1 Make sense of problems and persevere in solving them. (Rating – Performance: 3)

MP.3 Construct viable arguments and critique the reasoning of others. (Rating – Performance: 2)

MP.6 Attend to precision. (Rating – Performance: 3)

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DEBRIEF CAROL’S NUMBERS: ALIGNMENT WITH THE CCLS CONTENT STANDARDS

2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. (Rating – Content: 3, Performance: 3)

2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. (Rating – Content: 3, Performance: 2)

2.NBT.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. (Rating – Content: 3, Performance: 2)

2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram. (Rating – Content: 3, Performance: 2)

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INTRODUCTION TO DEPTH OF KNOWLEDGE

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How does DOK fit into the Citywide Instructional Expectations for 2012-13?

A key component of the Citywide Instructional Expectations is strengthening student work by examining and refining curriculum, assessment and instruction.

Rigorous questions, tasks and assessment are essential to driving the higher-order thinking and skills students need to become college and career-ready

Depth of Knowledge is a framework that helps educators examine the level of rigor to ensure students are being pushed to meet the demands of the new standards.

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Surfacing Definitions of Rigor

What is your current definition of rigor? Please record it in your note-taking guide

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DOK Video Guiding Questions

http://schools.nyc.gov/Academics/CommonCoreLibrary/ProfessionalLearning/DOK/default.htm

After watching the video, think about rigor in terms of your own practice.

> What sounded familiar to you? > What sounded new?

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1956 2001

Knowledge - Define, duplicate, label, list, name, order, recognize, relate, recall

Remember - Retrieve knowledge from long-term memory, recognize, recall, locate, identify

Comprehension - Classify, describe, discuss, explain, express, identify, indicate, locate, recognize, report, review, select, translate

Understand - Construct meaning, clarify, paraphrase, represent, translate, illustrate, give examples, classify, categorize, summarize, generalize, predict…

Application - Apply, choose, demonstrate, dramatize, employ, illustrate, interpret, practice, write

Apply - Carry out or use a procedure in a given situation; carry out or use /apply to an unfamiliar task

Analysis - Analyze, appraise, explain calculate, categorize, compare, criticize, discriminate, examine

Analyze - Break into constituent parts, determine how parts relate

Synthesis - Rearrange, assemble, collect, compose, create, design, develop, formulate, manage, write

Evaluate - Make judgments based on criteria, check, detect inconsistencies/fallacies, critique

Evaluation - Appraise, argue, assess, choose, compare, defend, estimate, explain, judge, predict, rate, core, select, support, value

Create - Put elements together to form a coherent whole, reorganize elements into new patterns/ structures

Bloom – 1956 to 2001

Webb’s Depth of Knowledge Levels DOK 1 - Recall & Reproduction - Recall a fact, term,

principle, or concept, perform a routine procedure DOK 2 - Basic Application of Skills/Concepts - Apply

information or conceptual knowledge to routine situations or problems, select appropriate procedures for a task, complete two or more steps with decision points along the way, organize/display data, interpret/use simple graphs

DOK 3 - Strategic Thinking - Use reasoning to develop a plan or sequence of steps to approach a problem, make a claim and justify it using evidence, solve abstract, complex, or non-routine problems with more than one possible solution or solution path

DOK 4 - Extended Thinking – Investigate multi-faceted real-world problems, use multiple sources or an interdisciplinary approach to create new understanding of a topic

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Curriculum

DOK

1-4 DOK

1-4

DOK

1-4

September June

Unit of S

tudyUnit o

f Study

Unit of S

tudyUnit o

f Study

Unit of S

tudyUnit o

f Study

Weaving DOK into our current units of study and curriculum maps can help schools transition to the CCLS…

College & Career Trajectory

ACTIVITY #2

USING DEPTH OF KNOWLEDGE TO ASSESS THE RIGOR OF A MATHEMATICS TASK

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Assessing Rigor Using DOK

1. Work the task

2. Analyze the rigor of the task using the Cognitive Rigor Matrix

3. Suggest changes to modify the rigor of the task, when appropriate

4. Consider instructional supports that would need to be included in the unit that builds towards this task

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Reflection

When can you use DOK throughout the school year?

How can this process apply to other aspects of curriculum, assessment, and instruction in addition to culminating tasks?

What further support do you need in using DOK to assess and increase rigor in your classroom?

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Bridge to Practice

Use the Task Alignment Protocol to check the alignment of your own culminating task to the targeted standards of your unit.

Assess your culminating task for rigor using the Cognitive Rigor Matrix.

Based on your analyses, make any appropriate adjustments to your culminating task

Bring an instructional task for your unit.

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