Transcript Implications for Instructional Modeling Transitioning from

Implications for Instructional Modeling:
Transitioning from Awareness to Implementation
of the Common Core State Standards in Mathematics
Facilitator: Beth Howard, EdD
Project Lead: Camille Chapman, MEd
Project Team Member: Concepcion Molina, EdD
November 29, 30, and December 1, 2011
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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 nonoverlapping rectangles and adding the areas of the nonoverlapping 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
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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 Practices
National 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.
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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?”
Standards for Mathematical Practice (Cont.)
2. Reason abstractly and quantitatively.
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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.
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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.
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Notice if calculations are repeated
Look for general methods and shortcuts
Maintain oversight of the process
Attend to details
Evaluate the reasonableness of results
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
References
Common Core State Standards Initiative. (2010). Common core
state standards for mathematics. Retrieved from
http://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-statestandards-for-mathematics---what-how-when-and-how-aboutyou
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
[email protected]
Camille Chapman, MEd
Program Associate
Southeast Comprehensive
Center at SEDL
3501 North Causeway Blvd.,
Suite 700
Metairie, LA 70002
800-644-8671
[email protected]