Social Creativity in the Design of Digital Resources Interweaving

Math with Environmental Education

The Case Study of the Climate Change C-Book

Maria Daskolia

1,2

, Angeliki Kolovou

1,3

and Chronis Kynigos

1,3

Computer Technology Institute (CTI) and Press "Diophantus”, 26-28 Mitropoleos, Athens, Greece

Environmental Education Lab, Department of Philosophy-Pedagogy-Psychology, University of Athens, Athens, Greece

Educational Technology Lab, Department of Philosophy-Pedagogy-Psychology, University of Athens, Athens, Greece

Keywords: Social Creativity, Socio-technical Environments, Communities of Interest, Creative Mathematical Thinking,

Climate Change, Design of Digital Educational Resources, Mathematics Education,

Environmental Education, MC

Project.

Abstract: This study focuses on how social creativity is manifested in the collective design of digital educational

resources (called “c-books”, c for creativity) aiming to foster students’ creative mathematical thinking. We

investigate social creativity as a process by focusing on the boundary-crossing encounters taking place

within a socio-technical environment constituted of teachers of diverse expertise interacting with each other

and with the C-Book technology, while designing a c-book on “Climate Change”. The analysis of two

critical episodes shows that during the design process the socio-technical environment allowed the

communication and coordination of diverse perspectives enhancing the designers/ teachers creativity and

leading to the transformation of initial ideas into ‘tangible’ objects.

1 INTRODUCTION

1.1 Social Creativity in the Design of

Digital Educational Resources

‘Social Creativity’ has been proposed as a

theoretical frame for understanding and fostering

creativity in collectives operating within particular

technological environments. This approach, which

was primarily put forward and developed by Gerald

Fischer (Fischer, 1999; 2000; 2001; 2004; 2005;

2011) and his team (Fischer and Ostwald, 2005;

Fischer et al., 2005), is based on the assertion that no

human creation has ever arisen in conditions of

absolute isolation from either other people or other

people’s ideas and works. It addresses creative

performance as it grows out of the interactions

among members of a specific group or community,

and between them and particular computational

media, technologies and artefacts.

The synergy between all participating parts

constitutes a ‘socio-technical environment’, an

appropriate and purposefully designed setting for

supporting social creativity to attain specific goals.

This system consists of a community of creative

practitioners, the Community of Interest, whose

performance is facilitated and/or boosted in close

interaction with ‘technical’ infrastructures

specifically designed to amplify the outcome of their

collaborative efforts towards fulfilling the task at

stake (Fischer, 2004; Fischer et al., 2005).

More particularly, a Community of Interest

(CoI), differs from a Community of Practice (CoP)

(Lave and Wenger, 1991; Wenger, 1998) in that CoI

members are representatives of more than one CoPs,

who were brought together to solve a particular

problem of common concern. A CoI is thus

‘defined’ both by heterogeneity in the disciplinary

and/ or professional backgrounds of its members,

and by the members’ shared interest in dealing with

a particular problem or task. This combination is

suggested as a prerequisite for developing new

insights to a problem or a practice (Bonifacio and

Molani, 2003; Csikszentmihalyi, 1996).

Social creativity as a construct has been mainly

conceived in relation to the design practice (Fischer,

1999; 2000). Design problems are recognized as

complex, open-ended, ill-defined and fuzzy

problems requiring the contribution of various

134

Daskolia, M., Kolovou, A. and Kynigos, C.

Social Creativity in the Design of Digital Resources Interweaving Math with Environmental Education - The Case Study of the Climate Change C-Book.

In Proceedings of the 8th International Conference on Computer Supported Education (CSEDU 2016) - Volume 1, pages 134-143

ISBN: 978-989-758-179-3

actors. Collaboration among professionals with

various backgrounds and expertise is therefore

considered a necessary prerequisite for addressing

them. ‘Learning design’ or ‘design for learning’

(Laurillard, 2012), defined as the practice of

devising effective learning experiences aimed at

achieving defined educational objectives in a given

context, is a more recent strand in the design

practice, opening up a new field for teachers’

professional development in the 21

century

education systems. Under this perspective, teachers

are encouraged to work collaboratively both within

their own Communities of Practice, but also and

more importantly beyond these, with other education

professionals or with experts outside the education

sector, and with the aid of emerging technologies, to

creatively design effective and innovative teaching

and learning processes and resources. Their

participation in such contexts can promote quality

and innovation in education along with their

professional development (Emin-Martínez et al.,

2014).

The 'Mathematical Creativity Squared' (MC2)

project, within which research presented here is

being conducted, builds on these theoretical

perspectives and rationale, with the aim to identify

new settings and methods for boosting creativity in

the collaborative design of digital educational

resources for creative mathematical thinking (CMT).

These collaborative designs are based among other

things on the synergies between designers from

diverse disciplinary domains, school levels or

teaching subjects, such as those of Math and

Environmental Education (Kynigos, 2015a; Kynigos

and Daskolia, 2014). This is being accomplished

through (a) the development and use of a new genre

of technological environment for the design of

digital educational resources for mathematics, that is

an authorable e-book we call 'the c-book' (c for

creative), and (b) the adoption of a specific

methodology based on the generation of particular

Communities of Interest (CoI) consisted of teachers

with different disciplinary, epistemological and/ or

teaching backgrounds, brought together to

collaborate and create new learning designs for

mathematics.

Two focal design specifications for the design of

such creative educational resources (the c-books) is

(a) to interweave learning activities with narratives,

and (b) to center them all around the identification

and investigation of real-life and real-world

problems. Both were decided with the aim to

motivate students to get them more actively and

creatively involved in ‘finding the mathematics’

hidden behind some of the challenging current issues

of societal concern. These issues are by nature ill-

defined, complex, controversial, value-laden, and

require the application of various perspectives

simultaneously to grasp them holistically (Daskolia

and Kynigos, 2012). However, it is exactly their

inherent messiness and complexity that make them

'good' examples of creativity-triggering topics, and

amenable to foster students' creative thinking. It also

turns them into “boundary objects” (Star and

Griesemer, 1989; Daskolia and Kynigos, 2012), that

is entities which can be interpreted and employed by

more than one groups or communities in ways that

make sense to them.

Dealing with issues of these characteristics at a

pedagogical level provides many opportunities for

teachers and learners to get engaged in dialogical

forms of meaning-construction and perspective-

sharing. This expands the “boundaries” of their

knowing of and being in the world, both inside and

across the realms of their discipline (Kynigos, 2007;

Daskolia and Kynigos, 2012). Processes of this kind

can be identified as creative appropriation of

subject-matter and pedagogical knowledge.

1.2 Boundary-crossing Interactions as

Agents of Social Creativity

One way of approaching and studying social

creativity in the context of M C Squared project is as

being located in and nurtured by the ‘boundary

crossing’ encounters taking place among the CoI

members, in the mechanisms and strategies

employed by them, and as outcomes of these

processes. ‘Boundary-Crossing’ and ‘Boundary

Objects’ have been proposed by Akkerman and

Bakker (2011) as a framework for approaching the

“sociocultural differences that give rise to

discontinuities in action and interaction” (p. 139). A

Community of Interest (CoI) is such a setting where

boundary crossing processes most expectedly can

occur. This is because the different 'worlds' of the

CoI members (represented in terms of their

knowledge background, disciplinary domain,

professional expertise, life experience, pedagogical

values and/or epistemological perspectives)

inevitably cause ‘discontinuities’. But, they can also

act at the same time as springboards for creativity,

by mobilizing learning processes and re-

conceptualisations of practice to overcome these

discontinuities, through “negotiating and combining

ingredients from different contexts to achieve hybrid

situations” (Engeström et al., 1995, p. 319).

Social Creativity in the Design of Digital Resources Interweaving Math with Environmental Education - The Case Study of the Climate

Change C-Book

135

Boundary objects are ‘objects’ employed by

people engaged in such interactions to be used for

the negotiation and overcoming of such

discontinuities and the ‘re-establishment of action

and interaction’ (Akkerman and Bakker, 2011).

They actually facilitate boundary crossing processes

by fulfilling a bridging function (Star, 2010)

between their ‘intersecting social worlds’.

According to Star and Griesemer (1989) what turns

an ‘object’ into becoming a boundary object is:

- its interpretative flexibility: boundary objects

have different meanings in different social

worlds, but at the same time they have a structure

that is common enough to make them

recognizable across these worlds,

- the fact they act as means of translation: they

allow different groups to work together, based on

a back-and-forth movement between ill-

structured use in cross-site work and well-

structured use in local work.

Akkerman and Bakker (2011) propose the following

four types of mechanisms as being employed during

boundary crossing encounters taking place between

or within individuals. These are:

(a) Identification of the boundaries between two (or

more) ‘worlds’, when people come to act in these

‘worlds’ simultaneously. Although

discontinuities may not be overcome, the

learning potential resides in a renewed sense-

making of different practices and related

identities related to each of these ‘worlds’.

(b) Coordination of activity flow acknowledging

diverse ‘sites’, leading to the overcoming of

boundaries, in the sense that continuity is

established, facilitating future effortless

movement between different ‘sites’.

through perspective-making and perspective-

taking, leading to a new and more enriched view

of the world and one’s identity.

(d) Transformation leading to changes in practices,

potentially the creation of a new, in-between

practice, through dialogue and collaboration

between individuals at either side of the

boundary.

2 THE “CLIMATE CHANGE”

C-BOOK: A CASE STUDY

The study presented here focuses on identifying and

understanding how social creativity was manifested

in the collective design of a specific c-book, namely

the “Climate Change” c-book, produced within the

context of M C Squared project. This c-book was

collaboratively designed by members of a Greek

CoI, comprised of educational designers/ teachers

from diverse disciplinary backgrounds, school levels

and teaching subject practices, making use of the C-

Book technology.

2.1 The “Climate Change” C-Book:

Theme, Design Process and

Product

The “Climate Change” c-book unit was designed

with the aim to foster creative mathematical thinking

(CMT) in its prospective users (secondary education

students), by inducing mathematical concepts and

mathematical thinking processes in reference to

identifying and/or analysing various dimensions of

the climate change issue, and by promoting the

students’ active engagement and experimentation

with them.

The selection of “climate change” as the

narrative theme of the c-book was not made

arbitrarily. Climate change is recognised as one of

the greatest societal challenges of our times,

encompassing various (environmental, economic,

health and safety, food production, and other)

dimensions (Intergovernmental Panel on Climate

Change, 2015). It is well-documented through

various observational records that the rate of climate

change is now much greater than in previous

periods. The last decade was the warmest ever

recorded since modern measurement on global

temperatures began. Continued global warming has

led to a systematic decline in the Arctic sea-ice

cover, and there is similar evidence with regards to

snow cover, glaciers and the Greenland ice sheet.

These phenomena have enabled acceleration of ice-

melting and an increase in the mean sea levels, both

with detrimental consequences for some coastal

areas. Extreme weather events, such as hurricanes,

cyclones and floods, seem to be also closely

connected with climate change. Although natural

causes play a role in enhancing climate change, there

is almost unanimous consensus that the greenhouse

gas emissions released from industrial,

transportation, agricultural and other human-related

activities are the main contributors to climate

change. Carbon dioxide resulting from the

combustion of fossil fuels (such as coal, oil and gas)

is the main culprit in human-induced climate

change.

However, although climate science has evolved

our understanding of these phenomena, there is still

much complexity about the climate system and

CSEDU 2016 - 8th International Conference on Computer Supported Education

136

acknowledged limitation in the potential of science

to address it, which leads to a great deal of

uncertainty, unpredictability and controversy as to

how climate change works and can be mitigated in

terms of sustainability. It is this fact that turns

‘climate change’ into a ‘wicked’ and ‘ill-structured’

problem’ (Rittel and Webber, 1973) and thus a

challenging topic to address and deal with in

educational practice (Daskolia and Kynigos, 2012).

This kind of ‘problems’ ask for transcending the

‘boundaries’ between mono-disciplinary approaches

and practices to inter-disciplinary and trans-

disciplinary collaboration in the construction of

knowledge (Lotz-Sisitka et al., 2015).

Six Greek CoI members were involved in this

challenging task of designing a digital educational

resource interweaving sustainability concerns about

climate change with mathematical concepts and

thinking processes. The whole design process lasted

four months (25/3/2015- 21/07/2015) and resulted in

a c-book comprising two sections: a) ‘The Living

Earth’, dealing with the causes and effects of

climate change (in 17 pages), and b) ‘Making the

Impossible Possible’, focusing on the human role in

inducing and enhancing climate change and practical

solutions to reduce its impact (in 8 pages).

The narrative devised revolves around George, a

12-year-old boy, inhabitant of an island located

somewhere in the Pacific Ocean, who is forced to

flee his homeland and become an ‘environmental

refugee’. Soon he decides to get into a journey

around the world and to set up a youth movement

using social media as a means to fight against

climate change. George first visits Venice (a coastal

city at high risk due to the sea level rise caused by

climate change) and then Athens (a city suffering

from air pollution). In each of these visits he comes

across several facets of climate change and becomes

aware of the causes (the greenhouse gases) and

consequences of it (global warming, sea-ice cover

decline, melting of the ice sheets, rise of the sea

levels, etc.), and the impact of various human

activities on disproportionally raising the levels of

carbon dioxide emissions (i.e., through calculating

the carbon footprint.

As the narrative unfolds, several mathematical

concepts ‘emerge’ or have to be ‘identified’ to

facilitate the understanding of the various facets of

the climate change issue. Students are prompted to

experiment and tinker with widget instances to

explore correlations between variables, estimate

mathematical models, construct and interpret

multiple representations, design 3D shapes (see, Fig.

1), make and investigate assumptions, draw and

extend conclusions related to climate change

dimensions, etc. The narrative together with the

respective widget instances form a challenging

learning environment in which the students build

and apply mathematical concepts to make sense of a

real-life issue. The students’ mathematical creativity

is triggered through the learning opportunities

provided to the students asking them to establish

connections between various representations of a

concept (e.g., students are asked to depict and

compare CO

emissions by drawing circles and

disks), or to pose and respond to open problems

(e.g., students use relevant information to estimate

footprint values).

Figure 1: A ‘Climate Change’ c-book page asking users/

students to get involved in finding the best procedure to

construct a 3D model of a water molecule.

2.2 Operational Definition for Social

Creativity

Within the context of M C Squared project, social

creativity in the design of c-books has been

operationally defined as: the generation of ideas and

digital artifacts (widgets instances and the c-books)

stemming from the combination of diverse

knowledge systems and disciplinary domains, which

result from the various boundary crossing

interactions among CoI members and between them

and the C-Book technology, and are considered – at

least by the CoI members – to be: i) novel, ii)

appropriate, and iii) usable to support creative

mathematical thinking (CMT) in their end-users

(students).

In this study we are interested in the processes

that took place among the Greek CoI members and

with the C-Book technology while designing the

“Climate Change” c-book to foster CMT in

Social Creativity in the Design of Digital Resources Interweaving Math with Environmental Education - The Case Study of the Climate

Change C-Book

137

prospective users/ students. Our focus is on

identifying the boundary crossing mechanisms that

were employed in these interactions and how they

affected the production of “creative” outputs, either

ideas or more tangible products.

3 METHOD

3.1 Participants

The six Greek CoI members involved in the design

of the “Climate Change” c-book were teachers with

different disciplinary backgrounds and teaching

expertise in mathematics, mathematics education,

environmental education, drama in education and the

design of digital tools for mathematics education.

This diversity in knowledge domains, perspectives

and cultures was meant to enhance the CoI’s

creative potential.

3.2 The C-Book Environment

The C-Book environment provides the “CoICode

workspace”, a mind-map communication and

collaboration platform for organized asynchronous

discussions with compulsory meta-data, pertaining

to the creativity aspects of the interaction process,

e.g., the status of a post being’ either ‘alternative’,

‘objectionable’, or ‘contributory (see, Fig. 2). In

their posts CoI members can also attach or refer to

‘objects’, such as online resources, text files or

widget instances, as part of their exchange over the

c-book under construction. Furthermore, the

CoICode tool provides the designers with the

possibility to rate any idea or widget production they

have suggested and posted in the form of CoICode

contribution. Their ratings can be against three

criteria: a) novelty, b) appropriateness, and c)

usability of the contribution, on a yes/no basis. A

creativity score per contribution is then

automatically calculated as the aggregate score from

the votes received on each criterion and across

raters.

In addition, the C-Book environment comprises

an ‘authoring and playing’ tool, which is a space

allowing the CoI members to collectively design and

construct the c-book (see, Fig. 3), and where the

students can interact with it. Authoring of a c-book

is based on the design and construction of a number

of ‘pages’, each of them incorporating some

dynamic widget instances (which can be configured

by the c-book authors in order to fulfil specific

design specifications) and are accompanied by

Figure 2: Excerpt from the CoICode workspace depicting

CoI members’ interactions as described in critical episode 1.

corresponding narratives. The designers/ authors can

write text, attach links, files or widget instances out

of a set of widget factories (e.g., MaLT, a 3D Logo-

Based Turtle Geometry software, is a ‘widget

factory’, and a microworld of this factory is a

‘widget instance’) which are available in C-Book.

Figure 3: Snapshot of the authoring tool of the C-Book

environment.

3.3 Data and Analytical Approach

The data collected and analyzed in the present study

were: a) the 270 contributions uploaded in CoICode

from the outset of the design process until the final

version of the c-book was released, b) the actual c-

book produced in terms of structure (pages) and

contents (the ‘script’, the widget instances and the

respective narratives per page), and c) the creativity

scores calculated per idea posted as contribution in

CoICode workspace.

The level of analysis employed in this case-study

is in terms of identifying and discussing critical

episodes of social creativity, i.e., selected segments

of an activity (including discourse activity) with a

single theme as a focus. The aim was to apply an in-

depth lens on the boundary-crossing processes that

CSEDU 2016 - 8th International Conference on Computer Supported Education

138

took place between the CoI members and with the

ideas and tangible artifacts produced out of their

exchanges and interactions with the C-Book

technology. This qualitative approach to

understanding social creativity in the design of c-

books was chosen to shed light on the social nature

of the processes involved in the design and

development of the c-book. The identification of

each critical episode was guided and supported by

the data automatically collected and analysed by

CoICode, such as time series interaction data and/or

creativity scores extracted per idea.

4 FINDINGS

4.1 Critical Episode 1: The Design of

Widget Instances as a Result of the

Creative Interactions between

Teachers of a Diverse Expertise

The first episode selected and presented here started

one month after the outset of the design process. It

lasted for 8 days and the participants in it were four

members of the Greek CoI: two researchers in

environmental education, a primary school teacher

with an expertise in math education and a

mathematician/ secondary school teacher. Their

exchange is part of the evolutionary path of a

specific idea, which received a high score in

creativity according to the votes of the CoI members

and was later reified as a widget instance in the c-

book.

The discussion (see, Fig. 2) begun with the

suggestion of a new idea about the narrative of the c-

book:

Rea (environmental education researcher),

26/4/2015: [...] I was thinking that for approaching

the issue on a global level we could create the main

character as an adventurous traveler (a backpacker),

who wanders around the world and is confronted

with the consequences of climate change. [...]

Irini (mathematician), 27/4/2015: I like the idea.

Let’s have a look on it.

This idea was followed by other CoI members’

contributions who were motivated to search for and

upload in CoICode external links to interactive maps

depicting the consequences of climate change or

portraying different aspects of it (e.g., the relation

between industrialization and greenhouse gas

emissions):

Kostas (environmental education researcher),

27/4/2015: This is a very nice idea! Adventure and

travelling appeal to kids of all ages [...] I believe that

these interactive maps that depict the dimensions of

climate change at several parts of the world will help

us develop both the script and the widgets. What do

you think? (attaches two links to interactive maps)

Angeliki (math education researcher) 29/4/2015:

This map can be compared with this one (attaches a

link to an interactive map with circles that depict

global carbon footprints), so that we can pose

questions like the following […]

It is noteworthy that Angeliki attempts to

establish a common space of communication and

exchange of ideas for the intersecting fields of

Mathematics and Environmental Education by

posting external links for others to comment upon.

Searching for sources in a field other than her own,

is for her a way to re-define her proper field and her

CoI identity. This is done by getting connected with

another field and trying to delineate how the former

differs from the latter. Such a dialogical process of

“othering” is a characteristic dimension of the

identification mechanism in boundary crossing

interactions.

Later on (13/5/2015), Irini picked up the idea of

visualizing the quantity of CO

emissions and

suggested the design of a widget instance, where the

students are asked to draw circles or disks on a map,

so to depict the carbon footprint of two main Greek

cities. The widget instance was reified by another

CoI member, Dimitris, a mathematician. Several

elaborations of this widget instance took place,

fueled by intense interactions between the CoI

members until the final version was released and

incorporated in the c-book unit (see, Fig. 4).

This episode shows how a communicative

exchange between an environmental and a

mathematical perspective were brought together

giving rise to a series of new, appropriate and usable

ideas and widget instances to be generated and

applied in the c-book. The interactive maps

suggested by some CoI members were used as

‘boundary objects’ to translate them in different

ways but also to enable understanding and bridge the

diversity in the perspectives. For environmental

educators, they were used to depict facets of the

climate change impact, whereas for mathematicians

they served as tools to represent and compare

different amounts of CO

emissions by the size of a

circle or a disk. However, at the same time they

enabled the coordination of the activity so that both

practices were combined efficiently in the design of

widget instances, which were consequently rated by

the designers themselves as creative.

Social Creativity in the Design of Digital Resources Interweaving Math with Environmental Education - The Case Study of the Climate

Change C-Book

139

Figure 4: The final version of the produced “Carbon

footprint” widget instance.

The widget instances were thus employed as

boundary objects, not only by facilitating

communication and collaboration between the CoI

members in the design of the c-book unit, but also

because they enabled perspective-making and

perspective-taking, managing this way to be

transformed into ‘creative’ ideas and constructions.

4.2 Critical Episode 2: Narratives and

Widget Instances Interweaved in

the Design of the C-Book

The selection of the second critical episode was

based on time series interaction data coupled with

creativity scores calculated and provided by

CoICode, helping us identify a segment of the

discourse activity of the CoI quite dense in posting

contributions, but also in putting forth and

elaborating a number of highly creative ideas with

regards to the narrative of the c-book. This episode

started two months after the outset of the design

process. It lasted for 18 days and all CoI members

participated in it. At that time, a number of instances

designed to afford mathematical creativity took the

role of boundary objects while they were gradually

evolving into more elaborated versions. These

included, among others, constructing multiple

representations of climate change dimensions (e.g.,

measuring the carbon footprint) and tinkering with

3D shapes. However, a decision on the narrative that

would incorporate and join together all these

elements was pending. The discussion (see, Fig. 5)

begun with a suggestion on the outline of the script,

based on an earlier idea about the main character, a

backpacker who travels around the globe and comes

across various consequences of climate change:

Sylvie (primary school teacher), 24/5/2015: […]

By having a look at the discussion on the script, it

came to me […] a story outline. Please send your

feedback on the attached document.

Rea (environmental education researcher),

24/5/2015: […] in such a way we introduce a

‘creative’ character in the narrative. […] However,

my idea was that our hero would travel and visit

more places, so that we could get more glimpses of

climate change as a global issue.

Eirini (mathematician), 26/5/2015: I don’t

understand this story. I can’t realise how it connects

with the widget instances already produced and the

initial questions we posed for the design of this c-

book. […] Whoever writes the story has to have a

good understanding of the structure and the

activities.

Kostas (environmental education researcher),

28/5/2015: […] trying to connect all the widget

instances, I thought of starting writing a story based

on a real incidence. Shall we go on this?

Figure 5: Excerpt from CoICode workspace depicting CoI

members’ interactions as described in critical episode 2.

This last idea turned yet into another boundary

object, since it was unanimously accepted as novel

and intriguing narrative with the potential to

incorporate all the previously suggested widgets

instances. Several refined versions of the narrative

followed as a result of the exchange between the CoI

members in CoICode. The flexibility of the scenario

allowed its customization to earlier and newer ideas

on the didactical design. And vice versa: it allowed

the modification of the widget instances that had

CSEDU 2016 - 8th International Conference on Computer Supported Education

140

already been produced, or inspired the design of new

ones.

A communicative connection was established

around the narrative as an evolving artifact bridging

diverse perspectives. Continuity and effortless

movement between these perspectives became the

norm of interaction, and boundary permeability was

enhanced, since mathematicians got involved into

the construction of the narrative, while

environmentalists connected dimensions of the

climate change issue with ideas about mathematical

widget instances. Perspective-making and

perspective-taking were essential for the

interweavement of widget instances with the

narrative into a concise whole. Social creativity

exemplified in the generation of a ‘creative’ script

idea, was thus facilitated by the boundary-crossing

exchanges that led to the transformation of the initial

idea into some more ‘tangible’ products.

5 DISCUSSION

Our research employs the Boundary Crossing

perspective as a framework to identify and study

social creativity in the design of c-books by

educational designers/ teachers. The findings

suggest that this kind of interactions enabled by an

appropriately designed socio-technical environment

enhanced the CoI designers’ capacity to come up

with ideas which they rated as creative. The

affordances of the C-Book technology, allowing for

the meshing of narratives with dynamic

constructionist artefacts-widgets, were at the center

of these interactions, facilitating the continuous

collaborative versioning of the various constituent

parts of the c-book.

Moreover, our approach values the engagement

of teachers in the design of digital educational

resources. It acknowledges them as active creators

of educational resources in participative cultures

(Fischer, 2011) and not as just ‘consuming’

practitioners involved in top-down integrations of

technology in the classroom as suggested by other

frameworks, such as TPaCK (Mishra and Koehler,

2006). Socio-technical environments, like the one

employed in this study, can serve as settings to

deploy and study the teachers’ collaborative design

of resources and act as a driving force for classroom

innovations (Kynigos, 2015b).

Regarding the CoI’s involvement in boundary

crossing interactions, four mechanisms seem to have

played a role as depicted in the two critical episodes

reported here: identification, through which new

hybrid ideas come up in the course of the CoI’s

discussion of an idea-theme; coordination, as an

important condition for establishing a

communicative connection between the CoI

members in terms of design suggestions and moves,

revealing their efforts of translating them to each

other’s ‘language’, so that dialogue is maintained

and shared design work proceeds and develops; and

finally, reflection and transformation, as two

important processes at the core of social creativity

processes, as for example when the CoI members

got into perspective-making and perspective-taking

to identify and build on the others’ contributions and

shared key resources, or when they actually

managed to collectively improve and turn an initial

idea about the narrative into a better elaborated idea

or new widget instance.

The design process of the “Climate Change” c-

book was mainly focused on interweaving the

widget instances with the narratives into a concise

whole, a creative and definitely demanding

endeavor, representing a focal characteristic of a

new generation of digital educational resources.

Integrating the various constituent parts of such an

‘object’ to bring it into existence in a complete and

creative form is ‘wicked’ and thus a genuine design

problem. As such, social creativity in the context of

socio-cultural environments is identified as a

necessary asset to invest on, since it can multiply the

impetus for appropriately addressing issues of this

kind. Solving dilemmas emerging while designing c-

books (or any other types of new mediations with

properties and functionalities which have never

existed before, at least in the all-brought-together

form), involves firstly articulating and posing these

dilemmas, if we allow ourselves to think with the

analogy of problem-posing and problem-solving.

This is a task which is inherently creative and, in

order to be facilitated and boosted, it needs to be

situated in appropriately designed contexts, where

designers collaboratively think and design not only

about new technologies but also with these

technologies.

Finally, ‘climate change’ worked well as a theme

that inspired and enabled creative boundary

transcendences from the part of all CoI members,

and boosted the collaborative construction of new

perspectives in teaching and learning about

traditionally mono-disciplinary and normal science

subjects, such as mathematics. This can be the case

with other current sustainability issues, all sharing

the characteristics of ‘ill-structured’ problems, by

thus allowing for creative thinking processes to take

place.

Social Creativity in the Design of Digital Resources Interweaving Math with Environmental Education - The Case Study of the Climate

Change C-Book

141

ACKNOWLEDGEMENTS

The research leading to these results has received

funding from the European Union Seventh

Framework Programme (FP7/2007-2013) under

grant agreement n° 610467 - project “M C Squared”,

http://mc2-project.eu. The c-book technology is

based on the widely used Freudenthal Institute's

DME portal and is being developed by a consortium

of nine partner organisations, led by CTIandPress

'Diophantus'.

REFERENCES

Akkerman, S. F. and Bakker, A. (2011). Boundary

Crossing and Boundary Objects. Review of

Educational Research, 81(2), 132-169.

Bakker, A. and Akkerman, S. F. (2014). A boundary-

crossing approach to support students’ integration of

statistical and work-related knowledge. Educational

Studies in Mathematics, 86(2), 223-237.

Bonifacio, M. and Molani, A. (2003). The richness of

diversity in knowledge creation: an interdisciplinary

overview. Journal of Universal Computer Science,

9(6), 491-500.

Csikszentmihalyi, M. (1996). Creativity: Flow and the

psychology of discovery and invention. New York:

Harper Collins.

Daskolia, M. and Kynigos, C. (2012). Applying a

Constructionist Frame to Learning about

Sustainability. Creative Education, 3, 818-823.

Emin-Martínez, V., Hansen, C., Rodríguez-Triana, M. J.,

Wasson, B., Mor, Y., Dascalu, M., Ferguson, R. and

Pernin, J.-P. (2014). Towards teacher-led design

inquiry of learning. eLearning Papers. Retrieved

March 6, 2015, from http://openeducationeuropa.eu

/en/article/Towards-Teacher-led-Design-Inquiryof-Le

arning?paper=134810.

Engeström, Y., Engeström, R. and Kärkkäinen, M. (1995).

Polycontextuality and boundary crossing in expert

cognition: Learning and problem solving in complex

work activities. Learning and instruction, 5(4), 319-

336.

Fischer, G. (1999). Symmetry of ignorance, social

creativity and meta-design. In Proceedings of the 3rd

conference on Creativity and cognition (pp. 116-123).

New York: ACM.

Fischer, G. (2000). Shared Understanding, Informed

Participation, and Social Creativity - Objectives for the

Next Generation of Collaborative Systems. In R.

Dieng, A. Giboin, L. Karsenty and G. De Michelis

(Eds.), Designing Cooperative Systems, The Use of

Theories and Models (pp. 3-16). Amsterdam, the

Netherlands: IOS Press. Retrieved May 23, 2015, from

http://l3d.cs.colorado.edu/~gerhard/papers/coop2000.p

df.

Fischer, G. (2001). Communities of interest: Learning

through the interaction of multiple Knowledge

Systems. Paper presented at 24th Annual Information

Systems Research Seminar in Scandinavia, Ulvik,

Norway.

Fischer, G. (2004). Social creativity: Turning barriers into

opportunities for collaborative design. In A. Clement

and P. Van den Besselaar (Eds.), Proceedings of the

eighth conference on Participatory design: Artful

integration: interweaving media, materials and

practices (Vol. 1, pp. 152-161). New York: ASM.

Fischer, G. (2005). Social Creativity: Making All Voices

Heard. In

Proceedings of the HCI International

Conference (HCII), (published on CD). Retrieved May

23, 2015, from http://l3d.cs.colorado.edu/~gerhard/pap

ers/social-creativity-hcii-2005.pdf.

Fischer, G. (2011). Social Creativity: Exploiting the Power

of Cultures of Participation. In SKG2011: The 7th

International Conference on Semantics, Knowledge

and Grids (pp. 1-8). Los Alamitos, Washington,

Tokyo: IEEE.

Fischer, G., Giaccardi, E., Eden, H., Sugimoto, M. and Ye,

Y. (2005). Beyond Binary Choices: Integrating

Individual and Social Creativity. International Journal

of Human-Computer Studies (IJHCS) Special Issue on

Computer Support for Creativity (E.A. Edmonds and

L. Candy, Eds.), 63(4-5), pp. 482-512. Retrieved May

23, 2015, from http://l3d.cs.colorado.edu/~gerhard/pap

ers/ind-social-creativity-05.pdf.

Fischer, G. and Ostwald, J. (2005). Knowledge

communication in design communities. In R. Bromme,

F. W. Hesse and H. Spada (Eds.), Barriers and Biases

in computer-mediated knowledge communication –

and how they may be overcome (pp. 213-242).

Dordrecht, the Netherlands: Kluwer Academic

Publishers.

Intergovernmental Panel on Climate Change (2015).

Climate Change 2014: Mitigation of Climate Change

(Vol. 3). New York: Cambridge University Press.

Kynigos, C. (2007). Half-Baked Logo Microworlds as

Boundary Objects in Integrated Design. Informatics in

Education, 6(2), 335–358, Institute of Mathematics

and Informatics, Vilnius.

Kynigos, C. (2015a). Designing Constructionist E-Books:

New Mediations for Creative Mathematical Thinking?.

Constructivist Foundations, 10(3), 305–313.

Kynigos, C. (2015b). Constructionism: Theory of

Learning or Theory of Design? In S. J. Cho (Ed.),

Selected Regular Lectures from the 12th International

Congress on Mathematical Education (pp. 417- 438).

Heidelberg New York, Dordrecht, London,

Switzerland: Springer International Publishing,

Kynigos, C. and Daskolia, M. (2014). Supporting creative

design processes for the support of creative

mathematical thinking. Capitalising on cultivating

synergies between Math Education and Environmental

Education. Proceedings of the 6th International

Conference on Computer Supported Education

(CSEDU 2014), Barcelona, Spain, 1-3 April (Paper

#256, pp. 342-347). doi:10.5220/0004965603420347.

CSEDU 2016 - 8th International Conference on Computer Supported Education

142

Laurillard, D. (2012). Teaching as a Design Science:

Building Pedagogical Patterns for Learning and

Technology. London: Routledge.

Lave, J. and Wenger, E. (1991). Situated learning:

Legitimate peripheral participation. Cambridge, UK:

Cambridge University Press.

Lotz-Sisitka, H., Wals, A. E., Kronlid, D. and McGarry,

D. (2015). Transformative, transgressive social

learning: rethinking higher education pedagogy in

times of systemic global dysfunction. Current Opinion

in Environmental Sustainability, 16, 73-80.

Mishra, P. and Koehler, M. J. (2006). Technological

pedagogical content knowledge: a framework for

integrating technology in teacher knowledge. Teachers

College Record, 108(6), 1017-1054.

Rittel, H. and Webber, M. (1973). Dilemmas in a general

theory of planning, Policy Sciences, 4(2), 155-169.

Star, S. L. (2010). This is not a boundary object:

Reflections on the origin of a concept. Science,

Technology and Human Values, 35(5), 601-617.

Star, S. L. and Griesemer, J. R. (1989). Institutional

ecology, ‘translations’ and boundary objects: amateurs

and professionals in Berkeley’s Museum of Vertebrate

Zoology, 1907-1939. Social Studies of Science, 19,

387-420.

Wenger, E. (1998). Communities of Practice: Learning,

Meaning, Identity. New York: Cambridge University

Press.

Social Creativity in the Design of Digital Resources Interweaving Math with Environmental Education - The Case Study of the Climate

Change C-Book

143