Common Core State Standards: Overview of CCSS Mathematics CSU STEM Conference March 14, 2014 Ivan Cheng CSU 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 student 1.Make sense of problems and persevere in solving them 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others 4.Model with mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure 8.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 8 Pre-Algebra Some “1997 HS Geometry” “1997 Algebra 1A” Common Core Algebra I “1997 Algebra 1B” “1997 Algebra 2A” Some AP Statistics topics Common Core Geometry More “1997 HS Geometry” Transformational Geometry Some AP Statistics topics Common Core Algebra II “1997 Algebra 2B” “1997 Trigonometry” Some Math Analysis Some AP Statistics topics Standards for Mathematical Content

N-Q 1-3 A-SSE 1 A-CED 1-4 A-REI 1, 3, 3.1, 5, 6, 10, 11, 12 F-IF 1-7, 9 F-BF 1-3 F-LE 1-3, 5 S-ID 1-3, 5-9 N-RN 1-3 A-SSE 2-3 A-APR 1 A-REI 4, 7 F-IF 8 F-BF 4 F-LE 6 G-CO 1-8, G-GPE 4, 5, 7 Algebra I Math I Underlined standards are California revised additions Standards for Mathematical Content

G-CO 9-11 G-STR 1-8, 8.1 G-C 1-5 G-GPE 1-2, 4 G-GMD 1, 3, 5, 6 S-CP 1-9 S-MD 6-7 G-CO 1-8,12-13 G-SRT 9-11 GPE 5-7 G-GMD 4 G-MG 1-3 N-RN 1-3 N-CN 1-2, 7-9 A-SSE 1, 2, 3 A-APR 1 A-CED 1, 2, 4 A-REI 4, 7 F-IF 4-7, 8, 9 F-BF 1, 3, 4 F-LE 3, 6 F-TF 8 Geometry Math II Underlined standards are California revised additions Standards in blue are also in Math I Standards for Mathematical Content

N-CN 8-9 A-SSE 1,2,4 A-APR 1, 2-7 A-CED 1-4 A-REI 2, 11 F-IF 4-9 F-BF 1, 3, 4 F-LE 4, 4.1, 4.2, 4.3 F-TF 1, 2, 2.1, 5 G-GPE 3.1 S-ID 4 S-IC 1-6 S-MD 6-7 N-CN 1-2, 7 A-REI 3.1 F-TF 8 G-SRT 9-11 G-GMD 4 G-MG 1-3 Algebra II Math III Underlined standards are California revised additions Standards in blue are also in Math I, II, and Algebra I Standards for Mathematical Content

Smarter Balanced Assessments

Smarter Balanced Blueprints  “Claims” integrate content and practices  Assessment “Targets”  Depth of Knowledge (“DOK”) ELAMath 1ReadingConcepts and Procedures 2WritingProblem Solving 3Speaking/ListeningCommunicating Reasoning 4ResearchModeling/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 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 3DOK 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

TOP-SCORE SCORING RUBRIC Sample Extended Response Item

From Smarter Balanced Assessments, MAT.06.TE.1.000EE.F.170 Sample Technology Enhanced Item

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 Cheng CSU Northridge

Online Resources  Key resources that might be useful  CA Common Core Standards  Smarter Balanced  Illustrative Mathematics K-8 StandardsK-8 Standards  MARS/Shell  Howard County  NYC Department of Education Common Core LibraryCommon Core Library  Achieve the Core (commentaries and links to tasks)commentaries and links to tasks  Sense-Making in Mathematics  Gates Foundation Learning/MathDesignCollaborativehttp://collegeready.gatesfoundation.org/ Learning/MathDesignCollaborative