Proceedings 2017, 1, 863; doi:10.3390/proceedings1090863 www.mdpi.com/journal/proceedings
Mathematical Operations Visual Dictionary: An
Interactive Support to Teach Math to Children Not
Speaking Italian †
Benedetta Frezzotti 1,* and Giulia Natale 2
1 Studio Platypus, Istituto Europeo di Design (IED), 20100 Milano, Italy
2 PubCoder, 10100 Torino, Italy; email@example.com
* Correspondence: firstname.lastname@example.org ; Tel.: +39-340-550-6094
† Presented at the International and Interdisciplinary Conference IMMAGINI? Image and Imagination
between Representation, Communication, Education and Psychology, Brixen, Italy, 27–28 November 2017.
Published: 21 November 2017
Abstract: The ever-increasing presence in Italian school of Italian L2 children is an established
reality. Language learning is a priority: it is the gateway to all school subjects and “social life” in the
new country. Unfortunately, language learning has its own times, which often collide with
schooling. Consequently, while a child is learning a language, he/she is excluded from many other
subjects, especially scientific, thus accumulating gaps. The mathematical operations visual
dictionary takes traditional language access tools (visual dictionaries) and verge them for
mathematical concepts, implementing traditional illustration with the interactive media declined
through the principle of understanding by doing.
Keywords: illustrations for children; digital book; Image based technologies for teaching;
understanding by doing
The ever-increasing presence in Italian school of Italian L2 children is an established reality.
Language learning is a priority: it is the gateway to all school (academic) subjects and "social life" in
the new country.
Unfortunately language learning has its own times, which often collide with schooling.
Consequently, while a child is learning a language, he/she is excluded from many other subjects,
especially scientific, and he/she might accumulate gaps: “Li Li and Alban, like many other foreign
children, are actually learning many languages at the same time: Italian oral, written language,
disciplinary knowledge and rhetoric, school communication” .
The Mathematical operations visual dictionary  takes traditional language access tools (visual
dictionaries) and verge them for mathematical concepts implementing traditional illustration with
the interactive media declined through the principle of understanding by doing.
The interactive dictionary was created by an Italian software PubCoder® that allows to create
multiplatform apps and books without having to program. The visual dictionary is divided into three
• The first one is a classical visual dictionary. It introduces a visual code, independent from the
language spoken by the users. This part contains the visual translation of numbers from zero to
twenty and introduce the symbol equal and different.
• The second one is the most interactive part. Here, the four basic operations will be explained by
adding the user’s gesture to the traditional visual dictionary: the user can then try the actions
Proceedings 2017, 1, 863 2 of 5
for adding, subtracting, multiplying, and dividing on a sort of augmented digital abacus built
with the shared code in the first part of the dictionary.
• The last part is an Exercise book. It will be physically and conceptually separated from the
dictionary: it is only available by turning the tablet or mobile phone vertically. Here you can
repeat the operations in the dictionary on several variants; have feedback whether you are
operating correctly or not. It also a way to check if a math operation was properly understood;
It is based on pure mathematical calculation with numeric symbols.
2. Materials and Methods
2.1. The Project
The choice of using the visual dictionary as a starting point was based on the knowledge of the
instrument, the experience gained in multicultural environments during years of didactic
laboratories, and on the study of Blissymbols or Blissymbolics: an ideographic writing system called
Semantography consisting of several hundred basic symbols, each representing a concept, which can
be assembled to generate new symbols that represent new concepts. Blissymbols differ from most of
the world’s major writing systems in that its characters do not correspond at all to the sounds of any
spoken language.[…] Blissymbols was invented by Charles K. Bliss (1897–1985), born Karl Kasiel Blitz
in the Austro-Hungarian city of Czernowitz (at present the Ukrainian city of Chernivtsi), which had
a mixture of different nationalities that “… hated each other, mainly because they spoke and thought
in different languages. […] Since the 1960s/1970s, Blissymbols have become popular as a method to
teach disabled people to communicate. In 1971 Shirley McNaughton started a pioneer program at the
Ontario Crippled Children’s Centre (OCCC), aimed at children with cerebral palsy, from the
approach of augmentative and alternative communication (AAC)” .
In Italy it was very useful for me follow Professor Gava  in schools and during some courses
to see how children combine Blissymbols to communicate abstract concept and actions.
2.2. Illustrations and Interactivity: Building a Universal Visual Code for Mathematical Operations
As previously mentioned, the dictionary will be divided into three parts:
• The visual dictionary to introduce the mathematical code: numbers from zero to twenty and the
same and different symbols, to be learnt before to the part related to mathematical operations.
• The interactive part: the visual dictionary for addition, subtraction, multiplication and division
• The exercises
All illustrations have been aesthetically cared but, following the principle that the form should
follow the function, they are not considered narrative illustrations, but visual codes . The first part
of the dictionary will work on the construction of this code by translating visually the equal and
different symbols. This is made possible by repeating a number of examples, sufficient to make it
easy to isolate the ‘=’ symbol meaning (See Figure 1a). Always in the attempt to disambiguate as
much as possible the concept of equal, it is also decided to introduce its opposite: different.
Once the meaning of the symbol ‘=’ is clarified, it will be used to introduce numbers from zero
to twenty (see Figure 1b).
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Figure 1. Creating the visual code. (1a) Equal and different; (1b) Numbers.
After establishing this first code level, the dictionary moves to translate the addition, subtraction,
multiplication and division concepts, mediated by their corresponding mathematical symbol ‘+’, ‘−’,
‘x’, ‘:’. This more complex transition needs interactivity. For its design, we have applied the same
methods applied by Munari in its laboratories : Do to understand.
Pages have been constructed as an interactive abacus on which a child can only do the actions
necessary to understand the concepts of ‘+’, ‘−’, ‘x’, ‘:’: add, subtract, multiply and divide.
This was possible thanks to the ductility of the PubCoder® software, which, although not
requiring programming, is sufficiently modular for experiments of this kind, and allows to update
the interactivity very quickly during the test phase (see Figure 2).
The last part of the tutorial is slightly different from the previous chapters: we add some real-
life photographs at iconic illustrations and mathematical symbols, to recall classroom problems and
to connect reality and abstract mathematical language.
Figure 2. Interactive abacus.
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2.3. Sound Environment
Choosing the sound environment in an app is not secondary to graphic or text choices and it is
extremely delicate. That is why we have made some very specific choices:
• The app could be used in silent mode without losing any basic information.
• It will not contain any continuous or gingle sound. That is because the app could be used by the
teacher to mediate the explanation in the spoken language according with our secondary
objective: use mathematics explanations as a language access tool by connecting sounds abstract
from the Italian language as more, less, equal, with their mathematical concept. Hence, a gingle
could be intrusive or disturbing.
• However, it was decided to give a very discreet sound feedback to the user’s actions. It makes
the app more clear and endearing in the case of child’s stand-alone use.
• As an iconic and functional style was chosen for the illustrations, we decided to take advantage
of the audio to make the app less aseptic: we created the sound feedback system with a
traditional South American toy, a bird ring in ceramic to warm the user experience.
One of the critical aspects in apps production is distribution: although we release a free content,
its visibility in stores is related to search for keywords and number of downloads. That’s why we
decided to include it in the Edook project, an APP/library that collects projects designed for children,
teenagers, teachers, educators, students and creatives; all contents are uploaded free of charge from
PubCoder® and released for free. Projects are available on tablets, cell phones, and LIMs.
There are already two visual dictionaries on the Edook platform: Benvenuto in ABC (Welcome in
ABC) , a multilingual visual dictionary designed for associations and operators who give the first
aid to refugees and asylum seekers. The dictionary consists of 189 interactive illustrations translated
into Italian, English and Arabic. The illustrations were made by about 120 volunteer illustrators and
mounted with the PubCoder® software. His twin app, Welcome to ABCinese, is expanded and declined
for Chinese language.
3. Expected Results
The expected result is to promote math learning in children who do not speak Italian yet, and at
the same time use the mathematical symbol as a moment of access to the second language by
connecting sounds belonging to the Italian language as more, less, equal with their mathematical
The visual dictionary project was born a few years ago as a pop-up book. The problems started
when we understood that is crucial for the child understanding to do a series of moving actions as
explained in the section on interactivity. To permit this kind of action on a pop-up page the project
would require a very complicated paper engineering and therefore an exaggerated user’s cost, in
addition the book would be extremely fragile: it could not be a real educational material, but an object
for enthusiasts of the matter.
Interactivity has freed itself from paperwork constraints and allowed to create the dictionary
and distribute it for free. Thanks to the version that can be used on the LIM, you can take advantage
of existing classroom equipment without additional costs for the school or teachers. We believe that,
in this case, choosing an interactive tool instead of paper does not impinge on the child’s experience
but it is an added value. The experience in traditional publishing was crucial in the final dictionary
review. We applied the same analysis method on our interactive dictionary that system artists such
as Suzy Lee do on paper book, for example in his The trilogy of limit : the plot and illustration are a
game about border between right and left page created by binding. The method of analysis on the
book is also applied by Hameling  network through their own magazine, and the Transbook 
Proceedings 2017, 1, 863 5 of 5
network. In doing so, we apply the traditional analysis on paper book on interactive book, we discard
what was not of interest and enhance what we needed. In concrete terms:
• We abandoned the binding issue, but we have exploited the possibility of having two
overlapping and interchangeable pages to explain the commutative property.
• In the matter of tactile experience, we realized that the screen took away all the possibilities of
paper and its variations, but we were able to explore all the possibilities related to the user’s
gesture and exploit and gesture/cause/effect concatenations.
So we think this dictionary is a reflection experiment on a new language and it certainly must
and will always have a lot to the book, but it cannot stop at a mere copy with a soundtrack of his
Author Contributions: Benedetta Frezzotti is the App Author, and wrote the paper; Giulia Natale and PubCoder
are Publisher on Edook and revised the paper.
Conflicts of Interest: The authors declare no conflict of interest.
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