Strengthening Instructional Leadership in Mathematics 10/6/2014.
Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies
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Transcript of Strengthening Mathematics Instruction Cognitive Complexity and Instructional Strategies
Strengthening Mathematics Instruction
Cognitive Complexity and Instructional Strategies
Dr. Vicki [email protected] [email protected]
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• California could add up
to 15%
• Indicated by underlined
text
• Adopted 2 options for
grade 8
• Added AP Probability
and Statistics and
Calculus
The Common Core State Standards - Mathematics
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The CCSS-M are divided into two groups:Mathematical Content StandardsDescribe what students should understand
and be able to do.Change from grade to grade.Standards for Mathematical PracticeDescribe ways in which students ought to
engage with mathematics.Carry across all grade levels.
Tulare County Office of Education
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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
Standards for Mathematical Practice
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The 8 Standards for Mathematical Practice require students to think at a
high level and place an emphasis on
student demonstrations of learning.
How do we give students the opportunity
to engage in the Practices?
Math Task #16
Martha was re-carpeting her bedroom which was 15 feet long and 10 feet wide.
How many square feet of carpeting will she need to purchase?
Math Task #27
Ms. Brown’s class will raise rabbits for their spring science fair. They have 24 feet of fencing with which to build a rectangular rabbit pen in which to keep the rabbits.
1. If Ms. Brown’s students want their rabbits to have as much room as possible, how long would each of the sides of the pen be?
2. How long would each of the sides of the pen be if they had only 16 feet of fencing?
3. How would you go about determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it.
Compare and Contrast8
How are Martha’s Carpeting Task and
the Fencing Task the same and how are they different?
Math Task 1: Possible SolutionsMethod 1:
A = l x wA = 15 x 10
A = 150 square feet
Method 2:
Area = 150
Math Task 2: Possible Solutions
AREA
LENGTH
A) B)
C)
Similarities and Differences
Similarities Differences
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• Both are “area” problems
• Both require prior knowledge of area
• The amount of thinking and reasoning required
• The number of ways the problem can be solved
• The way in which the area formula is used
• The need to generalize• The range of ways to enter
the problem• #1 a CST style problem,
#2 a SBAC style problem
Cognitive Levels of Tasks12
Higher-Level TasksProcedures with
ConnectionsDoing Mathematics
e.g. The Fencing Task, SBAC assessment items
Lower-Level TasksMemorizationProcedures without
Connectionse.g. Martha’s Carpeting Task, CST assessment items
Selected Response – Yes/No
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Research based
More complex than traditional multiple choice
Worth multiple points
http://www.smarterbalanced.org/?s=item+specifications+math
Selected Response – Scoring Rubric
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http://www.smarterbalanced.org/?s=item+specifications+math
CST Equivalent:
Communicating Reasoning16
http://www.smarterbalanced.org/?s=item+specifications+math
Communicating Reasoning17
http://www.smarterbalanced.org/?s=item+specifications+math
SBAC – Technology Enhanced
http://www.k12.wa.us/SMARTER/pubdocs/SBAC_Appendices.pdf
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http://www.k12.wa.us/SMARTER/pubdocs/SBAC_Appendices.pdf
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SBAC – TECHNOLO
GY ENHANCED(CONTINUE
D)
Sample Performance Task – High School
www.smarterbalanced.org
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• Addresses middle school and high school standards
• 2 sessions – no more than 120 minutes
• Calculator can be used
www.smarterbalanced.org
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www.smarterbalanced.org
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Cognitive Demands of CCSS-MCST items call for recall of procedures and
facts – low cognitive demand.SBAC items demand not only that recall,
but also the ability to apply and use that mathematical knowledge in meaningful ways – high cognitive demand
Mathematical Tasks24
It is the mathematical tasks selected and implemented by the
teacher that create the opportunity for students
to engage in these practices and learn mathematics.
SMI PD gives teachers tools to find tasks with high cognitive demands.
Outline of SMI PD Modules
Next Steps and Closure
Welcome
Value of SMI PDThe transition to the CCSS-M and the new
assessments needs to begin now.The obvious place to begin is with the
Standards for Math Practice.That shift calls for using math tasks with
high cognitive demand.SMI PD is focused on understanding,
finding, and creating such math tasks for high school courses.