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Introducing Connected MathWorlds: Navigator SimCalc

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... computer and hand-held versions of SimCalc MathWorlds (Calculator MW & Java MW) ... Math Needs to Be About Something. 9. Basic SimCalc Features ... – PowerPoint PPT presentation

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Title: Introducing Connected MathWorlds: Navigator SimCalc


1
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

2
Our friend and colleague
3
Big Picture Combine dynamic SimCalc
representations with the new ingredient,
Classroom Connectivity (CC) that is
4
Dynamical Mathematics (in the form of SimCalc
MathWorlds) Classroom Connectivity (in the form
of TI Navigator)
5
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

6
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

7
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

8
A SimCalc AssumptionMath Needs to Be About
Something
9
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)

10
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)

11
So lets try a few things! Well then return
reflect.
12
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

13
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

14
CD Contents Sample Lessons from theAlgebra
Subscription Sample Lessons from the forthcoming
Connected MathWorlds Subscription
15
Thank You!
  • Contact Stephen Hegedus (shegedus_at_umassd.edu)
  • www.simcalc.umassd.edu/workshops
  • www.simcalc.com
  • To download more free stuff
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