1. 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. 2 Our friend and colleague

3. 3 Big Picture Combine dynamic SimCalc representations with the new ingredient, Classroom Connectivity (CC) that is:

4. 4 Dynamical Mathematics (in the form of SimCalc MathWorlds) + Classroom Connectivity (in the form of TI Navigator)

5. 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. 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. 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. 8 A SimCalc Assumption: Math Needs to Be About Something

9. 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. 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. 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. 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 the Algebra 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