Embracing the Common Core Standards
in Mathematics Wholeheartedly
What has changed and why?
Dr. Lamont Holifield, CICS-Ralph Ellison
IMathination 2013 – January 26, 2013
St. Charles, IL
Agenda
CCSS Rationale: Why the Need to Change
The Need for Critical Thinking in Mathematics
The Shift in Cognitive Demand
What Common Core Is Not
Major Contentions
Professional Development
Paradigm Shift
First Look at the CCSS Eight Mathematical Practices
Common Core Implementation Ideas (Strategies, Sample Lessons,
Etc…)
Closing
THIS!
NOT THAT!
CCSS Rationale:
CCSS: www.corestandards.org/math
Toward greater focus and coherence
“Because the mathematics concepts in [U.S.]
textbooks are often weak, the presentation becomes
more mechanical than is ideal. We looked at both
traditional and non-traditional textbooks used in the
US and found this conceptual weakness in both.”
— Ginsburg et al., 2005
The Need for Critical
Thinking In Mathematics
Quote from How to Teach Thinking Skills Within the
Common Core
“The principal goal of education in the schools should
be creating men and women who are capable of doing
new things, not simply repeating what other
generations have done; men and women who are
creative, inventive, and discoverers, who can be critical
and verify, and not accept, everything they are offered.”
What Common Core Is Not!
Consider this quote from the National Governor’s
Association Center for Best Practices & Council of
Chief State School Officers.
“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 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 we intend to keep.”
The What, Why, and How
Major Contentions
There is a difference between the intended curriculum an
external authority establishes and the implemented
curriculum that individual teachers teach in the classroom
each day.
Students cannot learn what they are not taught.
The quality of instruction students receive each day is the
most important factor in their learning of mathematics.
Providing more good teaching in more classrooms more of
the time requires high-quality professional development for
those who deliver mathematics instruction.
Professional Development???
Must be ongoing rather than sporadic.
Embedded in the routine practice of the school.
Occur in the workplace rather than relying on
workshops.
Collective and Team-Based vs. Individualistic
Focused on Student Achievement vs. Adult Activities
Paradigm Shift Required
Is your focus on covering the mathematics curriculum
or is the focus on students’ learning?
Are you interested in creating documents in isolation
or collaborating and sharing collective responsibility?
Do you believe in the use of assessments to prove what
students have learned or do you look at them as tools
to improve students’ learning?
Do you use evidence of students’ learning to assign
grades or to inform or improve professional practice?
Think About This:
As a mathematics teacher, how often have you heard
from others or personally felt obligated to reteach
much of what students were supposed to have been
taught the previous year(s)?
Turn and Talk about some possible reasons
for this phenomenon!
CCSS – A Move In the Right
Direction
This standards offer possibilities and have the potential
to address the prevalent concern that U.S. students
have historically learned mathematical content in a
superficial manner in which concept and skills are
approached as discrete and unrelated topics without
application.
Although GREAT TEACHING looks different in
every classroom, the Common Core standards expects
us to commit to high-quality instruction as an essential
element of successful student learning.
Prerequisite for Teaching using
CCSS
Implementation of the standards with fidelity requires
us to:
•
•
•
Not just teach mathematics content
Teach students processes and proficiencies for ways of
thinking and doing mathematics—a habit of mind
Participate in collaborative team discussions—which is
the vehicle that aids us in creating and implementing
rigorous and coherent mathematics curriculum and
prevents ineffective instructional practices.
Collaboration
“The Same Old, Same Old . . .
NO!
Truly COLLABORATING requires one to:
“balance personal goals with collective goals, acquire
resources for [your] work and share those resources to
support the work of others.”
Think About It!
We are often accustomed to working toward success for
each of our students by ourselves, without an
articulated or shared image of what it would look like
in a mathematics classroom.
If we asked each teacher on your team to list his or her
top three non-discretionary teaching behaviors critical
to student success, would the top three reveal a
coherent and focused vision for instruction from your
team?
High Impact Collaborative
Teams Focus
Focused on student learning
Focused on assessment of the decision teacher team
members make
Focused on people rather than programs.
Seven Stages of Teacher
Collaboration
Stage 1: Filling the Time
Stage 2: Sharing Personal Practice
Stage 3: Planning, Planning, Planning
Stage 4: Develop Common Assessments
Stage 5: Analyzing student learning
Stage 6: Adapting Instruction to Student Needs
Stage 7: Reflecting on Instruction
Common Core Standards For
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.
Groupings of Mathematical
Practices
MP 1 and 6: Overarching Habits of Mind
(encompasses all of the practices).
MP 2 and 3: Reasoning and Explaining
MP 4 and 5: Modeling and Using Tools
MP 7 and 8: Seeing Structures and Generalizing
Essential Questions
Understanding CCSS
Mathematical Practices
1. What is the intent of this CCSS Mathematical
Practice, and why is it important?
2. What teacher actions develop this CCSS
Mathematical Practice?
3. What evidence is there that students are
demonstrating this CCSS Mathematical Practice?
Power Standard 1
Making Sense of
Problems and Persevering
in Solving Them
Intent and Importance
Problem Solving is one of the hallmarks of
mathematics and is the essence of doing mathematics.
When students problem solve, they draw on their
understanding of mathematical concepts and
procedures with the goal to reach a successful response
to the problem.
To students, this is a source of frustration!
Tendency
“Design lessons that remove
obstacles and minimize
confusion [where]
procedures for solving the
problems would be clearly
demonstrated so students
would not flounder or
struggle.”
In the Spirit of Mathematics
Removing
Obstacles
Minimization
of Confusion
Lack of
Perseverance
Teacher Actions that Support
Development of MP 1
Six Planning Questions
1.
Is the problem interesting to students?
2.
Does the problem involve meaningful mathematics?
3.
Does the problem provide an opportunity for students to
apply and extend mathematics?
4.
Is the problem challenging for students?
5.
Does the problem support the use of multiple strategies?
6.
Will students’ interaction with the problem reveal
information about the student’ mathematics understanding?
Sample Geometric Probability
Problem
Determine the probability that a point randomly
chosen in the square lands in each of the shaded
regions.
Students’ Methodology
Some will want to use a ruler as they solve the
geometric probability.
Some students will get stuck with the unfamiliar
shaded area in the middle of the square.
Some will want to use a formula for finding area.
Some may demonstrate an understanding of what area
means as a measure of so many square units of surface.
Question to Ponder
Without providing too much of a lead to the solution,
what types of advancing or assessing thinking questions
might you ask students who are stuck?
And what will be the expected precision of student
response regarding both the explanation of their
answer and the computation format of the answer.
In the first square are 25%, ¼, one out of four or 1:4
acceptable student responses? Attending to precision
becomes an important habit of mind.
Deconstructing Power
Standard 1
POOFPPOOF!
FROM
THIS
To this!
Power Standard 6
Attend to Precision
Is this okay?
ln(x + 1) = 2 = (x + 1) = e^2 = x = e^2 – 1 = 6.389
When Actually the Student Means
ln(x + 1) = 2
x + 1 = e^2
x = e^2 – 1
x= 6.389
not the ln(x + 1) = 6.389
Common Core Toolkit
Examination
Which can you immediately use?
What ideas have the session triggered?
What questions do you still have?
Next Steps . . . .
Common Core integration in
Lesson Planning
Resources
Common Core Mathematics in a PLC at Work (High
School) by Zimmerman, Carter, Kanold and Toncheff
How to Teaching Thinking Skills Within the Common
Core by Bellanca, Forgarty, and Brian M. Peter
go.solution-tree.com/commoncore
Special Thanks
I appreciate your participation in today’s session!
Should you desire to communicate with me further, please
contact me at:
Lamont Holifield
C.I.C.S. – Ralph Ellison High School
1817 W. 80th Street, Chicago, IL 60620
lholifield@cicsellison.org