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Draft – originally published in: Ebner, M. (2015) Mobile Learning and Mathematics. Foundations,
Design, and Case Studies. Crompton, H., Traxler, J. (ed.). Routledge. New York and London. pp. 20.32
Mobile Applications for Math Education – How Should
They Be Done?
Martin Ebner
Department Social Learning, Information Technology Services, Graz University of
Technology, Graz, Austria, martin.ebner@tugraz.at
Abstract. Math education in elementary schools is a necessity. In this
publication we introduce different math applications for iPhone and iPad
developed by students at Graz University of Technology. Both, the technical as
well as the pedagogical strategy of these apps are described. Furthermore, a
close look at the HCI guidelines are taken and finally enhanced with some
crucial facts that in principle an app is able to serve as a learning app for
elementary school children. It can be summarized that the successful use of
math apps in classroom is more than just a playing with the first app that comes
along; it is about a careful design of a didactical approach based on an
appropriate learning strategy.
Keywords: Interaction design, HCI, e-Learning, iPhone, app, learning, game-
based learning
1. Introduction
Looking back over the last 15 years an impressive technological progress has taken
place. On the one side the so-called Web 2.0 (O’Reilly, 2007) enriched our way of
dealing with the World Wide Web; we changed our roles from Internet consumers to
producers (Ebner & Nagler, 2010). With the help of weblogs, wikis, and even social
networks (Ebner, 2013) the way we work and learn (Downes, 2005; Ebner, 2007)
differs considerably from the time before Web 2.0. On the other side new (mobile)
devices were invented and spread the world in a remarkable way and within a
remarkable short time frame. These powerful technologies have made it to the pockets
of our today´s society for the first time; even school children in the age of ten (JIM
Study, 2013; Ebner et al, 2013) own a personal smartphone.
All this led to the famous A3 advantages of e-learning as already proposed in the
1990s – anytime, anywhere, and anybody (Salmon, 2002). The main problem of this
expression was that anytime and anywhere, which was referred to Personal
Computers (PC) with Internet connection, did not work simply because Internet
connections as well as PCs were very statically operating at that time. A learner had
to be on-site to receive all offered learning contents. Furthermore the pre-smartphone
period was dominated by mobile phones without a multi-touch interface, a bad
usability, and mostly no Internet connection. It can be stated that the first research
work in mobile learning done in the early 2000 (Göth, 2004; Taylor, 2006) was not
widely accepted, because of missing technological possibilities.
At least since Apple has placed its iPhone at the market and Google offered its
more open mobile operating system Android mobile learning has become a more
effective learning scenario characterized by the following three crucial factors (Ally et
al, 2014):
• Communication: We are able to communicate about learning content and
our learning processes (e.g. with the use of social media)
• Interaction: We are able to interact with learning content just in time (e.g.
podcasts).
• Applications: We are able to learn with a broad variety of different
applications for numerous learning problems.
In this publication different math applications are introduced according to the
needs of elementary school children in the age of 5-10. From a technical perspective
the developed apps strongly differ from each other; also from a pedagogical
perspective these apps are following different teaching and learning strategies. The
research work aims to ask whether and to what extend math apps can help to improve
the learning and teaching behavior in classrooms of elementary schools. The
introduced apps must be seen as first prototypes implemented following a predefined
didactical approach. Consequently the carried out evaluation is a proof-of-concept
from a technical point of view as well as the apps are working as intended.
2. Theoretical Background
Graz University of Technology (TU Graz) has a long tradition in mobile
application development with a special focus on iPhone development (Ebner et al,
2010). Since 2010 a lecture at the university focusing this subject instructs on average
50 students / year in order to let them build their own mobile application. The
programmed apps have a strong relationship to education especially for young
elementary school children. Due to the fact that math, especially addition, subtraction,
and the multiplication table are one of the most important learning objectives a
number of different apps has been developed on basic arithmetical operation.
Bearing in mind the Apple Definition Statement (ADS)
{your differentiator} {your solution} for {your audience}
and according to the iPad Human Interface Guidelines (2011, 2012) an application
is built for a specific target group. In the broadest sense the target group in our case is
“the learner"; in the strict sense it focuses on school children - to be exact – on
elementary school children. Of course, the official HCI-Guidelines from Apple do not
hold any didactical hints for how to create an adequate app for children; therefore a
research study has been carried out aiming to answer this question (Huber & Ebner,
2013). Huber (2011) also taught the first class in Austria’s elementary school where
school children got an iPad for learning purposes for free. She collected practical
experiences and summarized her results as a proposal about the way such HCI
guidelines must be enhanced in case an application addresses learning aims and is
built for to be used by school children. In this context, the following issues should be
taken into account:
• Aim to support all orientations
• Flatten your information hierarchy
• Add physically and heightened realism: Real life graphics to make user
comfortable
• Multi-touch gestures: Performance of more certain actions
• File handling: Problem of the differences to other PC-based operating
systems
• Keyboards: Use the hidden features (e.g. keyboard separation)
The research study (Huber & Ebner, 2013) concluded with the suggestion that “a
beautiful, intuitive and convincing graphical user interface adds to positive feelings”
of our school children.
3. IPhone Applications
In this chapter all different types of math apps are described which have been
developed by TU Graz for iPhone or iPad over the last four years. Please be sure that
each category addresses its own purpose. In relation to the ADS each category has
even its own differentiator. Finally, from the viewpoint of teaching and learning
strategy each category also has its own learning strategy.
Category 1: Stand-Alone-Learning-Apps
The first category is from both technical and pedagogical perspective the simplest
one. A stand-alone application is just a so-called native app, which is programmed for
a specific mobile operating system and is only able to run on that one. Furthermore, it
is also supposed that the app did not need any registration or date-exchange with a
server on the World Wide Web. In other words, there is no Internet connection
necessary to run the app and it can be really done anywhere and anytime if the mobile
device is available.
From a pedagogical perspective such apps assist self-directed learning. There have
been many further approaches since Diesterweg (1873), Montessori (1909), or Otto
(1914). Nevertheless, the main focus on self-directed learning began with Knowles
(1975) and his definition (Knowles, 1975, p. 18) “Self-directed learning is a process
in which the individual take the initiative, with or without the help of others, in
diagnosing their learning needs, formulating learning goals, identifying human and
material resources, for learning strategies, and evaluation learning outcomes …”. The
learners can use such applications to strengthen their knowledge on a specific topic
without further instructions; they decide it completely on their own. On the other side
instructors have no chance to follow the learning process; they simply get no
information about the performance of the learners.
Exactly for this purpose two mobile iPhone apps with a strong focus on math were
programmed at TU Graz (figure 1):
1. MatheZoo: This app is just a first possibility to get in touch with math. Its
goal is to educate children in the age of 5-6 about the first basic
calculation. The used numbers just range from 1-10. With the assistance
of a high-end graphics the app helps the child to learn addition and
subtraction. The story behind the app is that there is a zoo and in each
station of the zoo the learner have to solve a little math problem.
2. iLearn+: Similar to MatheZoo this app is also for young children who are
doing their first mathematical steps. The storyboard addresses a space
environment where children have to add nicely visualized planets and
stars to each other. Three different levels represent the difficulty of the
calculation as well as the used range of numbers. There is also no high
score implemented, just small graphical feedback.
Both apps have in common that they are just for training and self-determined
learning. There is no high score or similar kind of reputation schema. Also,
both apps end after finishing the provided levels.
Figure 1 MatheZoo and iLearn+
Category 2: Game-Based-Learning-Apps
This category is about learning through gaming. Game based Learning (GBL) is
very similar to Problem Based Learning (PBL), wherein different problem scenarios
are placed within a play framework (Barrows & Tablyn, 1980). Due to the fact that
games in general include many characteristics of problem solving (e.g. an unknown
outcome, multiple paths to a goal, construction of a problem context etc.) and also add
the elements of competition and chance, it can be stated that there is a huge potential
for learning (Zechner & Ebner, 2011; Hannak et al, 2012), more detailed for
incidental learning. Furthermore, already in 1980 Malone summarized three essential
characteristics for computer games in order to answer the question of what makes a
computer application enjoyable to work with: challenge, fantasy, and curiosity.
The problem of games in recent years was that they were very expensive to
program but the education sector only put aside less money for it. Since 2010
fortunately a “new” approach hit the market called Gamification. Deterding et al.
(2012. p. 10) stated that gamification can be defined as “video games [which] are
designed with the primary purpose of entertainment, and since they can demonstrably
motivate users to engage with them with unparalleled intensity and duration, game
elements should be able to make other, non-game products and services more
enjoyable and engaging as well”.
In other words, with the help of mobile technologies learning games distributed as
apps should be seen as an essential possibility for education. Bearing the theoretical
background in mind three game-based-learning apps were programmed by TU Graz
according to this category (figure 2 and figure 3):
1. iBubbleMath: This game was developed with the goal to learn the
multiplication table. It is therefore best for children in the age of 6-9.
There are two different modes: a training mode and a contest mode. The
story behind is that you are in the sea in different surroundings; when you
finish the game you become a specific character of the sea. This motivates
the children to play it again.
2. MatheFindIt: This game is just a digital variant of the well-known game
Memory. You have to find the right pair of a number and its related
calculation, e.g. 7 and 4+3. The game rewards the learner by presenting
him/her a picture after finishing one set. The picture´s themes are
adequate for preschool children and beginners. Both, the background of
the cards as well as the difficulty (represented by the range of numbers)
are selectable.
3. Super 1*1: This game corresponds to the gaming classification of Jump &
Run. Children in the age of 6-9 have to move forward their avatar through
a level full of barriers and enemies. On their way they have to find the
right solution to a given simple multiplication to finish the level and to get
points for the high score.
Figure 2 iBubbleMath and Super 1*1
Figure 3 MathFindIt
Category 3: Collaborative-Apps
The next category of math apps aims to promote collaborative learning. The goal
of collaborative learning is to assist teaching through a coordinated and shared
activity, by means of social interactions among the group members (Dillenbourg,
1999). Cooperative and collaborative peer learning has been frequently seen as a
stimulus for cognitive development, through its capacity to stimulate social
interaction and learning among the members of a group. Also Vgotsky (1978)
mentioned that social interactions are essential to achieve the desired learning.
So far a collaborative learning approach has been represented by the connection of
a learner with another learner. But if also the mobile devices are added to the
collaborative scenario, the collaboration not only connects people but also their
devices with each other. From a technical perspective this is just the idea of using
WiFi or Bluetooth to exchange data between different mobile phones.
As example of this category, the connection of devices to foster collaboration, the
following two apps were developed:
1. MatheBingo (figure 4): This app follows the idea of a classic Bingo
game. One device in the middle serves as the Bingo table where a
calculation in a predefined range of numbers is presented (e.g. 17+21).
Up to four devices can be connected to that table and serve as Bingo
cards. On each card 16 different numbers are displayed. If a learner finds
the right solution on his/her device he/she can simply mark it. The game
ends when one of the connected cards holds 4 marked numbers in a row.
Afterwards a new round can be started.
2. MathePairs: This app is more or less the same as the described app
MathFindIt. There is just one little difference: the memory cards are
distributed to two connected devices. Of course, one device holds the
calculation and one device the related solution. So the two learners are
forced to collaborate and talk with each other.
Figure 4 Collaborative App MatheBingo
Category 4: Learning-Analytics-Apps
The last category of math apps should overcome the lack of providing feedback to
the teacher. When instructor teacher educates a number of learners, he/she has to take
care about their learning progress regardless to the media used, However, any
collected data about their learning process can help the teacher to understand the
process in a broader view and therefore better. This is the goal of the research field of
learning analytics. Phil Long and George Siemens (2011) stated, learning analytics
can be seen as the mergence of big data and their interpretation to enhance the
didactical possibilities of teachers. From a technical perspective this means that
learners provide data through their devices, such will be sent to a server, interpreted,
and used for further statistical analyses. The teacher itself monitors the learning
process on a separate screen. The teacher knows at any time whether an obvious
problem has occurred or everything is running smoothly. Due to the fact that more
and more data is collected the analyses turn more and more accurate and can also be
used to recommend follow up calculations or even predict/disclose a general learning
problem (Ebner & Schön, 2013).
The developed app of this category, collecting and interpreting learners’ data, is the
so-called “1*1 Trainer” (figure 5). After a registration the learner gets examples of the
multiplication table. The provided example depends on the current learning stage of
the learner, which is computed in real time. Each single finished calculation is sent
back to the server and saved in the database. On base of this database entries teachers
are displayed an overall look at their class in general or a detailed one at each single
child. If failures are accumulated over a certain time period it will be highlighted by a
traffic light analogy.
Figure 5 1*1 Trainer
4. Discussion
Bearing the introduced HCI guidelines for children in mind and as a result of our
experiences in the field of math education with elementary school children, the
following issues have to be taken into account first:
• Language: One major problem of the already existing apps in the common
stores is the language in use. Especially for young children who have very
low reading competencies the native language is a necessary precondition.
From a technical point of view this results either in an own app for each
country-specific store or a multilingual app (language to be changed in the
preferences).
• Design vs. text: Because of the low reading competencies the visualizations
within the app should replace textual parts as much as possible. For
example, MatheZoo or MahthFindIt are only using design elements
without any text. Each single interaction can be done with visual
representations using gestures.
• Highscore: Due to the fact that children in the age of 5-10 mostly are not
enjoying the representation of their results in numbers (Huber, 2012) it
would be better to avoid high scores in game-based-learning apps or a
connection to the game center (which would allow a competition with
players all over the world) Young learners should be rewarded be
graphical add-ons, e.g. a new avatar or a nice picture.
• Target group: Bearing in mind the ADS it turned out that the target group is
essential for the whole app development. In primary math education the
provided range of numbers must be very seriously taken into account to
avoid frustrations on learner’s side.
• Convincing usability: Usability with a strong focus on children needs is the
key factor for the success in the process of app development. All observed
children quickly became used to work with those apps or learned the
handling within minutes. This intuitive comprehension must be picked up
by the apps´ visual interface.
Finally, the introduced apps were tested and used firstly in numerous schools
(Huber, 2011; Frühwirth, 2013; Schönhart, 2013) from a technical as well as a
pedagogical side. As one result it can be pointed out that first of all teachers have to
choose the appropriate learning strategy respectively their educational setting. If
children should do a kind of training, than maybe the self-directed learning approach
is the best. According to table 1 apps of the category 1 and 2 should be chosen.
Incidental Learning or informal learning is claiming an app of category 2 or 3.
Collaborative learning simply needs an app that supports collaboration through the
connection of the devices while working or learning on the same issue. Apps assisting
the teacher by providing detailed analyses are generally independent from the chosen
learning strategy; it is useful in any case. Nevertheless, the quality of the statistical
analyses depends on the provided data and how precisely it can be assigned to a single
learner (e.g. in the field of collaboration it is hard to address the results to single
learners).
Self-directed
Learning
Incidental
Learning
Collaborative
Learning
Learning
Analytics
Category 1
X
Category 2
X
X
Category 3
X
X
Category 4
X
X
X
X
Table 1 Learning Strategy vs. App-Category
5. Conclusion
In this publication different math apps are introduced. Both, the technical as well
as the pedagogical perspective of these apps are described. It can be summarized that
the use of any apps strongly follows a learning and therefore also a teaching strategy.
Most of the apps available in related stores1 can be categorized as stand-alone-
learning- or game-based-learning-applications aiming to assist a self-directed learning
strategy.
Apps for collaborative learning scenarios are quite rare so far due to their more
complex programming efforts and necessary environment to run it. On the other side,
the learning outcome is indeed promising, because the gaming environment and the
communication about the learning problem of the learners as well as the collaboration
through devices is a very powerful combination (Kienleitner, 2014). Finally it was
shown that educators of course need feedback and an overview about the learning
progresses of their students. This feedback can be provided by smart learning
analytics setups. On base of collected data from learners´ activities an intelligent
analysis helps to find recommended learning outcomes. The research field of
Learning Analytics is a very new one. First attempts (Ebner et al, 2012) point out that
new insights in and details about the learning progress can be discovered, even for the
basic math education in elementary schools.
At first glance it can be concluded that the introduced apps worked as intended at
first glance. Further research studies will be necessary to investigate the improvement
of the learners’ outcomes in more detail.
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