21st Century Mathematics & Common Core Standards

An Opportunity for South Carolina &

Beaufort School District

Ed DickeyCollege of Education

University of South Carolina

Mathematics Tools for the 21st 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 21st Century

Societal Need for•Competitiveness (Knowledge-based global economy)

•Fulfillment (sustainability in diverse society)

Competitiveness in the 21st Century

• Technology

• New tools for understanding and visualizing numerical ideas

• Web-based, hand-held, ubiquitous

• Hans Rosling

• “The Joy of Stats”

Competitiveness in the 21st Century

• Technology

• New tools for understanding and visualizing numerical ideas

• Computer Algebra Systems

• On iPads and Smartphones

• Wolfram Alpha

Wolfram Alpha

Competitiveness in the 21st Century

• Computer Algebra Systems

• Handheld Calculators

• Equation of a line

( y = mx + b) with sliders using

TI Nspire Calculator

Fulfillment in the 21st Century

• Teaching IS a gratifying profession…

Fulfillment the 21st Century

• Cultural Diversity

Understanding mathematical content in a manner that ENGAGES the learners who populate our classrooms

Cultural Diversity

Cultural Diversity

– Vedic Multiplication 21 x 13 video

Subtraction in Mexico

12

963-369

1

7

4

1

4

9

5

NCTM Affiliated Groups

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

• www.todos-math.org

NCTM Affiliated Groups

• Benjamin Banneker Association, advocating for the mathematics education of African-American students

• www.bannekermath.org

NCTM Affiliated Groups

• South Carolina Council of Teachers of Mathematics

• www.scctm.org

Mathematics for the 21st 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 www.corestandards.org

• 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 m 2 m 5 m

8 m

3 m 2m 10 m

Reasoning

8 m 2 m 5 m

8 m

3 m 2m 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

Grade Level Overview

Critical Areas Critical Areas – similar to – similar to

NCTM’s NCTM’s Curriculum Curriculum Focal PointsFocal Points

Format of K-8 Standards Grade Grade LevelLevel

DomainDomain

Format of K-8 Standards

ClusterCluster

ClusterCluster

StandardStandard

StandardStandard

Format of High School

StandardStandard

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 21st 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

www.nctm.org/cfp

www.nctm.org/FHSM

Ed Dickeyed.dickey@sc.edu