Mathematics and the Common Core

Principals’ ConferenceNovember 18, 2011

Common Core in Mathematics

Common Core Instructional Shifts in Mathematics

Video linking shifts to domains of focus

Domains of focus and DOE Expectations

What does this work look like in our schools?

Rigor: Tools and tasks

Important links/information to support Common Core Implementation

DOE EXPECTATIONS

Fall 2011 Teacher Teams engage in deep examination of

student work in comparison to expectations set out by

CCLS

Winter 2011 ELA and Math teachers work to adapt or

replace a unit so it is aligned with the CCLS and

includes a rigorous culminating task.

Teacher teams examine work generated by this unit to

determine a shared understanding of success (as

defined by the CCLS).

In partnership with the authors of the CORE…

The State has articulated shifts in Mathematics in order for us to have a framework through which to address the necessary changes in instruction

demanded by the Common Core.

These are the instructional shifts that are needed in order for students to

attain the standards.

6 Shifts in Mathematics

FocusCoherence

FluencyDeep Understanding

ApplicationDual Intensity

Instructional Shifts in MathRead, Pair, Share

Talking points:

How are these ideas similar or different than how teachers at your school have been teaching/thinking about math

instruction?

Which of these shifts is most urgent for your school?

What administrative supports can be made at your schools that will help teachers address the instructional shifts put forth by

the CCLS ?

Which shift/s appear to be most relevant to guide schools in achieving the winter citywide expectations?

Mathematics: Shift 1: FOCUS

Discussion between Commissioner King, David Coleman, and Kate Gerson, Senior Fellow for Educator Engagement & The Common Core, USNY Regents Research

Fund, regarding the importance of focused instruction to build on the necessary skills and concepts that

govern later success in mathematics.

http://vimeo.com/27068378

Shift 1:Focus

What challenges will we encounter as we make this shift?

Link Focus on a High-leverage areas of

mathematics

At least 1 Common Core aligned unit

Domains of focus

Embedded CC aligned rigorous task

Grade

Priorities in Support of Rich Instruction and Expectations of Fluency and

Conceptual Understanding

K–2Addition and subtraction, measurement using whole number quantities

3–5Multiplication and division of whole numbers and fractions

6Ratios and proportional reasoning; early expressions and equations

7Ratios and proportional reasoning; arithmetic of rational numbers

8 Linear algebra

Priorities in Math

12

How is NYC beginning the work of addressing Shift 1?

Schools have the flexibility to select the teachers who engage in this work, the types of tasks they teach, and the curriculum they

develop. Excerpted student work and diagnostic tasks aligned to the selected

Common Core math standards are available on the Common Core Library now:

http://schools.nyc.gov/Academics/CommonCoreLibrary .

Teachers will align at least one unit to Common Core in a high leverage area and embed culminating

performance task.

CCLS CONTENT AND MATHEMATICAL PRACTICES: NYC AREAS OF FOCUS

14

GRADE BAND

DOMAIN OF FOCUS

PreK-K Operations and Algebraic Thinking

1-2 Number and Operations in Base Ten

3 Operations and Algebraic Thinking

4-5 Number and Operations—Fractions

6-7 Ratios and Proportional Relationships

8 Expressions and Equations

Algebra Reasoning with Equations and Inequalities

Geometry Congruence

PLUS…

Targeted Standards of Mathematical

Practice:

MP.4 Model with Mathematics

and/or

MP.3 Construct Viable Arguments and Critique the Reasoning of Others

The Standards for Mathematical Practices are one of the most distinct portions of the

Common Core standards. Taken together, these standards paint a picture of a

mathematically proficient student. We understand that the Standards for

Mathematical Practice are interconnected and that a rich task may require students to

demonstrate many of the practices. However, for the winter task, we ask that schools focus on one or both of the high-leverage practices we’ve suggested and the domains of focus representing key content in each grade.

Model with Mathematics (#4) Construct Viable Arguments and

Critique the Reasoning of Others (#3)

Modeling is what real mathematicians do: using mathematics to represent and solve authentic problems in our world. Key to this process of

problem-solving is the ability to clearly construct and analyze mathematical arguments, evaluating

and articulating the reasoning behind claims. Facility with these two practices, and solid

knowledge of key concepts, will enable students to demonstrate their mathematical thinking by successfully analyzing authentic problems and

constructing and defending logical paths to solving problems.

How is this happening in our schools?

What are the differences and what are the commonalities happening in teacher teams?

What is different? Teacher teams are :

What is the same? All teams are:

•Working with existing curriculum units in the domain of focus and aligning to CCLS. “Rigoring up” an existing task•Planning from the DOE sample task bundle and using its’ performance task.• Some combination of the first two.•Other

•Looking at student work together to address instructional needs and measure instructional choices for future planning.•Aligning units of study to CCLS.•Looking at rigor of existing tasks and embedded tasks •Aligning tasks to the CCLS.•Refining rubrics/scoring for measuring progress on performance tasks.•Studying and learning about the domains of focus.

How are we assessing Rigor?

HESS’ Cognitive rigor matrix

Webb’s Depth of Knowledge

Stein and Smith’s Mathematical Task Analysis Guide

Hess’ Cognitive Rigor Matrix

Continued…

Grade 5 TasksChoose a Task Analysis Tool

Look at the problems

Discuss with a partner where you would place these tasks and why.

Upcoming Workshops

Grades K-2, November 30, PS 26, S.I.Grades 3-5, December 2, PS 69, BrooklynGrades 6-8, December 6, MS141, Queens

Thank you Principals for hosting!

ELEMENTARY WORKSHOPS:2 teachers from each school at each workshop

MIDDLE SCHOOL: 2-3 teachers from each school

Important Links

Videos links to Instructional ShiftsShift 1• http://vimeo.com/27068378 Shifts 2-6• http://vimeo.com/27066753Links for Standards, Tools and DOE Sample Tasks

• www.engageny.org• www.commoncore.org,• http://schools.nyc.gov/Academics/CommonCoreLi

brary.

Supporting DocumentsThe Model Content Frameworks serve two main purposes. They provide

support and guidance for implementation of the Common Core State Standards and information that will inform the design and development of PARCC assessments in grades 3–8 and high school.

 http://www.parcconline.org/parcc-content-frameworks

The Common Core State Standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics. These documents were spliced together and then sliced into grade level standards. From that point on the work focused on refining and revising the grade level standards. Please use these to deepen your content knowledge of the expectations of the CCLS and to inform your planning and instruction.

http://ime.math.arizona.edu/progressions/

THANK YOU!