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
A Little History
2 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
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
• • • • 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
Counting & Cardinality
1 2 3 4 5
Number and Operations in Base Ten Number and Operations – Fractions Operations and Algebraic Thinking Measurement and Data Geometry
6 7 8 HS
Ratios and Proportional Relationships The Number System Expressions and Equations Functions Number & Quantity Algebra Functions Statistics and Probability Geometry Statistics & Probability
Operations and Algebraic Thinking (OA)
Expressions and Equations (EE)
Number and Operations in Base Ten (NBT)
Number and Operations— Fractions (NF)
Number System (NSS
)
Algebra
COMPARING NCTM AND COMMON CORE
40% 30% 20% 10% 0% 100% 90% 80% 70% 60% 50% 2 3 4 5 6 7 8 12 2 3 4 5 6 7 8 12 Data & Prob Algebra Geometry Number
• • • 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
• • • • 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
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 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: Ex plai n 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 Mathematical Problem
Decontextualize
Represent as symbols, abstract the situation
½ P x x x x 5
Contextualize
Pause as needed to refer back to situation © 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 © 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 © 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 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 © 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 Multiply the number by 6 Add 8 to the product Divide the sum by 2 Subtract 4 from the quotient
4 x 6 = 24 24 + 8 = 32 32÷2 = 16
16 – 4 = 12 Original number input 7 11 Result of the process output 4 7 11 33 100 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 + 2 x 2x x x^3
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 7 18% Grade 8 18%
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=30 3&contentid=1491&emp=e9GNT9&mail_id=e9GNT9 http://www.insidemathematics.org/ http://educore.ascd.org/channels/02d1bb32-0584-4323-908e df822f4fc68f www.learnzillion.com