Common Core State Standards—Mathematics Introduction/Overview 1 Cathy Carroll

Characteristics of CCSS–M Fewer and more rigorous standards Rigorous content and application of higher-order skills Aligned with college and career expectations Research-based Build on strengths and lessons of current state standards Internationally benchmarked 2

Principles Underlying the Common Core State Standards Focus Identify key ideas, understandings and skills for each grade or course Stress deep learning, which means applying concepts and skills within the same grade or course Coherence Articulate a progression of topics across grades and connect to other topics Vertical growth that reflects the nature of the discipline 3

Shifts in Mathematics Shift 1 Focus Teachers significantly narrow and deepen the scope of how time and energy is spent in the math classroom. They do so in order to focus deeply on only the concepts that are prioritized in the standards. Shift 2 Coherence Principals and teachers carefully connect the learning within and across grades so that students can build new understanding onto foundations built in previous years. Shift 3 Fluency Students are expected to have speed and accuracy with simple calculations; teachers structure class time and/or homework time for students to memorize, through repetition, core functions. Shift 4 Deep Understanding Students deeply understand and can operate easily within a math concept before moving on. They learn more than the trick to get the answer right. They learn the math. Shift 5 Application Students are expected to use math and choose the appropriate concept for application even when they are not prompted to do so. Shift 6 Dual Intensity Students are practicing and understanding. There is more than a balance between these two things in the classroom – both are occurring with intensity. SOURCE: Engage NY

Design and Organization Standards For Mathematical Practice Describe habits of mind of a mathematically expert student, and are expected to be implemented at all levels Mathematical Content Standards K-8 standards presented by grade level Organized into domains that progress over several grades. High school standards presented by conceptual themes Number & Quantity, Algebra, Functions, Modeling, Geometry, Statistics & Probability

Standards for Mathematical Practice “The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important ‘processes and proficiencies’ with longstanding importance in mathematics education.” 6 National Governors Association Center for Best Practices and Council of Chief State School Officers (2010) Common Core State Standards for Mathematics

Underlying Frameworks Adding It Up— National Research Council Strands of Mathematical Proficiency Conceptual understanding Procedural fluency Strategic competence Adaptive reasoning Productive disposition Principles and Standards for School Mathematics— NCTM Process Standards Problem Solving Reasoning and Proof Communication Connections Representation

Standards for Mathematical Practice 8 Overarching Habits of Mind 1. Make sense of problems and persevere in solving them 6. Attend to precision Reasoning and Explaining 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others Seeing Structure and Generalizing 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning Modeling and Using Tools 4. Model with mathematics 5. Use appropriate tools strategically

Standards for Mathematical Practice On one hand, the Standards for Mathematical Practice describe mathematical content students need to learn. SP1. Make sense of problems “… students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends.” 9

Standards for Mathematical Practice On the other hand, they describe the nature of the learning experiences, thinking processes, habits of mind, and dispositions that students need to develop a deep, flexible, and enduring understanding of mathematics. SP1. Make sense of problems “….they [students] analyze givens, constraints, relationships and goals. ….they monitor and evaluate their progress and change course if necessary. …. and they continually ask themselves “Does this make sense?” 10

Mathematics Content Standards Modeling

Content Overviews Critical Areas of Focus Description of Critical Area

Format of Content Standards Grade Level or Conceptual Category DomainDomain StandardsStandards ClusterCluster

High School Conceptual Categories Rather than list HS content by course or by grade level, CCSSM identifies “Conceptual Categories.” These categories represent: The big ideas that connect mathematics across high school Such as Functions or Probability and Statistics A progression of increasing complexity Description of mathematical content to be learned elaborated through domains, clusters, and standards

High School Pathways The CCSSM Model Pathways are two models that organize the CCSSM into coherent, rigorous courses Pathway A—two algebra courses and geometry Pathway B—three integrated courses The CCSSM Model Pathways are NOT required. The two sequences are examples, not mandates A variety of year 4 courses can follow either pathway

Articulating the Challenge The Common Core State Standards are not intended to be new names for old ways of doing business. They are a call to take the next step. It is time…to work together to build on lessons learned from two decades of standards-based reforms. It is time to recognize that standards are not just promises to our children, but promises we intend to keep. — CCSS (2010, p.5)