Constructionism 2014, 19-23 August, Vienna
Social Creativity in designing Constructionist
e-books:
New mediations for creative mathematical thinking?
Chronis Kynigos
http://etl.ppp.uoa.gr www.cti.gr
Constructionism 2014, 19-23 August, Vienna
Infusing Constructionismstrategic and academic integrations
• The Kaleidoscope Network of Excellence (Balachef, Wasson, Noss, 2004)
• The Mathematics Education Theory group (Prediger, S., Bikner-Ahsbahs, A., & Arzarello, F., 2008)
Constructionism 2014, 19-23 August, Vienna
Infusing constructionism
• Turtle Geometry, Logo programming and Dynamic Manipulation of variable procedure values (turtleworlds, 2D – 3D)
• Navigation and cartography (c-cube)• Component computing (e-slate, SEED project) • Computer assisted collaborative learning (METAFORA
project) • Theoretical landscape of learning mathematics with DM
(ReMath project) • LMS – large portals – the Greek mathematics digital book • E-books (m c squared project)
Constructionism 2014, 19-23 August, Vienna
The Constructionist e-book
• Interactive vs constructionist e-books
• How does reading change?
• What roles will users of c-books adopt?
• How will readers be addressed?
• How can an author inspire creativity?
• How will the meaning of ‘a book’ change?
Constructionism 2014, 19-23 August, Vienna
The ‘m c squared’ project• To develop technologies to inspire
creativity in educational design
• 6 Academic and 3 industrial partner organizations from Europe
• Develop the ‘c-book’ for mathematical learning
• Show glimpses of creative collaborative design and creative mathematical thinking
Constructionism 2014, 19-23 August, Vienna
• Partner Organisations– Computer Technology Institute & Press “Diophantus” (CTI)
(coordinator), Greece– Universiteit Utrecht (UU), Netherlands– London Knowledge Lab, Institute Of Education, University Of
London (LKL), UK– Universitat De Barcelona (UB), Spain– Université Claude Bernard – LYON1 (UCBL), France– Martin-Luther-Universität Halle-Wittenberg (MLU), Germany– ARISTOD (ARI), France– Talent (TAL), Greece– TESTALUNA (TL), Italy
• Collaborators– UoA Educational Technology Lab– Uni. Southampton
Constructionism 2014, 19-23 August, Vienna
The ‘c-book’
• Can contain constructionist widgets from diverse widget factories (from Cinderella-E-slate-Geogebra to Scratch-NETLOGO etc)
• Supports collaborative design with CoIcode
• Will support authorable data analytics
Constructionism 2014, 19-23 August, Vienna
Socio-technical environments
• Social Creativity (S-C) in a design project (Fischer, 2001, 2011)– creativity as activity focusing on a design problem of
common concern (the “interest”) situated in a socio-technical environment
• Community of Interest (CoI)– specially designed computational media– fueled by a culture of participation – exemplified in social processes and practices– leading to novel/new, useful and desirable outputs
Constructionism 2014, 19-23 August, Vienna
CoI as SC enhancers• heterogenous • Members are representatives of CoPs
• to solve a design problem of common concern (joint “interest”) that requires the combination of multiple knowledge systems
• a rich environment for interconnecteness, different perspective-taking, knowledge exchange and integration between diverse domains and more opportunities for creative thinking and learning
• CoI members may be participants in more than one CoPs• One community can exhibit characteristics of both a CoI and a CoP
• can integrate aspects of both a CoI and a CoP its type may shift over time due to external factors
Constructionism 2014, 19-23 August, Vienna
Collaborative design: DG and BO
• Documentational genesis (Trouche et al)– Living documents– Instrumentation and instrumentalization
• Digital artifacts as boundary objects (Griesmeyer, Hoyles and Noss, Kynigos) – Boundary crossings– Improvable objects
Constructionism 2014, 19-23 August, Vienna
Starting points for CMT
• Narrative activity model (Vygotsky)– Exploration, inspiration, production, sharing
• Creative thinking spiral (Resnick)– Imagination Creation, Play, Sharing, Reflection, imagination
• Lateral, out of the box, playfulness, humor, imagination (Ackerman, DeCortis et al)
• Model of Collaborative Creativity (Aragon, Williams)– Focus, Frame, Create, Complete
• Product-process, general-specific, solving-posing problems interplay, ill structured open problems (Shriki, Jamir-Leikin)
• Creativity in techno-mathematical literacies and the importance of modeling and boundary crossings and artifacts as boundary objects (Hoyles-Noss)
Constructionism 2014, 19-23 August, Vienna
Collaborative designs with CoIcode
•Mind map – forum
•Semantics to encourage social creativity (alternative, contributory, objecting)
•Embedded tools for versioning
•Adornment and other tools for structuring and navigating through a discussion
Figure 1: The CoI’s discussion thread
Constructionism 2014, 19-23 August, Vienna
A glimpse at emerging c-book units
Constructionism 2014, 19-23 August, Vienna
Critical design episode 1: the windmil
• CoI: designers+teachers, in computer science, mathematics and engineering/vocational training, 75 postings in CoIcode
• Shapes of sails, symmetry by rotation, trigonometric functions, productivity ratios, 3d modeling of structure
• Strategies– Starting from designing a half baked widget instance or
an elaborate instance to deconstruct – Starting from the narrative (the story) – Scope and sequence (narrative, embedded math,
widgetry)
Constructionism 2014, 19-23 August, Vienna
Jolts to their initial widget – centric approach
• How to include an engineering and a coding element and integrate them with mathematical concepts.
• How to allow for and promote unpredictable student activity and personalized creative constructions with the instances and how to inspire such activity through the accompanying narrative.
• How to embed diverse mathematical ideas organized in ways not found in standard curricula.
Constructionism 2014, 19-23 August, Vienna
Critical episode 2: Bike in the city
• CoI: mathematics and environmental education, developers (82 CoIcode posts)
• Plethora of ideas and tensions • A widget instance as an expression of an idea to
contribute (GPS-distance meter, charting itineraries, orientation device)
• Free navigation, shortest route, program a route • Modifying a pre-existing instance, rejecting a
suggested instance: instances as improvable boundary objects
Constructionism 2014, 19-23 August, Vienna
Concluding questions
• A book as a ‘living document’ for the reader• A need for creativity in designing c-books to
promote creativity in their readers• A need for diverse views and methods to
integrate amongst them • A need to have information on what readers do
with a c-book • Improvable boundary objects to generate
boundary crossings within a CoI: widget instances and unit versionings
Constructionism 2014, 19-23 August, Vienna
thank you!!
• http://mc2-project.eu • http://mc2dme.appspot.com• www.cti.gr • http://etl.ppp.uoa.gr