math common core standards
DESCRIPTION
Math Common Core Standards. Jennie Winters Lake County ROE [email protected]. Focus for Today. 3 types of change Standards for Mathematical Practice Focus, Coherence & Rigor Assessment Curriculum: Quality Units/Lessons Q & A. Instructional Change. Curricular Change. - PowerPoint PPT PresentationTRANSCRIPT
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Math Common Core Standards
Jennie WintersLake County ROE
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Focus for Today
1. 3 types of change2. Standards for Mathematical Practice3. Focus, Coherence & Rigor4. Assessment5. Curriculum: Quality Units/Lessons6. Q & A
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Common Core Implementation
Curricular Change
Instructional Change
Assessment Change
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Practice Standards
1. Make sense of problems and persevere in solving them.
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Practice Standards
2. Reason abstractly and quantitatively.
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Practice Standards
3. Construct viable arguments and critique the reasoning of others.
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Practice Standards
4. Model with mathematics.
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Practice Standards
5. Use appropriate tools strategically.
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Practice Standards
6. Attend to precision.
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Practice Standards
7. Look for and make use of structure.
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Practice Standards
8. Look for and express regularity in repeated reasoning.
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Modes of Representation(Lesh, Post, & Behr, 1987)
Pictures
Manipulative Models
Written Symbols
Real-world Situations
Oral/WrittenLanguage
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Modes of Representation
Manipulative/ Tools
Picture/Graph
Table/Chart
Symbols (Equations,
etc.)
Oral & Written Language
Real-Life Situations
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The CCSS Requires Three Shifts in Mathematics
1. Focus: Focus strongly where the standards focus.
2. Coherence: Think across grades, and link to major topics
3. Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application
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Rigor
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• The CCSSM require a balance of: Solid conceptual understanding Procedural skill and fluency Application of skills in problem solving
situations
• Pursuit of all threes requires equal intensity in time, activities, and resources.
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Solid Conceptual Understanding
• Teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives
• Students are able to see math as more than a set of mnemonics or discrete procedures
• Conceptual understanding supports the other aspects of rigor (fluency and application)
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Fluency• The standards require speed and accuracy
in calculation.
• Teachers structure class time and/or homework time for students to practice core functions such as single-digit multiplication so that they are more able to understand and manipulate more complex concepts
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Required Fluencies in K-6Grade Standard Required Fluency
K K.OA.5 Add/subtract within 5
1 1.OA.6 Add/subtract within 10
2 2.OA.22.NBT.5
Add/subtract within 20 (know single-digit sums from memory)Add/subtract within 100
3 3.OA.73.NBT.2
Multiply/divide within 100 (know single-digit products from memory)Add/subtract within 1000
4 4.NBT.4 Add/subtract within 1,000,000
5 5.NBT.5 Multi-digit multiplication
6 6.NS.2,3 Multi-digit divisionMulti-digit decimal operations
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Application• Students can use appropriate concepts and
procedures for application even when not prompted to do so.
• Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations, recognizing this means different things in K-5, 6-8, and HS.
• Teachers in content areas outside of math, particularly science, ensure that students are using grade-level-appropriate math to make meaning of and access science content.
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Assessment
• Conceptual Assessment– Includes Observational Tools
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2nd Grade Example
Students each create their own paper airplane and take turns flying them. They use a tape measure to find the distance each has flown to the nearest foot.
What concepts are being assessed?
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Assessment
• Conceptual Assessment– Includes Observational Tools
• Procedural Skill & Fluency Assessment– Includes Extended Response
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Assessment
• Conceptual Assessment– Includes Observational Tools
• Procedural Skill & Fluency Assessment– Includes Extended Response
• Application– Includes Rich Tasks
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Curriculum
• Sequence of units (Coherence)• Prioritization• Sequence within units:
– Conceptual before procedural– Application throughout
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The Tri-State Quality Review Rubric Criteria
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4 Dimensions
• Alignment to the Rigor of the CCSS• Key Areas of Focus in the CCSS• Instructional Supports• Assessment
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1 – Alignment to the Rigor of the CCSS
The unit aligns with the letter and spirit of the CCSS:
• Targets a set of grade level mathematics standard(s) at the level of rigor in the CCSS for teaching & learning
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1 – Alignment to the Rigor of the CCSS
The unit aligns with the letter and spirit of the CCSS:
• Standards for Mathematical Practice that are central to the unit are identified, handled in a grade-appropriate way, and well connected to the content being addressed.
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1 – Alignment to the Rigor of the CCSS
The unit aligns with the letter and spirit of the CCSS:
• Presents a balance of mathematical procedures and deeper conceptual understanding inherent in the CCSS
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2-Key Areas of Focus in the CCSSThe unit reflects evidence of key shifts that
are reflected in the CCSS.• Focus Centers on the concepts,
foundational knowledge and level of rigor that are prioritized in the standards.
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2-Key Areas of Focus in the CCSSThe unit reflects evidence of key shifts that
are reflected in the CCSS.• Coherence Makes connections and
provides opportunities for students to transfer knowledge and skills within and across domains and learning progressions.
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2-Key Areas of Focus in the CCSSThe unit reflects evidence of key shifts
that are reflected in the CCSS.• Rigor Requires students to engage
with an demonstrate challenging mathematics in the following ways:
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2-Key Areas of Focus in the CCSS• Conceptual Understanding Requires
students to demonstrate conceptual understanding through complex problem solving, in addition to writing and speaking about their understanding.
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2-Key Areas of Focus in the CCSS• Procedural Skill & Fluency Expects,
supports and provides guidelines for procedural skill and fluency with core calculations, mathematical procedures and strategies (when called for in the standards for the grade) to be performed quickly and accurately.
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2-Key Areas of Focus in the CCSS• Application Provides opportunities for
students to independently apply mathematical concepts in real-world situations and problem solve with persistence, choosing and applying an appropriate model or strategy to new situations.
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3 – Instructional SupportsThe unit is responsive to varied student
needs:• Includes clear and sufficient guidance
to support teaching and learning of the targeted standards, including, when appropriate, the use of technology and media.
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3 – Instructional SupportsThe unit is responsive to varied student
needs:• Uses and encourages precise and
accurate mathematics, academic language, terminology, and concrete or abstract representations (e.g. pictures, symbols, expressions, equations, graphics, models) in the discipline.
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3 – Instructional SupportsThe unit is responsive to varied student
needs:• Engages students in productive
struggle through relevant, thought-provoking questions, problems, and tasks that stimulate interest and elicit mathematical thinking.
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3 – Instructional SupportsThe unit is responsive to varied student
needs:• Addresses instructional expectations
and is easy to understand and use.
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3 – Instructional SupportsProvides appropriate level and type of
scaffolding, differentiation, intervention, and support for a broad range of learners:
• Supports diverse cultural and linguistic backgrounds, interests and styles.
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3 – Instructional SupportsProvides appropriate level and type of
scaffolding, differentiation, intervention, and support for a broad range of learners:
• Provides extra supports for students working below grade level.
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3 – Instructional SupportsProvides appropriate level and type of
scaffolding, differentiation, intervention, and support for a broad range of learners:
• Provides extensions for students with high interest or working above grade level.
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3 – Instructional Supports• Recommend and facilitate a mix of
instructional approaches for a variety of learners such as using multiple representations, (including models) using a range of questions, checking for understanding, flexible grouping, pair-share, etc.
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3 – Instructional Supports• Gradually remove supports, requiring
students to demonstrate their mathematical understanding independently.
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3 – Instructional Supports• Demonstrate an effective sequence
and a progression of learning where the concepts or skills advance and deepen over time.
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3 – Instructional Supports• Expects, supports, and provides
guidelines for procedural skill and fluency with core calculations and mathematical procedures (when called for in the standards for the grade) to be performed quickly and accurately.
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4 – Assessment
The lesson/unit regularly assesses whether students are mastering standards-based content and skills:
• Is designed to elicit direct, observable evidence of the degree to which a student can independently demonstrate the targeted CCSS.**
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4 – Assessment
The lesson/unit regularly assesses whether students are mastering standards-based content and skills:
• Assesses student proficiency using methods that are accessible and unbiased, including the use of grade level language in student prompts.**
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4 – Assessment The lesson/unit regularly assesses
whether students are mastering standards-based content and skills:
• Includes aligned rubrics, answer keys, and scoring guidelines that provide sufficient guidance for interpreting student performance.
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4 – Assessment The lesson/unit regularly assesses
whether students are mastering standards-based content and skills:
• Use varied modes of curriculum embedded assessments that may include pre-, formative, summative and self-assessment measures.
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Questions and (Hopefully) Answers