Deep Dive into the Math Shifts

Deep Dive into the Math Shifts

Understanding Focus and Coherence in the Common Core State Standards for

Mathematics

The Three Shifts in Mathematics

•Focus: Strongly where the standards focus•Coherence: Think across grades and link to major topics within grades•Rigor: Require conceptual understanding, fluency, and application

http://www.parcconline.org/sites/parcc/files/PARCCMCFMathematics_August%202012rev2_FINAL.pdf

Algebra I Overview

http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf

http://www.parcconline.org/sites/parcc/files/PARCCMCFMathematics_August%202012rev2_FINAL.pdf

GeometryOverview

http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf

http://www.parcconline.org/sites/parcc/files/PARCCMCFMathematics_August%202012rev2_FINAL.pdf

Algebra II Overview

http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf

http://www.parcconline.org/sites/parcc/files/PARCCMCFMathematics_August%202012rev2_FINAL.pdf

Coherence Across and Within Grades

• It’s about math making sense.• The power and elegance of math comes out

through carefully laid progressions and connections within grades.

Taken from the Algebra II Course Description on C-Palms website: Don’t … Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Looking For Coherence Within Grades

• Examples: 6th grade: Solve problems by graphing in all 4

quadrants. (1st year of rational numbers) 8th grade: “Understand the connections between

proportional relationships, lines and linear equations.”

Algebra 1: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

Coherence Within A Grade

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

8.EE.6

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Coherence Within Geometry

Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

G-CO.5

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Looking for Coherence Across Grades

• Coherence is an important design element of the standards.

• “The Standards are not so much built from topics as they are woven out of progressions.”

DIVING IN! Let’s explore our new course descriptions for evidence of coherence!

Coherence Activity Form small groups with one teacher from each course in a progression such as

Algebra I, Geometry, and Algebra II; or Algebra II, Pre-Calculus, AP Calculus.

Goal: Find and chart two examples of coherence across courses and one example of

coherence within a course.

– Each group should study their course descriptions to find at least two progressions contained between courses.

– Progressions may be contained within a domain or may cross domains. (Refer to next slide the domains and their abbreviations)

– Find an example of coherence within a course and highlight the evidence of coherence.

– Use markers to indicate the standards as major, supporting, additional– If not a major focus of the course, discuss the supporting role of these standards to

the major work. 17

Domains for K-12K 1 2 3 4 5 6 7 8 HS

Counting

and Cardinality

(CC)

Number and

Quantity

Number and Operations in Base Ten (NBT) The Number System

Number and Operations-Fractions

(NF)

Ratios and Proportional Relationships

(RP)

Operations and Algebraic Thinking (OA)Functions (F)

Expressions and Equations (EE)

Algebra(A)

Geometry (G)

Measurement and Data (MD)

Statistics and Probability (SP)

(NQ)

Engaging with the HS ContentFocus Activity

1. How would you summarize the major work of grades 6-8, Algebra I, Geometry, or Algebra 2?

2. What would you have expected to be a part of the major work that is not?

3. Give an example of how you would approach something differently in your teaching if you thought of it as supporting the major work, instead of being a separate, discrete topic.

Engaging with the Content

Discuss the connection between focus and coherence and how the two work in tandem to influence instruction

Resources• Common Core Progressions http://ime.math.arizona.edu/progressions/

• PARCC Content Frameworkshttp://www.parcconline.org/sites/parcc/files/PARCCMCFMathematics_August%202012rev2_FINAL.pdf

• C-Palms Unpacking Maphttp://www.cpalms.org/cpalms/unpack_map.aspx

• Flip Chartshttp://www.azed.gov/azcommoncore/files/2012/11/high-school-ccss-flip-book-usd-259-2012.pdf