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/Expectations Is 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 DomainsK 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

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

Test Gr ade GLEs NOT Assessed in Fall 2013* NECAP Mathematics 3DSP 2-4 Combinations NECAP Mathematics 4DSP 3-5 Probability NECAP Mathematics 5 DSP 4-4, DSP 4-5, and GM 4-5 Combinations/Permutations Theoretical Probability Similarity NECAP Mathematics 6DSP 5-5 Experimental & Theoretical Probability NECAP Mathematics 7 DSP 6-4, DSP 6-5, FA 6-2, and GM 6-5 Combinations/Permutations Experimental & Theoretical Probability Slope Similarity NECAP Mathematics 8FA 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

New Hampshire Connection to 8 Mathematical Practices PreK-16 Numeracy Action Plan for the 21st Century ns/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 on whole numbers, initially with sets of objects; and (2) describing shapes and space. More learning time in Kindergarten 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 = 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 students increasingly 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 # of Critical Areas CourseAlg IGeoAlg IIMath I Math II Math III # of Critical Areas

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

Step #1: Common Core Standards Step #2: Content Specifications Step #3: Assessment Development

Mathematics Content Specs 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? 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 Downing Patty Ewen