1. Getting to 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: NCTM’s An Agenda for Action
1989: NCTM’s Curriculum and Evaluation Standards
2000: NCTM’s Principles and Standards for School Mathematics
2006: NCTM’s Curriculum Focal Points
2008: National Math Advisory Panel Report
2010: Common Core State Standards

3. 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:

4. 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

5. 6 Shifts in how we will teach mathematics using Common Core p. 1
Focus
Coherence
Fluency
Deep Understanding
Application
Dual Intensity

6. 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

8. 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
Coherence

9. CCSS Domain progression (page 2-5 )K 1 2 3 4 5 6 7 8 HS
Counting & Cardinality
Number and Operations in Base Ten
Ratios and Proportional Relationships
Number & Quantity
Number and Operations – Fractions
The Number System
Operations and Algebraic Thinking
Expressions and Equations
Algebra
Functions
Geometry
Measurement and Data
Statistics and Probability
Statistics & Probability
This diagram illustrates how the domains are distributed across the Common Core State Standards.
What is not easily seen is how a domain may impact multiple domains in future grades.
An example is K-5 Measurement and Data, which splits into Statistics and Probability and Geometry in grade 6.
Likewise, Operations and Algebraic Thinking in K-5 provides foundation Ratios and Proportional Relationships, The Number System, Expressions and Equations, and Functions in grades 6-8.

10. Algebra Operations and Algebraic Thinking (OA)
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)

11. COMPARING NCTM AND COMMON CORE

12. In reading students need to read fluently for comprehension to occur
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

13. 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.

14. 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.

15. 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

16. 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.

17. If not, what can be done to implement the CCSS in some
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

18. Looking at the mathematical practices
The Last Word (pp 6-7)

19. Mathematical Practices Activity What do they mean to you?

21. pages 17-19

23. 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

24. SMP 2: Reason abstractly and quantitatively
Decontextualize
Represent as symbols, abstract the situation
Contextualize
Pause as needed to refer back to situation 5
Mathematical Problem P
x x x x
© Institute for Mathematics & Education 2011

25. 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
Distinguish correct logic
Communicate conclusions
Explain flaws
Justify conclusions
Ask clarifying questions
Respond to arguments
© Institute for Mathematics & Education 2011

26. 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
© Institute for Mathematics & Education 2011

27. 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

28. 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:
© Institute for Mathematics & Education 2011

29. 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

30. If = 5 then
2/7 + 3/7 = 5/7 and
2x + 3x = 5x

31. 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

32. Select a number 4 7 11
100
Multiply the number by 6
4 x 6 = 24
Add 8 to the product
= 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

33. Which shape does not belong in the set?
Explain Why

34. Which one does not belong in the set?
2, 3, 15, 31
Explain why

35. Where would you place these on a number line?
3x x/2 x – x^2 x + 2
x 2x x
x^3

36. What Mathematical Practice(s) do you see illustrated in the activities?

38. Common Core standards on GED 2014

39. The Formula p. 37

40. A look at GED 2014 and the Common Core

41. Some resources for Common Core