convocation 2013

Convocation 2013

Common Core Mathematics Updates

Universal Design for Learning (UDL)

A set of principles forcurriculum development that applies

to the general education curriculum to promote learning environments that meet the needs of all

learners

UDL

UDL Principles

UDLPrinciple 1:

Representation

Multiple Means of Representation Improves Learning for All

Non-verbal

• Modeling• Pictures/videos• Realia/Concrete objects • Gestures• Movement• Manipulatives• Demonstrations• Hands-on• Picture dictionaries

Language Support• Word banks• Word walls• Labels• Graphic organizers• Sentence starters• Sentence frames

Represent

Act/Express Engage

Principle II:Multiple Means of Action and Expression

Judy Augatti

RepresentRepresent

ActionExpression

Engage

UDLPrinciple 2:Action and Expression

Multiple Means of Action and Expression• Role-play• Illustrations/ Drawings / Visuals • Gestures• First language use• Online tools (journaling, blogging, interactive

math problem solving, assessments)

Represent

ActionExpression

Engage

Principle III:

Multiple Means of Engagement

Represent

Act/Express

Engage

Principal 3:Engagement

Multiple Means of Engagement

• Graphics• Group Writing• Problem Solving

Teams• Role Plays• Interest Projects

•Response Cards •Student Presentations•Real Life Simulations •Online tools•Manipulatives

UDL RequiresMultiple Means of Engagement

How do you meet the needs ofStudents Identified as Gifted?

1. Complexity: Abstract-thinking, Variety of concepts, subjects and strategies

1. Depth: Higher levels of thinking, concepts

1. Creativity: Open-endedness, choice

1. Acceleration: Rapid pacing, Focus on Growth

1. Relevance: Personal interest, Real-world problems and audiences, Connections

Give One – Get One

Leigh Daniels AccelerationI love to use the NCCTM website to find acceleration opportunities for my students with Illuminations activities.

http://goo.gl/1RDZN

FocusWhat do we want students to know and be able to do?

CoherenceHow will we know when they know it? What will we do when they don’t know it?

RigorWhat will we do when they know it?

FOCUS

Rather than racing to cover everything in today’s mile-wide, inch-deep curriculum, teachers use the power of the eraser and significantly narrow and deepen the way time and energy is spent in the math classroom.

cc: Microsoft.com

Math I Wordle

“Math Content Emphases” Read the Introduction to the Major Work Booklet.

What is the relationship between the major work and the additional/supporting work?

How does this focus result in fewer objectives that go deeper?

cc: Microsoft.com

Content Emphasis After reading sample

CCSSM topics for their grade, ~80% say CCSSM is “pretty much the same” as their former standards

If CCSSM places a topic they currently teach in a different grade only about ¼ would drop it

- Bill Schmidt, Achieve

cc: Microsoft.com

Points to Ponder

• 85% of teachers say the textbook is main resource- rather than the standards.

Barbara Reyes

cc: Microsoft.com

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Effective Instructional Tasks

“Tasks that demand engagement with concepts and that stimulate students to make purposeful connections to meaning or relevant mathematical ideas which lead to a different set of opportunities for student thinking.”

Stein, Smith, Henningsen, & Silver, 2000, p. 11

What are Features of a Good Task?

• Challenges the learners to think for themselves and make decisions.

• Offers different levels of challenge.• Encourages collaboration and discussion.• Has the potential for revealing patterns or

leading to generalizations.

nrich.maths.orgnrich.maths.org

What are Features of a Good Task?

• Begins where the students are; accessible to wide range of learners.

• Requires justifications and explanations for answers and methods. – “Show the mathematics you used and explain

your reasoning” (Connecticut Dept. of Education)

• Has a focus on making sense of the mathematics involved and thereby increasing understanding.

Van de Walle, 2004

Why are Instructional Tasks Important?

….it is the level and kind of thinking in which students engage that determines what they will learn.

Stein, Smith, Henningsen, & Silver, 2000, p. 4

Three Mathematical Shifts

FocusWhat do we want students to know and be able to do?

CoherenceHow will we know when they know it? What will we do when they don’t know it?

RigorWhat will we do when they know it?

• Fragmenting the Standards into individual standards, or individual bits of standards, erases all these relationships and produces a sum of parts that is decidedly less than the whole.

Looking for Coherence “Measuring in the Round”

Using the sheet: Shift Two: CoherenceThinking Across Grades / Courses, Linking to Major Clusters copy all of the standards leading to and related to “Measuring in the Round” and note how coherence is evident in these standards.

Team Initiated Problem Solving

(TIPS)

(Newton et al, 2009)

CollectCollect& Use& UseDataData

Develop Hypothesis

Discuss &Select

Solutions

Develop &ImplementAction Plan

Evaluate &Revise

Action Plan

Problem SolvingMeeting Foundations

Identify Problems(Define & Clarify)

What’s the Area?

A square piece of paper is folded in half to form a rectangle with a perimeter of 12 cm. What is the area of the original square?

Not drawn to scale

Our Goals• Know the three shifts -- focus, coherence

and rigor.– Understand the importance of focus for the

coming year • Develop plans to ensure all NC teachers

know the major work (“focus”) of their grade or course.

• Plan your time, money, and effective PD around the major focus of your grade or course.

Our Goals• Establish how the three shifts address these

questions:1. What do we want students to know and be able to do?2. How can we ensure that all children have the opportunity to

learn?3. What do you do if they don’t know it?4. What do you do if they know it?

• Experience instruction that will support learning for all students.

• Identify strategies used to support diverse learners.

Looking at Student Work

Three Mathematical ShiftsFocus

What do we want students to know and be able to do?

CoherenceHow will we know when they know it? What will we do when they don’t know it?

RigorWhat will we do when they know it?

What Is Rigor?

• Conceptual Understanding:– Beyond mnemonics or discrete procedures– Problem-Based– Apply math in new situations– Speak/Write about their understanding

• Procedural Skill & Fluency:– Opportunities to practice core functions to increase speed & accuracy

in calculations• Application:

– Use math in “real world” situations– Choose the appropriate concept for application

RIGOR

ConceptualUnderstanding

Application

Skills and Procedures

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

JohannahMaynorHigh SchoolMathematics Consultant919-807-3842johannah.maynor@dpi.nc.gov

Mary KeelProfessional Development Lead Region 2252.725.2570mary.keel@dpi.nc.gov

Paul MarshallProfessional Development Lead Region 3919-225-0655paul.marshall@dpi.nc.gov

Gertrude Lyons-NewkirkDistrict and School Transformation919-gertrude.newkirk@dpi.nc.gov

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

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

DPI Contact Information