A Technological Storytelling Approach
to Nurture Mathematical Argumentation
Giovannina Albano
1a
, Umberto Dello Iacono
2b
and Giuseppe Fiorentino
3c
1
Department of Information and Electrical Engineering and Applied Mathematics, University of Salerno,
Via Giovanni Paolo II, 132, 84084 Fisciano (SA), Italy
2
Department of Mathematics and Physics, University of Campania “L. Vanvitelli”,
Viale Abramo Lincoln, 5, 81100 Caserta (CE), Italy
3
Naval Academy of Livorno, Viale Italia 72, Italy
Keywords: Argumentation, Collaborative Script, Digital Storytelling, Mathematics Education, Technology Enhanced
Learning.
Abstract: This research deals with how to foster the attitude of the mathematician facing a problem. In this regard, we
identified some fundamental steps, from the initial understanding to its solution, and some key attitudes, such
as critical thinking and insight. The steps have been translated into the phases of a digital interactive story-
telling in mathematics (DIST-M), while the attitudes have been embodied as characters/roles within the story.
The whole didactic design is based on collaborative scripts, and evolves according to the interactions between
the characters and the stimuli coming from the expert. In the paper we briefly report the design, it’s imple-
mentation using ICT tools, a taste of the analysis conducted and the results arising from a DIST-M trial in-
volving 26 first-year high school students.
1 INTRODUCTION
One of the aims of this research concerns how to fos-
ter in students the attitude of the mathematician fac-
ing a mathematical problem. For this purpose, we
identified some of his typical mental activities, fram-
ing them as distinct characters of a storytelling frame-
work. We also shaped the story into phases according
to the typical process that goes from the initial discov-
ery and inquiry to the conjecture, up to the final proof
and rethinking. These phases were translated into
learning activities (Leontiev, 1978) within the story-
telling.
More in depth, we considered the following fun-
damental phases involved in the understanding and
the formalization of a mathematical problem and its
solution:
Inquiry: the mathematician starts exploring the
problem, investigates about the assumptions,
makes trials, until a rough hypothesis arises.

a
https://orcid.org/0000-0002-5119-5413
b
https://orcid.org/0000-0003-0224-1046
c
https://orcid.org/0000-0003-1021-3969
Conjecture: the mathematician starts refining
the hypothesis to obtain a clear and complete
(though often verbal) conjecture.
Formalization: in most cases a verbal conjec-
ture is not enough to trigger the mathematical
tools needed to prove or disprove it; to this pur-
pose, a more formalized statement is obtained
using mathematical language and symbolic rep-
resentations.
Proof: the formal language allows to apply all
mathematical knowledge to prove (or confute)
the conjecture.
Refinement: once proved the conjecture, math-
ematicians often retrace their course and refine
the proof, producing a clear statement to share
with the mathematical community.
Along the above phases, we also foresaw the fol-
lowing key attitudes of a mathematician dealing the
solution of a problem:
420
Albano, G., Iacono, U. and Fiorentino, G.
A Technological Storytelling Approach to Nurture Mathematical Argumentation.
DOI: 10.5220/0009416904200427
In Proceedings of the 12th International Conference on Computer Supported Education (CSEDU 2020) - Volume 1, pages 420-427
ISBN: 978-989-758-417-6
Copyright
c
2020 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
Critical thinking: this is the ability to rethink
what is said in order to identify its weaknesses
and critical points.
Memory: as the ability of verbalizing and refin-
ing the partial and final formulations of the
reached results.
Coordination: is the ability of planning the ac-
tions and keeping track of them, taking into ac-
count the purpose of the various tasks.
Insight: this is the capability of generating new
germinal ideas which bring forward towards the
goal.
Knowledge: it stands for previous knowledge,
know-how, ability to seek information or to ask
for advice when own resources are not enough
to overcome difficulties.
These attitudes have been embodied in our story-
telling as different characters/roles that all students
play in turn, phase after phase.
With such roles and phases in mind, we designed
a digital interactive storytelling in mathematics
(DIST-M), based on a Vygotskian approach where
learning is first socialized and then internalized
(Vygotsky, 1980). The instructional design of a
DIST-M is based on collaborative scripts within a
digital storytelling framework. The narrative frame-
work allows contextualized learning through the inte-
gration of logical-scientific and narrative thinking
(Bruner, 1986).
In order to increase their cognitive engagement,
our storytelling approach does not foresee the con-
struction of the story by the students (which is hard to
drive towards the desired learning outcomes). On the
contrary, we start from a didactically interesting
mathematical problem well integrated in a consoli-
dated story, here students (divided into groups) and
experts (teacher or researcher) play as characters
along several possible learning paths. The narration
evolves according to the interactions between the
characters and the stimuli coming from the experts.
The analysis of the protocols arising from the class-
room experimentations is reported in Section 5.2 and
seems to confirm that, in this way, students remain
more focused on the plot and its (mathematical) ob-
jectives. More details on the implementation of the
DIST-M are given in Section 3.
Another aim of this research was to understand
whether technology is an essential component and to
which extent it can play an active role in teaching and
learning processes of this kind. We try a tentative an-
swer to this question in Section 6.
2 THEORETICAL
BACKGROUND
The design of the learning activities has been in-
formed by a network of theories (Bikner-Ahsbahs &
Prediger, 2014), where different approaches are com-
bined and coordinated to investigate the same phe-
nomenon from different points of view. In the follow-
ing, we briefly summarize the main theoretical refer-
ences taken into account in the instructional design.
Initially developed in the field of psychology and
social sciences, the Activity Theory studies individu-
als from the analysis of their activities. The key con-
cept is the activity, understood as something charac-
terized by interactions (it is an action in the world)
and intentionality (the action responds to a purpose).
The activity is therefore a high-level, usually collab-
orative, construct at the top of a hierarchy with two
other components: actions and operations, character-
ized respectively by awareness (having a goal) and
unconsciousness (task).
The intrinsic collaborative nature of these activi-
ties led us to explore some aspects of collaborative
learning, particularly computer-based learning. It is
well known that the effectiveness of collaborative
learning is not to be taken for granted, especially in
computer-supported environments (Weinberger et al.,
2009), where the need to pre-structure and regulate
social and cognitive processes is even more evident.
This is why researchers in the field have used the con-
cept of scripts as introduced in cognitive psychology.
It refers to an internal memory scheme corresponding
to a sequence of actions that define a well-known sit-
uation (Schank and Abelson, 1977). Here each actor
has a specific role and specific actions to perform and
the script is activated every time a similar situation
happens. In education, scripts are externally imposed
to support the students in collaborative learning con-
texts through the regulation of roles and actions that
students must take and perform to achieve a success-
ful learning (King, 2007). Over time, through social
practice, the expectation is that the student will inter-
nalize such scripts (Vygotsky, 1980) and shift from
hetero regulation to self-regulation.
In mathematics education, the importance of as-
signing roles to the members of cooperative groups
has been recognized in order to achieve a successful
learning. Pesci (2009) devises five roles: the first is
oriented to the task, in charge of getting the group to
solve the mathematical task as well as they can; the
second is oriented to the group, responsible of the ac-
tive participation of members of the group; the third
is the memory, who takes care of verbalizing the re-
sults of the group; the fourth is the speaker, in charge
A Technological Storytelling Approach to Nurture Mathematical Argumentation
421
of reporting the results outside of the group; the last
one is the observer, who takes notes of all the pro-
cesses and of the engagement of each member of the
group. A key remark highlighted by Pesci concerns
the importance of rotating such roles among the stu-
dents, so that each of them has the chance to experi-
ence each role and thus develops the corresponding
skill. A further role is foreseen for the teacher, who
acts as a supervisor, refraining from giving hints on
the mathematical side.
3 DESIGN OF DIST-M
EXPERIENCES
The theoretical background has informed our project
and suggested how to design the DIST-M experience
in order to engage students in developing the mathe-
matician attitudes outlined in the introduction. The
general framework of the DIST-M consists in a digi-
tal storytelling (Albano & Dello Iacono, 2018; Al-
bano, Dello Iacono, Fiorentino, Polo, 2018). The
story evolves along various episodes where students
and teachers are involved impersonating Characters
corresponding to the roles introduced in Section 1.
Following Pesci, the student plays different roles in
each episode, allowing him to experience the story
from different perspectives and to practice different
skills. Teachers and researchers play the Guru role.
and, differently from Pesci, in our design they can
also intervene mathematically, since their role em-
bodies the professional knowledge.
To cope with classes with more than 20 pupils,
one may be tempted to adopt two opposite solutions.
The first one foresees many students playing each
role/Character; however, the resulting “shared re-
sponsibility” can easily lead to situations where only
a few members of each group are really engaged. The
opposite approach allows many smaller teams to act
along the story as (nearly) isolated “threads”. How-
ever, it is hard to monitor all the teams by means of
their simultaneous real-time online conversations.
We tried a different approach, broadening the roles
and their rotation, with the Observers (Pesci, 2009).
Indeed, when a DIST-M is experienced in a class, var-
ious groups of four students (one for each role) are
created leading to five or six groups. For each epi-
sode, only one group is directly involved as the Char-
acters of the story, whilst the others are the Observers
(each member of the group observes a different Char-
acter). In the following episode, the active group and
all the roles are rotated. In this way, each students is
active once and will experience all the roles, either as
a Character or as an Observer. In this way, also the
Observers are engaged in the story, both on the cog-
nitive level (“What would I have done in his shoes?”)
and on the metacognitive one (“Is the observed Char-
acter playing well his role? Is he effective?”).
3.1 Macro Design
According to the Activity Theory, each phase corre-
sponds to an activity, characterized by interactions
(inside the digital environment, along the story, using
the available tools, with the other Characters) and in-
tentionality (each activity has a purpose). The macro
script consists of 5 activities corresponding to the
phases of a mathematician work introduced in Section
1: Inquiry, Conjecture, Formalization, Proof, Refine-
ment. Each phase corresponds to one episode of the
story. In the Inquiry phase (Episode 1) students ex-
plore a given mathematical situation. The aim of this
phase is to produce a short description of what has
been found. Subsequently, in the Conjecture phase
(Episode 2), the description is refined. The students,
starting from what was found, are required to formu-
late an agreed mathematical conjecture. The latter is
usually expressed in verbal form and, as such, it may
not be suitable for the formal manipulation required
to obtain a proof. So, in Episode 3 (the Formalization
phase), the students are asked to formalize the conjec-
ture in a proper mathematical language. This new
form is exploited in Episode 4 (the Proof phase) mak-
ing them organize the arguments in a deductive chain,
to build a (mathematical) proof. Finally, in Episode 5
(that is the Refinement phase) students are required to
write a report about the process carried out and the
results, explaining the purpose of each episode.
In order to fulfill the objective of each activity,
every student has some actions to perform, sometimes
individually, sometimes collaboratively. The actions
depend on the mathematical problem and are de-
signed to accomplish the purpose of the episode.
3.2 Micro Design
As already stated, the roles within the DIST-M arise
from the need to regulate group work in computer-
based environments, but they also represent functions
describing the attitude of a mathematician facing a
problem. Taking into account both the devised func-
tions (section 1) and the information from the theoret-
ical background (section 2), we have foreseen the fol-
lowing Characters, all played by students:
CSEDU 2020 - 12th International Conference on Computer Supported Education
422
The Boss (coordination): is both task and group
oriented (Pesci, 2009), takes care of the partici-
pation climate in the group, keeps the focus of
the group on the actions to be carried out accord-
ing to the purpose of the episode and to the
mathematical task; the responsibility of the
mathematical success, however, is in charge of
the whole group.
The Blogger (memory): is both memory and
speaker (Pesci, 2009), summarizing and com-
municating to the Guru the results obtained by
the whole group.
The Pest (critical thinking): acts as the devil’s
advocate (Soldano & Arzarello, 2016), asking
questions to check the robustness of all results
obtained by the group.
The Promoter (insight): is the creative of the
group, providing new insights to proceed to-
wards the objective of the episode.
We have also a Character played by the teacher or the
researcher:
The Guru (knowledge): is the one to ask for in-
formation and advice in case of lack of own re-
sources, the expert in the Vygotskian perspec-
tive.
To avoid deadlock situations, we have foreseen a
private communication channel between the Guru
and the Promoter. So if the Guru believes that the
group is in trouble, unable to ask for advice, or if
someone is not playing his role correctly without
someone else pointing it out, then the Guru can give
advice to the Promoter to overcome the difficulties.
In each episode, each member of the groups as-
sumes the perspective of one of the above roles, and
their role changes in the following episode. As al-
ready stated, in each episode only one group is active
playing the Characters of story while the members of
all other groups are Observers (of a different Charac-
ter). The rotation of the roles also involves the epi-
sodes where the group members are Observers. So, as
stated, all students will play all roles.
During the observation phases, the student is
asked to take the perspective of the assigned role,
watch the corresponding active Character and com-
ment in a personal spaces (the Logbook) how the
player behaves with respect to what is needed on the
mathematical plane to accomplish the episode objec-
tive. In these observation phases the student is urged
to switch from the cognitive to the metacognitive
level.
This continuous change of perspective, from
Character to Observer, from one role to another and
from the cognitive to the metacognitive level are in-
tended to help internalise all the roles and phases in-
troduced in Section 1.
3.3 The (self-)assessment
As each DIST-M experience is intended within the
curriculum, the assessment of such experience should
be part of the didactical contract. Thus we have fore-
seen two different kind of evaluation:
A Collective Assessment: it refers to the Epi-
sode 5 (section 3.1); each group of students is
asked to retrace all the previous episodes and
fill-in a report describing what happened in each
episode, both at the story level and at the math-
ematical level; in particular, students are ex-
pected to recognize and describe the purpose of
each episode.
An Individual Assessment: all students are re-
quired to review the whole activity, commenting
on how they played the assigned roles, both as a
Character and as an Observer; and say what they
would change in hindsight.
The collective assessment is essentially cognitive
and refers mainly to the mathematical content. How-
ever, it makes the students aware of the attitudes of a
mathematician and the steps he makes, as experi-
enced along the episodes Eventually, the whole path
(the script underpinning the story) will become clear
to the students and they will realize that it can be fol-
lowed every time they find themselves involved in
similar situations.
The individual assessment is essentially metacog-
nitive and affective. It concerns the functions in-
volved in a mathematician’s work and how they
showed up in the corresponding roles.
4 A CASE STUDY
The educational activities of the DIST-M take place
in a sci-fi setting. The Characters of the story are four
friends: Marco, Federico, Sofia and Clara. Marco is
the leader of the group and is trusted by his friends:
he is the Boss. Federico is a computer expert, con-
vinced of the existence of the aliens and always eager
to investigate and look for creative ideas: he is the
Promoter. Sofia loves reading and writing and wants
to become a journalist: she is the Blogger. Clara is
wary and often annoys her friends with countless
doubts and questions: she is the Pest. A further Char-
acter goes along with the four friends: Gianmaria,
A Technological Storytelling Approach to Nurture Mathematical Argumentation
423
Federico’s uncle. He is a smart adult, with a great
knowledge, experience and understanding: he is the
Guru.
4.1 The Mathematical Problem
As already stated, the DIST-M starts from a didacti-
cally interesting mathematical problem, and aims to
develop argumentative and proving skills in the stu-
dents. The problem is the following: given four con-
secutive numbers, the difference between the product
of the two middle ones and the product of the two ex-
tremes is always 2 (Mellone & Tortora, 2015). This
problem is suitable to introduce students to algebraic
proofs. In fact, to prove that the result is always 2
needs some algebraic modelling; for example, from n,
n+1, n+2, n+3, we may write the given statement as
(n+1) (n+2) - n(n+2) and manipulate it to obtain 2.
This problem is also suitable to promote discussions
on terms as “all” and “always” (i.e. universal quanti-
fier), encourages reflection on key mathematical con-
cepts such as “consecutive” in the set of natural num-
bers, integers, or within a generic numerical se-
quence.
Within the story, the mathematical problem has
been intentionally reformulated and partly hidden:
one day Federico (the Promoter), with a self-built su-
percomputer, finally picks up a strange message from
the aliens. It is made of numbers and mathematical
signs and demands a decipherment (Figure 1). Unfor-
tunately, due to interference, he cannot write down all
the numbers.
Figure 1: the mathematical problem in Episode 1.
Federico immediately involves his friends and
calls his uncle Gianmaria (the Guru) for help since he
is also fond of mathematical puzzles.
Starting from the recognition that each quadruple
on left side of Figure 1 is always formed by consecu-
tive integer numbers, pupils are guided by the story
towards the production of a conjecture about the mes-
sage such as that 2 is always the result of all opera-
tions on the right side of Figure 1.
To achieve this goal they will need and will be
guided by the story, to formulate their conjecture, for-
malise it in mathematical language, prove it and fi-
nally send a message back to the aliens, who are sup-
posed to understand mathematical language.
4.2 Implementation of the DIST-M
The DIST-M is mainly implemented using Moodle,
which provides useful tools for both educational ac-
tivities and social interactions (Albano, Dello Iacono,
Fiorentino, 2016).
Moodle’s tools and resources have been carefully
chosen and configured to meet the educational needs
of each design step. For instance, we used Chats for
all informal communication between students in the
same group and for the privileged channel between
Gianmaria the Guru and Federico the Promoter.
While Forums and Questionnaires (suitably adapted
to simulate the sending of an email) were used for all
formal communications between the Characters and
the Guru. This shift, which mimics the transition from
spoken to written language, is also intended to facili-
tate the transition to higher literate registers (Ferrari,
2004).
Figure 2: The comics setting and the 5 characters.
The whole learning environment has been customised
to look like a strip cartoon. The comics were made
with the online environment Toondoo and Power-
Point (as in Figure 2) and inserted into Moodle Books
to implement all episodes of the story. So, students
can navigate the story flipping through pages and
chapters. Moreover, a few lines of custom CSS, the
use links within of Moodle’s Labels allowed access
to “stealth” activities (available, but not shown on
course home page) so hiding some other elements of
Moodle’s user interface.
Making an extensive use of access condition,
some activities and resources are visible and available
only to specific roles; for instance, the Chat between
CSEDU 2020 - 12th International Conference on Computer Supported Education
424
Federico (the Promoter) and Gianmaria (the Guru) is
only visible to the Promoter role, while the Question-
naire that simulates the sending of an email can be
seen only by the Blogger role. The Observers were
implemented with a new Moodle role which allows to
see all chats and forums, without being able to edit
them.
Some digital application, implemented with Geo-
Gebra (Albano & Dello Iacono, 2019a), have been
embedded to support students in the production of
conjecture, argument and formalization process (Al-
bano & Dello Iacono, 2019b). In particular, in the first
episode, a GeoGebra spreadsheet is embedded in a
Moodle Page to support students in their exploration
in search of regularities. Students can exploit the po-
tential of spreadsheets quickly performing many tests
on all the quadruples. Another Moodle Page with an
embedded GeoGebra spreadsheet is also available
with a short tutorial on how to use it (assuming that
students were able to use technologies in a didacti-
cally meaningful way is a common mistake that we
tried to avoid). The student can choose if and when
follow the tutorial. In the second and third episodes
of the story, two Interactive Semi-open Questions
(ISQ) (Albano & Dello Iacono, 2019b) were imple-
mented to support students in the production of a con-
jecture and for its formalization respectively.
An ISQ is a digital GeoGebra application embed-
ded in Moodle that allows the student to build a state-
ment or a sentence by dragging digital tiles. Figure 3
and 4 show the digital tiles in the two ISQs needed to
construct a verbal statement and its symbolic expres-
sion, in Episodes 2 and 3 respectively.
Figure 3: Interactive Semi-open Question for Episode 2.
Figure 4: Interactive Semi-open Question for Episode 3.
These GeoGebra applications are initially hidden,
the expert (i.e. the Guru) can activate these resources
and make them available to students, according to the
technological literacy of the class.
All students are asked to keep a personal Logbook for
all episodes. The Observers will take notes while the
(observed) Characters are playing. The Characters
will describe the episode in which they were active at
the end of the experience. The Logbook is imple-
mented as a Google Doc with preloaded questions to
guide the (cognitive and metacognitive) analysis of
each episode. The same document will be useful in
the final (self-assessment) phase when all students are
asked (with an open text Moodle assignment) to re-
think about how they played during the whole story.
5 EXPERIMENTATION
In this section we briefly report the methodology and
a short analysis of some excerpts arising from an ex-
perimentation of the outlined DIST-M.
5.1 Methodology
This DIST-M was experimented with 26 first-year
high school students. The trial was carried out in a
computer lab at the University of Salerno. All stu-
dents worked individually on a computer and commu-
nicated with their classmates by means of one of the
platform’s tools. Groups of 4 or 5 students have been
set up. In groups with 5 members the Pest and Pest
Observer roles were duplicated. The role of the ex-
pert, Gianmaria, was played by a researcher together
with the teacher. In the following section we give a
taste of the engagement of the students in their roles
(as Characters or Observers), focusing on the first ep-
isode of the story (i.e. the Inquiry phase).
5.2 Data Analysis and Results
A qualitative analysis is conducted with the aim of
understanding how much the environment has influ-
enced the students’ appropriation of roles with respect
to the mathematical problem to be solved. In this re-
gard, we will look at the transcriptions produced by
A Technological Storytelling Approach to Nurture Mathematical Argumentation
425
the students in the Group Chat and in the private Chat
between Federico and Gianmaria, and the Observers
Google Doc files.
In the following we report an excerpt from the
discussion between the Characters in the Group Chat:
1 BOSS: since in the previous rows the difference
between the numbers was one, then in the seventh
row (the last one), as it ends with 15 and the dif-
ference is one, then the four numbers should be:
12, 13, 14, 15.
2 BOSS:So, it will be 12*14-13*15. Do you agree?
3 PEST: Ehm, excuse me, I don’t understand this
4 BOSS: sorry, I was wrong, 13*14-12*15
5 PROMOTER: guys, since I see the row with the
numbers 15,16 and 18, since in the row on the
right there is *17, in my opinion the missing num-
ber should be 17, yielding 16*17-15*18
6 PEST: product of the middle ones minus the prod-
uct of the extremes?
7 BLOGGER: row 5 I suppose should be 7-8-9-10
8*10-7*10. Do you agree?
8 BLOGGER: Boss, what do you think about?
9 PEST: Are we supposed to compute the result?
10 BLOGGER: we are expected to find the missing
numbers
In the above discussion, we can note how the
Boss, in explaining his idea to the group (line 1)
makes a mistake. The timely intervention of the Pest,
in search of clarification (line 3) allows the Boss to
correct his statement. The intervention of the Boss
leads both the Promoter and the Blogger to explain
their idea about the quadruples. The frequent ques-
tions of the Pest (e.g. line 9) lead the Blogger to come
back to the story request and to keep the teammates
focused on what they are expected to carry out. It’s
worthwhile to note how the members of the group
consider the Boss as a reference for the group, asking
his opinion (e.g. line 8).
The above dialogue can be considered fruitful, as
shown by the few interactions between Gianmaria
(the Guru) and Federico (the Promoter) in their pri-
vate chat:
11 GIANMARIA: ehm... how the numbers are ar-
ranged in each row? Have you and your friends
“solved” the enigma? What comes out?
12 PROMOTER: it appears that the second number
is multiplied by the third one minus the first num-
ber by the fourth one. For instance, looking at the
first row (15,16,17,18) we have (16*17-15*18)
13 PROMOTER: the result could change; we should
check computing the result for each row
The suggestions of Gianmaria are reported in the
Group Chat by the Promoter, allowing the whole
group to come out of a stalemate, as shown by the
following excerpt:
14 PROMOTER: my uncle said that we should check
whether the result changes from row to row
15 BLOGGER: I don’t understand
16 BOSS: maybe we should perform the computa-
tions shown in each row and see if the result
changes
17 PEST: we should check whether the result it is al-
ways the same one
18 BLOGGER: are we expected to compute the
mathematical expression?
19 PROMOTER: I think so
20 BOSS: the first one is 2
21 PEST: they are all 2!
22 PROMOTER: so, guys, we may state that in all
the rows the result is 2
The excerpts from the Characters show that they
were able to disclose the consecutivity relation and
regularity of the quadruples at the end of the first ep-
isode. The success of the activity seems to have been
influenced by the conscious appropriation of the roles
by the students and, therefore, by the responsibility
that each specific role implied. This is also high-
lighted by the Observers, as shown below.
BOSS OBSERVER: The fact that the boss recognises
his mistake and cares of the group work is a posi-
tive thing. At the end of the discussion he greatly
helped.
PEST OBSERVER: She [the Pest] is involved by fre-
quently asking questions. So she poses doubts,
stimulating the group to validate what has been
conjectured.
PROMOTER OBSERVER: He recognises the mis-
takes made by the group and look for a correct so-
lution.
BLOGGER OBSERVER: He helps the others and in
my opinion he is working well. He is carrying out
all the steps correctly and is arranging the email to
the promoter’s uncle despite the difficulties.
6 CONCLUSIONS
In this paper we presented an overview of a research
project aimed at investigating how to promote some
of the attitudes of a mathematician. To this aim, we
used an immersive storytelling approach where stu-
dents can experience the whole process and skills in-
CSEDU 2020 - 12th International Conference on Computer Supported Education
426
volved in a mathematical discovery. The mental ac-
tivities characterizing such process are the Characters
of the story with their specific roles, and the story it-
self has been carefully designed to address all the
problem-solving steps. Both cognitive and metacog-
nitive aspects were taken into account, engaging the
students with active playing and observation phases
from one episode to the other of the story. We think
that, in the long run, this will help them to interiorise
such roles. It is worth noting that the designed learn-
ing activity is part of their curriculum, so it also in-
cludes individual and collective assessment steps.
The first one allows to make evident to the students
the process and the mental activities constituting the
mathematician’s attitude, and to institutionalize the
mathematical knowledge. The second moves along
the affective level of learning, focusing on the en-
gagement of the student as Characters or Observers.
The implemented technological environment pro-
vides added-value to both students and teachers. In
fact, it allows immediate and persistent access to (far)
more information than in real situation (e.g. chat and
forum transcriptions with the details of all discus-
sions). So, students can really act as Observers with-
out losing any detail. Analogously, teachers have the
real chance to observe their students working in a
more authentic context.
The first trials show the engagement of the stu-
dents and some signs towards the appropriation of the
roles can be recognised.
ACKNOWLEDGEMENTS
This research has been funded by the Italian Ministry
of Education, University and Research under the Na-
tional Project “Digital Interactive Storytelling in
Mathematics: a competence-based social approach”,
PRIN 2015, Prot. 20155NPRA5. We also
acknowledge the teachers Piera Romano e Rossella
Ascione and their students involved in the trial.
REFERENCES
Albano, G., Dello Iacono, U., Fiorentino, G. (2016). An
online Vygotskian learning activity model in mathe-
matics. Journal of e-Learning and Knowledge Society
(Je-LKS), v.12, n.3, pp. 159-169.
Albano G., & Dello Iacono U. (2018). DIST-M: scripting
collaboration for competence based mathematics learn-
ing. In: Silverman J. Hoyos V. (eds). Distance Learn-
ing, E-Learning and Blended Learning of Mathematics,
(pp. 115-131), Cham:Springer.
Albano, G., Dello Iacono, U., Fiorentino, G., & Polo, M.
(2018). Designing mathematics learning activities in e-
environments. In Weigand, H. G., Clark-Wilson, A.,
Donevska-Todorova, A., Faggiano, E., Trgalova, J.
(Eds.), Proc. of 5th ERME Topic Conference “Mathe-
matics Education in the Digital Age” (MEDA), (pp. 2-
10), Copenhagen, Denmark.
Albano, G., & Dello Iacono, U. (2019a). GeoGebra in e-
learning environments: a possible integration in mathe-
matics and beyond. Journal of Ambient Intelligence and
Humanized Computing, 10 (11), pp. 4331-4343.
Albano, G., & Dello Iacono, U. (2019b). A scaffolding
toolkit to foster argumentation and proofs in Mathemat-
ics. International Journal of Educational Technology in
Higher Education 16:4, pp. 1-12.
Bikner-Ahsbahs & Prediger (2014). Introduction to Net-
working: Networking Strategies and Their Background.
In Networking of Theories as a Research Practice in
Mathematics Education (pp. 117-125). Springer.
Bruner, J. S. (1986). Actual Minds, Possible Worlds. Cam-
bridge, MA – London: Harvard University Press.
Ferrari, P.L. (2004). Mathematical language and advanced
mathematics learning. In: Johnsen Hoines, M. & Berit
Fugelstad, A. (Eds.), Proceedings of the 28th Confer-
ence of PME (pp. 383–390). Bergen, Norway.
King, A. (2007). Scripting collaborative learning processes:
A cognitive perspective. In: F. Fischer, I. Kollar, H.
Mandl, & J. Haake (eds.), Scripting computer-sup-
ported collaborative learning: Cognitive, computa-
tional and educational perspectives (pp. 13-37). New
York: Springer.
Leontiev, A.N. (1978). Activity, consciousness, and person-
ality. Englewood Cliffs: Prentice-Hall.
Mellone M., & Tortora R. (2015). Ambiguity as a cognitive
and didactic resource. In: Krainer K., Vondrová N.
(Eds.), Proc. of CERME 9, (pp. 1434-143), Prague.
Pesci A. (2009). Cooperative learning and peer tutoring to
promote students’ mathematics education. In L. Paditz,
A. Rogerson (eds.). Proc. of the 10th International Con-
ference “Models in Developing Mathematics Educa-
tion”. The Mathematics Education into the 21st Cen-
tury Project (Dresda, 11-17 Settembre 2009). Dresda:
Dresden University of Applied Sciences, pp.486-490.
Schank, R. C, & Abelson, R. P. (1977). Scripts, plans, goals
and understandings. Hillsdale, NJ: Erlbaum.
Soldano, C., & Arzarello, F. (2016). Learning with
touchscreen devices: game strategies to improve geo-
metric thinking. Mathematics Education Research
Journal, 28(1), 9-30.
Vygotsky, L. S. (1980). Mind in society: The development
of higher psychological processes
. Harvard university
press.
Weinberger, A., Kollar, I., Dimitriadis, Y., Makitalo-Siegi,
K., & Fischer, F. (2009). Computer-supported collabo-
ration scripts. Technology enhanced learning, Springer
Netherlands, pp. 155–173.
A Technological Storytelling Approach to Nurture Mathematical Argumentation
427