Teachers and Researchers Talk AboutTeachers and Researchers Talk AboutClassroom ConnectivityClassroom Connectivity

Stephen J. Hegedus, Catie Marchessault, Julie Sunderland, NicoleThuestad, Sara K. Dalton

shegedus@umassd.eduJames J. Kaput Center for Research and Innovation in Mathematics Education

SimCalc Research Projects,Department of Mathematics

University of Massachusetts Dartmouthwww.simcalc.umassd.edu

Developed under NSF-based Grants: REC-0087771, Understanding Classroom Interactions Among Diverse, Connected Classroom Technologies; REC-0337710,Representation, Participation and Teaching in Connected Classrooms; REC-0228515, Scaling Up SimCalc: Professional Development for Leveraging Technologyto Teach More Complex Mathematics, Phase I; REC-0437861, Scaling Up Middle School Mathematics Innovations, Phase II

Democratizing AccessDemocratizing Access

•Mathematical alienation

•Motivation repressed via opaque classroomobjectives

•Curriculum restrictions

•Classroom participation is an expectationrather than a phenomenological artifact ofproductive learning

SimCalc MathWorldsSimCalc MathWorlds

•Dynamic interactive representations that arelinked, e.g. edit a position function andautomatically see velocity graphs update

•Graphically and algebraically editable functions

• Import motion data and re-animate (CBR &CBL2)

• Simulations are at the heart of SimCalc -executable representations (Moreno, 2001)

SimCalc MathWorlds -SimCalc MathWorlds -The ProductThe Product

•The historic evolutions of two software intoone integrated product

• SMW for the TI 83+/84+ - Version 6.0

• SMW for the Desktop PC (cross-platform fornon-connected work) - Version 4.0

•Mental Model for users: Microsoft Office - Canbe used in integrated ways or independently -documents can be written to be used in otherapplications

SimCalc SimCalc ““ConnectedConnected”” MathWorlds MathWorlds

• TI-Navigator Network

• New generation of SimCalc that increasesparticipation, motivation and learning

• Exploits wireless networks to allow the aggregation ofstudent work in mathematically meaningful ways

• Teachers have powerful classroom management toolsto focus attention and pedagogical agenda

• Student work becomes contextualized into a class ofcontributions for comparison and generalization

• Mathematical thinking goes from a local to a socialactivity

Three fundamental powers ofThree fundamental powers ofconnectivityconnectivity

• To harvest students work to examine variation andcommon misconceptions (error analysis)• To aggregate students work in a mathematicallymeaningful way – use natural variation to examineparametric variation (i.e. each students varies aparameter)• To focus on connections across representations, i.e.students work with representation A (e.g. a velocitygraph) and the teacher displays/works withrepresentation B (e.g. a position graph) - cf. Kaput 1991

Parallel Software

From Student Device

To Teacher Display

Executable RepresentationsExecutable Representations

SimCalc in action!

Let’s demonstrate an activity!

Dynamic MathematicsDynamic Mathematics

•Dynamic representations are a new accessroute to new visions of mathematical ideas andproblem solving

•Connectivity is a foundation to allow publiccollaboration, mutual expression in dynamicmedia, physical expression through time andspace via gesture, discourse and action, andsocial cognition.

Classroom Management: a fundamental designClassroom Management: a fundamental designprinciple in a representationally-rich environmentprinciple in a representationally-rich environment

• Collecting/Receiving – allows two forms of agency inthe classroom/distributed agency• Post-Connectivity: Data management vsRepresentational management - role of filters to assessstudents’ progressive understanding (i.e.representational timestamps) and systematicallygenerate public reasoning and generalization•Note: This is not always about allowing students tohave ownership of the public display space - we tightlycontrol this• Design challenges and solution strategies - roster as acentral ordering principle

Exploiting ConnectivityExploiting Connectivity• Facilitate work-flow,• Aggregate student constructions to: i. vary essential

parameters on a per-student basis, ii. elevate studentattention from single objects to parameterized families ofobjects,

• Provide opportunity for generalization and expose commonthought-patterns (e.g. errors)

• Students make personally meaningful mathematical objects tobe publicly shared and discussed

• Students project their personal identity into the objects andconstructed motions

• Students math and social experience are deeply intertwined• Teachers are in a central role to orchestrate whole class of

events

• Students experience and contributions areembedded in a social workspace

•Mathematical structure and understanding canbe emergent, e.g. What do you expect to seebefore I show you the ...

• Representational infrastructure includes datamanagement systems to manage the flow ofinformation and examination of mathematicalsub-structures; such power serves a variety ofpedagogical needs, and sustains pedagogicalflexibility

Some Top-Level ThoughtsSome Top-Level Thoughts

Impact on LearningImpact on LearningConnectivity StudyConnectivity Study

All 9th grade High School Algebra 1 students in twodistricts took a pre- and post-test. A selection ofteachers in these schools participated in a SimCalcIntervention in which they temporarily replacedpart of their regular curriculum with SimCalcmaterials for 3-6 weeks.

The bar graph to the left illustrates the mean gains frompre to post for the Comparison versus Treatmentgroups. In the Treatment group the mean gain isabout 2 points out of a total of 26 points. In theComparison group the mean gain is about 1 point.This group difference is statistically significant,t=2.465 (p<0.015).

Along with Pre-post data, we have video data (todevelop student case studies), attitude survey data,student and teacher interviews.

Treatment n=162, Comparison n=235

ConclusionsConclusions•Research-to-date shows positive impact on

mathematical knowledge (necessary andadvanced) AND participation and motivation todo mathematics (attitude & behavioral data)

•Over 6 years of design & experimentation hasproduced a software environment thatredefines the educational landscape of themathematics classroom in the 21st century

•Dynamic Representations and in-classcommunication infrastructure + mathematicallymeaningful activities = powerful opportunitiesfor MORE students.

Other Sessions

• For more info go to TI booth - ask aboutSimCalc Activities

• Software

• Establishment of the Kaput Center

• 944. Exponential Motion! James Burke, DerekBeaton