Common Core State Standards for Mathematics

Christine Downing, CCSS Consultant NH DOE

Patty Ewen, Office of Early Childhood Education, NH DOE

Who’s in the room?

• Name, position, school/district• Tell me something you already know about

the CCSS for Mathematics?• Now tell me something you hope to learn

more about in terms of CCSS for Mathematics?

Goals of Presentation

1. Dig into the Common Core State Standards for Mathematics

2. Get down and dirty with SBAC– Content Specifications, Assessment Claims, Item

Specifications

Throughout we will sift through and mix the resources!

Instructional Shifts

• Focus• Coherence• Fluency• Deep Understanding• Application• Dual Intensity

Dig Into CCSS Mathematics

1

Context for Treasure Hunt

As you complete the treasure hunt, consider the following Common Core Message.

CCSS Solve Three Specific Problems:– Increased Skills Demand and Competition– Students Not College/Career Ready– Variance Across the Country in

Standards/ExpectationsIs there evidence in CCSS for Mathematics to support

this?

Treasure Hunt

• Form Small Groups that represent the grade ranges from K through 12

• As a group complete the Treasurer Hunt for Mathematics

• As you complete the Treasurer Hunt, keep track of what intrigues you? What do you want to investigate deeper? Also, what surprised you?

Let’s Do a Quick Overview of Mathematics

• Here are some common, key messages that can be used to begin the discussion

• Hang on…it’s going to be quite a ride!

Criteria for New Standards• Fewer, clearer, and higher (Consistent, rigorous, and

shared aligned with college and work expectations)

• Aligned with college and work expectations

• Include rigorous content and application of knowledge through high-order skills

• Build upon strengths and lessons of current state standards (think DNA of education)

• Internationally benchmarked, so that all students are prepared to succeed in our global economy and society

• Based on evidence and research

Mathematics• Focus and coherence– Focus on key topics at each grade level.– Coherent progressions across grade levels.

• Balance of concepts and skills– Content standards require both conceptual

understanding and procedural fluency.• Mathematical practices (8 practices)– Foster reasoning and sense making in mathematics.

• College and career readiness – Level is ambitious but achievable.

Topic Placement in Top Achieving Countries

Topic Placement in the U.S.

International Comparison

CCSS Distribution of Emphasis

CCSS K – 8 Domains Progression Domains K 1 2 3 4 5 6 7 8

Counting and Cardinality

Operations and Algebraic Thinking

Number and Operations in Base TenNumber and Operations – FractionRatios and Proportional ReasoningThe Number System

Expressions and Equations

Functions

Measurement and Data

Geometry

Statistics and Probability

CCSS versus GLE/GSE emphasis In NECAPCCSS K – 8 Domains Progression

Domains K 1 2 3 4 5 6 7 8

Counting and Cardinality

Operations and Algebraic Thinking

Number and Operations in Base Ten

Number and Operations – Fraction

Ratios and Proportional Reasoning

The Number System

Expressions and Equations

Functions

Measurement and Data

Geometry

Statistics and Probability

TestGrade

GLEs NOT Assessed in Fall 2013*

NECAP Mathematics

3 DSP 2-4 Combinations

NECAP Mathematics

4 DSP 3-5 Probability

NECAP Mathematics

5

DSP 4-4, DSP 4-5, and GM 4-5

Combinations/PermutationsTheoretical ProbabilitySimilarity

NECAP Mathematics

6 DSP 5-5 Experimental & Theoretical Probability

NECAP Mathematics

7DSP 6-4, DSP 6-5, FA 6-2, and GM 6-5

Combinations/PermutationsExperimental & Theoretical ProbabilitySlopeSimilarity

NECAP Mathematics

8 FA 7-2 Slope & Constant/Varying Rates of Change

NECAP Assessment Changes in Mathematics

CCSS Mathematics-High School

The high school standards are listed in conceptual categories:• Number and Quantity• Algebra• Functions• Modeling• Geometry• Statistics and Probability

Let’s Pause for a Bit

• Let’s Jigsaw the strands of mathematical proficiency.

• Please form groups of 5.• All read pages 115 to 118 and 133 to 135• Person 1 – reads conceptual understanding• Person 2 – reads procedural fluency• Person 3 – reads strategic competence• Person 4 – reads adaptive reasoning• Person 5 – reads productive disposition

How do the strands of mathematical proficiency

relate to the 8 mathematical habits of mind?

National Council of Teachers of Mathematics NCTM

Mathematical Process Standards•Communication•Connections•Representations•Problem Solving•Reasoning•Proof

www.nctm.org

New Hampshire Connection to 8 Mathematical Practices

PreK-16 Numeracy Action Plan for the 21st Century

http://www.education.nh.gov/innovations/pre_k_num/index.htm

Let’s Dig a Little Deeper…

• The new standards support improved curriculum and instruction due to increased:– FOCUS, via critical areas at each grade level– COHERENCE, through carefully developed

connections within and across grades– CLARITY, with precisely worded standards that

cannot be treated as a checklist– RIGOR, including a focus on College and Career

Readiness and Standards for Mathematical Practice throughout Pre-K-12

Structure of Knowledge

Structure of Knowledge in CCSS

Critical Areas

Domains

Clusters

Standards

Similar to STRANDS from GLEs and GSEs

Similar to STEMS from GLEs and GSEs

Top Level

Middle Level

Bottom Level

Critical Areas

• There are typically two to four Critical Areas for instruction in the introduction for each grade level or course.

• They bring focus to the standards at each grade by grouping and summarizing the big ideas that educators can use to build their curriculum and to guide instruction.

Example of a Critical Area_______________________________________________________________________________________

Kindergarten_______________________________________________________________________________________

In Kindergarten, instructional time should focus on two critical areas: (1) representing, relating, and operating onwhole numbers, initially with sets of objects; and (2) describing shapes and space. More learning time inKindergarten should be devoted to number than to other topics.

(1) Students use numbers, including written numerals, to represent quantities and to solve quantitative problems, such as counting objects in a set; counting out a given number of objects; comparing sets or numerals; and modeling simple joining and separating situations with sets of objects, or eventually with equations such as 5 + 2 = 7 and 7 – 2 = 5. (Kindergarten students should see addition and subtraction equations, and student writing of equations in Kindergarten is encouraged, but it is not required.) Students choose, combine, and apply effective strategies for answering quantitative questions, including quickly recognizing the cardinalities of small sets of objects, counting and producing sets of given sizes, counting the number of objects in combined sets, or counting the number of objects that remain in a set after some are taken away.

(2) Students describe their physical world using geometric ideas (e.g., shape, orientation, spatial relations) and vocabulary. They identify, name, and describe basic two-dimensional shapes, such as squares, triangles, circles, rectangles, and hexagons, presented in a variety of ways (e.g., with different sizes and orientations), as well as three-dimensional shapes such as cubes, cones, cylinders, and spheres. They use basic shapes and spatial reasoning to model objects in their environment and to construct more complex shapes.

The Standards for Mathematical Practice complement the content standards at each grade level so that studentsincreasingly engage with the subject matter as they grow in mathematical maturity and expertise.

How do critical areas promote focus?

What is the number of critical areas per grade level/course?

• How will/could it improve teaching and learning in our school/district when each grade focuses on a few Critical Areas?

Grade level

K 1 2 3 4 5 6 7 8

# of Critical Areas

2 4 4 4 3 3 4 4 3

Course

Alg I Geo Alg II Math I

Math II

Math III

# of Critical Areas

5 6 4 6 6 4

Main Activity: Focusing on the Critical Areas

• In small groups, read the Critical Areas for a grade level including the description.

• Read each content standard, marking the recording sheet with a:

√ when a standard strongly matches or supports your Critical Area and ? when you are not sure Leave blank if the standard does not match or support the Critical Area

Did every standard fall within a Critical Area?

Are there standards that fall within more than one Critical Area?

Do all the standards within a cluster fall within the same Critical Area?

How do the Critical Areas help organize and bring focus to your grade level standards?

How should we as a school (or district) use what we have learned today about Critical Areas in planning

for the implementation of the new standards?

How could this work be linked to existing curriculum built on GLEs/GSEs?

Down and Dirty with SBAC

• Content Specifications

• Assessment Claims

• Item Specifications

2

SMARTER Balanced

• Computer Adaptive– Multiple Choice, Constructed Response,

Technology Enhanced

• Performance Tasks– Writing, listening and speaking– Emphasis of mathematical practices

Components of SBAC System• Summative Assessments– Grades 3-8 and 11 in ELA and Mathematics– Computer Adaptive Testing– Performance Tasks

• Interim Assessments– Optional– Progress of Students– Linked to content clusters in CCSS

• Formative Tools and Processes– Evidence of progress toward learning goals

Mathematics ContentSpecs

• Claim #1 Conceptual Understanding and Procedural Fluency: Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.

• Claim #2 Problem Solving: Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.

Mathematics Content Specs

• Claim #3 Communicating Reasoning: Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.

• Claim #4 Modeling and Data Analysis: Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.

Let’s look at SBAC Resources

• Assessment Claims and Target Standards • Claim #1 of the Content Specifications• Design of Performance Tasks• Sample Items from Showcase 2 and 3

Where do you find all this for SBAC?

www.smarterbalanced.org

Now explore on your own!

Share…

So what aha’s did you have as you explored the wealth of information on SBAC?

What concerns do you have?

What will you do next?

Other Math Resources• MASS DOE presentation materials

• NCSM – Alignment Tool for CCSS resources

• NCTM – Reasoning and Sense Making Tools

• Indiana Resources – new??

• North Carolina Unpacking

Questions/Comments

Thank you!

Christine DowningChristine.downing@nh.gov

Patty EwenPatricia.ewen@doe.nh.gov