Designing creative electronic books for mathematical creativity
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”. This publication reflects only the author’s
views and Union is not liable for any use that may be made of the information contained therein.
Eirini Geraniou – UCL Institute of Education (firstname.lastname@example.org)
Christian Bokhove – University of Southampton (email@example.com)
Manolis Mavrikis – UCL Knowledge Lab (firstname.lastname@example.org)
Saturday, 12th of November 2016
Designing creative electronic books
for mathematical creativity
• 5 mins – Introduce the MC2 project and its aims
• 10 mins – Introduce MC-squared platform, the different
functionalities, tools, such as widgets
• 15 mins – Present the list of current c-books and focus on 3 c-books
• 8 mins – Show some data
• 2 mins – Share Key messages
• Design and develop a new genre of authorable e-book, which we call 'the c-
book' (c for creative)
• Creative Mathematical Thinking (CMT)
• Initiate a ‘Community of Interest’ (CoI)
• A community of interest consists of several stakeholders from various
‘Communities of Practice.
• England, Spain, Greece, France
• Within these, teachers who co-design and use resources for teaching, can
contribute to their own professional development.
• Social Creativity
• UK CoI: learning analytics and feedback
(e.g. Fischer, 2001; Wenger, 1998; Jaworski, 2006)
MC Squared Platform
• C-books available
• Widget list
• At the end, we can demo the platform:
and login as guest
stores student work.
can have several
This is the ‘edit’ mode of
the environment : this c-
book is about planets
c-books can have several pages: each
circle indicates a page. Other options
are available as well
C-book pages can have random
elements, like random values.
Pages consist of ‘widgets’, which can
range from simple text to simulations
(here: Cinderella). Some widgets can give
(a) Social creativity (SC) in the design of CMT resources (c-book units)
(b) Creative mathematical thinking (CMT) has been drawn on Guilford’s (1950)
• fluency (the ability to generate a number of solutions to a problem),
• flexibility (the ability to create different solutions),
• originality (the ability to generate new and unique solutions), and
• elaboration (the ability to redefine a problem).
Tryingtooperationalizecreativity Geometry example
Create a certain object with a widget that
can produce these objects. If ‘certain’ is
not included then (originality)
Create a (certain) quadrilateral Create a (certain) number
We should be able to ask the widget what
classes/types have been produced
From the 9 types of
quadrilaterals 3 were made by
the student: square, rhombus
Different numbers or
expressions were made
We should be able to ask the widget how
these classes/types were produced
The square and rhombus were
made once. The trapezium in
two distinct ways.
were made in very distinct
If the outputs are numbers they can be
compared over a group of students
Student was only one who made
a rhombus. / Teacher submitted
‘non original’ answers.
Student was only one who
made this expression. /
Teacher submitted ‘non
Explain what you created and how you
created them in your own words
Student supplies an elaboration
on the types and processes of
Student supplies elaboration
on the types and processes of
Case Study – Reflections c-book
We considered CMT as
• (i) the ‘construction’ of math ideas or objects,
in accordance to constructionism that sees CMT being expressed
through exploration, modification and creation of digital artefacts
• (ii) Fluency (as many answers as possible) and
Flexibility (different solutions/strategies for the same problem)
• (iii) novelty/originality (new/unusual/unexpected ways of applying
mathematical knowledge in posing and solving problems).
(Daskolia & Kynigos, 2012; Papadopoulos et al. 2015; 2016)
• as a thinking ‘process’ in a mathematical activity in order to produce a
‘product’ (e.g. a solution to a mathematical problem).
Case Study - Aims
• explore the potential of the Reflection digital book and of automated
feedback and reflection
• focus on building ‘bridges’ to the maths involved (and may be ‘hidden’) in
Bridging activities = short tasks or questions used to intervene and encourage students
to reflect upon mathematical concepts and problem-solving strategies they use
throughout a sequence of activities (or simple interactions) with a digital tool.
Such activities could take various forms from questions or prompts within the digital tool
to paper-based worksheets or verbal teacher’s interventions.
• METHODOLOGICAL TOOL:
• “design experiment” (Collins et al., 2004; Cobb et al., 2003).
• 21 Grade-7 students and their class teacher
• 2 lessons in the school’s computer lab.
• DIFFERENT ROLES:
• Researchers as ‘participant observers’
• Teacher as COI member to design the Reflections c-book, offered assistance in
technical issues and ensured that all students were on task and answered the
• logged answers in the MC2 platform, voice recordings of students’ elaborations
on their interaction/answers and a student evaluation questionnaire
Case Study – Reflections c-book
(A – F) Excerpts from the Reflection c-book and (G) a sample solution of (F)
A Likert multiple-choice questionnaire consisting of questions such as:
• (1) How satisfied were you after completing the c-book activities?
• (2) How easy to use do you think the c-book is?
• (3) How free did you feel to experiment with the c-book and try out your ideas?
• (4) I feel I understand Reflection now.
• Another two questions (5 and 6) gave them options to pick on their thoughts on
the c-book and their preferred features.
• The questionnaire finished with three more questions to request suggestions
• Language. Moving from informal terminology (“the other shape moves”, “we
have to flip the shape” or “count how many down from the mirror line”) to using
mathematical terms (“the reflected church” or the “reflection line”).
• Superficial responses.
• “if you move the green shape, the orange shape moves with it”.
• They seemed to have noticed that the 2 shapes (green and orange ‘F’) are
linked, but only 2 were able to articulate that they maintain the same distance
from the Reflection line.
• Bridging activities revealed students’ solving strategies and their CMT.
• Competition task. 3 different strategies:
(i) counting boxes across and down,
(ii) tilt the head so that the reflection line becomes vertical and then find the
reflected image and
(iii) imagine using tracing paper on the screen to find the reflected image.
(Q4) I feel I understand
85% (18/21) responded on with an answer above 4 in the Likert scale
thoughts on the c-book
and their preferred
43% (9/21) said that it included problems that they would not have
tried to solve.
60% (13/21) answered that it helped them see the idea of reflection in
3 students made comments that showed that they appreciate the
advantages of digital technologies:
“the digital book help[s] because you could have actually test[ed]
out your ideas and improve if it’s wrong or not”
Students’ Suggestions They recognized the dynamicity of such resources and how seeing the
immediate feedback on their actions helps them validate an answer or
• Teacher’s keenness to use Digital Technologies was re-enforced through
• authoring activities,
• designing bridging activities and
• participating in the creation of the Reflection c-book
• Reflection c-book was further developed
• The most notable improvement was breaking down the bridging questions to smaller
questions with guidance, and using the feedback affordances to encourage the CMT
aspect of flexibility in terms of the strategies.
The c-book technology can be integrated in the mathematics classroom and
promote a positive learning experience through the use of playful activities for
students, matched with carefully designed bridging activities, followed by
constructionist activities that allow deeper exploration of the subject matter.
• Operationalising creativity: challenging
• Added value of technology: more than the sum of the parts
• Widgets with different features
• Storing student data
• Different people can work together in participatory design (Community of Interest) with
c-books acting as boundary objects
• Creative and interactive activities made by designers (creative process authoring)
• Collaboration within CoI between designers, teachers and computer scientists.
• Interactivity: feedback design
• More than one widget factories used
• All student data stored
• Sum is more than the parts…
MC Squared Platform
• To demo the platform, go to:
and login as guest
• Eirini Geraniou
• Christian Bokhove
• Twitter: @cbokhove
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