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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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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)

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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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A SimCalc Assumption:Math 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)

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

(shegedus@umassd.edu)www.simcalc.umassd.edu/

workshopswww.simcalc.com

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