A Technological Storytelling Approach

to Nurture Mathematical Argumentation

Giovannina Albano

, Umberto Dello Iacono

and Giuseppe Fiorentino

Department of Information and Electrical Engineering and Applied Mathematics, University of Salerno,

Via Giovanni Paolo II, 132, 84084 Fisciano (SA), Italy

Department of Mathematics and Physics, University of Campania “L. Vanvitelli”,

Viale Abramo Lincoln, 5, 81100 Caserta (CE), Italy

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.

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https://orcid.org/0000-0002-5119-5413

https://orcid.org/0000-0003-0224-1046

https://orcid.org/0000-0003-1021-3969

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● 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

● 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.

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