common core dissection 1

Common Core Dissection

Staff Development Day Friday, March 23, 2012

Stages of CCSS in Mathematics

Denial

This can’t be happening! I

finally understand the 2005

standards!

Anger

It’s unfair! They are changing

the curriculum, the test, and the

evaluation system at the same time!!

BargainingI promise I’ll be a good teacher, if you will

just leave the math curriculum alone.

Depression

I don’t care anymore. I’ll

teach whatever they

tell me.

Acceptance

OK-I’m ready to take on the Common

Core. Where do I start?

Common Core Introduction

The State has provided each grade level with its own introduction to the Common Core Learning Standards

What do you notice about the focus of the introduction in your grade-level?

Math Practices

• On posters around the room, you will find the eight math practices.– These represent the 8 ’habits of mind’ that connect

the entire pre-K through 12 continuum.

• Please take a few minutes to reflect on each math practice statement and consider– What does it mean?– What does it look like?

1. Make Sense of Problems and Persevere

in Solving Them• Read and understand the problem

• Organize information to make a plan (more than one approach is acceptable)

• Solve and adjust the process as necessary

• Evaluate the solution and decide how you will use the solution to answer the question

2. Reason Abstractly and Quantitatively

• Take a given situation and represent it symbolically (decontextualization)

• Assign meaning to the symbols by putting them back in context (contextualize)

3. Construct Viable Arguments and Critique the

Reasoning of Others

• Listen to or read the arguments of others

• Decide whether the arguments make sense

• Ask useful questions to clarify or improve the arguments

4. Model With Mathematics

• Apply math concepts to solve problems that arise in every day life

• Simplify a complicated situation and make revisions as needed

• Use tools such as diagrams, graphs charts to analyze math relationships and draw conclusions

• Interpret results and reflect, “Does this make sense?”

• Make adjustments, if necessary

5. Use Appropriate Tools Strategically

• Consider available tools such as paper/pencil, concrete models, rulers, software

• Develop a familiarity with tools

• Make sound decisions about which tools to use for the situation

• Use technological tools to deepen the understanding of concepts

6. Attend to Precision

• Calculations are accurate and efficient

• Explanations include clear definitions, correct use of symbols (especially the equal sign), units of measure, axes labels, etc.

7. Look For and Use Structure

• Look for patterns and use what is known to apply or extend the pattern

• Look for structure by identifying the conceptual way that we think about math

• Find and follow the “rules” that mathematicians use to solve problems

8. Look For and Express Regularity in Repeated Reasoning

• Notice repetitive actions in counting and computation

• Look for shortcuts such as rounding

• Continuously check work to see if answers are reasonable

• Ask, “Does the answer match the question?”

The Six Shifts in Mathematics• SHIFT 1: FOCUS• SHIFT 2: COHERENCE• SHIFT 3: FLUENCE• SHIFT 4: DEEP

UNDERSTANDING• SHIFT 5: APPLICATION• SHIFT 6: DUAL INTENSITY

Group Discussion:• What does this shift mean?• What does it look like in the classroom?

From the teacher’s perspective?From the students’ perspectives?

Mathematics Shift 1: FocusWhat the Student Does… What the Teacher Does… What the Principal Does…•Spend more time thinking and working on fewer concepts.•Being able to understand concepts as well as processes (algorithms).

•Make conscious decisions about what to excise from the curriculum and what to focus•Pay more attention to high leverage content and invest the appropriate time for all students to learn before moving onto the next topic.•Think about how the concepts connects to one another•Build knowledge, fluency and understanding of why and how we do certain math concepts.

•Work with groups of math teachers to determine what content to prioritize most deeply and what content can be removed (or decrease attention). •Determine the areas of intensive focus (fluency), determine where to re-think and link (apply to core understandings), sampling (expose students, but not at the same depth).•Determine not only the what, but at what intensity.•Give teachers enough time, with a focused body of material, to build their own depth of knowledge.

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An Examination of Focus

• The standards were written to reflect a deepening of key understandings at certain grade levels.

• There are 2-4 focal areas per grade-level.

• To ensure the degree of understanding and application required, more time and practice will need to be devoted to these particular concepts.

Intense focus70%

Rethink and link20%

Sampling10%

K - 2 Addition and Subtraction

Concepts Skills Problem Solving

Geometry and Measurement

PatternsStatistics and Data

ProbabilityEstimating Arithmetic

3 - 5 Multiplication and Division of Whole Numbers and Fractions A good balance of

o Conceptso Skillso Problem

Solving

AreaVolume

PatternsStatistics and Data

Probability

6 - 8 Proportional Reasoning & Linearity

AlgebraGeometric

Measurement

Quantitative Relationships &

Functions

Statistics

GradePriorities in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding

K–2 Addition and subtraction, measurement using whole number quantities

3–5 Multiplication and division of whole numbers and fractions

6 Ratios and proportional reasoning; early expressions and equations

7 Ratios and proportional reasoning; arithmetic of rational numbers

8 Linear algebra

Priorities in Math

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Mathematics Shift 2: CoherenceWhat the Student Does… What the Teacher Does… What the Principal Does…

•Build on knowledge from year to year, in a coherent learning progression

•Connect the threads of math focus areas across grade levels•Think deeply about what you’re focusing on and the ways in which those focus areas connect to the way it was taught the year before and the years after

•Ensure that teachers of the same content across grade levels allow for discussion and planning to ensure for coherence/threads of main ideas

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Mathematics Shift 3: Fluency

What the Student Does… What the Teacher Does… What the Principal Does…

•Spend time practicing, with intensity, skills (in high volume)

•Push students to know basic skills at a greater level of fluency•Focus on the listed fluencies by grade level•Create high quality worksheets, problem sets, in high volume

•Take on fluencies as a stand alone CC aligned activity and build school culture around them.

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The Special Case of Fluency

• Fluency is more than just “knowing facts by memory”

• It is the fast and accurate completion

of a continuum of mathematical operations and procedures

• Each grade level has 1-2 key fluency goals

Mathematics Shift 4: Deep Understanding

What the Student Does… What the Teacher Does… What the Principal Does…

•Show, through numerous ways, mastery of material at a deep level•Use mathematical practices to demonstrate understanding of different material and concepts

•Ask yourself what mastery/proficiency really looks like and means•Plan for progressions of levels of understanding •Spend the time to gain the depth of the understanding•Become flexible and comfortable in own depth of content knowledge

•Allow teachers to spend time developing their own content knowledge•Provide meaningful professional development on what student mastery and proficiency really should look like at every grade level by analyzing exemplar student work

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Mathematics Shift 5: ApplicationWhat the Student Does… What the Teacher Does… What the Principal Does…

•Apply math in other content areas and situations, as relevant•Choose the right math concept to solve a problem when not necessarily prompted to do so

•Apply math including areas where its not directly required (i.e. in science)•Provide students with real world experiences and opportunities to apply what they have learned

•Support science teachers about their role of math and literacy in the science classroom•Create a culture of math application across the school

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Mathematics Shift 6: Dual IntensityWhat the Student Does… What the Teacher Does… What the Principal Does…

•Practice math skills with an intensity that results in fluency•Practice math concepts with an intensity that forces application in novel situations

•Find the dual intensity between understanding and practice within different periods or different units•Be ambitious in demands for fluency and practice, as well as the range of application

•Provide enough math class time for teachers to focus and spend time on both fluency and application of concepts/ideas

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FLUENCYDEEP UNDERSTANDING

APPLICATION

Procedural Fluency

Conceptual Understanding Application

Shift 6 Dual Intensity

Highlight

• In one color, highlight the content that we currently teach

• In another color, highlight the content that is NEW to our grade level

An example from 4th grade

Skill (verb) Content (noun) Method (using…)Recognize Relationship between digits

(any place is 10 times the digit to its right)

Read Multi-digit whole numbers Base-ten numerals, number names, expanded form

Compare Multi-digit whole numbers Place value

Let’s Continue

• We will break into groups

• Each group will complete a portion of the Skills-Content-Method activity

• Be ready to share out with the entire grade-level group

How to Access Go-Math Online

1. Go to www-k6.thinkcentral.com2. Click on the blue “Evaluators Click

Here” button3. Access word: gocommoncore4.  Check the boxes for the Privacy Policy

and Terms of Use5.  Fill out your name and email address

CCLS aligned Performance tasks and instructional supports (units)

A small but growing list of sample activities for the CCLS

Some still in draft form but its getting there!

Bring together some of the best math minds…

A collection of videos, open-ended problem solving task

NYS math teacher-created break down of each standard

http://illustrativemathematics.org/standards/k8

http://schools.nyc.gov/Academics/CommonCoreLibrary/SeeStudentWork/default.htm

http://commoncoretools.wordpress.com/category/progressions/

http://ime.math.arizona.edu/commoncore/

http://insidemathematics.org/index.php/classroom-video-visits

http://nymathstandards.pbworks.com/w/page/45609650/Unpacking%20the%20Content%20Standards%20for%20Math

Resources