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 Math1 Reading Concepts and Procedures2 Writing Problem Solving3 Speaking/Listening Communicating Reasoning4 Research Modeling/Data Analysis

Smarter Balanced Blueprints “Claims” address content and practices

1. 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 practices

1. 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 practices

1. 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 recognizing2. Using procedures3. Explaining and concluding4. 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