21 st Century Mathematics & Common Core Standards An Opportunity for South Carolina & Beaufort School District Ed Dickey College of Education University of South Carolina

Mathematics Tools for the 21 st Century Classroom U.S. Secretary of Education Arne Duncan at NCTM Annual Meeting, 15 April 2011 “Curricular materials cover so much ground too superficially, failing to provide students with an understanding of the concepts that are essential for success.” “Tests don’t always measure what’s important, or provide information back to you to help you improve.”

Mathematics for the 21 st Century Societal Need for Competitiveness (Knowledge-based global economy) Fulfillment (sustainability in diverse society)

Competitiveness in the 21 st Century Technology New tools for understanding and visualizing numerical ideas Web-based, hand-held, ubiquitous Hans Rosling “The Joy of Stats”The Joy of Stats”

Competitiveness in the 21 st Century Technology New tools for understanding and visualizing numerical ideas Computer Algebra Systems On iPads and Smartphones Wolfram Alpha

Competitiveness in the 21 st Century Computer Algebra Systems Handheld Calculators Equation of a line ( y = mx + b) with sliders using TI Nspire Calculator

Fulfillment in the 21 st Century Teaching IS a gratifying profession…

Fulfillment the 21 st Century Cultural Diversity Understanding mathematical content in a manner that ENGAGES the learners who populate our classrooms

Cultural Diversity

–Vedic Multiplication 21 x 13 video21 x 13 video

Subtraction in Mexico

NCTM Affiliated Groups TODOS advocating for equitable, high quality mathematics education for all, in particular, Hispanic/Latino students

NCTM Affiliated Groups Benjamin Banneker Association, advocating for the mathematics education of African-American students

NCTM Affiliated Groups South Carolina Council of Teachers of Mathematics

Mathematics for the 21 st Century Common Core State Standards for Mathematics An opportunity to address… –Competitiveness –Fulfillment

Common Core Standards Sponsored by the Council of Chief State School Officers (CCSS) and the National Governors Association (NGA) First significant attempt to systematically align K-12 standards across the U.S. Building on NCTM’s standards documents from 1980, 1989, 2000, 2006, and 2009 NCTM among groups providing feedback

Common Core Standards Different from most current state standards Based on most recent research regarding students’ learning trajectories related to mathematics content Includes detailed description of the way mathematics is learned and used by students (Mathematical Practice)

Common Core Development Initially 48 states and three territories signed on As of April 1, 2011, 41 states have officially adopted (plus DC and US VI) Final Standards released June 2, 2010, at Adoption required for Race to the Top funds

Common Core Development Each state adopting the common core either directly or by fully aligning its state standards may do so in accordance with current state timelines for standards adoption not to exceed three (3) years. States that choose to align their standards to the common core standards accept 100% of the core. States may add additional standards.

Benefits for States and Districts Allows collaborative professional development based on best practices Allows development of common assessments and other tools (SC in SMARTER Balanced and PARCC) Enables comparison of policies and achievement across states and districts Creates potential for collaborative groups to get more economical mileage for: –Curriculum development, assessment, and professional development

CCSSM CCSSM stands for Common Core State Standards for Mathematics

Arne Duncan at NCTM “... today’s tests don’t measure higher-order thinking skills or deep understanding of subject material. American students deserve better than the fill-in-the-bubble tests that are now common across states.” New assessments “… are the ones that you’ve longed for. They will measure critical thinking skills and complex student learning.”

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

Intent of the Common Core The same goals for all students Coherence Focus Clarity and Specificity

Coherence Articulated progressions of topics and performances that are developmental and connected to other progressions Conceptual understanding AND procedural skills stressed equally NCTM states coherence also means that instruction, assessment, and curriculum are aligned

Focus Key ideas, understandings, and skills are identified Deep learning of concepts is emphasized –That is, time is spent on a topic and on learning the topic well. This counters the “mile wide, inch deep” criticism leveled at most current U.S. standards.

Clarity and Specificity Skills and concepts are clearly defined Being able to apply concepts and skills to new situations is expected

Word Cloud CCSSM

CCSSM Mathematical Practices Common Core includes a set of Standards of Mathematical Practices that all teachers should develop in their students. Similar to NCTM’s Mathematical Processes from the Principles and Standards for School Mathematics. Practices MUST be assessed

8 CCSSM Mathematical Practices 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.

Geometry Lesson from Japan

Make Sense / Critique Reasoning Find the area of the shaded region: 8 m2 m 5 m 8 m 3 m2m 10 m

Reasoning 8 m2 m 5 m 8 m 3 m2m 10 m

Learning Trajectories Area is invariant under transformations

8 CCSSM Mathematical Practices 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.

Look for and make use of structure What is the result when you add… Even + Even ? Odd + Odd ?

Mod 2 Arithmetic Modular arithmetic used in encryption codes..

Vi Hart’s Binary Hand Dance

Mathematical Structures Vi Hart Blog at vihart.com Base 2 Modular arithmetic Mathematical food And other engaging ideas about mathematics … BUT now back to the Common Core

Common Core Format Domains are large groups of related standards. Standards from different domains may sometimes be closely related. Look for the name with the code number on it for a Domain.

Common Core Format Clusters are groups of related standards. Standards from different clusters may sometimes be closely related, because mathematics is a connected subject. Clusters appear inside domains.

Common Core Format Standards define what students should be able to understand and be able to do – part of a cluster.

Common Core Format High School Conceptual Category Domain Cluster Standards K-8 Grade Domain Cluster Standards (There are no preK Common Core Standards)  Domains are NOT courses   Clusters are NOT units 

Grade Level Overview

Critical Areas – similar to NCTM’s Curriculum Focal Points

Format of K-8 Standards Grade Level DomainDomain

Format of K-8 StandardsClusterCluster ClusterCluster StandardStandard StandardStandard

Format of High SchoolStandardStandard ClusterCluster DomainDomain

Common Core - Domain Domains are overarching big ideas that connect topics across the grades Descriptions of the mathematical content to be learned elaborated through clusters and standards

Common Core - Standards Standards are content statements. An example content statement is: “Use properties of operations to generate equivalent expressions.” Progressions of increasing complexity from grade to grade

Common Core - Clusters May appear in multiple grade levels in the K-8 Common Core. There is increasing development as the grade levels progress What students should know and be able to do at each grade level Reflect both mathematical understandings and skills, which are equally important

High School Conceptual Categories 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 The CCSSM Model Pathways are NOT required. The two sequences are examples, not mandates

High School Pathways Four years of mathematics: –One course in each of the first two years –Followed by two options for year three and a variety of relevant courses for year four Course descriptions –Define what is covered in a course –Are not prescriptions for the curriculum or pedagogy

High School Pathways Pathway A: Consists of two algebra courses and a geometry course, with some data, probability and statistics infused throughout each (traditional) Pathway B: Typically seen internationally that consists of a sequence of 3 courses each of which treats aspects of algebra, geometry and data, probability, and statistics.

NCTM President Michael Shaughnessy An Opportune Time to Consider Integrated Mathematics March, 2011 “Students need to see mathematics as an integrated whole, with connections across the content domains... …the United States will never show well in international comparisons of mathematics performance as long as other countries have an integrated mathematics, and we take a “layer cake” approach. … we have an unprecedented opportunity… to integrate the content of our secondary mathematics…”

Promising, Opportune… but Perfect? Problem areas: CCSSM has never been field tested Can the assessments address understanding and measure the Practices? How to accommodate exceptional learners? Learning trajectories require careful vertical articulation

Not Perfect … Problem areas: Too little technology particularly in K-8 No statistics in K-5 How can this be 21 st Century competitive? Piling on in Grade 6

Ideal (according to Ed) CCSSM as standards and not mandated curriculum Give districts choices for implementation (avoiding a lock-step approach) Assessment includes parts addressed by teachers at the local level (as in Europe) Reward success, don’t punish non-success TRUST teachers to do the work we hire them to do

Ideal We don’t buy a dog, then bark for it. Invest in the best pre- and in-service teacher development…. Then get out of the way and let teachers do what these very intelligent professionals were educated to do (Finland)

Beaufort CORE Vision for STEM An investment in the education of high quality teachers Graduate level course work tied to mathematics and science Core knowledge and emphasis on building students’ understand Research-based professional development

Institute for Middle/High School Mathematics Teachers Keynote: Math Curriculum Makeover with Dan Meyer

Additional Information For grades preK-8, a model of implementation can be found in NCTM’s Curriculum Focal Points For the secondary level, please see NCTM’s Focus in High School Mathematics: Reasoning and Sense Making

Ed Dickey