### Common Core PD

```Common Core State Standards:
Overview of CCSS Mathematics
CSU STEM Conference
March 14, 2014
Ivan Cheng
CSU Northridge
Overview of the Standards
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
Standards for Mathematical Practice
 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
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
Standards for Mathematical Content
 Similar names but different content
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
 “These standards are not intended to be new names
for old ways of doing business.” (CCSS, 2010, p. 5)
Smarter Balanced Assessments
Smarter Balanced Blueprints
 “Claims” integrate content and practices
ELA
Math
1
Concepts and Procedures
2
Writing
Problem Solving
3
Speaking/Listening
Communicating Reasoning
4
Research
Modeling/Data Analysis
 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”
 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 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
Types of Assessment Items
 Selected Response (SR)
 Constructed Response (CR)
 Extended Response (ER) (math only)
 Technology Enhanced (TE)
Sample Selected Response Item
From Smarter Balanced Assessments, MAT.07.SR.1.000EE.C.162
Sample Constructed Response Item
From Smarter Balanced Assessments, MAT.07.CR.1.000EE.C.296
Sample Extended Response Item
From Smarter Balanced Assessments, MAT.08.ER.3.000EE.D.137
Sample Technology Enhanced Item
From Smarter Balanced Assessments, MAT.06.TE.1.000EE.F.170