Transcript Implementing Standards and Incorporating Mathematical

Implementing Standards and
Incorporating Mathematical
Practices
Sandra M. Alberti
AMTNJ
October 24, 2013
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Student Achievement Partners – Who We Are
• SAP is a nonprofit organization founded by three of
the contributing authors of the Common Core State
Standards
• Currently a team of approximately 30; office in NY and
team members located throughout the country
• Funded by foundations: GE Foundation, Hewlett
Foundation, Bill & Melinda Gates Foundation and The
Helmsley Charitable Trust
Our mission:
• Student Achievement Partners is devoted to
accelerating student achievement by supporting
effective and innovative implementation of the CCSS.
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Our Principles – How we approach the work
WE HOLD NO INTELLECTUAL PROPERTY
Our goal is to create and disseminate high quality materials as widely as
possible. All resources that we create are open source and available at no
cost. We encourage states, districts, schools, and teachers to take our
resources and make them their own.
WE DO NOT COMPETE FOR STATE, DISTRICT OR FEDERAL
CONTRACTS
Ensuring that states and districts have excellent materials for teachers and
students is a top priority. We do not compete for these contracts because we
work with our partners to develop high quality RFPs that support the Core
Standards.
WE DO NOT ACCEPT MONEY FROM PUBLISHERS
We work with states and districts to obtain the best materials for teachers
and students. We are able to independently advise our partners because we
have no financial interests with any publisher of education materials. Our
independence is essential to our work.
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Why are we doing this? We have had
standards.
• Before Common Core State Standards
we had standards, but rarely did we
have standards-based instruction.
Long lists of broad, vague statements
Mysterious assessments
Coverage mentality
Focused on teacher behaviors – “the
inputs”
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Results of Previous Standards, and Hard
Work
Previous state standards did not improve student
achievement.
 Gaps in achievement, gaps in expectations
 NAEP results
 High school drop out issue
 College remediation issue
This is about more than just working hard!
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Principles of the CCSS
Fewer
-
Clearer
-
Higher
• Aligned to requirements for college and
career readiness
• Based on evidence
• Honest about time
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Implications
• What implications do the CCSS
have on what we teach?
• What implications do the CCSS
have on how we teach?
This effort is about much more than implementing
the next version of the standards: It is about
preparing all students for success in college and
careers.
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Mathematics: 3 shifts
1. Focus: Focus strongly where the
standards focus.
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The shape of math in A+ countries
Mathematics topics intended at
each grade by at least
two-thirds of A+ countries
1 Schmidt,
Mathematics topics intended
at each grade by at least twothirds of 21 U.S. states
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
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3
4
Algebra
The Number
System
Number and
Operations—
Fractions



5
6
7
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High School
Priorities 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
7
8
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Ratios and proportional reasoning; early
expressions and equations
Ratios and proportional reasoning; arithmetic of
rational numbers
Linear algebra, linear functions
Where to focus in mathematics – K
example
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14
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Mathematics: 3 shifts
1. Focus: Focus strongly where the
standards focus.
2. Coherence: Think across grades, and
link to major topics
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Coherence: Link to major topics within grades
Example: data representation
Standard 3.MD.3
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Mathematics: 3 shifts
1. Focus: Focus strongly where the
standards focus.
2. Coherence: Think across grades, and
link to major topics
3. Rigor: In major topics, pursue
conceptual understanding,
procedural skill and fluency, and
application
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Conceptual
understanding of
place value…?
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Conceptual
understanding
of place value…?
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Conceptual Understanding of Fractions
Resource/Tool:
http://www.illustrativemathematics.org/standards/k8
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Required Fluencies in K-6
Grade
Standard
Required Fluency
K
K.OA.5
Add/subtract within 5
1
1.OA.6
Add/subtract within 10
2
2.OA.2
2.NBT.5
Add/subtract within 20 (know single-digit sums from
memory)
Add/subtract within 100
3
3.OA.7
3.NBT.2
Multiply/divide within 100 (know single-digit products
from memory)
Add/subtract within 1000
4
4.NBT.4
Add/subtract within 1,000,000
5
5.NBT.5
Multi-digit multiplication
6
6.NS.2,3
Multi-digit division
Multi-digit decimal operations
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Mathematical Practices
1. Make sense of problems and persevere in
solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the
reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated
reasoning.
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1. Make sense of problems and
persevere in solving them
6. Attend to precision
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique
the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
7. Look for and make use of structure
8. Look for and express regularity in
repeated reasoning
Overarching habits of mind of a
productive mathematical thinker.
Modeling and using tools
Reasoning and explaining
Seeing structure and
generalizing
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AM I DOING THE CORE?
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Standards for Mathematical Practice
•
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There is not a one-to-one
correspondence between
the indicators for Core Action
3 and the Standards for
Mathematical Practice.
These indicators and the
associated illustrative
student behavior collectively
represent the Standards for
Mathematical Practice that
are most easily observable
during instruction.
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Core Action 3: Provide all students with opportunities to exhibit
mathematical practices in connection with the content of the
lesson.
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Some or most of the indicators and student behaviors should be
observable in every lesson, though not all will be evident in all lessons.
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Evidence Observed or Gathered
1 = The teacher does not provide students opportunity and
very few students demonstrate this behavior.
2 = The teacher provides students opportunity inconsistently
and very few students demonstrate this behavior.
3 = The teacher provides students opportunity consistently
and some students demonstrate this behavior.
4 = The teacher provides students opportunity consistently
and some students demonstrate this behavior.
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Am I doing the Core?
Indicators
Illustrative Student Behavior
A. The teacher uses strategies to keep
all students persevering with
challenging problems.
Even after reaching a point of
frustration, students persist in efforts
to solve challenging problems.
B. The teacher establishes a classroom
culture in which students explain
their thinking.
Students elaborate with a second
sentence (spontaneously or prompted
by the teacher or another student) to
explain their thinking and connect it to
their first sentence.
C.
Students talk about and ask questions
The teacher orchestrates
about each other’s thinking, in order
conversations in which students talk
to clarify or improve their own
about each other’s thinking.
mathematical understanding.
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Am I doing the Core?
Indicators
Illustrative Student Behavior
D. The teacher connects students’
informal language to precise
mathematical language appropriate
to their grade.
Students use precise mathematical
language in their explanations and
discussions.
E.
F.
The teacher has established a
classroom culture in which students
choose and use appropriate tools
when solving a problem.
Students use appropriate tools
strategically when solving a problem.
The teacher asks students to explain Student work includes revisions,
and justify work and provides
especially revised explanations and
feedback that helps students revise justifications.
initial work.
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Evidence-Centered Design (ECD)
Claims
Evidence
Design begins
with the
inferences
(claims) we
want to make
about
students
Tasks
In order to
support
claims, we
must gather
evidence
Tasks are
designed to
elicit
specific
evidence from
students in
support of
claims
ECD is a deliberate and systematic approach to assessment
development that will help to establish the validity of the
assessments, increase the comparability of year-to year results, and
increase efficiencies/reduce costs.
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Claims Structure: Mathematics
Master Claim: On-Track for college and career readiness. The degree to which a student is college and career ready (or “ontrack” to being ready) in mathematics. The student solves grade-level /course-level problems in mathematics as set forth in
the Standards for Mathematical Content with connections to the Standards for Mathematical Practice.
Total Exam Score Points:
82 (Grades 3-8), 97 or 107(HS)
Sub-Claim A: Major Content1 with
Connections to Practices
The student solves problems
involving the Major Content1 for her
grade/course with connections to
the Standards for Mathematical
Practice.
~37 pts (3-8),
~42 pts (HS)
Sub-Claim B: Additional & Supporting
Content2 with Connections to
Practices
The student solves problems involving
the Additional and Supporting
Content2 for her grade/course with
connections to the Standards for
Mathematical Practice. ~14 pts (3-8),
~23 pts (HS)
Sub-Claim D: Highlighted Practice MP.4 with Connections to Content
(modeling/application)
The student solves real-world problems with a degree of difficulty appropriate to the
grade/course by applying knowledge and skills articulated in the standards for the
current grade/course (or for more complex problems, knowledge and skills articulated
in the standards for previous grades/courses), engaging particularly in the Modeling
practice, and where helpful making sense of problems and persevering to solve them
(MP. 1),reasoning abstractly and quantitatively (MP. 2), using appropriate tools
strategically (MP.5), looking for and making use of structure (MP.7), and/or looking for
and expressing regularity in repeated reasoning (MP.8).
12 pts (3-8),
Sub-Claim C: Highlighted Practices
MP.3,6 with Connections to Content3
(expressing mathematical reasoning)
The student expresses grade/courselevel appropriate mathematical
reasoning by constructing viable
arguments, critiquing the reasoning of
others, and/or attending to precision
when making mathematical statements.
14 pts (3-8),
14 pts (HS)
4 pts (Alg II/Math 3 CCR)
Sub-Claim E: Fluency in applicable
grades (3-6)
The student demonstrates fluency as set
forth in the Standards for Mathematical
Content in her grade.
18 pts (HS)
6 pts (Alg II/Math 3 CCR)
For the purposes of the PARCC Mathematics assessments, the Major Content in a grade/course is determined by that grade level’s Major Clusters as identified in
the PARCC Model Content Frameworks v.3.0 for Mathematics. Note that tasks on PARCC assessments providing evidence for this claim will sometimes require
the student to apply the knowledge, skills, and understandings from across several Major Clusters.
2 The Additional and Supporting Content in a grade/course is determined by that grade level’s Additional and Supporting Clusters as identified in the PARCC
Model Content Frameworks v.3.0 for Mathematics.
3 For 3 – 8, Sub-Claim C includes only Major Content. For High School, Sub-Claim C includes Major, Additional and Supporting Content.
1
7-9 pts (3-6)
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Implementing Standards and
Incorporating Mathematical
Practices
Sandra M. Alberti
AMTNJ
October 24, 2013
achievethecore.org