Social Creativity in designing Constructionist e-books: new mediations for creative mathematical thinking

1. 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

2. Constructionism 2014, 19-23 August, Vienna
Infusing Constructionism
strategic 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)

3. 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)

4. 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?

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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)

12. 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

13. Constructionism 2014, 19-23 August, Vienna
A glimpse at emerging
c-book units

14. 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)

15. 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.

16. 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

17. 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

18. Constructionism 2014, 19-23 August, Vienna
thank you!!
• http://mc2-project.eu
• http://mc2dme.appspot.com
• www.cti.gr
• http://etl.ppp.uoa.gr