Common Core State Common Core State Standards in Standards in MathematicsMathematics

For Cluster 2 Network Leaders and TeamsPrepared and presented by Louise Antoine, Kerry Cunningham, Linda Curtis-Bey,

George Georgilakis, Carol Mosesson-Teig, Rose Shteynberg, Suzanne Werner 9/21/10

What are Standards?What are Standards?

Standards define what students should understand and be able to do.

Standards must be a promise to students of the mathematics they can take with them.

CCSS Mathematical PracticesCCSS Mathematical Practices

The Common Core proposes a set of Mathematical Practices that all teachers should develop in their students. These practices are similar to the mathematical processes that NCTM addresses in the Process Standards in Principles and Standards for School Mathematics.

CCSS Mathematical PracticesCCSS Mathematical Practices

The Common Core proposes a set of Mathematical Practices that all teachers should develop with their students. These practices are similar to the mathematical processes that NCTM addresses in the Process Standards in Principles and Standards for School Mathematics and informed by the Strands of Proficiency from Adding it Up from the National Research Council.

CCSS Mathematical PracticesCCSS Mathematical Practices

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

2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the

reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated

reasoning.

Common Core FormatCommon Core Format

High School

Conceptual Category

Domain

Cluster

Standards

K-8

Grade

Domain

Cluster

Standards

(There are no Pre-K Standards)

Grade Level OverviewGrade Level Overview

Grade Level OverviewGrade Level Overview

Critical AreaCritical Area

Cross- Cutting Themes

Cross- Cutting Themes

Format of K-8 StandardsFormat of K-8 Standards

StandardStandard

ClusterCluster

ClusterCluster

StandardStandard

Format of High School StandardsFormat of High School Standards

StandardStandard

ClusterCluster

DomainDomain

Common Core - DomainCommon Core - Domain

Overarching “big ideas” that connect topics across the grades

Descriptions of the mathematical content to be learned, elaborated through clusters and standards

Common Core - StandardsCommon Core - Standards

Content statements

Progressions of increasing complexity from grade to grade

High School High School Conceptual CategoriesConceptual Categories

The big ideas that connect mathematics across high school

A progression of increasing complexity

Description of the mathematical content to be learned, elaborated through domains, clusters, and standards

High School Conceptual High School Conceptual CategoriesCategories

Number & QuantityAlgebraFunctionsModelingGeometryStatistics & Probability

High School PathwaysHigh School Pathways

The CCSS Model Pathways are NOT required. The two sequences are examples, not mandates

Two models that organize the CCSS into coherent, rigorous courses

Four years of mathematics: ◦ One course in each of the first two years

◦ Followed by two options for year 3 and a variety of relevant courses for year 4

Course descriptions ◦ Define what is covered in a course

◦ Not prescriptions for the curriculum or pedagogy

High School PathwaysHigh School Pathways

Pathway A: Consists of two algebra courses and a geometry course, with some data, probability, and statistics infused throughout each (traditional)

Pathway B: Typically seen internationally, consisting of a sequence of 3 courses, each of which treats aspects of algebra; geometry; and data, probability, and statistics.

Answer Getting vs. Learning Answer Getting vs. Learning MathematicsMathematics

United StatesHow can I teach my kids to get the answer to this problem?Use mathematics they already know. Easy, reliable, works with bottom half, good for classroom management.

JapanHow can I use this problem to teach mathematics they don’t already know?

How might a fourth grader solve How might a fourth grader solve these problems?these problems?

145-100= 145 -100

145-98= 145 - 98

Students Ideas About MathStudents Ideas About MathD. Schifter and M. RiddleD. Schifter and M. Riddle

Read pages 28, 29, 30. STOP at Dig into Content Go back to Mathematical Practices in the

StandardsFind evidence for students’ use of some of

the Practices described in the CCSS document.

Domain Trace: Number and Domain Trace: Number and Operations in Base Ten: Grade 2Operations in Base Ten: Grade 2

Use place value understanding and properties of operations to add and subtract5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

DDomain Trace Number and omain Trace Number and Operations in Base Ten Grade 3Operations in Base Ten Grade 3

Use place value understanding and properties of operations to perform multi-digit arithmetic.

2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Trail Mix ProblemTrail Mix Problem

At your tables, begin solving the problem on your own.

Discuss and share solutions and strategies at your table.

Choose one solution to share. Put it on chart paper.

Take a BREAKTake a BREAK

Sharing Strategies Sharing Strategies

Listen

Connect

Compare

Looking at Student Work:Looking at Student Work:Trail Mix ProblemTrail Mix Problem

Look at samples of student work

Analyze for evidence of understanding through the CCSS Mathematical Practices

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LUNCH

Using Video to Using Video to Examine Teacher Examine Teacher

PracticePractice

Framework for ViewingFramework for Viewing

What does the teacher do to foster learning?

What is the impact on student learning?

What Are Mathematical Tasks?What Are Mathematical Tasks?

Mathematical tasks are a set of problems or a single complex problem the purpose of which is to focus students’ attention on a particular mathematical idea.

Why Focus on Mathematical Why Focus on Mathematical Tasks?Tasks?

Tasks form the basis for students’ opportunities to learn what mathematics is and how one does it;

Tasks influence learners by directing their attention to particular aspects of content and by specifying ways to process information;

Why Focus on Mathematical Why Focus on Mathematical Tasks?Tasks?

The level and kind of thinking required by mathematical instructional tasks influences what students learn; and

Differences in the level and kind of thinking of tasks used by different teachers, schools, and districts, is a major source of inequity in students’ opportunities to learn mathematics.

“Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.”

Stein, Smith, Henningsen, & Silver, 2000

“The level and kind of thinking in which students engage determines what they will learn.”

Hiebert et al., 1997

The Cognitive Level of TasksThe Cognitive Level of Tasks

• Lower-Level Tasks Memorization Procedures without connections

• Higher-Level Tasks Procedures with connections Doing mathematics

Task Analysis GuideTask Analysis Guide

Read over the Task Analysis Guide and highlight important words, phrases or ideas for each level.

Discuss at your table.

What type of task was the Trail Mix problem? Why?

Adapt-a-Task ActivityAdapt-a-Task ActivityChoose a standard from the 4th Grade or

from the 8th Grade CCSS in Mathematics.

As a group, write a low-level demand task on a large post-it note.

Discuss why the task is low-level demand using the Task Analysis Guide.

Adapt-a-Task Adapt-a-Task Three Stay-One Stray• Designate one person as the Traveler. The

Traveler takes the group’s low-level demand task and moves to the next table. The rest of the group stays.

• The Traveler explains why the task is a low- level demand task to the new group.

Adapt-a-Task Adapt-a-Task The new group creates a high-level

demand task from the low-level demand task using the Task Analysis Guide and the CCSS Standards for Mathematical Practices and writes their new task on chart paper.

Facilitator Walk

• Facilitators move the charted tasks from table to table.

Facilitator Walk (continued)

• Table groups evaluate the cognitive level of each task presented by the facilitator using the criteria from the Task Analysis Guide and writes the demand level (M, PwoC, PwC, DM) on a post-it note.

• The facilitator moves from table to table adding the post-it notes from each group to their charts.

• The facilitators discuss feedback on the tasks with the whole group.

ReflectionReflection Review of the CCSS in Mathematics

Article - Students Ideas About Math

Trail Mix Problem

Looking at Student Work

Using Video to Examine Teacher Practice

Adapt-a-Task (Low and High Level Tasks)

A Sample Plan for Year 1A Sample Plan for Year 1Explore and integrate at least one Mathematical

Practice, into your students’ repertoire of doing mathematics.

Integrate a Mathematical Practice into an existing unit of study in your curriculum map.

Explore and collect mathematical tasks that will support students’ use of the CCSS Mathematical Practices.

Collect student work and integrate looking at student work into your school’s inquiry team work.

Use classroom talk to support the CCSS Mathematical Practices.

Develop one Domain strand trace covering the grade spans of your school (e.g. K-5, K-8, 6-8, 6-12, etc)