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Gettin
g to th
e co
re o
f
Comm
on C
ore
Mat
h Sta
ndards
Effective Transitions in Adult Education
ConferenceNovember 8, 2012
Pam Meader, presenterPortland Adult Education
Portland, Maine
A Little History
1980: NCTM’s An Agenda for Action1989: NCTM’s Curriculum and Evaluation
Standards2000: NCTM’s Principles and Standards for
School Mathematics2006: NCTM’s Curriculum Focal Points2008: National Math Advisory Panel Report2010: Common Core State Standards
2
What are they?Common Core State Standards
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
• 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• Focus• Coherence• Fluency• Deep Understanding• Application• Dual Intensity
Focus• 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
Coherence
• 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
CCSS Domain progression (page 2-5 )
K 1 2 3 4 5 6 7 8 HS
Counting & Cardinality
Number and Operations in Base TenRatios and Proportional
Relationships Number & QuantityNumber and Operations –
FractionsThe Number System
Operations and Algebraic Thinking
Expressions and Equations Algebra
Functions Functions
Geometry Geometry
Measurement and Data Statistics and ProbabilityStatistics & Probability
Operations and Algebraic
Thinking (OA)
Expressions
and
Equations
(EE)
Algebra
Number and Operations in
Base Ten (NBT)
Number
System (NSS)
Number and
Operations—
Fractions
(NF)
2 3 4 5 6 7 8 120%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
2 3 4 5 6 7 8 12
Data & ProbAlgebraGeometryNumber
COMPARING NCTM AND COMMON CORE
fluency
• 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
Deep understanding• 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?
What are the possibilities in the mathematical shifts?
What could be the barriers?
Take a minute and discuss with each other
*McGraw Hill Research Foundation, Common Core Standards, 2012.
Common Core White Paper: McGraw Hill Research Foundation
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, and productive lifelong careers?
*McGraw Hill Research Foundation, 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 somemeaningful 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 arecurrently available?
The Last Word (pp 6-7)
Looking at the mathematical practices
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
Continuously evaluate progress
Check results
Question sense of solutions
© Institute for Mathematics & Education 2011
SMP 2: Reason abstractly and quantitatively
DecontextualizeRepresent as symbols, abstract the situation
ContextualizePause as needed to refer back to situation
x x x x
P
5
½ Mathematical Problem
© Institute for Mathematics & Education 2011
SMP 3: Construct viable arguments and critique the reasoning of others
Use assumptions, definitions, and
previous results 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
Justify conclusionsRespond to
arguments
Communicate conclusions
Distinguish
correct logic
Explain flaws
Ask clarifying
questions
© Institute for Mathematics & Education 2011
SMP 4: Model with mathematics
Problems in everyday life…
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
…reasoned using mathematical methods
© Institute for Mathematics & Education 2011
SMP 5: Use appropriate tools strategically
Proficient students• 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
© Institute for Mathematics & Education 2011
SMP 6: Attend to precisionMathematically 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 © 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
© Institute for Mathematics & Education 2011
If 2 + 3 = 5 then
2/7 + 3/7 = 5/7 and
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
© Institute for Mathematics & Education 2011
Select a number
4 7 11 100
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
Result of the process output
4 12
7
11
33
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 2x x x^3
What Mathematical Practice(s) do you see illustrated in the activities?
Quantitative problem solving45%
Algebraic problem solving55%
GED 2014
Common Core standards on GED 2014
Grade 3 to 515%
Grade 615%
Grade 718%
Grade 818%
High school35%
The Formula p. 37
A look at GED 2014 and the Common Core
Some resources for Common Core http://ime.math.arizona.edu/progressions/
http://commoncoretools.me/
http://illustrativemathematics.org/
http://www.mathsolutions.com/index.cfm?page=nl_wp2b&crid=303&contentid=1491&emp=e9GNT9&mail_id=e9GNT9
http://www.insidemathematics.org/
http://educore.ascd.org/channels/02d1bb32-0584-4323-908e-df822f4fc68f
www.learnzillion.com
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