1 introducing connected mathworlds: navigator + simcalc stephen j. hegedus sara dalton jim kaput...
Post on 19-Dec-2015
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Introducing Connected MathWorlds: Navigator +
SimCalcStephen J. HegedusSara DaltonJim Kaput (1942-2005)
University of Massachusetts DartmouthDepartment of Mathematics
www.simcalc.umassd.edu/workshopswww.simcalc.com
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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 Navigator’s communication infrastructure to move data (especially MathWorlds functions) between device-types
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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)
So let’s try a few So let’s try a few things!things!
We’ll then return & We’ll then return & reflect.reflect.
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Strategically, What Are We Doing?
• We enable the teacher to render an individual’s 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
CD Contents:CD Contents:
Sample Lessons from theSample Lessons from theAlgebra SubscriptionAlgebra Subscription
Sample Lessons from the Sample Lessons from the forthcoming forthcoming Connected Connected MathWorlds SubscriptionMathWorlds Subscription
Thank You!Thank You!
Contact: Stephen Hegedus ([email protected])
www.simcalc.umassd.edu/workshops
www.simcalc.comTo download more free stuff