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Cognitive Demand - UW-Milwaukee

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					                           Exploring
                     Cognitive Demands of
                      Mathematical Tasks
                                Milwaukee Public School

                                Bernard Rahming
                          Mathematics Teaching Specialist
                               rahminbv@milwaukee.k12.wi.us


                                   April 16, 2011
                    National Council of Teachers of Mathematics
                                  Indianapolis, IN


Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation
                                    Agenda
Participants will :
Develop their understanding of cognitive
 demand levels of mathematical task
Engage in activities of identifying cognitive
 demand levels of mathematical tasks
Discuss factors of maintenance and decline of
 mathematical tasks during setup and
 implementation.


                                                                                                      2
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation
                        Success Criteria
We will be successful if at the end of the
 session..
We understand and can identify the features
 of the levels of cognitive demand of
 mathematical tasks.
We can articulate the factors of maintenance
 and decline of cognitive demand levels
 during setup and implementation.

Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation
                                                                                                           3
Building Academic Vocabulary
Discuss with your shoulder partner what
  you think Cognitive Demand is.

What picture comes to mind when you
 think of Cognitive Demand?



                                                                                                           4
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation
           Cognitive Demand…
“The kind and level of thinking required of
students in order to successfully engage with
and solve the task.”

                                              Stein, Smith, Henningsen, & Silver, (2009)




Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation   5
     Reading: “Analyzing Mathematics
           Instructional Tasks”

Individually read the entire article.

Each person share one idea from the article at
your table.

  Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation




                                                                                                             6
   Four Levels of Cognitive Demand in
          Mathematical Tasks
Low Level Cognitive               High Level Cognitive
  Demands                           Demands

 Memorization Tasks               Procedures With
                                    Connections to
 Procedures Without                understanding, meaning
  Connections to                    or concepts/Tasks
  understanding, meaning
  or concepts Tasks                Doing Mathematics
                                    Tasks
                 Stein, Smith, Henningsen, & Silver, (2009)


                                                              7
             Table Group Sort Activity
 Lay out the 4 green category cards
 Deal out the 8 blue Mathematical Task
 Cards to everyone in the group.
 Refer to the “Task Analysis Guide” for
 criteria.
 As you place your Mathematical Task cards
 into a category, explain your reasoning.
 Help each other justify the placements.
                                                                                                           8
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation
  Table Group Sort Activity
Sample activity cards were adapted from
Stein, Smith, Henningsen, & Silver, (2009).
“Implementing standards-based mathematics
instruction: A casebook for professional
development”. 2nd Edition, pg. 9, Fig. 1.3




                                              9
10
                   Cognitive Demands and Features
                             Sample Tasks

           Task                 Level of                    Explanation of              Features
                            Cognitive Demand                Categorization


             A          Doing Mathematics                 There is no              •Requires an
                                                          pathway                  explanation
                                                          suggested by the         •Uses
                                                          task. The focus is       manipulatives
                                                          on looking for the       •Involves multiple
                                                          underlying               steps
                                                          mathematical
                                                          structure.               •Uses a diagram




                                                                                                           11
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation
                                      Reflection
Respond to the following:

Which of the four levels of cognitive demand
 are you most comfortable with -why?

Which one do you understand the least -why?

Something I want to know more about is…?


    Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation
                                                                                                               12
   Four Levels of Cognitive Demand in
          Mathematical Tasks
Low Level Cognitive        High Level Cognitive
  Demands                    Demands

  Memorization Tasks         Procedures With
                             Connections to
  Procedures Without         understanding, meaning
  Connections to             or concepts Tasks
  understanding, meaning
  or concepts Tasks          Doing Mathematics
                             Tasks


                                                  13
Mathematical Tasks Framework

 Figure 1.3

   TASKS                 TASKS                TASKS
   As they               As set up by         As
   appear in             teachers             implemented
   curricular/                                by students
   instructional                                                   Student
   materials                                                       Learning

A representation of how mathematical tasks unfold
during classroom instruction.
(Stein & Smith, 1998, Mathematics Teaching in the Middle School)



                                                                              14
 Factors associated with the decline of High-
          Level cognitive Demand

• Students press teacher to reduce complexity of the
  task, explicit steps
• Teacher rescue students from struggle
• Teacher shifts emphasis from meaning, concepts, or
  understanding to correctness or completeness of
  answer
• Not enough time or too much time
• Classroom management

      (Adapted from Stein & Smith, 199 Stein, Smith, Henningsen, & Silver, (2009)


                                                                                    15
 Factors associated with the maintenance of
        High-Level Cognitive Demand

• Scaffolding of student thinking and reasoning
• Students provided with means of monitoring
  their own progress
• Teachers of capable students model high-
  level performance
• Task build on students’ prior knowledge
• Sufficient time to explore
(Adapted from Stein, Smith, Henningsen, & Silver, (2009))


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www.mmp.uwm.edu


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