Grade Level Overview

Critical Area Critical Area of Focusof Focus

Cross-Cross-cutting cutting themes themes

Format of K-8 StandardsGrade Grade LevelLevel

DomainDomain

StandardStandard

ClusterCluster

• Assessment and Instructional Priorities http://www.parcconline.org/classroom • CCSS-IAS Alignment Documents

www.doe.in.gov/commoncore • PARCC Content Frameworks

http://www.parcconline.org/parcc-content-frameworks • Arizona’s Content and Practice

Alignmentwww.ade.az.gov/standards/math/2010mathstandards

• www.InsideMathematics.org

District Preparation for CCSS

CCSS Domain ProgressionK 1 2 3 4 5 6 7 8 HS

Counting & Cardinality

Number and Operations in Base Ten Ratios and Proportional Relationships Number &

QuantityNumber and Operations – Fractions The Number System

Operations and Algebraic ThinkingExpressions and Equations Algebra

Functions Functions

Geometry Geometry

Measurement and Data Statistics and Probability Statistics & Probability

Phase 1 (2011-2012): •Standards for Mathematical Practice•Essential Standards (IAS & CCSS)

Phase 2 (2012-2013 •Standards for Mathematical Content

Full Implementation (2014-15)

Transition in Two Phases

•“The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important ‘processes and proficiencies’ with longstanding importance in mathematics education.”

• (CCSS, 2010)

Phase 1: Mathematical Practices

CCSS Mathematical Practices

1. Make sense of problems and persevere in solving them

2. 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

Integration of Standards for Mathematical Practices

(SMPs)• Not “Problem Solving Fridays”• Not “enrichment” for advanced students• Most lie in the process of arriving at an

answer, not necessarily in the answer itself

• Every lesson should seek to build student expertise in Content and Practice standards

Standards for Mathematical Practice in a Classroom

Traditional U.S. ProblemWhich fraction is closer to 1: or ?

Same Problem with SMP integration is closer to 1 than is . Using a number line,

explain why this is so.(Daro, Feb 2011)

45

54

54

45

It’s About Instruction• We don’t have an achievement gap• We have an instruction gap

– Matt Larson

• So how can we reduce the discrepancies in instructional quality within and among schools?– Increase the mean and reduce the variance

• How can harness the expertise of our best teachers?

Maintain Focus and Coherence• Focus and coherence are not in the

CCSS document• Focus and coherence are in

interpretations of the document

• The goal is coherence in the heads of teachers and students– Think in chapters, not lessons (Daro)– Standards are taken as atoms, but the

power is in the bonds (Zimba)

• Crosswalk documents may encourage rearrangements of low-quality curricular materials and frameworks– Aim for focused, forward-thinking crosswalk

documents at the level of clusters or big ideas

• Unpacking standards may perpetuate the atomized check-list mentality– Unpack clusters of standards via descriptive

paragraphs

Challenges

• Response to Instruction may be misused to sort students into groups that receive fundamentally different instruction – Standards are the minimum level, our daily

instruction must go beyond with high-quality Tier 1 instruction for all

• Data-driven decision making may remain only about numbers– Use data to provoke targeted discussions

about instruction

Challenges

• Formative assessment may be misconstrued as a task bank– Formative assessment must provide insight

into student thinking

• Professional development may be largely generic and unfocused– Develop strategies for content-based

professional learning communities

Challenges

• Publishers may add chapters to existing materials– Insist on materials with focus and coherence

• Local control and limited resources may create excuses– Share and borrow materials– Leverage resources– Take advantage of the assessment

consortia

Challenges

What Should Districts Do Now?• Get to know the CCSSM through Professional

Learning Communities– Use the “critical areas” – Take a “progressions view”

• Begin developing the Mathematical Practices • Develop support structures for struggling students

– Use previous mathematics in service of new ideas

– All students need access to the regular curriculum, a la Response to Instruction

• Be skeptical of easy alignment and quick fixes