2013. Vol.4, No.7A1, 1-10
Published Online July 2013 in SciRes (http://www.scirp.org/journal/ce) http://dx.doi.org/10.4236/ce.2013.47A1001
Copyright © 2013 SciRes. 1
Using Mobile Devices for Teaching Realistic Mathematics in
Nicholas Zaranis1, Michail Kalogiannakis1, Stamatios Papadakis2
1Department of Preschool Education, Faculty of Education, University of Crete, Crete, Greece
2Ph.D Candidate, Secondary Education Teacher, Crete, Greece
Email: firstname.lastname@example.org, email@example.com, firstname.lastname@example.org
Received April 16th, 2013; revised May 17th, 2013; accepted May 24th, 2013
Copyright © 2013 Nicholas Zaranis et al. This is an open access article distributed under the Creative Commons
Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the
original work is properly cited.
New ICT tools allow children to take advantage of new learning platforms as well aiding them effectively
in attaining new knowledge through activities related to their immediate interests and real life scenarios.
Nowadays, computers and digital applications are a part of the daily life of children. In kindergarten edu-
cation, properly designed digital educational activities can become a very powerful educational tool for
efficient and effective learning. The utilization of interactive activities may contribute towards the growth
of learning incentives as well as proper mental development in particular areas; such as mathematics and
science. Mobile devices have new attractive features and provide considerable advantages in the teaching
of mathematics in kindergarten education. Our study proposes the integration of mobile devices, running
our own specially designed learning activity applications, in kindergarten classrooms. These applications
are based on the three levels of Realistic Mathematics Education (RME) targeting fundamental mathe-
matical concepts for the kindergarten level. We intend to gather information on effectiveness of the in-
corporation of these devices and applications as leaning tools for kindergarteners.
Keywords: Preschool Education; ICT; Mobile Learning; Digital Learning Activities; Realistic
The introduction of ICT (Information and Communication
Technologies) in the field of Preschool Education has been a
point of debate and controversy among researchers for an ex-
tended period of time. Due to the highly dynamic introduction
of computers in the educational reality among the Western
society and the influence of related research, computer aided
learning is more realistic than it once was; thus gradually re-
placing any initial resistant reactions towards the use of ICT in
a learning environment. A wide variety of ITC applications
have become increasingly accepted as developmentally appro-
priate education resources for children of preschool and pri-
mary school age (Druin & Fast, 2002; Plowman & Stephen,
2003; Zaranis & Kalogiannakis, 2011a; Zaranis, 2012).
Moreover, modern researchers have expanded the content of
the term ICT to deal not only with the desktop computer but
well as mobile technologies embedded in various devices
(Plowman & Stephen, 2005; Gjelaj, 2013) such as e-toys, digi-
tal cameras, smart games, electronic tables and smart mobile
devices (Voithofer, 2005). Via the Internet, children are now
able to surf and search for information, play games, watch vid-
eos and even make use of numerous online services such as
making and receiving VoIP calls using Skype. There have even
been reported cases of kindergarten children creating and
maintaining their own blog and engaging in online social net-
working. Now digital media and interfacing with new tech-
nologies is a part of day-to-day life for children of all ages (Fi-
Computers not only isolate children but also act as a catalyst
in their social interaction and provide children with additional
opportunities for rich learning activities that are relevant to
their growth characteristics regardless of age. International re-
search studies (Yelland, 2002; Druin & Fast, 2002; Plowman &
Stephen, 2003; Musawi, 2011; Zaranis, 2011; Zaranis, 2012) on
the introduction of computers in preschool education show that
computers in the classroom have positive results in regard to
the learning of different subjects.
ICT can play an essential role in achieving the goals of the
kindergarten curriculum in all areas and subjects (Plowman &
Stephen, 2003; Chronopoulou & Riga, 2012) if the provided
developmentally appropriate software applications (Haugland,
1999; Lee, 2009) are embedded in appropriate educational sce-
narios (Zaranis & Kalogiannakis, 2011b). In addition to the
educational purpose, the use of computers in kindergarten is
characterized mainly as a learning activity while the common
child will see it as a game of sorts. Like many researchers, in
formal and informal settings, we strongly endorse the need to
focus our investigations on meaningful learning through play-
ing. It is now clear that the use of this learning process is more
than adequate in achieving given educational goals for children
at the preschool and primary school levels (Plowman &
Stephen, 2005; Zaranis, 2012).
In the classroom, ICT is treated as a learning tool (Zaranis &
Kalogiannakis, 2011a). For the students, ICT is a means for
achieving familiarity with new technologies as well as being a
N. ZARANIS ET AL.
tool of investigation, communication and understanding across
the full range of the cur riculum.
In recent years, with the emergence of smart mobile devices,
several researchers (Lam & Duan, 2012) have proposed the use
of mobile devices for learning. There are multiple advantages
with respect to the use of said devices in the learning process
including stimulus, motivation, ease of use, availability, etc.
(Vavoula & Karagiannidis, 2005). Such devices are becoming
highly valuable tools in the educational process because of their
attractive features (Klopfer, Squire, & Jenkins, 2002). Mobile
devices are portable, more affordable, in relation to desktop
computers, offer the opportunity for learning without local
restrictions, use the possibilities offered by the wireless mobile
technologies for easy access to information, promote the de-
velopment of digital literacy, provide opportunities for inde-
pendent learning, facilitate people with disabilities etc.
Shuler (2009) stated that applications on smart mobile de-
vices have the potential to become the new means of providing
educational content to students. As mobile technologies play an
increasingly prominent role in the lives of children worldwide,
national ministries and schools are experimenting with the use
of these popular devices for a wide range of alternative methods
of teaching and learning objectives. Smartphones and tablets
are among of the six new emerging technologies that may have
a major impact on teaching, learning, and research in primary
education (Johnson, Smith, Willis, Levine, & Haywood, 2011).
Particularly in the subject matter of mathematics, Zaranis
(2011) made a comparison between the learning outcomes of
computer based teaching and mathematical thematic teaching;
more specifically, targeting the teaching of “Realistic Mathe-
matics” for children ages 4 to 6 years old in Greek Kindergar-
ten. Compared to the traditional thematic teaching method,
results showed that computer-assisted learning may signifi-
cantly enhance the development of mathematical skills and the
cultivation of a deeper perceptual ability for the pupils (Zaranis,
2011; Zaranis & Kalogiannakis, 2011b).
The main purpose of this study is to provide a better under-
standing of the characteristics and the effect of ICT, especially
mobile learning, in the context of kindergarten education. We
will try to achieve the above through a systematic literature
review on the introduction and use of ICT and smart mobile
devices in kindergarten education. In particular, we will study
the use of educational applications in the form of digital activi-
ties for preschool education. This paper will also present the
first phase of an instructional intervention that utilizes a series
of educational applications designed according to the principles
of Realistic Mathematical Education. Our research materializes
in the form of digital activities performed on smart mobile de-
vices. These activities consist of comparison, sorting, matching,
structured counting, efficient counting and the general knowl-
edge of numbers exercises.
The originality of this work lies in the fact that it is the first
study carried out in the field of kindergarten education in
Greece. It attempts to take advantage of the children’s existing
familiarity with the use of smart mobile devices (tablets) to
provide a benefit to the learning process. In the context of this
document, a detailed and systematic effort will be made to-
wards achieving a theoretical justification for the implementa-
tion of reformed teaching proposals.
ICT and Children as “iLearners”
Researchers Christie and Johnson (2009) indicate that digital
media has now permanently settled in the lives of young chil-
dren. As pointed out by Lavidas, Komis, & Gialamas (2012),
many times children surpass adults in their modern technologi-
cal knowledge even before attending kindergarten. Hertzog and
Klein (2005) define a distinct line between the current genera-
tion of children and their parents. They very aptly report that
children do not need to adapt to the new technological society
because they were born in it; unlike their parents who have
acquired their technological knowledge as somewhat of a for-
eign language at an advanced age. Consequently, according to
Prensky (2001), young children can be described as “digital
natives” since they are growing up in the digital world. Most
recently, Prensky (2010) refers to today’s students as “iLearn-
ers” deriving from the fact that digital devices such as smart-
phones and tablet computers dominate the daily lives of chil-
dren in Western societies from the age of 6 months.
The Lieberman, Bates and So (2009a) report that several
studies have shown that digital media can introduce children to
abstract concepts that were previously considered too advanced
for their age. In her research, Yelland (2005) has shown that
activities entailing the use of digital media, within the school
environment, facilitate collaborative learning for young chil-
dren and the development of logical thinking while reinforcing
their ability to solve problems. Digital learning activities may
encourage children to work together. They have been found to
be more effective than traditional learning activities (Zaranis,
2011; Zaranis & Kalogiannakis, 2011a).
Young children have access to new technologies not just in
the school environment but also out of school, at home (Plow-
man & Stephen, 2005; Somekh, 2007). For some children, the
first educational experience with computers begins in the kin-
dergarten age, between 4 to 6 years old. Existing studies have
shown that children of this age can successfully handle com-
puters with the appropriate instruction (Zaranis, 2011; Zaranis
& Kalogiannakis, 2011a). In a study of the comparison between
learning at home and in the kindergarten classroom, Plowman,
Stephen and McPake (2010) found out that ICT is used to pro-
mote three main areas of learning. The extension of knowledge
about the world (cognitive objects), the acquisition of func-
tional skills (such as the operation of the mouse) as well as the
development of the propensity for learning (by strengthening a
range of emotional, social and cognitive functions of learning).
Recent studies have identified a number of emerging digital
devices, such as tablets, as being appropriate for the education
and entertainment of children (Verenikina & Kervin, 2011).
Lieberman et al., (2009a) commented that young children age
three to six years old play with a vast variety of digital learning
activities, now available on desktop monitors and portable
screens, spending a constantly increasing amount of time doing
Furthermore, Couse and Chen (2010) state the advantages
offered by the use of mobile devices with touch screens com-
pared to typical computer applications controlled by a mouse.
The significant potential offered by tablets should also be noted,
as they are not only useful and portable, but also more afford-
able compared to laptops (Leoni, 2010). The acquisition cost of
applications is very competitive and often includes the ability
of a user to download a “light,” often free, or trial version of
applications. Fuegen (2012) identifies tablets as compact lap-
tops with optimized operating systems, devoid of a physical
keyboard, however, provide interactive capabilities via built-in
functionality and the use of third party applications (mobile
Copyright © 2013 SciRes.
N. ZARANIS ET AL.
apps). Similarly, the term smartphone describes mobile phones
which, besides the usability of voice data over cellular networks,
have similar features and characteristics of tablets but with a
smaller screen size.
Orlando (2012) commented that portable devices fit perfectly
in the lifestyle of young children as they do not need to sit at a
table or an office to use the device, they do not need to handle a
mouse, while the interface offered with a single touch on the
touchscreen is irresistible. Children now use the new technol-
ogy at a younger age than ever before (Common Sense Media,
2011). A study including Australia, New Zealand, USA and
Great Britain showed that most children ages two to five years
are more able to interact with a tablet than to tie their shoes
(Orlando, 2012). Moreover, the possession of smart mobile
devices by children ages four to fourteen years old has doubled
since 2005 (NPD Group, 2008).
According to a survey by the MDG Advertising Company
(2012), preschoolers today make use of mobile devices more
than ever in the past. The same survey indicated that more than
half of all first time iPad and iPod device users are children
under the age of five. However, not all researchers explicitly
support the use of smart mobile devices by young children.
Banister (2010) notes the lack of research on the use of tablets
in education as they have only recently been introduced into the
market. In addition, Marsh (2010) advocates the “dichotomy”
that arises between the activities at hand and the technology
supporting it. He claims that the emerging phenomenon of
“digital activities” differs from that of the spontaneous chil-
dren’s play because the digital activity depends largely on, and
is often limited by, the actual design of the software and hard-
Learning via Mobile Devices
Sharples, Taylor and Vavoula, (2007) define mobile learning
as any kind of learning that takes place in learning environ-
ments and areas which take into account the mobility of tech-
nology, the mobility of learners and the mobility of learning.
Mobile learning through the use of tablets and smartphones
presents new opportunities for strengthening the learning ex-
periences in ways that simply other devices cannot achieve
(Lam & Duan, 2012).
High-resolution screens allow tablet users to share static
content and resources such as images and videos in an easy way.
Most tablets have no phone features making them ideal tools
for education since disruptive elements for the learners’ atten-
tion such as incoming text messages or unwanted calls that are
present in phones and smartphones alike, are absent. Tablets are
able to offer the benefits of mobile applications in a broader
context in all levels of education, not only as an affordable
solution for one-to-one learning but also as a feature rich tool
for work inside and outside the classroom.
Wakefield and Smith (2012) indicate that the technological
analysts characterize the tablet as an ideal tool for all levels of
education. After the introduction of tablets in the classroom of
several schools in the United States, students report that they
want to participate in learning activities due to the novelty of
the medium, the visual characteristics and ease of use. In the
classroom, tablets can be used to create text, audio or video
notes. Students, independent of age, can store educational ma-
terials in a digital portfolio. Using a tablet, learning can be
achieved through the active participation of students and the
use of interactive activities and animations. Additionally, the
attractive appearance of the working environment and the in-
novative touch interface are considered key learning facilitators
for young children and students with learning disabilities. The
characteristics of tablets including light weight, portability,
touch screen, large icons, speakers, voice commands, zoom
features and the cognitive simplicity are some of the key ad-
vantages that make them an affordable and more than efficient
tool for the education of young children (Buchanan, 2010).
At least 1000 universities and colleges create and distribute
free educational content in a format suitable for reproduction on
smart mobile devices (MDG Advertising, 2012). According to
McManis and Gunnewig (2012), this fact creates new require-
ments from the devices users as well as other opportunities for
innovative services through these devices.
Several governments worldwide have given special attention
to the development and implementation of mobile learning in
order to improve teaching and learning effectiveness. Lam and
Duan (2012) state that pioneers in this initiative are not only the
governments of developed countries but also of developing
countries that have begun to adopt policies and measures for the
development of mobile learning. Characteristically, they indi-
cate that the Royal Thai Government plans to provide tablets to
800,000 students of all educational levels by the next school
year. As early as 2011, an initiative of the Indian government
was to build the cheapest tablet in the world. It was sold to
students at a subsidized price of 35 dollars, implementing the
transition from the traditional to mobile learning in a faster and
easier way. Simultaneously, the Turkish government announced
that it plans to spend 8 billion dollars for the purchase of 15
million tablets, which will be distributed among school-age
children throughout the country.
Finally, as reported by Kenny and McDaniel (2011), while
overcoming past misconceptions that perceived the use of
technology only as electronic gaming and play among students,
many teachers and schools united are beginning to allow stu-
dents to bring their own smart mobile devices into the class-
room; especially since recent studies have shown that video
games, including learning activities, have become an integral
and essential part of the way in which young people learn.
Mobile Devices in Kindergarten Education
Egan and Hengst (2012) show that, even though educational
software has been available almost 30 years now, the educa-
tional community of kindergarten education initially resisted
the use of computers in the teaching of young children. Many
educators, inspired by Piaget’s theory of the developmental
stages of children, considered that young children need only the
physical activity and the ability to handle tangible objects in
order to consequently achieve understanding of the various
abstract concepts. However, since the mid-1990s, researchers
found that virtual manipulations which are facilitated by com-
puter software are similar to physical manipulations and there-
fore, the use of ICT could effectively support the learning
process, particularly in mathematics, and the educational de-
velopment of children as a whole (Yelland, 1998; Clements,
Nowadays, the use of ICT in the education of young children,
as well as the development of educational software and relevant
activities in preschool education, has already spread in many
educational systems (Druin & Fast; 2002; Plowman & Stephen,
Copyright © 2013 SciRes. 3
N. ZARANIS ET AL.
2003; Zaranis, 2011; Zaranis, 2012). Research results point out
the potential of ICT as a teaching tool (Segers & Verhoeven,
2005) and as a cognitive tool (Clements, 2000; Klein, Nir-Gal,
& Darom, 2000). Such results seem to formulate a common
agreement at the level of educational policy and school prac-
tices that promote the rational integration of ICT in early
childhood education (NAYEC, 1996; Yelland, 2002; Plowman
& Stephen, 2003; Bolduc & Lefebvre, 2012). Several studies
indicate that computers are developmentally appropriate tech-
nological resources for pupils of preschool and primary school
education and show how technology can be used to support and
encourage the development and learning in these age groups
(Musawi, 2011; Zaranis & Kalogiannakis, 2011a).
The integration of mobile devices into the preschool curric-
ula aims at strengthening the interest of young learners and in
enhancing their participation and cooperation with their class-
mates and teachers (Lindahl & Folkesson, 2012). According to
Nix (2005) this type of learning attracts the interest of young
students and it is considered both an enjoyable experience and
an attractive learning environment. Rushton, Juola and Larkin
(2009) point out the need for proper learning conditions and
indicate that children learn more easily in positive and encour-
aging learning environments. These said learning environments
allow the students to make their own decisions regarding which
topic to study out of their own free will. Rushton (2008) states
that the creation of a classroom environment that enhances
student expression and selection opportunities provides a wel-
coming atmosphere towards helping children to learn at their
own pace. Learning environments, which through various me-
diums provide differentiated teaching to young learners, allow
children to be actively responsible for their learning, by simul-
taneously stimulating various areas of their brain thus resulting
in better intellectual development (Rushton & Larkin, 2001).
The portability of tablets allows children and kindergarten
teachers to make use of various locations in the classroom ena-
bling the creativity and collaboration of small groups of stu-
dents. Additionally, the sophisticated user interface of tablets
allows both individual interaction and often, mutual interaction,
depending on the application at hand, between two or more
children (Wakefield & Smith, 2012).
Research findings (Abrams, 2009; Jenkins, 2009; Dickens &
Churches, 2011 as cited in Peluso, 2012) correlate the effect-
tiveness of learning through educational content delivery based
on touch screen technology. A study by Chiong and Shuler
(2010) in the United States involving iPod touch devices and
audiovisual material properly configured for children ages three
to seven years old showed that children drew remarkable gains
in vocabulary and phonological awareness. Another recent
survey by Bebell, Dorris and Muir (2012) on kindergarten stu-
dents selected randomly to use tablets for the study of literacy,
showed that infants who used tablets recorded remarkably
strong performance in their phonological awareness and their
ability to represent sounds with letters in relation to other chil-
dren that did not.
Sandvik, Smørdal, and Østerud (2012) point out that as well
as tablets are highly portable technology, learning can take
place in a variety of everyday activities in the kindergarten, in a
formal and informal context, inside and outside the classroom.
As reported by McManis and Gunnewig, (2012), the new digi-
tal tools, such as smart mobile devices and their accompanying
applications, can offer unique opportunities for kindergarten
children to participate in useful and targeted activities; either
individually or collectively with their peers and their kinder-
Digital Activities and Children
The introduction of smart mobile devices in the daily life of
children positively supports integration of digital applications
in childhood education. There is a positive continuum between
the everyday life of children and their school life. Moreover, it
is important that the technological instruction offered by the
school equips children with the necessary knowledge and skills
for later life as well.
Digital learning activities on mobile platforms are very
popular among students, especially at younger ages. Particu-
larly, in the last few years, the accession bid of educational
digital activities as teaching tools in the educational process has
increased. The term electronic or digital activity refers to all
categories of activities that are implemented through digital
technology. It concerns activities and games that run on large
classic game consoles, specialized consoles, personal com-
puters, smartphones and tablets (Chiong & Shuler, 2010). Re-
searchers such as Klein et al., (2000), Lewin (2000), Segers and
Verhoeven (2005), Comaskey, Savage and Abrami, (2009),
Zaranis and Kalogiannakis (2011b) document the positive im-
pact of digital applications in the educational development of
preschool age children. Other studies show that electronic ac-
tivities and games attract children and seem to stimulate them
in a more constructive manner than the standards the conven-
tional education has adopted so far (Klawe, 1999; Prensky,
2001; Zaranis & Kalogiannakis, 2011a).
Since the early 1990s, the trend has been that of edutainment.
This refers to the blend of gaming and educating based on the
logic of activities developed with clear educational orientation
(Shaffer, Squire, Havelson, & Gee, 2005). The contribution of
digital activities lies in the fact that they allow children to par-
ticipate in worlds in which they learn to think, speak and act in
new ways. Being rich in features, these virtual worlds constitute
a very promising framework for learning, as children can play
many different roles (Squire & Jenkins, 2003; Shaffer et al.,
2005; Squire, 2006). Digital activities are considered to be par-
ticularly effective when they are designed to examine a specific
problem or to teach a specific skill. For example, encouraging
learning in the thematic areas of the curriculum such as mathe-
matics, natural sciences and language where the specific objec-
tives can be determined and when it is selectively developed
within a context relevant to the learning activity and the spe-
cific target (Johnson et al., 2011).
For children aged three to five years old, educational digital
activities often focus on readiness skills for the kindergarten,
including reading (letter recognition, letter formation, correla-
tion of sounds and letters, simple spelling), mathematics (rec-
ognition of numbers, formation of numbers, counting, group-
ing), thinking and reasoning skills, perceptual skills, daily life
skills (hygiene), social skills, creativity and self-expression; as
well as the understanding of concepts such as family relations,
emotions, professions, etc. (Lieberman, Fisk, & Biely, 2009b).
Lieberman et al., (2009b) distinguish the quality of digital
learning activities in the following categories:
Well-designed activities—provide powerful interactive ex-
periences which can enhance the learning of young children,
fostering skills development, as well as their healthy de-
Copyright © 2013 SciRes.
N. ZARANIS ET AL.
Poorly designed activities—simple sedentary activities that
contribute little in children’s learning, skills development or
their healthy development while potentially associated with
obesity and poor physical condition;
Very poorly designed activities—can potentially cause con-
siderable damage to child ren either through st rengthening the
aggressi ve or antiso cial be haviour, appr obating e thnic or trans-
gender stereotypes and promoting bad eating standards.
A finding of several studies in children three to six years old
correlates the benefits of using digital activities in different
sectors (Figure 1).
More specific benefits are identified in the following sectors:
Learning—Digital activities can provide considerable edu-
cational services to children. Comparative studies have sug-
gested that well-designed educational activities provide po-
tentially more motivation and result in encouraging learning
compared to traditional teaching methods (Swing & An-
Cognitive skills—Using digital activities, children learn
cognitive skills through repetition, as relevant studies have
found improvements in operating memory, spatial ability,
visual attention, etc. (Thorell, Lindqvist, Bergman, Bohlin,
& Klingberg, 2009);
Social interaction—In preschool education, young children
often engage in cooperative social interaction when playing
digital activities (Christie & Johnson, 2009).
If materials for play and learning (including computer active-
ties) are designed to indulge the interests and abilities of chil-
dren, as well as their instinct to learn, students are more likely
to develop and strengthen their initiative, their attention, their
industriousness and their love for learning (Kagan & Scott-
Little, 2004; Sadowski, 2006).
However, as pointed out by Garrison and Christakis, (2005)
not all digital activities are developmentally appropriate or
meticulously designed to enhance the procedure according to
which young children play and learn.
The foundations of children’s mathematical thinking form in
the early years of their life. They gradually acquire their first
experiences with time and space then with basic mathematical
processes (measurement, calculation, sorting and comparison)
(Gadzichowski, 2012). Research findings prove the existence of
logical principles for counting from the age of three (Gelman &
Meck, 1983). Other researches indicate that numbers and nu-
merical phenomena sparks the intense interest of children from
an early age (Zaranis & Kalogiannakis, 2012). Mathematics in
preschool education is approached as a foundation that will
help children learn about the world around them and to adapt to
this world (Tzekaki, 2007; Zaranis, 2012). Egan and Hengst
Benefits of the use of digital activi-
ties by young children.
(2012) report that a large body of research shows that the time
spent in the kindergarten is a crucial period for children to de-
velop fundamental numeric skills. In their research on the de-
velopment of mathematical concepts in kindergarten, Clements
and Samara (2007) concluded that the numerical abilities of
children, developing before they enter the first grade of primary
school, are the best predictors of their subsequent mathematical
progress; more than other skills. When monitoring 200 students
from the kindergarten up to the third grade, Jordan, Kaplan,
Ramineni and Locuniak, (2009) concluded that the conquest of
mathematical concepts in the kindergarten is positively corre-
lated with the achievement of high mathematical performance
at the end of the third grade.
Consequently, the teaching of mathematical concepts in the
kindergarten has a huge significance, as it assists children to
acquire the necessary mental condition and the necessary cog-
nitive foundation for the systematic learning of “real” mathe-
matical concepts, later on, in primary school. The aim of kin-
dergarten is not just to teach mathematics but to initiate chil-
dren in ways of thinking that characterize the mathematical
science while providing a parallel realization of their social
For many years, the central theme for scientific debate was
the formulation of a comprehensive mathematical theory to-
wards interpreting phenomena related to the teaching and
learning of mathematics. Such a theory aimed to provide edu-
cators with the ability to help students understand mathematics
as a subject and as a tool for solving everyday problems. Over
the last few years and in the context of the above considerations,
various reform proposals for the teaching of mathematics have
been developed internationally, posing their focus on the prob-
lem solving procedure. One of these proposals is the Realistic
Mathematical Education (RME) which was developed in the
Netherlands and supports the view that the same phenomena
through which the mathematical concepts acquire content,
should be used as a basis for a teaching process that aims to
impart these concepts (Freudenthal, 1983).
According to Freudenthal (1983), mathematics is a human
activity and therefore it must constitute a human value, must be
close to reality of fact, be close to children and have a relation-
ship with society. The central idea of the Realistic Mathemati-
cal Education is when saying, “I know math” really means “I
know how to do math” (Streefland, 1991). The student becomes
able to easily handle the mathematical language, to solve and
construct problems, but mainly, to recognize mathematical
concepts within specific situations. The term “Realistic Mathe-
matics” refers to mathematics, which relate to problems of the
real world as well as to phenomena, which appear in our daily
life (De Lange, 1996). This form of mathematical education is
characterized as “realistic” because it relates to the real world,
in addition, to that special emphasis given in situations in which
the students can envisage with their imagination.
The digital learning media can contribute to the learning of
mathematical concepts by young children. Many aspects of
early informal learning of mathematical concepts, such as enu-
meration, arithmetic problem solving, and spatial syllogism
along with general geometrical knowledge, are developed dra-
matically during the preschool age. Therefore, digital technolo-
gies and accompanying software that teach early learning of
mathematical concepts have received considerable attention
from the scientific community (Lieberman et al., 2009a). The
use of mathematics-related computer programs in preschool
Copyright © 2013 SciRes. 5
N. ZARANIS ET AL.
children leisure activities enhanced the mathematical knowl-
edge of those children (Starkey, Klein, & Wakeley, 2004). Jor-
dan et al., (2009) report in a similar study, that young children
were able to develop mathematical skills and relevant reasoning
and thinking skills while using developmentally appropriate
Today, the use of mathematical technology in kindergarten
education and the first primary grades is a standard. It is in-
cluded as one of eight Standards for Mathematical Practice in
the Common Core State Standards for Mathematics (Common
Core State Standards Initiative, 2010). The principles that un-
derpin the Realistic Mathematical Education constitute a
framework in which technology could offer significant assis-
tance in the teaching and learning of mathematics (Clements,
A Proposal for Teaching Realistic Mathematics
through Mobile Devices
Currently, within the Faculty of Education, Department of
Preschool Education, University of Crete, systematic research
is being carried out in order to investigate whether there are
compelling benefits to using tablet computers in preschool
education in an attempt to implement teaching reform proposals,
such as Realistic Mathematical Education and the Natural Sci-
ences. This proposition is carried out by creating educational
applications for the mobile device platform in the form of digi-
tal learning activities, using specialized software (App Inven-
tor). These applications intend to help preschool children in
learning mathematics by following the principles of RME, fo-
cusing primarily on the existence of rich thematic frameworks
associated with a child’s experiences. For this reason, digital
applications are combined with group and individual activities
without the use of a tablet including board games, dice, active-
ties with given and hidden objects, etc. This form of digital
application was chosen because studies (Nix, 2005; Vavoula,
Pachler, & Kukulska-Hulme, 2009) have shown that digital
educational activities are not only appealing to the students’
interest but are also considered to be a pleasurable pastime
while establishing a new and attractive learning environment.
Today’s students are more likely to enjoy a learning experience
embedded with digital activities because these games are based
on the primordial form of learning “play and learn” from which
they derive their benefits as an educational tool (Squire, 2006).
Specifically, we have developed sixteen different activities
that cover four levels of mathematical intervention (ground or
zero, first, second and third) based on the principles of RME for
preschool education (Van Den Heuvel-Panhuizen, 2008; Zara-
nis, 2011, 2012). The purpose of the next step of the research is
to extensively implement such applications and other educa-
tional activities in kindergarten classrooms in order to system-
atically evaluate their integrity and educational use compared to
the traditional method of teaching.
According to Van Den Heuvel-Panhuizen (2008), the knowl-
edge of formal mathematical concepts may differ considerably
from child to child when entering into kindergarten. To elabo-
rate, some of these children are quite familiar with simple
counting while other children are not. Likewise, the extents to
which they are capable of distinguishing between the different
meanings of numbers may vary. The understanding of resulta-
tive counting children have developed upon entering to kinder-
garten differs significantly too. The somewhat variable initial
situation in which the children’s different initial levels of ma-
thematical knowledge upon beginning the kindergarten could
be described as the ground level. In general, an elementary
numerical sense develops before and during the preschool edu-
cation, in four general levels (Figure 2).
In addition to the pre-existing ground level, the three general
levels that are developed during kindergarten education are as
First level—The level of context-bound counting and calcu-
lating simple addition and subtr action;
Second level—The level of object-bound counting and cal-
culating simple addition and subtraction problems where
the objects are displayed and then hidden;
Third level—The level of pure counting and calculating ad-
dition and subtraction with the use of a missing variable.
The first level consists of context-bound situations in which
pupils are instructed to count up to ten, organize numbers in the
proper order, and make reasonable estimations or comparisons
of numbers through concepts of more than, less than or equal
too. Basic addition and subtraction problems are introduced at
The relevant object-bound counting and calculating of the
second level, which occurs in problem situations, focus directly
on the quantitative aspect. In contrast to the first level, ques-
tions asking that the students count and state the number of
given objects, in a given scenario, are presented and understood
in the second level. This applies, however, only if the questions
asked are associated with specific objects involving natural
numbers. The second level also consists of activities in which
pupils able to choose an appropriate strategy for solving simple
addition and subtraction problems in which the objects at hand
are displayed for a brief period of time before they are hidden.
The following are several examples of level two questions:
How many pieces of candy are in the box? How many chairs
are there? How many people are waiting in line? Which box
has the most sweets? How many of the seven candles will re-
main lit if the wind blows out three?
Finally, the third level consists of pure counting and calcu-
lating, questions using real numbers, rather than objects, focus-
ing on the aspect of a missing variable. For instance, “What
will remain if you subtract three from seven?” By previously
hiding objects after a brief period of time (second level), chil-
dren were obliged to use their fingers or other representations
for more the complex tasks as the visual objects were being
removed from the equation. This way, the enumeration is no
longer dependant on the objects themselves, and is instead put
into perspective using physical or mental representations of
these objects. These representations can occupy different levels
of abstract problems including the use of real numbers in addi-
Levels of realistic education in kindergarten education.
Copyright © 2013 SciRes.
N. ZARANIS ET AL.
tion and subtraction problems with a missing variable.
As Van Den Heuvel-Panhuizen (2008) claims, this can occur
by using a “birthday hat” but there are other possibilities, such
as the kindergarten teacher asking the children to describe their
age without using words. At the third level, children can repre-
sent the numbers one to ten using their fingers, as well as by
using lines and dots. They are then able to use these skills for
addition and subtraction activities. The use of numbers and the
execution of the arithmetic operations used in the third level are
not generally one of the targeted objectives of the kindergarten
curriculum but there are usually children who are able to work
at this level.
At the ground or zero level, students are instructed to use
various portable applications. In one of the applications, for
example, they have to place a certain number of chicks in their
nest or to count the number of animals that appear on the screen
(Figure 3). Variables are randomized numbers from one to ten
for each round.
The other tasks at hand are to help a climber pass over
mountains, counting each mountain on the way and to a help a
monkey down a ladder, counting each rung as it descends (Fig-
At the first level the children are expected respond to ques-
tions such as, “How many of the apples in her basket can Helen
buy with 5 euro if each fruit costs 1 euro?” Another example
problem is, “Each child needs a ticket to enter the castle. How
many children will not be able to enter?” (Figure 5).
At the second level the children are asked to solve problems
such as, “Place as many eggs as you would like in the fridge,”
after the selection is made the eggs are concealed. “Helen came
and took 1 egg from the fridge. How many eggs are left?” (Fig-
Finally, for the third level applications, pupils are told to
answer more complex questions such as, “Johnny has 5 pieces
of candy. His uncle came and gave him some more candy . Now
Johnny has 8 pieces of candy. How many pieces of candy did
his uncle give him?” Alternatively, in the case of subtraction,
the children are told that a monkey has cut a number of bananas
from the tree. Some of his animal friends suddenly appear and
Examples of ground le ve l portable applications.
Examples of ground le ve l portable applications.
Examples of fir s t l ev el portable applications.
Example of a second level p o rtable applications.
eat an unknown number of those bananas. The remaining ba-
nanas are displayed and the children are asked to find the num-
ber of bananas that were eaten (Figure 7).
Considering the categorization of Naismith et al., (2004), we
can claim that from a pedagogical point of view, the mobile
applications we created follow either the behavioral or the con-
structivist teaching method. Some applications follow the be-
haviorist perspective by providing fast and immediate feedback
while utilizing reinforcing learning elements like the confirma-
tion of the correctness of an answer. Others utilize the construc-
tivist perspective as they provide open type learning experi-
ences for the students. All applications provide feedback both
in the case of error as well as the successful completion of an
activity. This feedback is in both visual and audible form so
that it is easily understandable by pupils. Simple feedback is
provided through graphic characters (e.g. the appearance of a
happy or sad face), while more complex feedback is provided
by the narrator through an audio message (e.g. “Try again,” or
“Well done, you did it!”).
The applications were created using the application devel-
opment software App Inventor (AI) and were tested on the
Android operating system. Android was preferred over the iOS
operating system (Apple) mainly because of its flexibility for
the creation of applications as well as the existence of a very
large variety of available devices with various price ranges and
features. AI was first announced as a small project of Google
Labs at the end of 2010. In late 2011, it was moved to the cen-
ter of mobile learning in MIT (Massachusetts Institute of
Technology) for public use as open source software (http://
appinventor.mit.edu/). AI is a new free online block based vis-
ual development environment for creating mobile applications
of the Android operating system (Hsu et al., 2012).
The design process of the educational software had three
The research and development of the original applications
prior to their impl ementation in kinder garten;
The modification of the existing applications during the
pilot test in order to respond more effectively to the needs
of children and kindergarten educators;
Copyright © 2013 SciRes. 7
N. ZARANIS ET AL.
Examples of thir d level portable applications.
The creation of new applications that meet the demands of
The produced software should have the following character-
istics: 1) It should be user-friendly so that children can easily
handle it without any special assistance from an adult; 2) It
should not require any reading and writing knowledge for its
use so that it is suitable for the preschool age; 3) It should com-
bine animation and sound. At the preschool age, sound is es-
sential, as speaking is the only way to give instructions to chil-
In order to examine the children’s knowledge in the compa-
rison, classification, matching, structured counting, efficient
counting, basic addition and subtraction and general knowledge
of numbers, we will most likely use the Utrecht Early Mathe-
matical Competence Test (for children aged 4.00 - 7.05). This
criterion was designed by a team of scientists from the depart-
ment of special education at the University of Utrecht in the
Netherlands, in order to be used for the assessment of early
mathematical competence in preschool age children (4.06 - 7. 05)
(Van de Rijt, Van Luit, & Pennings, 1999). In 2008, the
weighting of this criterion in Greece led to the expansion of the
age range for six months. We will use all of the worksheets
from this test, because we assume that it is suitable for the pur-
pose of our research.
As already mentioned, the purpose of this paper was to pro-
vide a better understanding of the characteristics and the effect
of ICT and mobile learning in the context of preschool educa-
tion. In addition, we will try to examine children’s knowledge
by comparing the learning outcomes of teaching using specially
designed applications for smart mobile devices (tablets) and the
thematic teaching in mathematics; specifically targeting “Real-
istic Mathematics”, for children ages 4 to 6 years attending
Although the research is still in a preliminary stage, initial
results of the statistical analysis of pre tests (which were held in
a small sample of kindergarten students in specific geographic
regions of Greece) allow us to assume the following:
The tablet aided learning compared to the traditional teach-
ing method produces better learning outcomes for the stu-
The teaching of Realistic Mathematics with the use of edu-
cational software for tablets produces better learning out-
comes in relation to teaching based on the Greek Cross
Thematic Curriculum Framework (CTCF, 2003).
With great interest, we look forward to the learning outcomes
that result from the teaching intervention using a large and
properly weighted sample of kindergarten students. We intend
to expand our research in kindergartens located in all geo-
graphical regions of Greece in order achieve a larger possible
representative sample distribution.
Quite often, the debate on the use of ICT in mathematical
education is limited by and focused on the tool itself rather than
on the activities and in the specific problem situation that the
student is presented. In contrast, the activities and applications
that we have created refer to real world problems and situations.
The next stage of the research will be carried out in kindergar-
ten education in order to systematically evaluate the integration
of ICT and its educational benefits compared to the traditional
method of teaching.
This study is preliminary in its nature, as our research serves
to demonstrate a potentially greatly beneficial installation of
mobile learning in childhood education. With the execution of a
systematic study, we believe that our findings will contribute to
the acceptance that the positive effects derived from the use of
mobile devices and ICT in kindergarten in general, do not exist
only in the presence of a computer in the classroom, but also by
the way in which the technology is used by teachers. The pri-
mary concern, therefore, is how to maximize the benefits of
these new instruments in order to enhance, rather than hinder,
children’s ICT experiences for the benefit of learning.
This publication was supported by the Research Committee
of University of Crete (ELKE) http://www.elke.uoc.gr/.
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