teachers and researchers talk about classroom connectivity€¦ · developed under nsf-based...

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Teachers and Researchers Talk Abo Teachers and Researchers Talk Abo Classroom Connectiv Classroom Connectiv Stephen J. Hegedus, Catie Marchessault, Julie Sunderland, N Thuestad, Sara K. Dalton shegedus@umassd . edu James J. Kaput Center for Research and Innovation in Mathematics Educa SimCalc Research Projects, Department of Mathematics University of Massachusetts Dartmouth www.simcalc.umassd.edu Developed under NSF-based Grants: REC-0087771, Understanding Classroom Interactions Among Diverse, Connected Classroom Technologies; REC Representation, Participation and Teaching in Connected Classrooms; REC-0228515, Scaling Up SimCalc: Professional Development for Leveraging T to Teach More Complex Mathematics, Phase I; REC-0437861, Scaling Up Middle School Mathematics Innovations, Phase II

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Page 1: Teachers and Researchers Talk About Classroom Connectivity€¦ · Developed under NSF-based Grants: ... CBL2) • Simulations are ... develop student case studies), attitude survey

Teachers and Researchers Talk AboutTeachers and Researchers Talk AboutClassroom ConnectivityClassroom Connectivity

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

[email protected] 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

Page 2: Teachers and Researchers Talk About Classroom Connectivity€¦ · Developed under NSF-based Grants: ... CBL2) • Simulations are ... develop student case studies), attitude survey

Democratizing AccessDemocratizing Access

•Mathematical alienation

•Motivation repressed via opaque classroomobjectives

•Curriculum restrictions

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

Page 3: Teachers and Researchers Talk About Classroom Connectivity€¦ · Developed under NSF-based Grants: ... CBL2) • Simulations are ... develop student case studies), attitude survey

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)

Page 4: Teachers and Researchers Talk About Classroom Connectivity€¦ · Developed under NSF-based Grants: ... CBL2) • Simulations are ... develop student case studies), attitude survey

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

Page 5: Teachers and Researchers Talk About Classroom Connectivity€¦ · Developed under NSF-based Grants: ... CBL2) • Simulations are ... develop student case studies), attitude survey
Page 6: Teachers and Researchers Talk About Classroom Connectivity€¦ · Developed under NSF-based Grants: ... CBL2) • Simulations are ... develop student case studies), attitude survey

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

Page 7: Teachers and Researchers Talk About Classroom Connectivity€¦ · Developed under NSF-based Grants: ... CBL2) • Simulations are ... develop student case studies), attitude survey

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

Page 8: Teachers and Researchers Talk About Classroom Connectivity€¦ · Developed under NSF-based Grants: ... CBL2) • Simulations are ... develop student case studies), attitude survey

Parallel Software

From Student Device

To Teacher Display

Executable RepresentationsExecutable Representations

Page 9: Teachers and Researchers Talk About Classroom Connectivity€¦ · Developed under NSF-based Grants: ... CBL2) • Simulations are ... develop student case studies), attitude survey

SimCalc in action!

Let’s demonstrate an activity!

Page 10: Teachers and Researchers Talk About Classroom Connectivity€¦ · Developed under NSF-based Grants: ... CBL2) • Simulations are ... develop student case studies), attitude survey

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.

Page 11: Teachers and Researchers Talk About Classroom Connectivity€¦ · Developed under NSF-based Grants: ... CBL2) • Simulations are ... develop student case studies), attitude survey

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

Page 12: Teachers and Researchers Talk About Classroom Connectivity€¦ · Developed under NSF-based Grants: ... CBL2) • Simulations are ... develop student case studies), attitude survey

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

Page 13: Teachers and Researchers Talk About Classroom Connectivity€¦ · Developed under NSF-based Grants: ... CBL2) • Simulations are ... develop student case studies), attitude survey

• 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

Page 14: Teachers and Researchers Talk About Classroom Connectivity€¦ · Developed under NSF-based Grants: ... CBL2) • Simulations are ... develop student case studies), attitude survey

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

Page 15: Teachers and Researchers Talk About Classroom Connectivity€¦ · Developed under NSF-based Grants: ... CBL2) • Simulations are ... develop student case studies), attitude survey

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.

Page 16: Teachers and Researchers Talk About Classroom Connectivity€¦ · Developed under NSF-based Grants: ... CBL2) • Simulations are ... develop student case studies), attitude survey

Other Sessions

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

• Software

• Establishment of the Kaput Center

• 944. Exponential Motion! James Burke, DerekBeaton