Exploring the Impact of Common Core Standards on Math Instruction in your School.

Exploring the Impact of Common Core Standards on

Math Instruction in your School

Program

8.30 - 9.15 - Brief review of the components that drive changeRevisit characteristics of a professional learning community Brief introduction to the Four P’s - sustaining change in

schools9.15-9.45 - Review of lesson framework for CCS and its implications on

teaching instruction and assessment.9.45-10.00 - Review of CCS common language

10.00 – 10.45 -Deepening understanding of the impact of Mathematical Practices on teaching instruction.

10.45- 11.15 - Following a domain to identify implications for planning 11.15-12.00 - Use of the milestones as a framework for transitioning towards

the Common Core Standards12.00-1.00 - Lunch1.00-2.00 - Using essential questions to drive teaching instruction. Tiering

an exemplar based on schools current performance. Developing an understanding of the standard of the four levels of the rubric2.00-2.15 - Where to next

.

Characteristics of practice based professional learning

• Directly relates to school goals and teacher’s ability to meet these goals.

• Supports teachers in making explicit connections between what they do and what their students learn

• Everyone accepts personal responsibility for others learning and therefore shares knowledge, insights and experiences

• Everyone accepts personal accountability for learning and outcomes

• Teachers are empowered to design conduct and follow through on their own learning to attain greater depth of understanding.

• A safe environment that encourages teachers to take risks exists to enable them to explore, practice, reflect and refine.

Leading a Learning Community

Connecting

LearningOrganization

Engaging

Principles How do I make this work?

Parameters Rules of engagement

Purpose Why is this important?

Priorities Will this make a difference?

Sustaining Change in Schools Daniel P Johnson

Concrete – Abstract Balance in Schools

Concrete

Parameters

and

Priorities

Abstract

Purpose

and

Principles

People need to be engaged not interrupted

• Research has identified the following regard to peoples focus in schools

• Purpose – Why is it important?- focus on people – idealists (20-25%) • Parameters – What are the rules of engagement? (65-70%)• Principles – How do I make this work? – (5 – 7%) – principles that

define success• Priorities – Will this make a difference? – (35-40%) - value facts,

probability and possibility, beginning and end. Refocusing resources to the priorities.

• Two main groups • Concrete – Parameters or Guardians / Priorities or Artisians – • Abstract – Purpose or idealists / Principles or Rationals – relationship

between people and ideas.

The secret to sustaining quality is to link purpose to practice

Quality questions to consider• Purpose - What should students know and be able to do as

a result of their school experience? – Strategic Planning• Parameters – What will staff need to know and be able to

do in order to create programs and services that address students needs? – Shared decision making

• Principles – Who will monitor, align and adjust programs and services to ensure all students are successful? – Accountability

• Priorities – How will the resources support the quality programs and services – Resource alignment

“Everyone wants progress but no one wants to change”

1. Engaging peoples moral purpose- closing the gap on student achievement.

2. Building Capacity – policies, strategies, resources and actions used collectively to move forward. New knowledge skills and understandings competencies and shared commitment to work together.

3. Understanding the change process – ownership is acquired

through a quality change process. Establishing conditions for continuous improvement. Recognize the rise and flats issue.

8 Factors of Change - continued4. Developing cultures for learning – learning from one another,

networking

5. Developing a culture of evaluation- assessment for learning not just assessment of learning.Confronting the brutal facts through the use of technology supported systems.

6. Focusing on Leadership for change – how many leaders are left behind – leadership density.

7. Fostering coherence making – articulating how the change is impacting on the big picture, joining the dots.

8. Cultivating tri-level development – recognition of the interrelationship between school goals, district priorities and state policy.The presence of the core concepts does not guarantee success but their absence guarantees failure.

The Challenge of Change Michael Fullan

Assessment in the New World

“Assessment will alter teacher instruction”

• Multi-staged scenarios• Designing products or experiments• Manipulating parameters• Running tests and recording data• Incorporate audio and visual input• Problems posited in the real world requiring application of

critical thinking, creativity, collaboration and communication.

New Ways of PlanningUsing the pilot example provided identify the implications on Planning Teaching Assessment

GUIDING QUESTIONS

– What are the main components of this unit?– How do the essential questions drive the planning and teaching of this unit?– What are some of the differences to your current planning documents?– What do you see as the essential roles of the teacher?– What might be the impact on teaching with the inclusion of the two questioning types ?

(assessing and advancing)– To what degree does this example strive to construct meaning from the student’s current

experiences?– What mathematical practices underpin these lessons?– How do the activities promote the transfer of knowledge and skills to new situations?

REFLECTION

– What will need to change in your school/room to see lessons of this type as the norm?

Focus

Through • Concentration on number in elementary years• Emphasis on conceptual learning to counter

text book skill and drill• Emphasizing engagement of students

‘A mile wide and an inch deep’

Intent

• “These Standards are not intended to be new names for old ways of doing business.

• They are a call to take the next step. It is time for states to work together to build on lessons learned from two decades of standards based reforms.

• It is time to recognize that standards are not just promises to our children, but promises we intend to keep.”

CCSSM page 5

Are Standards the Curriculum?

“The standards do not dictate curriculum or teaching methods”

(p. 5)

Developing Common Language: How to read the grade level standards

Three Key Words

Domain Clusters

Standards

Turn to page 15.What do you think is the domain/the cluster/the

standard?

Organization of Mathematics Standards

• Mathematical PracticesEach grade level (K-8)• Critical Areas• Overview including the mathematical practices• Domains that progress over several grades• Clusters/Standards • High school standards presented by conceptual

theme ( Number & Quantity, Algebra, Functions, Modeling, Geometry, Statistics and Probability)

Organization of Mathematics Standards

Standards for Mathematical Practice

Grade LevelsCritical Areas of Instruction

Grade Level OverviewDomain & Cluster headings

Grade Level DomainsClusters

Standards

Match the Practice Heading to the Description

• You will find an envelope on your table• Your task is to match the Mathematical Practice heading with the matching description, using

the template providedNOTE:Where are the five current Process strands embedded within these

practices?Where are the Mathematical Proficiencies?

Understanding the Mathematical Practices

1. Make sense of problems and persevere in solving them2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning

of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated reasoning.

CoherenceStandards are coherent if they ….• are “articulated over time as a sequence of

topics and performances that are logical and reflect, where appropriate, the sequential or hierarchical nature of the disciplinary content from which the subject matter derives …”

• ”evolve from particular to deeper structures inherent in the discipline …which serve as a means of connecting the particulars”

William Schmidt and Richard Houang (2002)

How the Core Standards seek to achieve coherence

1. “Stressing conceptual understanding of key ideas”

2. “Continually returning to organizing principles, such as place value or properties of operations to structure those ideas”

3. “Respect what is known about how students learn”

CCSSM page 4

NOTE

Standards from different clusters may sometimes be closely related,

because mathematics is a connected subject

Intentional Design Limitations

What the Standards do not define:• How teachers should teach• All that can or should be taught• The nature of advanced work beyond the core• The interventions needed for students well below

grade level• The full range of support for English Language

Learners and students with special needs• Everything needed to be college and career ready

Understanding Mathematics

• “One hallmark of mathematical understanding is the ability to justify, in a way appropriate to a student’s mathematical maturity why a mathematical statement is true or where a mathematical rule comes from”

• “Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness”

CCSSM page 4

Differentiation

• “The standards should be read as allowing the widest possible range of students to participate fully from the outset, along with appropriate accommodates to ensure maximum participation of students with special education needs.”

CCSSM page 4

Reflect a Moment…

* Turn to the person beside you

* Recount three key ideas that you have reflected on to this point

Standards for Mathematical Practice

Standards for Mathematical Practice

• “Describe varieties of expertise that mathematic educators at all levels should seek to develop in their students”

• Based on important processes and proficiencies:

NCTM Process Strands & National Research Council’s proficiencies

Critical Focus Areas – Descriptions of Student Learning

• Based on NCTM’s Focal Points• Articulate some of the most important aspects of the

core standards• Language explicitly integrates process and

conceptual development• They provide an effective lens to look at growth

across grade levels• A natural starting point for developing rubric

development associated with rich assessment tasks

Trends - Discussion Points

1. Links through grade levels that provide content coherence

2. Evidence in the language that suggests changing requirements with respect to student thinking

3. Differences in content requirements compared with the NY standards

5 Levers of School Improvement

1. Curriculum -What are the academic tasks that we ask students to do?

2. Pedagogy- How do the teachers support student learning?

3. Assessment and data- How do we know students are learning?

4. Professional Collaboration- How do adults learn and improve their practice?

5. Structure- How do we use time, space and other resources to enable student learning?

Milestones for the Common Core Standards

Guide to help teams, schools and networks figure out where they are and where

they should go next on the road to full implementation of the Common Core

Standards

Milestones for Common Core Standards

• Highlight in each area the current reality for your school.

• Asterisk the next milestone in each area- this can become the basis for your school’s CCS action plan

Curriculum

Pedagogy

Assessment

Collaboration

Structure

Pivotal School Structures• Strategic Action Plan-embedded within CEP/PPR• Embedded within Yearly Professional Development Plan• Balanced Mathematics• Workshop Model- whole/part/whole model• Guided Mathematics• Focus on Writing Mathematically/Problem Solving• Curriculum Maps/pacing calendars linked to current and

common core standards• Scheduling- common preps/teacher teams to investigate CCS

further • Part of Data Inquiry Work

Questions – Doorways to

Understanding

Stage One Review Cycle

Stage One

Identify the big ideas

Align big ideas to the standard

The student will understand that

…Identify key

knowledge and skills

Assess against the rubric

identify possible confusion

Develop essential

question to guide inquiry

What is an Essential Question?Characteristics of Essential Questions• They have no simple right answer.• They are designed to foster the development of critical

thinking skills and higher order capabilities.• It is the principle component of inquiry based learning.• They probe for deeper meaning and set the stage for

learners to ask further questions.• Often address the conceptual or philosophical

foundations of a discipline.• Stimulate vital, ongoing rethinking of big ideas,

assumptions and prior lessons.

Grant Wiggen’s response • A question is essential when it: • Causes genuine and relevant inquiry into the big ideas and core

content;• Provokes deep thought, lively discussion, sustained inquiry, and new

understanding as well as more questions;• Requires students to consider alternatives, weigh evidence, support

their ideas, and justify their answers;• Stimulates vital, on-going rethinking of big ideas, assumptions, and

prior lessons;• Sparks meaningful connections with prior learning and personal

experiences;• Naturally recurs, creating opportunities for transfer to other

situations and subjects.

Exploring the Eight Mathematical Practices

• In pairs identify the various Mathematical Practices that will be required to complete the exemplar – labeling them 1 -8

• Read the details of these practices in the Common Core Standard document and underline any significant words.

• Can you identify any challenges in regard to current teaching and learning to ensure the Mathematical Practices are incorporated in the daily Math Lesson.

• Are some of the Mathematical Practices more easily incorporated into the daily Math lesson than others?

• If so how might this issue be addressed?

• Understanding - Numbers can represent, quantity, position, location and relationship.How is math relevant to me?

– Relate and apply concepts & skills to daily life

What do numbers convey? – Identify amount (cardinal) – Name position (ordinal) – Indicate location (nominal) –

How can numbers be expressed, ordered, and compared? – Read and write positive numbers, decimals, and fractions – – Sequence numbers: zero through one billion – Compare quantities as more, less, equal (>, <, =)

Understanding - Numbers can be classified by attributes What are properties of whole numbers?

– Understand odd and even– Identify prime and composite– Create figurate numbers (ex: square, triangular)

Understanding - Counting finds out the answer to how many in objects or setsWhat are different ways to count?

– Count all – Count on – Count back – Skip count – Count groups

What are efficient ways to count? - count up (or back) from largest number– Count sets of items – Count to using landmark numbers (ex: 10, 25, 50, 100)

Slide to support reflection activity

Do the students in your class know before the unit of work

• What they are required to learn• The Unit goals• The performance requirements• The evaluative criteria• The reason for engaging in the task in relation to furthering understanding of real life

problems

Are the students in you class provided with • Adequate opportunities to explore and experience the big ideas and receive

instruction to equip them for the required performance.• Sufficient opportunities to rethink, rehearse, revise and refine their work based on

timely feedback• Opportunities to evaluate their work , reflect on their learning and consider whether

they achieved their personal goals. • What evidence do you have to justify your assessment? • What strategies do you implement to hook the student into wanting to be engaged in

the unit of work?

Action Planning Brainstorm

Focus Area 2011 2012 2013

Curriculum

Pedagogy

Assessment

Collaboration

Structures

Time to reflect on your learning’s from this workshop

• What are you going to share with others when you are back in your school?

• What are you going to change when you return to your school?• What are you going to consider when you return to your school?

Managing tasks and leading people – It’s a hard, it’s bumpy and it takes as long as it takes

Michael Fullan p.21

Reflection

Where to from here?• Start small think BIG• Use the 6 facets of understanding and the Mathematical

Practices as a guide when planning.• Use the notes you made today on your reflection sheet to

view your teaching through a different lens.• During grade meetings share with your team how you are

striving to incorporate some of the learning’s from this workshop into your teaching practice.

• Look for resources to support you into diving into the world of tasks. A good place to start is looking at the material available on National Council of Teachers of Mathematics www.nctm.org

If you don’t put your toe in the water you will never learn to swim