Transcript Slide 1

21st 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 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
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1
963
-369
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7
5 94
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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
CCSSM
• Word Cloud
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:
8m
5m
2m
8m
3m
2m
10 m
Reasoning
8m
5m
2m
8m
3m
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
K-8
High School
Grade
Conceptual Category
Domain
Domains are NOT courses 
Cluster
Domain
Clusters are NOT units 
Standards
(There are no preK Common Core Standards)
Cluster
Standards
Grade Level Overview
Grade Level Overview
Critical Areas –
similar to
NCTM’s
Curriculum
Focal Points
Format of K-8 Standards
Grade Level
Domain
Format of K-8 Standards
Standard
Cluster
Standard
Cluster
Format of High School
Domain
Standard
Cluster
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
www.nctm.org/cfp
• For the secondary level, please
see NCTM’s Focus in High School
Mathematics: Reasoning and
Sense Making
www.nctm.org/FHSM
Ed Dickey
[email protected]