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