Transcript Long Island Higher Education Forum

An Update from the NYSED Office
of Curriculum & Instruction
AMTNYS November 2012
Mary Cahill, Director
John Svendsen, Associate in Mathematics
www.engageNY.org
Agenda
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Why the change in standards
•
Opportunity for questions
Brief overview of the shifts required by the
NYS P-12 Common Core Learning
Standards for Mathematics
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“Our country is in a slow decline, just slow
enough for us to be able to pretend - or believe
- that a decline is not taking place.”
“Our problem is us - what we are doing and not
doing, how our political system is functioning
and not functioning, which values we are and
are not living by.”
Friedman & Mandelbaum – That Used to Be Us
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High School Graduation & College Completion
• Nationally, out of 100 middle school students…
‒ 93 say they want to go to college.
‒ 70 will graduate from high school.
‒ 44 enroll in college.
‒ 26 earn a college degree within six years
Conley, David. 2012, “The Complexities of College and Career Readiness.” https://epiconline.org/files/pdf/07102012_Keene_NH.pdf
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Our Challenge
Graduating All Students College & Career Ready
New York's 4-year high school graduation rate is 74% for All Students
However, the gaps are disturbing.
June 2011 Graduation Rate
Calculated College and Career Ready*
Graduation under Current Requirements
% Graduating
% Graduating
All Students
74.0
All Students
34.7
American Indian
59.6
American Indian
16.8
Asian/Pacific Islander
82.4
Asian/Pacific Islander
55.9
Black
58.4
Black
11.5
Hispanic
58.0
Hispanic
14.5
White
85.1
White
48.1
English Language Learners
38.2
English Language Learners
6.5
Students with Disabilities
44.6
Students with Disabilities
4.4
*Students graduating with at least a score of 75 on Regents English and 80 on a Math Regents, which correlates with success in first-year college courses.
Source: NYSED Office of Information and Reporting Services
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College Instructors and Employers Say Graduates
Are Not Prepared for College and Work
Average estimated proportions of recent high
school graduates who are not prepared
100%
75%
50%
42%
45%
College Instructors
Employers
25%
0%
Source: Peter D. Hart Research Associates/Public Opinion Strategies, Rising to the Challenge: Are High
School Graduates Prepared for College and Work? prepared for Achieve, Inc., 2005.
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College Graduation and Remediation Rates
The more remedial classes students take, the less likely they are to stay in college.
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Higher Education Has Never Mattered More
Unemployment Rate By Degree: 2010
1.9%
Professional Degree
2.4%
Doctorate
4.0%
5.4%
7.0%
9.2%
10.3%
14.9%
Median Annual Earnings by Educational Degree: 2010
$83,720
$80,600
Masters
$66,144
Bachelors
$53,976
Associate
$39,884
Some College, No Degree
HS Diploma
No HS Diploma
$37,024
$32,552
$23,088
Education pays in higher overall earnings and lower unemployment rates.
SOURCE: 2010 Bureau of Labor Statistics, Current Population Survey
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International Competitiveness
The U.S. has fallen from 1st place to 13th place in high school graduation
Note: Approximated by percentage of persons with upper secondary or equivalent qualifications in the age groups 55-64, 45-54, 35-44, and 25-34 years.
Sources: Pathways to Prosperity Project, Harvard University, February 2011; Organization for Economic Cooperation and Development.
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International Competitiveness
College Completion Rank Declining: Percentage of 25- to 34-Year-Olds with an
Associate Degree or Higher, 2007
Sources: Pathways to Prosperity Project, Harvard University, February 2011; College Board, The College Completion Agenda 2010 Progress Report, 2010; Organization for Economic Cooperation and
Development.
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Job Readiness
Labor Market Has Become More Demanding
A post-secondary education is the
“Passport to the American Dream”:
Of the projected 47 million job openings between 2009-2018, nearly
two-thirds will require workers to have at least some post-secondary
education.
14 million job openings will go to people with an associate’s degree or
occupational certificate and pay a significant premium over many jobs
open to those with just a high school degree.
Sources: Pathways to Prosperity Project, Harvard University, February 2011; Georgetown Center on Education and the Workforce, Help Wanted: Projections of Jobs and
Education Requirements Through 2018, June 2010.
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Job Readiness
College Completion is Crucial for Employment
Since 1973, jobs that require at least some college have exploded while opportunities for those with just a high school
education have shrunk dramatically
Source: Pathways to Prosperity Project, Harvard University, February 2011, http://www.gse.harvard.edu/news_events/features/2011/Pathways_to_Prosperity_Feb2011.pdf
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International Competitiveness
%
70
College and university graduation rates in 1995 and 2006 (first-time
graduation)
2006
60
1995
2nd
Decline in relative position
of U.S. from 1995 to 2006
50
15th
40
30
20
10
Iceland1
Australia1
New Zealand1
Finland1
Poland1
Denmark1
Netherlands1
Norway1
Sweden1
Italy
Ireland
United Kingdom1
Japan
OECD average
Israel
United States
EU19 average
Canada1,2
Slovak Republic1
Portugal1
Spain
Hungary
Switzerland1
Czech Republic1
Austria1
Germany1
Slovenia
Greece1
Turkey
0
1. Net graduation rate is calculated by summing the graduation rates by single year of age in 2006.
2. Year of reference 2005.
Countries are ranked in descending order of the graduation rates for tertiary-type A education in 2006.
Source: OECD. Table A3.2 See Annex 3 for notes (www.oecd.org/edu/eag2008 )
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These Standards are not intended to be
new names for old ways of doing
business. They are a call to take the next
step. … It is time to recognize that
standards are not just promises to our
children, but promises we intend to keep.
CCSSM, p. 5
Principles of the CCSS
Fewer
Clearer
Higher
CCSS
Aligned to requirements for college and career readiness
Based on evidence
Honest about time
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Some Old Ways of Doing Business (1 of 2)
• A different topic every day
• Every topic treated as equally important
• Elementary students dipping into advanced topics at
the expense of mastering fundamentals
• Infinitesimal advance in each grade; endless review
• Incoherence and illogic – bizarre associations, or
lacking a thread
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Some Old Ways of Doing Business (2 of 2)
•
Lack of rigor
• Reliance on rote learning at expense of concepts
• Aversion to repetitious practice
• Severe restriction to stereotyped problems lending themselves to
mnemonics or tricks
From....
To….
856 = ___ hundreds, ___ tens, ___ ones
x2 – 10x + 21 = 0
1 hundredth = ___ tenths
¾ c(c –1) = c
• Lack of quality applied problems and real-world contexts
• Lack of variety in what students produce
– E.g., overwhelmingly only answers are produced, not arguments, diagrams, models, etc.
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The Three Instructional Shifts Demanded by the Core
• Focus strongly where the standards
focus
• Coherence: Think across grades and
link to major topics within grades
• Rigor: In major topics, pursue
conceptual understanding,
procedural skill and fluency, and
application with equal intensity
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Mathematics Shift 1: Focus
What the Student Does…
What the Teacher Does…
•Spend more time on fewer
concepts.
•excise content from the curriculum
•Focus instructional time on priority
concepts
•Give students the gift of time
Shift #1 in Research
“Move away from "mile wide, inch deep" curricula identified in TIMSS.”
Ginsburg et al., 2005
“Although high school English standards and courses tend to emphasize literature, most of the reading
students will encounter in college or on the job is informational in nature (e.g., textbooks, manuals, articles,
briefs and essays).”
Achieve, Inc. http:// www.achieve.org/files/50-s tate-07-Final.pdf
Students need sustained exposure to expository text to develop important reading strategies
Afflerbach, Pearson, & Paris, 2008; Kintsch, 1998, 2009; McNamara, Graesser, & Louwerse, in press; Perfetti, Landi, & Oakhill, 2005; van
den Broek et al., 2001; van den Broek et. al, 1995
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Key Areas of Focus in Mathematics
Grade
Focus Areas in Support of Rich Instruction and Expectations
of Fluency and Conceptual Understanding
K–2
Addition and subtraction - concepts, skills, and problem solving
and place value
3–5
Multiplication and division of whole numbers and fractions –
concepts, skills, and problem solving
6
Ratios and proportional reasoning; early expressions and
equations
7
Ratios and proportional reasoning; arithmetic of rational
numbers
8
Linear algebra and linear functions
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Major Areas of Work: P-2
Grade
K
Major Areas of Work
Counting and Cardinality
•Know number names and count sequence
•Count to tell the number of objects.
•Compare numbers.
Operations and Algebraic Thinking
•Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
Number and Operations in Base Ten
•Work with numbers 11-19 to grain foundations for place value.
1
Operations and Algebraic Thinking
•Represent and solve problems involving addition and subtraction.
•Understand and apply properties of operations and the relationship between addition and subtraction.
•Add and subtract within 20.
•Work with addition and subtraction equations.
Number and Operations in Base Ten
•Extend the counting sequence.
•Understand place value.
•Use place value understanding and properties of operations to add and subtract.
Measurement and Data
•Measure lengths indirectly by iterating length units.
2
Operations and Algebraic Thinking
•Represent and solve problems involving addition and subtraction.
•Add and subtract within 20.
•Work with equal groups of objects to gain foundations for multiplication.
Number and Operations in Base Ten
•Understand place value.
•Use place value understanding and properties of operations to add and subtract.
Measurement and Data
•Measure and estimate lengths in standard units.
•Relate addition and subtraction to length.
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Major Areas of Work: 3-5
Grade
3
Major Areas of Work
Operations and Algebraic Thinking
•Represent and solve problems involving multiplication and division.
•Understand the properties of multiplication and the relationship between multiplication and division.
•Multiply and divide within 100.
•Solve problems involving the four operations, and identify and explain patterns in arithmetic.
Number and Operations - Fractions
•Develop understanding of fractions as numbers.
Measurement and Data
•Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
•Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
4
Operations and Algebraic Thinking
•Use the four operations with whole numbers to solve problems.
Number and Operations in Base Ten
•Generalize place value understanding for multi-digit whole numbers.
•Use place value understanding and properties of operations to perform multi-digit arithmetic.
Number and Operations - Fractions
•Extend understanding of fraction equivalence and ordering.
•Build fractions from unit fractions by applying and extending previous understandings of operations on whole
numbers.
•Understand decimal notation for fractions, and compare decimal fractions.
5
Number and Operations in Base Ten
•Understand the place value system.
•Perform operations with multi-digit whole numbers and with decimals to hundredths.
Number and Operations - Fractions
•Use equivalent fractions as a strategy to add and subtract fractions.
•Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Measurement and Data
•Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
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Major Areas of Work: 6-8
Grade
6
Major Areas of Work
Ratios and Proportional Relationships
•Understand ratio concepts and use ratio reasoning to solve problems.
The Number System
•Apply and extend previous understandings of numbers to the system of rational numbers.
•Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
Expressions and Equations
•Apply and extend previous understandings of arithmetic to algebraic expressions.
•Reason about and solve one variable equations and inequalities.
•Represent and analyze quantitative relationships between dependent and independent variables.
7
Ratios and Proportional Relationships
•Analyze proportional relationships and use them to solve real-world and mathematical problems.
The Number System
•Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational
numbers.
Expressions and Equations
•Use properties of operations to generate equivalent expressions.
•Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
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Expressions and Equations
•Work with radicals and integer exponents.
•Understand the connections between proportional relationships, lines, and linear equations.
•Analyze and solve linear equations and pairs of simultaneous linear equations.
Functions
•Define, evaluate, and compare functions.
Geometry
•Understand and apply the Pythagorean theorem.
•Understand congruence and similarity using physical models, transparencies, or geometry software.
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Sample Grade 5
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Mathematics Shift 2: Coherence
What the Student Does…
What the Teacher Does…
•Build on knowledge from year to year, •Connect the threads of math focus
in a coherent learning progression
areas across grade levels
•connect to the way content was
taught the year before and the years
after
•Focus on priority progressions
Shift 2 in Research:
“The coherence and sequential nature of mathematics dictate the foundational skills that
are necessary for the learning of algebra. The most important foundational skill not
presently developed appears to be proficiency with fractions (including decimals,
percents, and negative fractions).
Final Report of the National Mathematics Advisory Panel (2008, p. 18)
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The shape of math in A+ countries
Mathematics
topics
intended at
each grade by
at least twothirds of A+
countries
Mathematics
topics
intended at
each grade by
at least twothirds of 21
U.S. states
1 Schmidt,
Houang, & Cogan, “A Coherent Curriculum: The Case of Mathematics.” (2002).
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Traditional U.S. Approach
K
12
Number and
Operations
Measurement
and Geometry
Algebra and
Functions
Statistics and
Probability
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Focusing Attention Within Number and Operations
Operations and Algebraic
Thinking
Expressions
→ and
Equations
Number and Operations—
Base Ten
→
K
1
2
3
4
Algebra
The Number
System
Number and
Operations—
Fractions
→
→
→
5
6
7
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High School
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Mathematics Shift 3: Rigor through Fluency
What the Student Does…
What the Teacher Does…
•Spend time practicing, with
intensity, skills (in high volume)
•Push students to know basic skills at
a greater level of fluency
•Focus on the listed fluencies by
grade level
•Uses high quality problem sets, in
high volume
Use should be made of what is clearly known from rigorous research about how children learn, especially by recognizing
a) the advantages for children in having a strong start; b) the mutually reinforcing benefits of conceptual understanding,
procedural fluency, and automatic (i.e., quick and effortless) recall of facts; and c) that effort, not just inherent talent,
counts in mathematical achievement.
-Foundations for Success The Final Report of the National Mathematics Advisory Panel, 2008
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Key Fluencies
Grade
Required Fluency
K
Add/subtract within 5
1
Add/subtract within 10
Add/subtract within 20
2
3
Add/subtract within 100 (pencil and
paper)
Multiply/divide within 100
Add/subtract within 1000
4
Add/subtract within 1,000,000
5
Multi-digit multiplication
6
Multi-digit division
Multi-digit decimal operations
7
Solve px + q = r, p(x + q) = r
8
Solve simple 22 systems by inspection
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Math Shift 4: Rigor through Deep Understanding
What the Student Does…
What the Teacher Does…
•Show mastery of material at a deep level •Create opportunities for students to
understand the “answer” from a variety
•Articulate mathematical reasoning
of access points
•demonstrate deep conceptual
understanding of priority concepts
•Ensure that EVERY student GETS IT
before moving on
•Get smarter in concepts being taught
Shift 4 in Research
Research has shown that learners become more engaged in the learning process when they are asked to explain and
reflect on their thinking processes.
-Surbeck, 1994; Good & Whang, 1999; Hettich, 1976
Researchers have found that students’ conceptual understanding and problem-solving skills improve when they are
encouraged to make sense of mathematics by writing about… their mathematical thinking.
-Putnam, 2003
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Mathematics Shift 5: Rigor through Application
What the Student Does…
What the Teacher Does…
•Apply math in other content areas
and situations, as relevant
•Apply math including areas where
its not directly required (i.e. in
science)
•Choose the right math concept to
solve a problem when not
necessarily prompted to do so
•Provide students with real world
experiences and opportunities to
apply what they have learned
Principal’s Role:
Ensure that math has a place in science instruction
Create a culture of math application across the school
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Mathematics Shift 6: Rigor through Dual Intensity
What the Student Does…
What the Teacher Does…
•Practice math skills with an intensity that •Find the dual intensity between
results in fluency
understanding and practice within
different periods or different units
•Practice math concepts with an intensity
that forces application in novel situations •Be ambitious in demands for fluency and
practice, as well as the range of
application
Research #6:
Use should be made of what is clearly known from rigorous research about how children learn,
especially by recognizing a) the advantages for children in having a strong start; b) the mutually
reinforcing benefits of conceptual understanding, procedural fluency, and automatic (i.e., quick and
effortless) recall of facts; and c) that effort, not just inherent talent, counts in mathematical
achievement.
-Foundations for Success The Final Report of the National Mathematics Advisory Panel, 2008
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Shifts in Assessments
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Thank You
Mary Cahill [email protected]
John Svendsen [email protected]
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More Questions?
Office of State Assessment
[email protected]
Teacher Evaluation (APPR), Student Learning
Objectives (SLO) [email protected]
Teacher Certification
http://www.highered.nysed.gov/tcert/contact.html
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WEBSITES
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Engageny
http://engageny.org/
PARCC Model Content Frameworks 3-11/Content Emphases
http://www.parcconline.org/parcc-model-content-frameworks
PreK-2 Content Emphases
http://engageny.org/wp-content/uploads/2012/03/nys-mathemphases-k-8.pdf
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• Common Core Toolkit (includes Mathematics toolkit)
• http://engageny.org/resource/common-core-toolkit/
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www.engageNY.org
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