The Cognitive Demand of Tasks How does the selection of high level tasks prepare our students to meet the demands of the Common Core Learning Standards?

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The Cognitive Demand of TasksHow does the
selection of high level tasks prepare our
students to meet the demands of the Common Core
Learning Standards?

• CFN 609 Principals Conference
• February 7, 2013

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As we move into the second decade of the 21st
century, one thing is clear

• Our country needs highly trained workers who can
  wrestle with complex problems. Especially needed
  are individuals who can think, reason and engage
  effectively in quantitative problem solving.
  Research shows the instructional practices used
  in many of our nations classrooms will not
  prepare students for these new demands.
• National studies have shown that American
  students are not routinely asked to engage in
  conceptual thinking or complex problem solving.
• If we want students to develop the capacity to
  think, reason, and problem solve then we need to
  start with high-level, cognitively complex tasks.
• Tasks are central to students learning, shaping
  not only their opportunity to learn but also
  their view of the subject matter. We learn
  through a process of knowledge construction that
  requires us to actively manipulate and refine
  information and then integrate it with our prior
  understandings.
• Quote 1 5 Practices for orchestrating
  Productive Mathematics Discussions, Smith and
  Stein, Quote 3 Educational Research and
  Evaluation, 2(4) Stein, M.K, 1996, Quote 2
  Stigler and Hiebert 1999, Quote 4 Adding it up,
  NRC 2001

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Quality Review Rubric 1.1Designing engaging,
rigorous and coherent curricula.

• Well Developed
• B) Rigorous habits and Higher- order skills are
  emphasized in curricula and academic tasks and
  are embedded in a coherent way across grades and
  subjects so that all learners, including ELLs and
  SWDs, must demonstrate their thinking.
• C) Curricula and academic tasks are planned and
  refined using student work and data so that
  individual and groups of students, including the
  lowest and highest achieving students, ELLs and
  SWDs, are cognitively engaged.

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Danielsons Framework for Teaching 1e

• Highly Effective
• Plans represent the coordination of in-depth
  content knowledge, understanding of different
  students needs and available resources
  (including technology), resulting in a series of
  learning activities designed to engage students
  in high-level cognitive activity. These are
  differentiated, as appropriate, for individual
  learners. Instructional groups are varied as
  appropriate, with some opportunity for student
  choice. The lessons or units structure is clear
  and allows for different pathways according to
  diverse student needs.

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• How can we make sure we are providing our
  students with opportunities to engage with high
  level tasks?

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The Task Analysis Guide ( Smith and Stein 1998)

• The Task Analysis Guide provides a general list
  of characteristics of low-level and high level
  mathematical tasks and thus can be used to
  analyze the potential of tasks to support
  students thinking and reasoning. The guide is
  intended to help teachers match tasks with their
  goals for student learning.
• 5 Practices for Orchestrating Productive
  Mathematics Discussions, Smith and Stein 2011

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Mathematics Task Analysis Guide
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At your tables

• Take a moment to review the Task Analysis Guide
  (TAG).
• Work through the four tasks independently (or
  with a partner). Use the TAG to determine the
  cognitive demand of each of the tasks.
• Share your categorization in pairs then as a
  table. Be prepared to justify your conclusions
  using the TAG. Come to consensus at the table.

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Proportional Relationships
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Use the TAG to determine the cognitive demand of
each of the tasks. Share your categorization in
pairs then as a table. Be prepared to justify
your conclusions using the tag.Identify the CCSS
for Mathematical Content and Practices used.
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Subtraction Tasks
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Use the TAG to determine the cognitive demand of
each of the tasks. Share your categorization in
pairs then as a table.. Be prepared to justify
your conclusions using the tag.Identify the CCSS
for Mathematical Content and Practices used.
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Math Task Analysis Guide Reflections

• What are your thoughts on the process of
  identifying the characteristics that best
  describe the cognitive demand of each task?
• How might teams of teachers integrate this tool
  and what are the implications?

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At your tables

• Identify the CCLS for Mathematical Content and
  which Math Practices students will have the
  opportunity to use.
• Which standard/s are best addressed by these
  tasks?

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Relating the cognitive demand of tasks to the
Mathematical Practices

• What relationships do you notice between the
  cognitive demand of the written tasks and the
  CCSS for mathematical Practices listed?

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Characteristics of Tasks that align with CCLS
standards for Mathematical Practice

• High Cognitive Demand (Stein et. al., 1996
  Boaler Staples, 2008
• Significant Content, meaning they have the
  potential to leave behind important residue
  (Hiebert et.al, 19970
• Require justification or explanation (Boaler and
  Staple, 2008)
• Make connections between two or more
  representations (Lesh, Post Behr, 1987)
• Open Ended (Lotan, 2003 Borasi Fonzi, 2002)
• Multiple ways to enter the task and show
  competence (Lotan, 2003)

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Increasing the Cognitive Demand of
TasksStrategies for Modifying Textbook Tasks
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Sources for Developing Rich tasks

• Exemplars
• Modifying existing Textbook/Program tasks
• DOE Instructional Bundles
• www.Parrconline.org
• www.georgiastandards.org
• www.schools.utah.gov
• www.EngageNY.org
• www.illustrativemathematics.org
• www.map.mathshell.org
• www.insidemathematics.org

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Tasks

• There is no decision that teachers make that has
  a greater impact on students opportunities to
  learn, and on their perceptions about what
  mathematics is, than the selection or creation of
  the tasks with which the teacher engages students
  in studying mathematics.
• Lappan and Briars, 1995
• Not all tasks are created equal, and different
  tasks will provoke different levels and kinds of
  student thinking.
• Stein, Smith, Henningsen, Silver, 200
• Not all tasks are created equal, and different
  tasks will provoke different levels and kinds of
  student thinking.
• Stein, Smith, Henningsen, Silver, 2000

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• Thank you for your attention.