Transcript New York State Common Core Learning Standards

New York State Common
Core Learning Standards
Mathematics
Presented by
Joyce Bernstein
East Williston UFSD
Elaine Zseller, Ph.D.
Nassau BOCES
Why Common Core State Standards?
 Preparation: The standards will help prepare
students with the knowledge and skills they need to
succeed in education and training after high school
 Competition: The standards are internationally
benchmarked
 Equity: Expectations are consistent for all
Why Common Core State Standards?
 Clarity: The standards are focused, coherent, and
clear
 Collaboration: The standards will create a
foundation to work collaboratively across states and
districts
 pool resources and expertise
 create curricular tools, professional development,
assessments and other materials
 compare policies and achievement across states
and districts
Overview of New York State
P-12 Common Core Learning Standards
for Mathematics
 Includes 450 College and Career Readiness
Standards for all students
 New York State added pre-kindergarten standards to
the national common core to provide foundational
support for kindergarten standards and beyond and
two grade level standards, one at the kindergarten
level and one at the first grade level
 No new standards were added to the national
common core for the rest of the grade levels (2-12)
Overview of CCLS for Mathematics
 The CCLS for Mathematics are organized as:

Standards for Mathematical Practice

Standards for Mathematical Content
Overview of CCLS for Mathematics:
Standards for Mathematical Practice
 There are eight Standards for Mathematical
Practice that are to be woven throughout the
curriculum
 taught in conjunction with content and procedures
 correspond to NYS’s current Process Strands in
mathematics
 Unlike our experience with the current Process
Strands, we are warned to take the Standards for
Mathematical Process seriously.
Mathematical Practices
Make sense of problems and persevere in
solving them.
 Mathematically proficient students start by
explaining to themselves the meaning of a
problem and looking for entry points to its
solution. Students learn to monitor their
solution path and change course if
necessary.
 Help student to build
PERSEVERANCE and STAMINA!
Mathematical Practices
2 Reason abstractly and quantitatively.
 Quantitative reasoning entails habits of
creating a coherent representation of the
problem at hand; considering the units
involved; attending to the meaning of
quantities, not just how to compute them;
and knowing and flexibly using different
properties of operations and objects.
Mathematical Practices
Construct viable arguments and critique the
reasoning of others.
 Elementary students can construct arguments
using concrete referents such as objects,
drawings, diagrams, and actions. Such
arguments can make sense and be correct,
even though they are not generalized or
made formal until later grades
Mathematical Practices
Model with mathematics.
 In early grades, this might be as simple as
writing an addition equation to describe a
situation.
Students should understand WHY they are
learning mathematics.
Mathematical Practices
Use appropriate tools strategically.
These tools might include pencil and paper,
concrete models, a ruler, a protractor, a
calculator.
Mathematical Practices
Attend to precision.
 Mathematically proficient students try to
communicate precisely to others. They try to
use clear definitions in discussion with others
and in their own reasoning.
 In the elementary grades, students give
carefully formulated explanations to each
other.
 Correct mathematical language is essential!
Mathematical Practices
Look for and make use of structure.
Young students, for example, might notice
that three and seven more is the same
amount as seven and three more, or they
may sort a collection of shapes according to
how many sides the shapes have. Later,
students will see 7 × 8 equals the well
remembered 7 × 5 + 7 × 3, in preparation for
learning about the distributive property.
Mathematical Practices
Look for and express regularity in repeated
reasoning.
For example: The rule “Add 3” results in a
pattern of odd-even-odd-even-
How to Read the
Common Core Learning Standards
 Domain
 Cluster
 Standard
 Be sure teachers are reading the examples. The
standards are written on a level designed to be read
by mathematicians. The examples clarify the content
in terms of the past experience of the teacher.
Domain Progression
PK - 8 Domain Progression
Domain
Counting and Cardinality
Operations and Algebraic Thinking
Number and Operations in Base Ten
Number and Operations - Fractions
Ratios and Proportional Relationships
The Number System
Expressions and Equations
Functions
Measurement and Data
Geometry
Statistics and Probability
PK
K
1
2
3
4
5
6
7
8
Mathematics Curriculum Mapping
 Sequence content


There will be multiple lessons for one standard
 Lessons should be logically sequenced to
scaffold knowledge
 Each math lesson should have one, maybe two,
objectives, reflective of the standard to be
covered.
Method – begin with CCLS
 Break down into lessons
 Find text lessons or other resources to match
objective.
 Don’t let your textbook series define your scope
and sequence.
Shifts in Mathematics
 1. Focus
Teachers must significantly narrow and deepen
the scope of what they each. They must focus
on content prioritized in the standards.
They must let go of several topics they are
currently teaching.
Spend Time on
Important Mathematics
Key topics demand that we slow down and devote more
time to allow for reasoning/ thinking/ interactive
discussion as well as the necessary drill and practice.
e.g
place value in K - 2
fractions in grades 3 – 5
We are moving away from the mile wide – inch deep
pattern we learned as children and taught to this
point.
Shifts in Mathematics
 2. Coherence
 Teachers must connect learning within and
across grades. Standards become extensions
of prior learning.
 The study of fractions in grades 3 – 6 is a
wonderful example of coherence.
Coherence
Write plans for a unit coherently:
 Big Idea (Grant Wiggins UBD)
 Essential Understanding
 Interactive Learning
 Articulated progressions and alignment of topics and
performance. Your sequence of units should make
sense.
The Number Line – K – 5
(Coherence Starts Here)
 Compare quantities, especially length
 Compare by measuring: units
 Add and subtract with ruler
 Diagram of a ruler
 Diagram of a number line
 Arithmetic on the number line based on units
 Representing time, money and other
quantities with number lines
Fractions
(Coherence Continues)
 Understanding the arithmetic of fractions draws upon




four areas introduced in prior grades:
equal partitioning,
understanding of a unit amount
number line
operations
Shifts in Mathematics
 3. Students are expected to have speed and
accuracy with simple calculations.
 Find fluencies by grade, beginning in
Kindergarten. (engageny.org)
 This is an important talking point with parents.
Shifts in Mathematics
 4. Deep Understanding
 Students must have understanding beyond
memorized procedures and mnemonics.
 Students, even in early grades, must be able
to apply the mathematics they know to new
situations.
 Relate to ELA – students must be able to
speak and write about their mathematical
understanding.
Mile deep: Operations:
Algebraic Thinking Grade 3
Apply properties of operations as
strategies to multiply and divide.
 Commutative Property
 Associative Property
 Distributive Property
Mile deep: Operations:
Algebraic Thinking Grade 3
 If 6 x 4 = 24 is known, then 4 x 6 = 24 is
also known. (Commutative property of
multiplication.)
 3 x 5 x 2 can be found by 3x 5 = 15, then
15x 2 = 30, or by 5 x 2 = 10, then 3 x 10 =
30. (Associative property of multiplication.)
 Knowing that 8 x 5 = 40 and 8 x 2 = 16, one
can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x
2) = 40 + 16 = 56. (Distributive property.)
Mile deep:
Fractions Building Grades 3 to 5
Shifts in Mathematics
 5. Application
 Link to the CCSS standards for modeling.
Students must be able to choose an
appropriate strategy, even when not
prompted to do so.
 Tie to real world experiences, including
learning in science.
 Students must be able to use the
mathematics they are learning.
Mile deep:
Connections to Prior Learning
Shifts in Mathematics
 6. Dual Intensity
 Teachers have to create a fine balance
between practice and understanding.
 Students must be fluent.
 Students must know how to use the math
they are learning.
 The balance is reset for every new topic.
Priorites (engageny.org)
Middle School Acceleration
 Appendix A, p. 80 ff
 Compacted courses for Grades 7 and 8
 Identifies specific standards to teach in each
of these grades
 Does not require acceleration earlier than
Grade 7
 Accomplishes three years in two by removing
redundancies
Algebra in 2012-13
This is a much more robust course, based
upon a more rigorous middle school
experience.
Some topics are left to earlier
grades:……..
What’s Out
 Scientific notation
 Percent
 Permutations and Combinations
 Line graphs, circle graphs
What’s Reduced
 Simple linear equations for grades 5 – 8.
 Some statistics
What’s New:
Modeling, including domain constraints
Slope in terms of instant rate of change
Functional vertical shifts
Cube root functions
Derivation of the Quadratic Formula
Recursion
Standard Deviation
Two-Way Frequency Tables
The Big Picture-Teacher Practice
In order to be successful teaching the New York
Learning Standards for Mathematics, teachers
must:
 Support the development of number sense.
 Use multiple representations of mathematical
entities.
 Create language rich classroom routines.
 Embed the mathematics in realistic, realworld contexts.
The Big Picture – Teacher Practice
 Incorporate cumulative review by building
coherent bridges within the curriculum.
 Minimize what is no longer a priority
 Make “Why?” and “How do you know?”
routine responses to student answers.
 Insist on holding all students responsible for
mastering fluency.