“FOCUS” Common Core State Standards for
Mathematics
Summer Institute 2012
NCDPICurriculum and Instruction and
Educator Recruitment and Development
Overview• Assessment• Shifting Professional Development• Three Mathematical Shifts• Focus on “Focus”• Digging Deeper Conceptually• Developing and Implementing Resources • Time for Math
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning
of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.
Standards for Mathematical Practices
DuFours’ Four Questions• What do we want all students to know and be
able to do ?(initiated Summer 2011)
• How will we know when they have learned it?
• How will we respond when a student has difficulty learning it?
• What will we do when they already know it?
Mathematical Shift One: Focus
– What is the focus of your grade level?
–Linking to major topics: Instead of allowing less important topics to detract from the focus of the grade, these topics (additional and supporting) are taught in relation to the grade level focus.
Mathematical Shift Two: Coherence
• Principals and teachers carefully connect the learning within and across grades
• students can build new understanding onto foundations built in previous years
• Each standard is not a new event, but an extension of previous learning.
•
Coherence• Vertical– connections across the grades
• Horizontal – choose a major focus for your grade level / course and identify any standards that help to develop the concept (Bublus.com)
Coherence• Universal Design for Learning UDL
– Access
– Minimize need for remediation
• Navigations alignment
Dufour Question 2: How will you knowwhen they know it?
Looking at Student Work: LASW
• Analyze student work for rigor, coherence, and focus on standards.
• Build an in-depth understanding of mathematical practices
ASSESSMENT
www.smarterbalanced.org
2012 – 2013 and 2013 – 2014
School Years North Carolina written tests aligned to the
COMMON CORE State Standards
will be administered.
Technology and Testing Content of the North Carolina
assessments is aligned to the CCSS-M; however, the technology will not be as sophisticated as in assessments created by the Smarter Balanced Assessment Consortium (SBAC).
DuFour Question 3:
What will we do if they don’t learn it?
Dufour Question 4:
What if they already know it?
DAY 2: SHIFT THREE: RIGOR
• Rigor: Rquires a balance of the three discrete components of mathematics instruction required by the Standards.– Conceptual understanding,
– Application
– Fluency of Skills & procedures
Educating the Whole Child
1. How does this content area prepare students to be future ready?
2. How does this area connect to other content areas?
3. What are the implications for meeting the needs of all learners as related to this content area?
By the time many students hit middle school, disengagement has become a learned behavior
Keely Potter, Reading Specialist
Universal Design
Universal Design
for Learning (UDL) isUniversal Design for Learning
(UDL)A set of principles for curriculum
development that applies to the general
education curriculum to promote learning
environments that meet the needs of all
learners
Universal Design
Individualized
Instruction
Differentiated Instruction
Universal Design
Representation
EngagementActions and Expressions
UDL
UDL Principles
•
Principle I: Multiple Means of Representation:
The what of learning
• To give diverse learners options for acquiring information and knowledge
• Present content in a variety of formats and modalities
UDL requires:Multiple Means of Representation
Multiple Means of RepresentationExamples:
Manipulatives
Visual Displays
Anticipatory Guides
Graphic Organizers
Artifacts
Videos
Music
Movement
Text Readers
Principle II: Multiple Means of Action and Expression:
Judy Augatti
UDL requires:Multiple Means of Action and Expression
Examples:Thumbs Up/Thumbs Down
Gallery Walks
Pair/Share
Chalkboard/Whiteboard Splash
Response Hold-Up Cards
Quick Draws
Numbered Heads Together
Line-Ups
and
Principle III: Multiple Means of Engagement
Taps into learners’ interests, offers appropriate challenges, and increases
UDL requires:Multiple Means of Engagement
Examples:
Bounce Cards
Air Writing
Case Studies
Role Plays
Concept Charades
Response Hold-Up Cards
Networking Sessions
Simulations
With UDL more students are:
• Engaged
• Learning
• Achieving
• Motivated
Multiple Means of Representation for ELLs
Non-verbal• Modeling
• Pictures
• Realia/Concrete objects
• Gestures
• Manipulatives
• Demonstrations
• Hands-on
• Picture dictionaries
Language Support• Word banks
• Word walls
• Labels
• Graphic organizers
• Sentence starters
• Sentence frames
Multiple Means of Expressing for ELLs
• Role-play
• Illustrations/ Drawings / Visuals
• Gestures
• First language
Multiple Means of Engagement
• Student Interaction– Oral comprehension supports reading and
writing development
– Differentiate Collaborative Activities
Learning about Language• What does it say?
• What does it mean?
• What does it matter?
Implications for the Classroomexplicit teaching of language
• Create a language-sensitive classroom
• Deconstruct/reconstruct complex text
• View other languages as assets
Just as there are strategies for assisting the ELL student, there are strategies to move the AIG student even farther…
Gifted Education and new NCSCOS• An opportunity for growth and collaboration with regular
education and within the field of gifted.
• Students may access more rigorous standards throughout the day, which would impact direct gifted education services and ensure access to more advanced education throughout the day.– A rising tide raises all ships.
• CC/ES standards align with and validate gifted education best practices, such as concept-based learning, integration of disciplines, and inquiry-based options.
Why Gifted Students Need Differentiated Learning
For most.…•Faster pace of learning (2-3 repetitions)•Precocity for information•Ability to synthesize information within and across disciplines (conceptual understanding)•Intensity of learning in area of interest•Asynchronous development
What do gifted learners need in order to maximize their
learning?
Learning Needs of Gifted: Some, Not All
• Complexity: Abstract-thinking, Variety of concepts, subjects and strategies
• Depth: Higher levels of thinking, concepts• Creativity: Open-endedness, choice• Acceleration: Rapid pacing, Focus on
Growth• Relevance: Personal interest, Real-world
problems and audiences, Connections
What does this mean for my classroom?
• Enrich, extend and accelerate the SCOS.
• Differentiate through content, process and product.
Tools and Strategies for Challenging Gifted
Learners– Concept-Based Teaching– Tiered Assignments– Project-Based Learning– Curriculum Compacting– Independent Study with Rubrics– SeminarsOther:
All with appropriate challenge!
Non–Negotiables for Gifted Learners
• Gifted Children Vary in Needs and Strengths• Mindset of Differentiation in Class, School, LEA• Pre-assessment to understand needs and
strengths; Flexible Grouping• Social and Emotional Needs Addressed• Academic and Cognitive Growth Addressed
AIG: ALL DAY, EVERY DAY
NCDPI Arts Education Literacy Institute 2004
46
Serving All is a Process
Problems & Problem Solving
• Problem: Difference between expected/desired outcome and current outcome
• Problem identification: Finding a difference & determining if it is significant enough to require action now
• Problem solving: Figuring out how to eliminate or reduce difference
(Newton et al, 2009)
RtI• NC DPI has identified RtI
as a research-based school improvement model and provides support to district and school implementation through professional development, technical assistance, and coaching.
Problem-Solving, Data, & Decision-Making
• Decision making is aided by access to data• Providing instruction on a problem-solving model
(TIPS) will result in problem solving that is – Thorough– Logical– Efficient– Effective
• Structure of meetings lays foundation for efficiency and effectiveness
(Newton et al, 2009)
Collect & UseData
Develop Hypothesis
Discuss & Select
Solutions
Develop &ImplementAction Plan
Evaluate &Revise
Action Plan
Problem Solving Meeting Foundations
Team Initiated Problem Solving (TIPS) Model
Identify Problems
(Define & Clarify)
(Newton et al, 2009)
The Problem-Solving “Mantra”
• Do we have a problem?
• What is the precise nature of our problem?
• Why does the problem exist, & what can we do about it?
• What are the actual elements of our plan?
• Is our plan being implemented, and is it working?
• What is the goal?
(Newton et al, 2009)
Addressing the whole child prepares future-ready students who are competitive for work and post-secondary education and prepared for life in the 21st century.
Shifting Gears….
How did you become an effective teacher?
Where did this occur?
PHI DELTA KAPPA InternationalResearch Bulletin
“If we spend more money on traditional form of professional development, such as workshops, conferences, presentations, and courses remotely related to the daily challenges of teaching, we can expect little return on our investments.”
http://www.pdkintl.org/research/rbulletins/resbul27.htm
Key Points
Phi Delta Kappan, 2005
Professional development should involve teachers in the identification of what they need to learn and, when possible, in the development of the learning opportunity and/or process.
Phi Delta Kappan, 2005
Key Points Professional development
should provide opportunities to engage in developing a theoretical understanding of the knowledge and skills to be learned.
What Works?Effective Teacher Development
–Collaboration
–Coaching
–PLCsSteve Leinwand, 2012
Time to Reflect
Three Mathematical ShiftsFocus
Coherence
Rigor
PLC for Today• Norm
– Keep our focus on the students
• Goal
– Know and articulate the major work or your grade level or course.
– Experience and become familiar with rich lessons that go deeper into content
A focus on “FOCUS”In your PLC:
• Discuss the three topics provided for each grade level.
• Decide which of the three should not receive intense focus at the indicated grade.
• Identify clusters/standards as either– major work of the grade level
– supporting work of the grade level
– additional work of the grade level
• Indicate standards that seem to be similar to a 2003 standard but are different
In Your Grade Level Groups
Time to Reflect
LUNCH
Digging Deeper
• How is the task you did different from this typical worksheet found online or in textbooks?
“Turn and Talk”
Digging Deeper – Your Turn
• Choose one identified major standard.
• Discuss how to move from the “inch deep” model to a model that promotes deeper understanding?
When planning, ask
“What task can I give that will build student
understanding?”rather than
“How can I explain clearly so they will understand?”
Grayson Wheatley, NCCTM, 2002
Can “Good Tasks” Be Made Bad?
Time to Reflect
Food for Thought• NCTM’s Navigation Series
Until we meet again
• Performance metrics
www.ncdpi.wikispaces.net
Time to Reflect
DPI Contact Information
Kitty RutherfordElementary Mathematics [email protected]
Amy ScrinziElementary Mathematics [email protected]
Robin BarbourMiddle Grades Mathematics [email protected]
Johannah MaynorSecondary Mathematics [email protected]
Barbara BissellK – 12 Mathematics Section [email protected]
Susan HartProgram [email protected]