ICTCM: New Forms of ParticipationICTCM: New Forms of Participationwith Wireless Classroomswith Wireless Classrooms
Stephen J. Hegedus, Sara K. Dalton, James P. [email protected], [email protected], [email protected]
James J. Kaput Center for Research and Innovation in Mathematics EducationSimCalc Research Projects,Department of Mathematics
University of Massachusetts, Dartmouthmerg.umassd.edu
www.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 are
linked, 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 SimCalc MathWorlds 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
• 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
Parallel Software
From Student Device
To Teacher Display
Executable RepresentationsExecutable Representations
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. Kaput1991
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 (cf. Stroup)- we tightly control this• Design challenges and solution strategies - roster as acentral ordering principle
Let’s Try Another
Make a motion for Actor B so that Actor B travelsat a constant speed and starts at three timesyour group number in feet ahead of Actor ABUT ends in a tie with Actor A.
ExtensionsExtensions
• SimCalc MathWorlds: Using it to lay thefoundation for Calculus and broadening accessfor more students
•Y=MX+B
•Dealing with Rate graphs - Averages, MeanValue Theorem, Fundamental Theorem ofCalculus
CMW Supports Three NewCMW Supports Three NewClasses of FunctionsClasses of Functions
Class 1: Piecewise editable functions graphically and algebraically
1. Piecewise Linear Functions 2. Piecewise Quadratic Functions
Class 2: Parametrically DefinedClass 2: Parametrically DefinedFunctionsFunctions
1. Linear: Y = MX + B
2. Quadratic: Y + AX2 + BX + C3. Quadratic (product of roots): Y= A(X– alpha)(X – beta)
Class 2: Parametrically DefinedClass 2: Parametrically DefinedFunctionsFunctions
4. Exponential: Ae(BX+C) 5. Periodic: Y=Asin(BX+C)+D
Class 3: Sampled Data: CBR & CBL2Class 3: Sampled Data: CBR & CBL2
• Ability to support a wide variety ofprobes
• Ability to disconnect on collectionand use a variety of smoothingmethods
• Ability to count inseconds/minutes/hours to offer“faster” animation
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 objectsto be 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 gainsfrom pre to post for the Comparison versusTreatment groups. In the Treatment group themean gain is about 2 points out of a total of 26points. In the Comparison group the mean gain isabout 1 point. This group difference is statisticallysignificant, 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.
For further Interest:
•There is a session pertaining to TI-Navigatortomorrow morning. “Experiencing TI-Navigator In A Calculus Classroom” at 8AM (inEssex South) with Robert Kowalczyk and AdamHausknecht
ICTCM: New Forms of Participation withICTCM: New Forms of Participation withWireless ClassroomsWireless Classrooms
Dr Stephen J. Hegedus, Sara K. Dalton, James P. [email protected], [email protected], [email protected]
James J. Kaput Center for Research and Innovation in MathematicsEducation
SimCalc Research Projects,Department of Mathematics
University of Massachusetts, Dartmouthmerg.umassd.edu
www.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