Transcript CCSS Math Breakout Session

CCSS Math
Breakout
Session
Where Are You?
Get a Post-It Note
Write your favorite math topic on it
Find the Consensograph on the wall
Place your post-it above where you feel
your level of understanding is about the
CCSS Math Standards
“Building A Box” Activity
Find the math problem on your table
With a partner work out the problem
Consider the following question:
“What does it look like when students
are doing math?”
Be ready to share
Session Objectives
To deepen understanding of CCSS Math
Standards
To become familiar with the Mathematical
Practice Standards
To understand the coding of the standards
To explore the glossary and appendix of
the math standards
First Step
Standards are essential, but inadequate. Along
with standards,
Educators must be given resources, tools, and
time to adjust classroom practice.
Instructional materials aligned to standards are
needed.
Assessments must be developed to measure
student progress.
Federal, state, and district policies need to be
reexamined to ensure they support alignment of
the CCSS with student achievement.
CCSSI 2010, www.corestandards.org
Key Advances
Focus and coherence
Focus on key topics at each grade level.
Coherent progressions across grade levels.
Balance of concepts and skills
Content standards contain both conceptual
understanding and procedural fluency.
Mathematical practices
Foster reasoning and sense-making in mathematics.
College and career readiness
Level is ambitious but achievable.
Standards, Curriculum and
Pedagogy
“For over a decade, research studies of
mathematics education in high-performing
countries have pointed to the conclusion
that the mathematics curriculum in the US
must become substantially more focused
and coherent in order to improve
mathematics achievement in this country.”
CCSS 2010, p. 3
Standards, Curriculum and
Pedagogy
“…the development of these standards
began with research-based learning
progressions detailing what is known
today about how students’ mathematical
knowledge, skill, and understanding
develop over time.”
CCSS 2010, p. 4
Standards, Curriculum and
Pedagogy
“One hallmark of mathematical
understanding is the ability to justify, in a
way appropriate to the student’s
mathematical maturity, why a particular
mathematical statement is true or where a
mathematical rule comes from…..
Mathematical understanding and
procedural skill are equally important, and
both are assessable using mathematical
tasks of sufficient richness.”
CCSS 2010, p. 4
Standards, Curriculum and
Pedagogy
“No set of grade-specific standards can
fully reflect the great variety in abilities,
needs, learning rates, and achievement
levels of students in any given classroom.
However, the Standards do provide clear
signposts along the way to the goal of
CCR for all students.”
CCSS 2010, p. 4
Standards, Curriculum and
Pedagogy
“These standards do not dictate curriculum
or teaching methods. For example, just
because Topic A appears before Topic B in
a given grade, it does not mean that Topic
A must be taught before Topic B.”
CCSS 2010, p. 5
Standards, Curriculum and
Pedagogy
“One promise of common state standards
is that over time they will allow research
on learning progressions to inform and
improve the design of standards to a much
greater extent than is possible today.”
CCSS 2010, p. 5
Standards, Curriculum and
Pedagogy
“It is time for states to work together to
build on lessons learned from two
decades of standards based reforms.
It is time to recognize that standards
are not just promises to our children,
but promises we intend to keep.”
CCSS 2010, p. 5
Building from past work
NCTM process standards:
Problem solving
Reasoning and proof
Communication
Representations
Connections
Building from past work
Five Strands of Mathematical Proficiency:
Adaptive reasoning
Strategic competence
Conceptual understanding – comprehension of
math concepts, operations and relations.
Procedural fluency – skill in carrying out procedures
flexibly, accurately, efficiently and appropriately.
Productive disposition – habitual inclination to see
math as sensible, useful, and worthwhile, coupled with a belief in
diligence and one’s own efficacy.
Adding It Up, NRC 2001
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.
Mathematical Practices
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.
Mathematical Practices
They are what students “do” with
the content standards.
Go across all grades.
Describe expertise or proficiencies
expected for all students.
How do your comments from earlier match
the Practice Standards?
Focus on Understanding
“The standards for Mathematical content
are a balanced combination of procedure
and understanding. Expectations that
begin with the word ‘understand’ are often
especially good opportunities to connect
practices to the content.”
CCSS 2010, p.8
Math Structure
Practice Standards
Describe an expertise that college & career ready
math students at all levels should develop in
order to effectively engage mathematical
concepts.
K-8
High School
Grade Level
Conceptual Category
Domain
Domain
Grade-Specific
Standard
Content-Specific
Standard
4.G.1
G-C.1
Design and Organization
Content standards define what students
should understand and be able to do
Clusters are groups of related standards
Domains are larger groups that progress
across grades
Design and Organization
Design and Organization
Take a look at the laminated
“posters” to help with learning the
coding process for the Math
CCSS.
Design and Organization
Critical Areas
Design and Organization
Critical Areas
Design and Organization
Critical Areas
Design and Organization
Design and Organization
Design and Organization
Design and Organization
Design and Organization
Design and Organization
Design and Organization
Design and Organization
Design and Organization
Design and Organization
Glossary
Appendix
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Course Development
(Traditional vs. Integrated)
Accelerating Students
Where is Michigan?
Fordham Institute’s Article – “The State of
the State Standards”
MI GLCE vs. CCSS Visual
Overview
MI “Crosswalk” Documents
Dig In
Time to Explore
& Ask Questions
Exploration Activity
Using the “Exploration” handout and the CCSS
document, correlate the standards from CCSS
with the “Building A Box” activity.
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Identify the big idea of the lesson.
Which standard does this lesson target?
What are students doing throughout the lesson?
Which standards were necessary for the student to
understand this lesson?
Which standards will the knowledge from this lesson
lay a foundation for?
Be ready to share.
Level of Understanding
What more do we need to
know/do?
Does the consensograph
change?