© 2013 boise state university1 what the shifts in the standards mean for learning and instruction...
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© 2013 Boise State University 1
What the Shifts in the Standards Mean for Learning and InstructionMichele Carney, PhD
Spring 2014
© 2013 Boise State University 2
Agenda• What does it mean to engage students in the
practice of mathematics?• Examine assessment items and categorize the
type of cognitive demand that are required from students
• What does this mean for instruction?
What does it mean to say students need to engage in the ‘Practice of ELA/Mathematics’Language Arts Mathematics• We teach phonics,
grammar, punctuation, spelling, etc. for the purpose of students’ engaging in the practice of language arts: – Reading – Writing
• Focused on teaching skills, facts, algorithms, procedures, etc.
• Now we are asking that students be able to put these into the practice of mathematics:– Problem solve– Model situations– Reason quantitatively– Critique the reasoning of
others
© 2013 Boise State University 4
Claim 1:Concepts & Procedures
Claim 2:Problem Solving
Claim 3:Communicate
Reasoning
Claim 4:Modeling & Data
Analysis
DOK 1
DOK 2
DOK 3
DOK 4
SBAC Assessment & Reporting Areas
Areas assessed by the ISAT
Areas assessed by SBAC
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If we are going to ask students to meaningfully engage in the practice of mathematics:
Then we must vary the type and depth of cognitive demand we are asking from students in classroom tasks, activities and assessments.
Level of Cognitive Demand
Rote, Skill or Recall
Concepts
Problem Solving
Reasoning & Justification
Modeling and Data Analysis
Mathematics Practices
Problem Solve
Model Situations
Reason Quantitatively
Critique the reasoning of others
© 2013 Boise State University 7
Porter (2002)
Memorize
Perform Procedures
Communicate Understanding
Solve Nonroutine Problems
Conjecture, Generalize, or
Prove
Webb (2007)
Recall
Skill/Concept
Strategic Thinking
Extended Thinking
SBAC Claims
Concepts and Procedures
Problem Solving
Communicate Reasoning
Model with Mathematics
Type DMT Description Example
Claim 1
Rote, Skill or Recall
Rote, Skill, Recall items require students to produce a response by following a set of rote procedures, demonstrating procedural skills or recalling information (Webb, 2002).
Typically procedural or algorithm focused problems
ConceptsConcept items require students to respond by producing models and diagrams or demonstrate an understanding of mathematical properties and their applications (Webb, 2002)
Often involves asking for visual or iconic representation of a topic
Claim 2
Problem Solving
Problem Solving items require students to produce a response to a given problem for which there can be a variety of answers or problem-solving strategies. Solution methods are not readily apparent and require students to make decisions about how to solve the problem (Hiebert et al, 1992; Porter, 2002).
Typically multi-part, contextual questions but must go beyond skill level applications
Claim 3
Reasoning & Justification
Reasoning and Justification items require students to justify their own reasoning or critique the reasoning of others through careful analysis and by explaining and modeling how a response is either correct or incorrect (de Lange, 1999)
Identifying the incorrect solution strategy from two examples and how to correct it
Claim 4
Modeling and Data Analysis
Modeling and Data Analysis performance tasks require students to analyze complex, real-world scenarios and/or use mathematics models to interpret and solve problems (SBAC, 2011).
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Type of Cognitive Demand• As a group:– Solve each problem– Identify the type of cognitive demand required by
each item
Type of Cognitive Demand: __________________________________
https://sat2.sbacpt.tds.airast.org/Student/Pages/TestShellModern.aspx
https://sat2.sbacpt.tds.airast.org/Student/Pages/TestShellModern.aspx
Type of Cognitive Demand: __________________________________
Type of Cognitive Demand: __________________________________
https://sat2.sbacpt.tds.airast.org/Student/Pages/TestShellModern.aspx
Type of Cognitive Demand: __________________________________
http://www.smarterbalanced.org/smarter-balanced-assessments/
https://sat2.sbacpt.tds.airast.org/Student/Pages/TestShellModern.aspx
Type of Cognitive Demand: __________________________________
http://www.smarterbalanced.org/wordpress/wp-content/uploads/2012/09/performance-tasks/tulips.pdf
Type of Cognitive Demand: ___________________________
p.5
p.6
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• Reflect upon the different types of cognitive demand:– How should these be integrated into classroom
practice?– How do they promote different aspects of the
mathematical practice standards?– Is there a particular order in which tasks with
different cognitive demands should be sequenced?
Discuss in your small groups and select one to two items to share with the whole group.
6th Grade Focus Areas
Rate and ratio
Dividing fractions and understanding rational (e.g.,
negative) numbers
Writing, interpreting, and using expressions and equations
Statistical thinking
6th Grade Math Topics # of Days
Expectations for Students
Rote, Skill or Recall Concepts Problem
SolvingReasoning & Justification
Modeling and Data Analysis
Rate and ratio A B C D A B C D A B C D A B C D A B C D
Dividing fractions and understanding rational (e.g., negative) numbers
A B C D A B C D A B C D A B C D A B C D
Writing, interpreting, and using expressions and equations
A B C D A B C D A B C D A B C D A B C D
Statistical thinking A B C D A B C D A B C D A B C D A B C D
Other A B C D A B C D A B C D A B C D A B C D
(A) no emphasis; (B) slight emphasis (less than 25% of time spent on this topic); (C) moderate emphasis (accounts for 25–33% of time spent on this topic); and (D) sustained emphasis
Adapted from Porter, A. C. (2002). Measuring the content of instruction: Uses in research and practice. Educational Researcher, 31(7), 3-14.
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Sample ISAT/NWEA MAP item Sample SBAC item
Is the level of cognitive demand in the CCSS and assessed on the Smarter Balanced test what Idaho students need?
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Describe the relationship you see between the mathematical practice standards and the levels of cognitive demand.Level of Cognitive Demand
Rote, Skill or Recall
Concepts
Problem Solving
Reasoning & Justification
Modeling and Data Analysis
Mathematics Practices
Problem Solve
Model Situations
Reason Quantitatively
Critique the reasoning of others