Introducing Connected MathWorlds: Navigator SimCalc

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Introducing Connected MathWorlds Navigator
SimCalc

• Stephen J. Hegedus
• Sara Dalton
• Jim Kaput (1942-2005)
• University of Massachusetts Dartmouth
• Department of Mathematics
• www.simcalc.umassd.edu/workshops
• www.simcalc.com

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Our friend and colleague
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Big Picture Combine dynamic SimCalc
representations with the new ingredient,
Classroom Connectivity (CC) that is
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Dynamical Mathematics (in the form of SimCalc
MathWorlds) Classroom Connectivity (in the form
of TI Navigator)
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Plan for the Session

• Orient ourselves to the bigger picture goals
• Do some warm-up MathWorlds activities to get a
  feel for Mathworlds on the TI-83 (CMW)
• Use CMW to make, Navigator to collect, and JMW to
  examine individual mathematical constructions
• Use CMW to make, Navigator to collect, and JMW to
  aggregate parametrically varying functions
• Step back and reflect on what we have been doing
• Plan for future interactions

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Our Larger Goals

• Integrate two families of technologies (SimCalc
  Navigator) to achieve uniquely powerful
  educational advantage for students
• Exploit connectivity across device types
• To take advantage of the strengths of each to
  compensate for weaknesses of the other, and
• To create learning and teaching opportunities
  that transcend the powers of each

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Technologically, What Is Happening?

• We have a common data-structure across computer
  and hand-held versions of SimCalc MathWorlds
  (Calculator MW Java MW)
• We integrate with Navigators communication
  infrastructure to move data (especially
  MathWorlds functions) between device-types

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A SimCalc AssumptionMath Needs to Be About
Something
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Basic SimCalc Features

• Dynamic simulations hot-linked to graphs
  formulas (which are about the motions)
• Graphically definable editable functions,
  including piecewise-defined functions
• Import re-animate CBR/L motion data
• Visualization tools (e.g., dropping marks
  during motions)
• Hot-linked rate accumulation data (e.g.,
  velocity position)

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How Do We Exploit Connectivity?

• Facilitate work-flow to from students
  activities, assessments, homework, etc.
• Make individual mathematical constructions
  public, e.g., mathematical performances
• Aggregate student constructions to
• Vary essential parameters on a per-student basis
• Elevate student attention from single objects to
  parametrized families of objects
• Provide opportunity for generalization across
  cases
• Expose common thought-patterns (e.g., errors)

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So lets try a few things! Well then return
reflect.
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Strategically, What Are We Doing?

• We enable the teacher to render an individuals
  mathematical activity public in a shared display
• We interlink mathematical structures and
  classroom social structures (both designed and
  naturally occurring) to create new forms of
  learning, new activity structures
• We intensify, focus manage student attention
• We promote the infusion of personal social
  identity in students mathematical constructions

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Reflections on the Projection-of-Identity Into
the Public Space

• Each person/group is up there (no place to
  hide)
• What is given what is hidden is tightly
  manipulable to serve a wide range of pedagogical
  curricular aims
• Personal identity is projected into the public
  object
• Attention can be explicitly managed by the
  teacher by showing/hiding/grouping students
  constructions
• Classroom is infused with affect social
  authenticity
• The above features in combination enable the
  teacher to enhance the intensity of classroom
  learning in new ways

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CD Contents Sample Lessons from theAlgebra
Subscription Sample Lessons from the forthcoming
Connected MathWorlds Subscription
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Thank You!

• Contact Stephen Hegedus (shegedus_at_umassd.edu)
• www.simcalc.umassd.edu/workshops
• www.simcalc.com
• To download more free stuff