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 Navigator’s communication infrastructure to move data (especially MathWorlds functions) between device-types

8. A SimCalc Assumption:Math 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 let’s try a few things! We’ll then return & reflect.

12. 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

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@umassd.edu) www.simcalc.umassd.edu/workshops www.simcalc.com To download more free stuff