Embracing the Common Core Standards in
Mathematics Wholeheartedly
What has changed and why?
Dr. Lamont Holifield, CICS-Ralph EllisonIMathination 2013 – January 26, 2013St. Charles, IL
AgendaCCSS Rationale: Why the Need to Change
The Need for Critical Thinking in MathematicsThe Shift in Cognitive Demand What Common Core Is NotMajor ContentionsProfessional DevelopmentParadigm 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
MathematicsQuote 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 ContentionsThere 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 RequiredIs 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 CCSSImplementation 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
FocusFocused on student learning
Focused on assessment of the decision teacher team members make
Focused on people rather than programs.
Seven Stages of Teacher CollaborationStage 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 QuestionsUnderstanding 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
In the Spirit of Mathematics
Teacher Actions that Support Development
of MP 1Six 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
FROM THIS
To this!
POOFPPOOF!
Power Standard 6Attend 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