common core state standards: overview of ccss mathematics csu stem conference march 14, 2014 ivan...
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Common Core State Standards: Overview of CCSS Mathematics
CSU STEM ConferenceMarch 14, 2014
Ivan ChengCSU Northridge
Overview of the Standards
Standards for college and career readiness Focus and coherence
Focus on key topics at each grade level Coherent progressions across grade levels
Balance of concepts and skills Conceptual understanding Procedural fluency
Mathematical practices Fosters reasoning and sense-making in mathematics Describe habits of mind of a mathematically expert student
Overview of the Standards
Habits of mind a mathematically expert student1. 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
Carry across all grade levels
Standards for Mathematical Practice
Standards for Mathematical Content
K-8 standards presented by grade level Organized into domains that progress over several grades 2-4 focal points at each grade level
HS standards presented by conceptual theme Number and quantity Algebra Functions Modeling Geometry Statistics and probability
Similar names but different content
“These standards are not intended to be new names for old ways of doing business.” (CCSS, 2010, p. 5)
Common Core Grade 8Pre-AlgebraSome “1997 HS Geometry”“1997 Algebra 1A”
Common Core Algebra I“1997 Algebra 1B”“1997 Algebra 2A”Some AP Statistics topics
Common Core GeometryMore “1997 HS Geometry”Transformational GeometrySome AP Statistics topics
Common Core Algebra II“1997 Algebra 2B”“1997 Trigonometry”Some Math AnalysisSome AP Statistics topics
Standards for Mathematical Content
Smarter Balanced Assessments
Smarter Balanced Blueprints
“Claims” integrate content and practices
Assessment “Targets” Depth of Knowledge (“DOK”)
ELA Math
1 Reading Concepts and Procedures
2 Writing Problem Solving
3 Speaking/Listening Communicating Reasoning
4 Research Modeling/Data Analysis
Smarter Balanced Blueprints
“Claims” address content and practices1. Students can explain and apply mathematical concepts and carry out
mathematical procedures with precision and fluency.
2. Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.
3. Students can clearly and precisely construct viable arguments to support their own reasoning and critique the reasoning of others.
4. Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.
Assessment “Targets” Depth of Knowledge (“DOK”)
Smarter Balanced Blueprints
“Claims” address content and practices1. Students can explain and apply mathematical concepts and carry out
mathematical procedures with precision and fluency.
2. Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.
3. Students can clearly and precisely construct viable arguments to support their own reasoning and critique the reasoning of others.
4. Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.
Assessment “Targets” specify what will be tested Depth of Knowledge (“DOK”)
Smarter Balanced Blueprints
“Claims” address content and practices1. Students can explain and apply mathematical concepts and carry out
mathematical procedures with precision and fluency.
2. Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.
3. Students can clearly and precisely construct viable arguments to support their own reasoning and critique the reasoning of others.
4. Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.
Assessment “Targets” specify what will be tested Depth of Knowledge (“DOK”) refer to complexity of
item types
Depth of Knowledge (DOK)
Cognitive rigor for each type of thinking Remember (Level 1 only) Understand (Levels 1 – 4) Apply (Levels 1 – 4) Analyze (Levels 1 – 4) Evaluate (Levels 3 – 4) Create (Levels 1 – 4)
Examine the levels for “Analyze”
Depth of Knowledge (DOK)
Webb’s Depth of Knowledge levels
1. Recalling and recognizing
2. Using procedures
3. Explaining and concluding
4. Making connections, extending and justifying
What is the DOK for current CSTs?
Depth of Knowledge (DOK)
DOK 3 DOK 4
Current CST <2% 0%
New SB Assessment 49% 21%
Yuan & Le (2012); Herman & Lin (2013), from Linda Darling-Hammond Assembly Testimony, 3/6/13
Selected Response (SR) Constructed Response (CR) Extended Response (ER) (math only) Technology Enhanced (TE) Performance Task (PT)
Types of Assessment Items
From Smarter Balanced Assessments, MAT.07.SR.1.000EE.C.162
Sample Selected Response Item
From Smarter Balanced Assessments, MAT.07.CR.1.000EE.C.296
Sample Constructed Response Item
From Smarter Balanced Assessments, MAT.08.ER.3.000EE.D.137
Sample Extended Response Item
From Smarter Balanced Assessments, MAT.06.TE.1.000EE.F.170
Sample Technology Enhanced Item
Sample Performance Task
Sample Performance Task
Sample Performance Task
From Smarter Balanced Assessments, MAT.06.PT.4.REMOD.4
Sample Performance Task
Common Core State Standards: Overview of CCSS Mathematics
Thank You
Ivan ChengCSU Northridge