Transcript CCSS Verbs of Math: Habits of a Mathematical Thinker

CCSS Verbs of Math: Habits of a
Mathematical Thinker
July 30 - 31, 2013
Our Presenters
Sean Timmons
Project Coordinator, STEM
Carolyn Viss
Project Coordinator, Mathematics
Goals and Outcomes
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Establish familiarity with the Common Core
Standards for Mathematical Practice (SMP)
Distill key elements of each SMP
Analyse assessment items through the lens
of the SMP
Identify SMP in an instructional segment
Refine an existing lesson or task to more
fully align with one or more SMP
Two Types of Math Standards
Math Content Standards
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Vary by grade level and
conceptual category
Describe what students
should know,
understand, and be able
to do at that grade level
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Standards for Math
Practice
Same eight standards
common to all grade
levels K-12
Capture:
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Mathematical processes
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Habits of mind and thinking
skills specific to math
Focusing on our Materials
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Let's take a moment to walk
through our Common Core
spirals for mathematics.
Where are the Standards for
Mathematical Practices
located?
Let's also locate the Standards
for Mathematical Practices
grade-level overview and
mark its location.
Standards for
Mathematical Practice
Sean Timmons
Standards for Mathematical Practice
What is the focus for the practices?
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Place an emphasis on student
demonstrations of learning that describes
their thought process.
Require students to develop the disposition
to acquire a deep, flexible, and enduring
understanding of mathematics.
adapted from Briars & Mitchell (2010)
Getting Started with the Common Core State Standards
Let's look at the eight standards.
Standards for Mathematical Practice:
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.
The Verbs in Mathematics
The practice standards describe actions that:
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require students to think differently about
mathematics.
ask students to solve problems and apply mathematics.
are crucial to developing an enduring understanding of
mathematics.
The Verbs in Mathematics
Let's look at an example:
Standard for MP6: 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. They state the meaning of the symbols they choose, including
using the equal sign consistently and appropriately. They are careful about
specifying units of measure, and labeling axes to clarify the correspondence
with quantities in a problem. They calculate accurately and efficiently,
express numerical answers with a degree of precision appropriate for the
problem context. In the elementary grades, students give carefully
formulated explanations to each other. By the time they reach high school
they have learned to examine claims and make explicit use of definitions.
Taking a Closer
Look
Let's take a look at the Standards for
Mathematical Practices.
After carefully examining the Standards for
Mathematical Practices, summarize your
standard or your thoughts.
Working Together
In groups of two, take a moment to share your
thoughts and understanding about the
practices.
Summarize your thoughts and understanding
about the practices in the "Pair" section.
Together, develop a common understanding
about your Standard for Mathematical Practices
and record it in the "Share" section.
Developing a Collective
Understanding
Create a poster for your standard. Please be prepared to present a
1-2 minute presentation to the group.
Standard for Mathematical Practice
Summarize the SMP in a bulleted list of key
ideas.
Describe the literacy skills that students will
need to be able to engage in this practice. You
can be very general in describing these skills.
Examples of what this might look like in action with students.
Why are the math practices
important?
The Hunt Institute and Council of Chief State School Officers (CCSSO)
Reflection and Discussion
Take a moment to think about the Standards
for Mathematical Practice.
How will math teaching and learning change in
your classroom or at your site?
Take a moment to discuss the implications of
this change with your table group.
Analysing the Assessment, Identify
the SMPs in Instruction, and
Refining Existing Activities
Carolyn Viss
Will this be on the test?
Find X
Smarter Balanced Assessment Consortium
SBAC
Consider some sample tasks and look for
alignment to Standards for Mathematical
Practice
www.smarterbalanced.org
Grade 3, CCSS3.NF.3a
smarterbalanced.org sample equiv fractions
Grade 6: CCSS 6.SP.3
smarterbalanced.org sample sandbags
Grade 6: CCSS 6.SP.3
Scoring Rubric
Grade 6 Performance Task
Taking a field trip
smarterbalanced.org sample field trip
SMP in the Classroom
As you reflect on the types of tasks students will
be required to do, consider the implications
for classroom instruction.
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What are the teacher's actions?
What are the students' actions?
Dip into the Classroom
Identify Standards for Mathematical Practice in a lesson
SMP 2 Reason abstractly and quantitatively
SMP 3 Construct viable arguments and critique the
reasoning of others
SMP 6 Attend to precision
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InsideMathematics.org
Stephanie Letson, 2nd Grade
Dip into the Classroom
Identify Standards for Mathematical Practice in a lesson
Dave Younkin, 4th grade, Public School 234 NY
Dip into the Classroom
Consider a math task or activity that:
exemplifies one or more of the standards for
mathematical practice
your students will be tackling in the next
weeks
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How might you modify the task to more fully
align with the SMP?
...not to reinvent the wheel
Task Analysis
Reflection on Shifts
Reflect on shifts you see in the transition from
1997 Standards to CCSS.
Create a seven word bumper sticker
summarizing the shift you see in
mathematics as we transition into the
Common Core
Contact Information
Carolyn Viss
[email protected]
Sean Timmons
[email protected]