Common Core State StandardsMathematics

Digital Learning Cadre

Renee Parsley James Dick Mathematics Education Associate Mathematics Education Associate

Common Core Standards

These Standards are not intended to be new names for old ways of doing

business. They are a call to take the next step…It is time to recognize that standards are not just promises to our

children, but promises we intend to keep.

-CCSS pg. 5

Why the Common Core?

Rationale for the CCSS

Declining US competitiveness with other developed countries

NAEP performance that is largely flat over the past 40 years in 8th grade

Slight improvement at the 4th grade level

Slight decline at the high school level

High rates of college remediation

4

Principles of the CCSS

Aligned to requirements for college and career readiness

Based on evidence

Honest about time

5

The Core Shifts 3 Core Shifts in Math

Shifts offer a way to focus on the few things that have the most significant return for students

Shifts should guide all aspects of implementing the Standards Professional Development Assessment Design Curriculum

College Math Professors Feel HS Students Today are Not Prepared for College Math

Why Math Common Core? For over a decade, research studies of

mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more FOCUSED and COHERENT in order to improve mathematics achievement in this country.

To deliver on the promise of common standards, the standards must address the problem of a curriculum that is “a mile wide and an inch deep.” The Common Core Standards are a substantial answer to that challenge.

The Mathematics Standards: Key Changes and Their Evidence by Dr.

William McCallum

The CCSS Requires Three Shifts in Mathematics

1. Focus: Focus strongly where the standards focus

2. Coherence: Think across grades, and link to major topics

3. Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application

Shift #1: Focus Strongly where the Standards Focus

Significantly narrow the scope of content and deepen how time and energy is spent in the math classroom.

Focus deeply on what is emphasized in the standards, so that students gain strong foundations.

Focus

Move away from "mile wide, inch deep" curricula identified in TIMSS.

Learn from international comparisons.

Teach less, learn more.

“Less topic coverage can be associated with higher scores on those topics covered because students have more time to master the content that is taught.”

– Ginsburg et al., 2005

Mathematics topics intended at each grade by at least two-thirds of A+ countries

Mathematics topics intended at each grade by at least two-thirds of 21 U.S. states

The Shape of Math in A+ countries

1 Schmidt, Houang, & Cogan, “A Coherent Curriculum: The Case of Mathematics.” (2002).

FOCUS 1st Grade CCSS: 21 Standards (1 every 9 days) 1st Grade G.L.E.’s: 30 Standards (1 every 6 days)

2nd Grade CCSS: 26 Standards (1 every 7 days) 2nd Grade G.L.E.’s: 34 Standards (1 every 5 days)

3rd Grade CCSS: 25 Standards (1 every 7 days) 3rd Grade G.L.E.’s: 36 Standards (1 every 5 days)

Focus 4th Grade CCSS: 28 Standards (1 every 6.4 days) 4th Grade G.L.E.’s: 45 Standards (1 every 4 days)

5th Grade CCSS: 26 Standards (1 every 7 days) 5th Grade G.L.E.’s: 52 Standards (1 every 3.5

days)

6th Grade CCSS: 29 Standards (1 every 6 days) 6th Grade G.L.E.’s: 39 Standards (1 every 5 days)

Focus

7th Grade CCSS: 24 Standards (1 every 7 days) 7th Grade G.L.E.’s: 46 Standards (1 every 4 days)

8th Grade CCSS: 28 Standards (1 every 6 days) 8th Grade G.L.E.’s: 45 Standards (1 every 4 days)

GradeFocus Areas in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding

K–2Addition and subtraction – concepts, skills, and problem solving and place value

3–5Multiplication and division of whole numbers and fractions – concepts, skills, and problem solving

6Ratios and proportional reasoning; early expressions and equations

7Ratios and proportional reasoning; arithmetic of rational numbers

8 Linear algebra

Key Areas of Focus in Mathematics

Shift #2: Coherence: Think Across Grades, and Link to Major Topics

Within Grades

Carefully connect the learning within and across grades so that students can build new understanding on foundations built in previous years.

Begin to count on solid conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.

One of several staircases to algebra designed in the OA domain.

Alignment in Context: Neighboring Grades and Progressions

Shift #3: Rigor: In Major Topics, Pursue Conceptual Understanding, Procedural Skill and Fluency, and Application

The CCSSM require a balance of: Solid conceptual understanding Procedural skill and fluency Application of skills in problem solving situations

Pursuit of all three requires equal intensity in time, activities, and resources.

Solid Conceptual Understanding

Teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives

Students are able to see math as more than a set of mnemonics or discrete procedures

Conceptual understanding supports the other aspects of rigor (fluency and application)

Fluency

The standards require speed and accuracy in calculation.

Teachers structure class time and/or homework time for students to practice core functions such as single-digit multiplication so that they are more able to understand and manipulate more complex concepts.

Required Fluencies in K-6Grade Standard Required Fluency

K K.OA.5 Add/subtract within 5

1 1.OA.6 Add/subtract within 10

2 2.OA.22.NBT.5

Add/subtract within 20 (know single-digit sums from memory)Add/subtract within 100

3 3.OA.73.NBT.2

Multiply/divide within 100 (know single-digit products from memory)Add/subtract within 1000

4 4.NBT.4 Add/subtract within 1,000,000

5 5.NBT.5 Multi-digit multiplication

6 6.NS.2,3 Multi-digit divisionMulti-digit decimal operations

Application Students can use appropriate concepts and

procedures for application even when not prompted to do so.

Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations, recognizing this means different things in K-5, 6-8, and HS.

Teachers in content areas outside of math, particularly science, ensure that students are using grade-level-appropriate math to make meaning of and access science content.

The Coming CCSS Assessments Will Focus Strongly on the Major Work of Each Grade

MATH CCSS Grade-Level Standards

• K-8 grade-by-grade standards organized by domain.• 9-12 high school standards organized by conceptual

categories.

Standards for Mathematics Practice• Describe mathematical “habits of mind”.• Connect with content standards in each grade.• Standards for mathematical proficiency:

reasoning, problem solving, modeling, decision making,

and engagement.

OVERVIEW OF K-8 CCSS

OVERVIEW OF K-8 CCSS Domains: big ideas that connect topics across the

grades. Clusters: illustrate progression of increasing

complexity from grade to grade. Standards: define what students should know and

be able to do at each grade level.

High School Math Standards Content Categories: big ideas that describe

strands of content in high school.

Domains/Clusters: groups of standards that describe coherent aspects of the content category.

Standards: define what students should know and be able to do.

High School Math Standards Organized around five conceptual categories:

Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability.

Modeling Standards are distributed under the five major headings and are indicated with a (*) symbol.

Standards marked as (+) are beyond the college and career readiness level but are necessary for advanced math courses.

Overview of High School

Model Course Pathways Developed by a panel of experts convened

by Achieve, including many of the standards writers and reviewers.

Organize the content of the standards into coherent and rigorous courses.

Illustrate possible approaches - models, NOT mandates.

Model Course Pathways 4 Pathways Indentified:

1. Traditional Pathway

2. Integrated Pathway

3. Compact (Advanced) Traditional

4. Compact (Advanced) Integrated

Model Course Pathways

Model Course Pathways All of this information is contained in

Appendix A of the CCSS.

Resources Common Core State Standards Website

What is Being Done? Math Cadre is developing grade specific

instructional shifts modules for use during in-service/PLC time

“Common Ground” Training- ongoing PD around the CCSS. School Teams participate.

Next Steps? How can the Digital Learning Cadre assist

in the implementation of the CCSS?