“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 Consultant919-807-3934kitty.rutherford@dpi.nc.gov

Amy ScrinziElementary Mathematics Consultant919-807-3839amy.scrinzi@dpi.nc.gov

Robin BarbourMiddle Grades Mathematics Consultant919-807-3841robin.barbour@dpi.nc.gov

Johannah MaynorSecondary Mathematics Consultant919-807-3842johannah.maynor@dpi.nc.gov

Barbara BissellK – 12 Mathematics Section Chief919-807-3838barbara.bissell@dpi.nc.gov

Susan HartProgram Assistant919-807-3846susan.hart@dpi.nc.gov