facilitator: beth howard, edd project lead: camille chapman, med project team member: concepcion...
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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
800-476-6861 | www.sedl.org
Copyright ©2011 by SEDL. All rights reserved.Designated staff of the state departments of education for Alabama, Georgia, Louisiana, Mississippi, and South Carolina as well as staff in their respective school districts are granted
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copyright holders whose work SEDL included after obtaining permission as noted to reproduce or adapt for this document and related handouts.
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.
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
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