Facilitator: Beth Howard, EdDProject Lead: Camille Chapman, MEd

Project Team Member: Concepcion Molina, EdD

November 29, 30, and December 1, 2011

Implications for Instructional Modeling: Transitioning from Awareness to Implementation

of the Common Core State Standards in Mathematics

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Status of the Common Core

• As of today, 44 states and the District of Columbia have adopted the Common Core State Standards for Mathematics (CCSSM).

• Two consortia are developing assessments for the CCSSM.

• Textbooks are already being adapted and written to address the CCSSM.

Source: Content on slides 2–9 and 11–18 adapted by SEDL with permission from the Common Core State Standards Initiative (2010)

Benefits from the Common Core• Development of common assessments

• Policy and achievement comparisons across states and districts

• Development of curriculums, professional development, and assessments through collaborative groups

• Common learning goals for all students

• Coherence

• Focus

Reading the CCSSM• The CCSSM are composed of

– Standards (what students understand and should be able to do)

– Clusters (groups of related standards)

– Domains (larger groups of related standards, these are the big ideas that connect across topics)

All three of these are incorporated into the conceptual strands, such as Geometry.

CCSSM Example Grade 3

Measurement and Data (Domain)

Geometric measurement: understand concepts of area and relate area to multiplication (Cluster Heading)

3.MD.7. Relate area to the operations of multiplication and addition. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. (Standard)

K–2 Domains

• Counting and Cardinality (K only)

• Operations and Algebraic Thinking

• Number and Operations in Base Ten

• Measurement and Data

• Geometry

3–5 Domains

• Operations and Algebraic Thinking

• Number and Operations in Base Ten

• Number and Operations – Fractions

• Measurement and Data

• Geometry

6–8 Domains

• Ratios and Proportional Reasoning

• The Number System

• Expressions and Equations

• Geometry

• Statistics and Probability

High School Domains

• Number and Quantity• Algebra• Functions• Modeling• Geometry• Statistics and Probability

Note on course and transitions: Course sequence, K–7 standards prepare students for Algebra I in grade 8.

Standards for Mathematical Practice

CCSS Mathematical PracticesNational Council Teacher of Mathematics Processes

Make sense of problems and persevere in solving them

Problem Solving

Reason abstractly and quantitatively Reasoning and Proof

Construct viable arguments and critique the reasoning of others

Reasoning and Proof, Communication

Model with mathematics Connections

Use appropriate tools strategically Representation

Attend to precision Communication

Look for and make use of structure Communication, Representation

Look for and express regularity in repeated reasoning

Reasoning and Proof

Source: Fennell, 2011, adapted by SEDL with permission of the Center on Instruction

Standards for Mathematical Practice

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

– Look for entry points to a problem’s solution– Change course if necessary– Rely on concrete objects to conceptualize a problem– Check answers using alternate methods– Ask, “Does this make sense?”

2. Reason abstractly and quantitatively.

– Make sense of quantities and their relationships– Decontextualize and contextualize– Create a coherent representation of the problem– Attend to the meaning of quantities– Use different properties, operations, and objects

Standards for Mathematical Practice (Cont.)

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

– Understand and use assumptions and definitions in constructing arguments

– Make conjectures– Justify conclusions and explain to others– Decide whether arguments make sense– Ask questions to clarify arguments

Standards for Mathematical Practice (Cont.)

4. Model with mathematics.

– Apply mathematics to solve problems in everyday life– Make assumptions and approximations to simplify a

complicated situation– Identify quantities– Analyze relationships– Interpret mathematical results

Standards for Mathematical Practice (Cont.)

5. Use appropriate tools strategically.

– Consider available tools Pencil and paper Concrete models Ruler and protractor Calculator Software

– Identify relevant external mathematical resources

Standards for Mathematical Practice (Cont.)

6. Attend to precision.

– Communicate precisely to others– Use the equal sign consistently and appropriately– Specify units of measure– Label accurately– Calculate accurately and efficiently– Give carefully formulated explanations– Examine claims and make use of definitions

Standards for Mathematical Practice (Cont.)

7. Look for and make use of structure.

– Look for patterns or structure– Shift perspective– See complicated things as composition of simple

objects

Standards for Mathematical Practice (Cont.)

8. Look for and express regularity in repeated reasoning.

– Notice if calculations are repeated– Look for general methods and shortcuts– Maintain oversight of the process– Attend to details– Evaluate the reasonableness of results

Standards for Mathematical Practice (Cont.)

Crosswalk of the Measurement Strand in the 2007 South Carolina Mathematics Standards and the Measurement Domain in the Common Core State Standards for Mathematics for Grades 3–5

Differentiated Instruction: Learner-Centered Classrooms

To what extent are students provided instruction based on consideration of their individual needs?

Source: Content on slides 20–25 from Lewis (2011)

Differentiated Instruction: Learner-Centered Classrooms (Cont.)

Limited – All students are provided access to the same content, using the same materials, at the same time. Work products and assignments are the same for all students.

Ideal – The teacher uses multiple sources of data to guide the learning tasks and assignments that are challenging for all students. Formative assessment is used throughout the lesson.

Differentiated Instruction: Flexible Grouping

To what extent do students experience instructional processes that foster cooperation and collaboration?

Differentiated Instruction: Flexible Grouping (Cont.)

Limited – The teacher leads all instruction in a whole group format. Students, as an entire class, work independently on nearly all tasks and projects.

Ideal – The teacher provides whole group instruction for specific, planned tasks. Students work in temporary, flexible pairs/groups that are formed by the teacher, by student choice, or based on specific criteria.

Differentiated Instruction: Instructional Strategies and Learning Experiences

To what extent do students experience lessons that are varied and tailored to their instructional needs and interests?

Differentiated Instruction: Instructional Strategies and Learning Experiences (Cont.)

Limited – The teacher leads all instruction and learning tasks. Students have no choice in what they are doing and are told to work on homework if they finish a task early. Instructional materials are generally textbook, paper, pens, or pencils. Nonprint media is rarely used.

Ideal – The teacher provides instruction and creates opportunities for students to choose products and processes for their learning. Enrichment is provided for early finishers, and instructional materials are varied and rich.

Resources and Questions

ReferencesCommon Core State Standards Initiative. (2010). Common core

state standards for mathematics. Retrieved fromhttp://www.corestandards.org/the-standards/mathematics

Fennell, F. (2011). Common core state standards: Where are we and what’s next? (PowerPoint presentation). Retrieved from http://www.centeroninstruction.org/webex-common-core-state-standards-for-mathematics---what-how-when-and-how-about-you

Lewis, D. (2011). Differentiated instruction: An innovation configuration. Austin, TX: SEDL. 

For more information contact

Beth Howard, EdD

Program Associate

Southeast Comprehensive

Center at SEDL

681 Broughton Street

Orangeburg, SC 29115

803-240-1748

beth.howard@sedl.org

Camille Chapman, MEd

Program Associate

Southeast Comprehensive

Center at SEDL

3501 North Causeway Blvd.,

Suite 700

Metairie, LA 70002

800-644-8671

camille.chapman@sedl.org