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