Transcript Cracking the core of Common Core Math Standards

Effective Transitions in Adult
Education Conference
November 8, 2012
Pam Meader, presenter
Portland Adult Education
Portland, Maine
2
A Little History
1980:
1989:
2000:
2006:
2008:
2010:
NCTM’s An Agenda for Action
NCTM’s Curriculum and Evaluation Standards
NCTM’s Principles and Standards for School Mathematics
NCTM’s Curriculum Focal Points
National Math Advisory Panel Report
Common Core State Standards
What are they?
Common Core State Standards
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Define the knowledge
and skills students
need for college and
career
Developed voluntarily
and cooperatively by
states; 46 states and
D.C. have adopted
Provide clear,
consistent standards
in English language
arts/Literacy and
mathematics
Source: www.corestandards.org
Characteristics of Common
core
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Fewer and more rigorous
Aligned with career and college
expectations
Internationally benchmarked
Rigorous content and application
of higher order skills
Builds on strengths and lessons of
current state standards
Research based
6 Shifts in how we will teach
mathematics using Common
Core p. 1
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Focus
Coherence
Fluency
Deep Understanding
Application
Dual Intensity
Focus
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Focus only on topics in CC
This helps students develop a strong foundation
and deeper understanding
Students will be able to transfer skills across grade
levels
Focus allows each student to think, practice, and
integrate each new idea into a growing
knowledge base
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Builds on strong
conceptual
understanding
Each standard is
not a new event
but an extension of
previous learning
“Is necessary
because
mathematics
instruction is not just
a checklist of topics
to cover, but a set
of interrelated and
powerful ideas”
Bill McCallum
Coherence
CCSS Domain progression (page 2-5 )
K
1
2
3
4
5
6
7
8
HS
Counting &
Cardinality
Number and Operations in Base Ten
Number and Operations –
Fractions
Ratios and Proportional
Relationships
The Number System
Expressions and Equations
Number &
Quantity
Algebra
Operations and Algebraic Thinking
Functions
Geometry
Measurement and Data
Functions
Geometry
Statistics and Probability
Statistics &
Probability
Operations and Algebraic
Thinking (OA)
Expressions

and Equations
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(EE)
Number and Operations in Base
Ten (NBT)

Algebra
Number
System (NSS)
Number and
Operations—
Fractions (NF)
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COMPARING NCTM AND COMMON CORE
100%
90%
80%
70%
60%
Data & Prob
Algebra
50%
Geometry
Number
40%
30%
20%
10%
0%
2
3
4
5
6
7
8
12
2
3
4
5
6
7
8
12
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In reading students
need to read fluently
for comprehension to
occur . The same is
true with mathematics
Students are expected
to have speed and
accuracy with simple
calculations
Fluency allows
students to understand
and manipulate more
complex problems
fluency
Deep understanding
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It’s more than just getting the right answer.
We need to support student’s ability to access
concepts from a variety of perspectives.
Students need to see math as connected and not
separate tasks
Students need to demonstrate deep
understanding by applying concepts to new
situations as well as write and speak about them.
Application
•
Students are expected to use math and choose
the correct application even when not prompted
to do so.
•
Teachers must give students opportunities to apply
math to “real world” situations.
What do you think?
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What are the
possibilities in the
mathematical shifts?
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What could be the
barriers?
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Take a minute and
discuss with each other
Common Core White Paper: McGraw Hill
Research Foundation
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How can the adult education community adapt to the
CCSS to raise educational achievement and reduce the
marginalization and stigmatization that adult education
carries?
How can the instructional guidelines now being
established for the CCSS in English Language Arts and
Literacy and Mathematics in K-12 be adapted to be
relevant (and realistic) for adult education students?
How can adult learners – especially those who did not
finish high school– be supported to meet higher
academic standards?
How can learners be motivated to pursue an education
with enhanced rigor?
What services can be implemented to support transition
into postsecondary education, advanced job training,
*McGraw Hill Research Foundation,
and productive lifelong careers?
Common Core Standards, 2012.
What can be done to support instructors and administrators in
all areas of adult education to ensure that they are provided
with the professional development necessary to ready them
to meet the challenges that might result from the
implementation of the CCSS?
In a time of fiscal austerity, will there be sufficient resources to
adapt and adequately implement the CCSS?
If not, what can be done to implement the CCSS in some
meaningful form without a substantial increase in funding?
Is there a consensus that can be achieved in the adult
education field regarding what needs to be done to adapt
and implement the CCSS based on the resources that are
currently available?
*McGraw Hill Research Foundation,
Common Core Standards, 2012
Looking at the mathematical
practices
The Last Word
(pp 6-7)
Mathematical
Practices Activity
What do they
mean to you?
pages 17-19
SMP 1: Make sense of problems and persevere in solving them
Mathematically Proficient Students:
 Explain the meaning of the problem to themselves
 Look for entry points
 Analyze givens, constraints, relationships, goals
 Make conjectures about the solution
 Plan a solution pathway
 Consider analogous problems
 Try special cases and similar forms
 Monitor and evaluate progress, and change course if
necessary
 Check their answer to problems using a different method
 Continually ask themselves “Does this make sense?”
Gather
Information
Make a
plan
Anticipate
possible
solutions
Check
results
Continuously
evaluate
progress
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Question
sense of
solutions
© Institute for Mathematics & Education 2011
SMP 2: Reason abstractly and quantitatively
Decontextualize
Represent as symbols, abstract the situation
5
½
Mathematical
Problem
P
x x x x
Contextualize
Pause as needed to refer back to situation
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© Institute for Mathematics & Education 2011
SMP 3: Construct viable arguments and critique the
reasoning of others
Make a conjecture
Build a logical progression
of statements to explore
the conjecture
Analyze situations by
breaking them into cases
Recognize and use
counter examples
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© Institute for Mathematics & Education 2011
SMP 4: Model with mathematics
Problems in
everyday life…
…reasoned using
mathematical methods
Mathematically proficient students
• make assumptions and approximations to simplify a
situation, realizing these may need revision later
• interpret mathematical results in the context of the
situation and reflect on whether they make sense
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© Institute for Mathematics & Education 2011
SMP 5: Use appropriate tools strategically
Proficient students
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are sufficiently familiar
with appropriate tools to
decide when each tool is
helpful, knowing both the
benefit and limitations
detect possible errors
identify relevant external
mathematical resources,
and use them to pose or
solve problems
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© Institute for Mathematics & Education 2011
SMP 6: Attend to precision
Mathematically proficient students
• communicate precisely to others
• use clear definitions
• state the meaning of the symbols they use
• specify units of measurement
• label the axes to clarify correspondence with problem
• calculate accurately and efficiently
• express numerical answers with an appropriate degree
of precision
Comic: http://forums.xkcd.com/viewtopic.php?f=7&t=66819
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© Institute for Mathematics & Education 2011
SMP 7: Look for and make use of structure
Mathematically proficient students
• look closely to discern a pattern or structure
• step back for an overview and shift perspective
• see complicated things as single objects, or as
composed of several objects
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© Institute for Mathematics & Education 2011
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If 2 + 3 = 5 then
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2/7 + 3/7 = 5/7 and
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2x + 3x = 5x
SMP 8: Look for and express regularity in repeated
reasoning
Mathematically proficient
students
• notice if calculations are
repeated and look both for
general methods and for
shortcuts
• maintain oversight of the
process while attending to
the details, as they work to
solve a problem
• continually evaluate the
reasonableness of their
intermediate results
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© Institute for Mathematics & Education 2011
Select a number
4
Multiply the
number by 6
4 x 6 = 24
Add 8 to the
product
24 + 8 = 32
Divide the sum
by 2
32÷2 = 16
Subtract 4 from
the quotient
16 – 4 = 12
Original number
input
4
7
11
33
100
7
11
Result of the process
output
12
100
Which shape does not belong
in the set?
Explain Why
Which one does not belong in
the set?
2, 3, 15, 31
Explain why
Where would you place these on a
number line?
3x x/2 x – 4
x+2
x 2x
x
x^3
x^2
What Mathematical
Practice(s) do you see
illustrated in the activities?
GED 2014
Algebraic problem solving
55%
Quantitative problem
solving
45%
Common Core standards on
GED 2014
Grade 3 to 5
15%
High school
34%
Grade 6
15%
Grade 8
18%
Grade 7
18%
The Formula p. 37
A look at GED 2014 and the Common Core
Some resources for Common Core
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http://ime.math.arizona.edu/progressions/
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http://commoncoretools.me/
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http://illustrativemathematics.org/
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http://www.mathsolutions.com/index.cfm?page=nl_wp2b&crid=30
3&contentid=1491&emp=e9GNT9&mail_id=e9GNT9
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http://www.insidemathematics.org/
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http://educore.ascd.org/channels/02d1bb32-0584-4323-908edf822f4fc68f
www.learnzillion.com
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