2011 Lima, Filho, Ribeiro, Andrade, Viana, Junior Guidelines for the Development and Use of MLearning Applications in Mathematics

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Abstract– Mobile Learning (m-Learning) emerges as a new research branch of e-learning, in which mobile devices are used during the learning process. M-learning applications are in essence mobile educational software that contains multimedia and interactivity. The development of these applications, however, is a non trivial task since it requires skills and knowledge of various domains, well-established methodologies and tools to support the process. In this paper, we present guidelines for the development of m-learning applications in Mathematics. First, from a survey of existing research projects, we identify the main requirements in the development of this kind of software. Then, we propose an extension of an existing development methodology and a RAD (Rapid Application Development) tool to assist the task of meeting these elicited requirements. In order to evaluate the proposal, we also develop three m-learning applications, using the Theory of Meaningful Learning of Ausubel, which help mathematics teaching. Finally, we conclude this paper, presenting directions for a future exploratory study in the classroom using these applications.

Index Terms–Mobile Learning, Meaningful Learning, Requirements Elicitation, Mathematics Education, Agile Methods.

I. INTRODUCTION

he Mobile Learning (m-learning) concept has been attracting interest from researchers since it provides flexibility, brings back a sense of responsibility and autonomy, and encourages teaching and learning practices according to an educational perspective [1][2][3]. M-learning represents a natural extension of distance education via computer-mediated communication (e-learning), while facilitating access to learning, for example, to obtain specific content for a particular subject, without a pre-established time and place.

Specifically speaking, researchers have investigated how m-learning can promote mathematics education [4][5] using embedded resources of mobile devices (e.g., mobile phones,

Manuscript received Feb. 9, 2011.

Luciana de Lima, Edgar Marçal de Barros Filho, Júlio Wilson Ribeiro, Rossana Maria de Castro Andrade, Windson Viana, Antonio José Melo Leite Júnior are with FACED (Faculdade de Educação), Universidade Federal do Ceará.

Publisher Identification Number 1558-7908-2011-7

palmtops, tablets, etc.), such as cameras or microphones, or using educational software designed to promote meaningful and telecollaborative learning [6][7]. In general, digital technologies open up possibilities for Mathematics classes and lectures, allowing simulations, visualizations, experiments, capture of hypotheses, among other actions. In addition to these technologies benefits, mobile devices provide students with collaboration and interactive communication tools, and encourage learning experiences outside of the teacher-managed classroom environment.

Although researchers have recognized the large potential of m-learning, few practical applications have been implemented. One reason is that the development of software for mobile devices, called mobile software, is not a simple task due to the peculiar characteristics of the support devices: heterogeneity, limited battery, reduced computing resources, among others [8]. Another reason is that m-learning software is, in essence, mobile and multimedia software that usually integrates a range of innovative technologies (photo camera, accelerometer, video, etc.), which increase the challenges of mobile software development. Mobile software also inherits the problems of design and development of traditional software. Pfleeger [9], based on the report by the Standish Group1_{that states that over} 30% of the problems in building software is related to problems with requirements either in their removal, in the changes in specifications or in the lack of user involvement.

In the process development steps of educational software, besides conventional requirements, software engineers should also emphasize the pedagogical and methodological aspects. According to Tarouco et al., the development of m-learning systems should submit their assembled content on demand, in order to help users in their contextual and cognitive needs [10]. It is important to maintain the meaningful learning in a dynamic and motivating way. Thus, software engineers must keep in mind that m-learning applications should contain multimedia and interactivity. In this way, students, with the help of these applications, should be able to build new content, developing a learning cycle of the type: action-reflection-debugging-new action [6].

In this context, m-learning applications using the Theory of Meaningful Learning of Ausubel [11] can be considered as pedagogical resources to improve student experience while

1_{http://www.standishgroup.com/}

Guidelines for the Development and Use of

M-Learning Applications in Mathematics

Luciana de Lima, Edgar Marçal de Barros Filho, Júlio Wilson Ribeiro, Rossana Maria de Castro Andrade, Windson Viana, Antonio José Melo Leite Júnior

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one firstly considers relevant the prior knowledge that the student has, it should be possible to make the learning of concepts more meaningful for students, creating a potentially helpful learning strategy in order to build new knowledge. Mobile technologies can assist teachers in characterizing this knowledge and help them to observe, continually and individually, how the students are learning in the classes.

The development of m-learning applications is then a complex task requiring skills and knowledge of various domains, well-established methodologies and tools to support this process. In this context, this paper discusses and proposes guidelines for the development of mobile software designed to help students to learn mathematical concepts based on the Theory of Meaningful Learning [11].

From a survey of existing related research projects, we first identified the main requirements in the development of m-learning applications, especially those in mathematics education. We also described some solutions that can be adopted in order to meet these requirements. These solutions are based on both literature and our experience in the development of three applications for m-learning in Geometry. As a result of this study, we also present an extension of a mobile software development methodology created to guide the integration of pedagogical and technological aspects in the construction of m-learning software. Some steps of the methodology are automated by an authoring tool that assists the creation of m-learning applications without demanding knowledge of software programming languages.

The remainder of the paper is organized in seven sections. Section II presents the theoretical foundations. In section III, we describe our first contribution: a survey of requirements for the development of m-learning applications in Mathematics. In Section IV, we propose an extension of an existing methodology, and an authoring tool. Section V presents three m-learning applications created in this work and Section VI describes some solutions we find during the development of these m-learning applications which meet a major part of the elicited requirements. In Section VII, we specify a proposal to apply m-learning software in Mathematics according to the principles of the Theory of Meaningful Learning. Finally, we present the conclusion and some suggestions for future works in the last section.

II. THEORETICAL AND METHODOLOGICAL ASPECTS

Aiming at identifying the main challenges in software development for m-learning with focus on mathematics learning, this section does a brief survey of m-learning applications in mathematics and examines common processes and tools involved in the development of this kind of mobile software. Furthermore, we present the main concepts of the Meaningful Learning Theory and their connections with m-learning.

A. M-Learning Applications in Mathematics

Rytkönen and Silander believe that mobile devices define a

new dimension in education, especially because they allow learning in specific contexts, easily extendable to the real world [12]. Thus, due to the ubiquity of such devices, students can virtually access digital material at any place, building knowledge, from observations of the real world. Therefore, m-learning experiments are usually designed based on this idea of user friendly interfaces and availability at any time. Based on the concept of easy access to information, Krajcsi et al. determine five most common usages of m-learning in mathematics: i) Text Books, ii) Assistant tools, iii) Models for Experimentation, iv) Programmed Learning, and v) Intelligent Tutoring [13]. We briefly present these five common usages illustrating them with some recent m-learning applications as follows.

Text Books

This kind of m-learning application exploits the basic functions of mobile devices. They present text and images that can be accessed by using a hyperlinked model or linear navigation. For example, Nokia proposes a mobile application for the resolution of mathematical exercises that are solved step by step on the tiny screen of mobile phones [14]. The main advantage of these simple applications is the possibility of joining a larger number of mobile device models since these m-learning applications require only standard device resources.

Assistant Tools

M-learning applications can also act as assistant tools during the learning process. These applications perform specialized calculations in the resolution of specific problems, such as calculating the area of geometric figures, measuring the volume of solids, or measuring dimensions and angles from images captured by the camera of a mobile phone [5].

Models for Experimentation

Another way to obtain benefits from mobile devices in the Mathematics learning is to simulate real situations on the device screen that can be solved pedagogically explored by applying some mathematical model. For example, students are confronted with a kind of arrangement-of-shoes problem. The shoes should later be arranged in closets according to certain rules that must be defined by mathematical functions [15].

Programmed Learning

Programmed Learning or Programmed Instruction is a learning proposal that involves administered and self-paced learning in small bytes of information. Some applications for m-learning in Mathematics adopt this strategy. First, the mobile software shows certain content and, later, it presents questions that must be answered by the student. As a simple feedback, such applications are limited to reporting mistakes and successes obtained by the students [16].

Intelligent Tutoring

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problems and analyze the student´s answers making use of artificial intelligence resources. These applications can infer how to help the students whenever necessary. As an example of such applications, the Cognitive Tutor has several guided exercises, from the calculation of the roots of a first degree equation to trace graphs of complex functions [17].

It is important to note that is hard to classify m-learning applications in one of the five aforementioned categories [13], since often current m-learning applications try to exploit the main advantages of each model. This occurs mainly due to recent advances in mobile devices that allow hybrid solutions to become increasingly common. This is the case of the mobile applications presented in this paper, discussed in the following sections.

B. Processes and tools for the development of M-Learning applications

These requirements are reinforced in mobile application development, since the mobile market is highly dynamic where the reduction of time to market (TTM) is really important. For these reasons, Rapid Application Development (RAD) and Agile methods are core concepts among the existing methodologies and tools that should also be taken into account when discussing mobile application development [18][19][20][21].

RAD methodology claims minimal planning, from the software point of view, in favor of rapid prototyping. The software engineers use the building of prototypes for to quickly demonstrate, evaluate or test a mobile application with less effort. Classical mobile development tools (e.g., NetBeans, Android SDK, and iOS Xcode) provide form-builders for drawing working interfaces by dragging components from a palette and positioning them on a screen that emulates the mobile device. Research projects such as iStuff Mobile [18], Visual RDK [19] and XMobile [23] go a step forward by providing high level features and models to be composed in order to generate both low-functional and high-fidelity prototypes. In general, the development process supported by these tools is a refinement cycle of the design-prototyping-evaluation [1] steps in which tools hide common design challenges for mobile application development (e.g., platform heterogeneity, multimedia, and sensors access complexity, wireless communication issues, adaptation, etc.).

Instead of focusing on low level aspects (implementation-oriented) of mobile software, Agile approaches, such as Mobile-D [24] and Hybrid Methodology Design [25], are more interested in high level (methodology-oriented) concepts of the mobile software development process. For instance, Mobile-D proposes a User-Centric approach with the disciplines of Designing, Architecture Line, Test-Driven Development, Continuous Integration and Pair-Programming. Thus, RAD tools and Agile methodologies seems to give the right directions to conduct the development of general mobile software. However, m-learning applications have some

peculiarities that avoid the direct application of these approaches. Similarly to other educational systems, the development of m-learning applications requires a multidisciplinary team which should be composed by teachers, multimedia designers and mobile developers. In general, they have different kinds and levels of knowledge and skills that often create tension in the development process [26]. Some methodologies are proposed to deal with this issue for general educational software [27][28]. Most of them propose a layered approach based on the ADDIE model [29]: Analyses, Design, Development, Implementation and Evaluation. In ADDIE, the first two phases are centred on the pedagogical perspective and are conducted by the teachers. The Development phase is destined to multimedia creation and the Implementation and Evaluation is related to the software development process itself.

However, there is an approach that seems to deal better with multidisciplinary team issues, since it involves domain experts (e.g., mathematics teachers) as first-class members of the design team and tries to avoid conflicts promoting a co-design methodology. This methodology, proposed by Millard et al. [26], combines techniques found in HCI (personas, scenarios, and storyboarding) with agile methodologies (incremental and iterative development) and lightweight software engineering notations (use cases, interaction diagrams). This co-design methodology is divided in into stages. Each stage is supported with workshops and meetings in which both domain and technical experts participate. The five stages of co-design methodology are:

I. Scoping. The definition of the stakeholders (learning experiences and knowledge) is made during this phase. First, requirements of the m-learning application are specified.

II. Shared Understanding. Is devoted to the presentation of the technology’s opportunities and restrictions. Domain experts also present the application’s educational purpose.

III. Brainstorming. The application’s scenarios are sketched.

IV. Refinement. More concrete software requirements are specified during this phase by using text tools or design diagrams.

V. Implementation. Iterative and incremental

development process models are used in an agile perspective for the creation of the multimedia content and the mobile application itself

In fact, stages III, IV and V are a cycle where some bad decisions can be more easily detected and corrected before the final delivery of the m-learning application. RAD tools can also be integrated during the implementation stage in order to promote fast development of the m-learning application increments. Section IV of this paper shows how we adapt the co-design methodology for the development of m-learning

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C. Aspects of the Meaningful Learning Theory

Ausubel developed his pedagogical work in the 60’s following cognitive psychology principles. He aimed to explain how the process of meaningful learning could be easily developed [30]. He defended the assumption that learning through meta-cognition can be more effective and meaningful.

According to Ausubel, meaningful learning occurs if the learner has previous knowledge in his cognitive structure, known as subsumers. They act as anchoring mechanisms that establish correlations between prior knowledge and new knowledge, which is willing to be internalized into the cognitive structure. Generally, subsumers is a concept, idea or proposition that already exists in the cognitive structure of the learner, which makes it easy to fix new information and to assign new meaningful learning [11][30].

Mobile applications can assist teachers during the task of determining the prior knowledge of students. For example, questionnaires and activities can be deployed in students’ devices in order to give individual and segmented information about each student. In this way, teachers can have a better synthesis of the knowledge of the group to which the students belong.

According to Praia, cognitive development is a dynamic process in which new knowledge is constantly interacting with existing knowledge [31]. Thus, Ausubel proposed four principles known as Programmatic Principles [32][33], as illustrated in Figure 1, to help the development of the meaningful learning process in the teaching practice and knowledge building by the students: Progressive Differentiation, Integrative Reconciliation, Sequential Organization and Consolidation.

Fig. 1. Programmatic Principles of Ausubel´s Meaningful Learning Theory

We believe that m-Learning applications can help to

improve these Programmatic Principles since these applications are deployed in the students’ devices and can provide real-time feedback of objective evaluations. At the end of the activities, which can be proposed for each programmatic principle, the student can answer questionnaires that address some questions, including those used in the initial evaluation. Given the responses, the mobile device itself could indicate the major difficulties of the student. This helps teachers to understand the conceptual and procedural difficulties presented by the students. Hence, the teacher can react more quickly. For instance, he can propose new explanations on the topic or can suggest new interactive activities to be done by students in the classroom or at home, improving their learning process construction.

They can become aware of the problems faced through self-evaluation or by a remote action by the teacher (e.g., messages sent using wireless technologies).

III. REQUIREMENTS ELICITATION

Correct requirements gathering is crucial in traditional software development, and, for m-learning applications, this is not different. In this section, we present functional and non-functional requirements in the development of m-learning applications. First, we present requirements already enumerated in literature. Afterwards, we describe new requirements that were identified from a survey of m-learning applications, especially those in mathematics education (some of them were described in Section II).

A. Requirements for M-learning Applications

Economides presents a set of requirements for educational applications in mobile devices, grouping them into four dimensions: Economic, Socio-Cultural, Technical and Pedagogical [34].

Regarding the economic aspects, one should consider costs whenever the application is used, cost benefit and the types of agreements required by the software developer (e.g. data transfer costs or software licensing costs). Attitude, social trends, acceptability, methods of social interaction and sociability are the main requirements related to the socio-cultural aspect. In the pedagogical dimension, it is important to mention the following requirements, which are close to the subject of this work: learning theories, presentation and quality of content, content organization and support of student feedback.

In the technical dimension, the requirements are divided into eight groups as follows: user interface, functionality, perception, adaptation, reliability, efficiency, connectivity, and security. In the aspect of the user interface, for example, the application should be easy to use, intuitive, and employ different media. The functionality requirement is related to the quality and interactivity of the application. Regarding the perception requirement, this should be linked to the type of device used, the activities to be implemented, and the environment in which the application will be used. The adaptation requirement is related to the ability of the

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transparent, and remain consistent after adaptations. The reliability of the application is related to the absence of errors, application availability, and the facility of installation, configuration and upgrade. The efficiency requirement is related to application performance, speed of information transmission, energy consumption and data input and output. Regarding connectivity, this requirement is related to ways of application data transmission as well as to its portability and autonomy. The safety requirement is related to access control and protection of the exchanged information.

Moreover, Petrova and Li enumerate a set of seven application requirements of m-learning obtained from a survey of students' needs, which are: adaptability of the content, availability of information, possibility of customization, understandable content, if the application permits self-instruction, if the application fits into the curriculum of the educational institution, and if the application contains interesting and enjoyable content [35]. Two other factors are highlighted as obstacles in the expansion of m-learning: the cost of data transmissions and the limited resources of mobile devices for storage of large amounts of text.

Besides these requirements, Georgieva shows a comparison between twelve m-learning applications, of which six were developed in universities and six commercially [36]. The requirements used to analyze and compare the applications are: type of mobile device supported, programming language, content type, if the application requires an Internet connection, type of content adaptation, and if the application is compatible with any Virtual Learning Environment (VLE). Among the findings, the author notes that most applications require transmission of information and business applications are integrated with existing VLEs.

B. Requirements for M-learning Applications in Mathematics

Based on the Krajcsi classification, presented in Section II, we enumerate six types of mobile software requirements for m-learning in mathematics: i. M -l e a r n i n g

applications should support texts and images that can be accessed linearly or by using hyperlinks; M-learning applications should support calculations of specific problems, such as areas of geometric figures and volumes of solids;

ii. M-learning applications should use simulations of situations in which mathematical models can be applied to solve problems;

iii. M-learning applications should integrate questionnaires to be answered by the student; iv. M-learning applications should offer methods for

measuring the learners’ feedback; and

v. M-learning applications should support some artificial intelligence resources for the creation of guided exercises.

Figure 2 shows a summary of sub-sections A and B with the main requirements to be elicited during the development process. However, it is important to note that an application of m-learning in mathematics does not always need to attend all these requirements.

IV. DEVELOPMENT PROCESS AND AUTHORING TOOL

A. Software Development Process Adopted for M-Learning Applications

As mentioned before, the development of m-learning applications is not a trivial task and to fulfill the requirements elicited in Section III it is necessary to follow a well planned process created to take into account the specificities of the mobile learning domain. For this reason, we have adopted the Co-design Methodology, described in Section II.

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Fig.2. Requirements of M-learning Applications in Mathematics.

Once we had captured all requirements, the next step was to design and implement three applications of m-learning for teaching Mathematics. From that experience, some steps of the Co-design Methodology were extended in order to better guide decision making during the software development process. Figure 3 shows the five co-design stages and the new steps we have added.

In the first stage of the methodology (Scoping), meetings are held with teachers of mathematics, who are stakeholders of our applications. During these meetings, the Agile team defines the application’s main objective and the roles of all participants in the process of the application development (teachers, programmers and designers).

In Stage 2 (Shared Understanding), after all stakeholders are identified, meetings are held to promote knowledge exchange. Scenarios for using the application are described and presentations of various existing applications of M-Learning are carried out. At this stage, during the development of our applications, we have a need to add two more steps that were not clearly defined in [26]: technology and pedagogical methodology selections.

The technological selection expresses the definition of which technical resources should be used by the applications. In fact, some decisions made here can limit the options available for achieving other application requirements. For instance, the selection of which mobile platform will be adopted and what type of connection is made during this step. These decisions influence both the economics and the technological aspects of the application. Moreover, the choice of the connection may interpose the use of certain Learning Styles or Methodologies. For example, offline applications forbid direct collaboration among learners, but they offer reduced costs since do not use paid communication. Attewell describes more deeply the technological selection and its impacts on m-learning applications [37]. The pedagogical methodology selection is related to the decision of which learning styles will be used by the teachers. In our applications, Meaningful Learning Theory was adopted.

During Stage 3 (Brainstorming), the initial script of the application is specified. It describes the order in which the screens will be displayed, multimedia resources that will be used, messages that should be presented, etc. This step is mainly conducted by Mathematics teachers, and developers have the task of guiding them in order to indicate what is possible to implement and what is not, as well as to propose alternatives in the case of impossibilities.

Stage 4 (Refinement) is characterized as a finer description of the application scripts and a formalization of the application requirements and requested features. We have added to this stage a step of Requirements Analysis in order to bring more importance to the requirements elicitation and requirements resolution. The main idea here is to use the requirements list

presented in Section III as a starting point. This stage also includes a more detailed description of the application features by using UML diagrams (Use Cases and Activity Diagrams).

Finally, in Stage 5 (Implementation), the applications are developed based on the artefacts produced in the previous stages. Given the broad relevance of multimedia elements for applications, at this stage a specific step was added to establish these elements. Once the multimedia resources are created, software development implementation is then initiated to group, manipulate and connect the multimedia elements, following the script established by the teacher.

It is important to note that the Interactive Development step encompasses the activities of the Agile methodologies (e.g., organization of sprints, daily meetings, and unit and integration tests) and the codification itself. Moreover, stages 3, 4 and 5 are, in fact, a cycle of refinements of both application specification and implementation.

We have also added to the final stage a step of Evaluation in situ, since we believe that the mobile application features must be experimented in a real situation (e.g., in a classroom) by the team.

B. The Authoring Tool

Taking as foundation the methodology shown in the last sub-section and aiming at optimizing the construction of educational software for mobile devices, this paper also proposes a computational tool for the preparation of material to support Mathematics teaching, called Mobile Authoring Tool. The material is designed to support interactive applications that will run on students’ mobile devices and assist teachers in Mathematics classes.

Our tool follows the design principles of MLCAT (Mobile Learning Content Authoring Tool) [38]. The tool tries to fulfill the requirements of a useful MLCAT in the three dimensions: technological, pedagogical and usability. For instance, our Mobile Authoring Tool supports text, image and videos as multimedia content, and it generates m-learning applications for diverse mobile platforms. The interface was designed to be used by people without programming knowledge (e.g., most of the teachers). Then, our tool proposes a flexible way to compose and organize the content to be presented to the students. This flexibility allows the creation of material to be applied using different kinds of learning styles, from Instructional Methodology to Meaningful Learning. Our tool is the only one that is fully in Portuguese since the potential users are Brazilian teachers.

The Mobile Authoring Tool consists of a web application that the teacher, previously registered, uses to produce interactive content to help students on the teaching material. Students will receive applications on their mobile devices using wireless networks and can use them anywhere and anytime without the need for an Internet connection.

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building mobile support material for their classes, which will be converted into a mobile application. In the current version, the tool will generate applications for the following formats: JME (Java Micro Edition), Android, and HTML. A version for generating content for iPhone is under development. After the development of educational materials, the Mobile Authoring Tool may send it directly to the application built for the student's mobile device through a wireless local network, or the application can be made available for installation via Internet. Figure 4 shows the image of the Mobile Authoring Tool's main screen. The tool has a Preview feature, which allows the user an approximate estimate of how the educational material built on the mobile displays. The teacher may, at any time, change the properties of the components of the class, including modifying and deleting elements. Nowadays, the tool is available only in Portuguese as shown in Figure 4.

V.PROTOTYPES DEVELOPED FOR M-LEARNING

APPLICATIONS IN MATHEMATICS

As mentioned previously, the process presented in Section IV was refined by using as case studies the development of three educational applications for teaching Mathematics with mobile devices. All application contents are in Portuguese as observed in Figures 5, 6 and 7. In all three applications (M-Prism, M-Pythagoras, and M-Queops), we used the JME platform that consists of the Java environment for mobile devices. This choice occurred because of the large number of

devices supporting this technology, including those of lower financial cost. These applications work locally on the mobile device without the need for a network connection.

The three applications have similar characteristics and performance: navigation between screens is simple, the student just clicks on the commands 'previous' and 'next'; the screens are composed of text, images, videos or questions; and after installed, there is no need for connection to the Internet. As for the content, the developed applications address different issues that are described in the following subsections.

A. M-Queops

This application, as one can see on the screen shown in Figure 5, works concepts of spatial geometry, more specifically around the pyramid tool. Since this is a subject with a greater level of difficulty of understanding for high school students, the concepts are presented in a contextualized format, beginning from the demonstration of a video, with narration, which specifically addresses the most famous Pyramids of Egypt. Then, animations are presented to students with the goal of showing the geometric constructions from more general concepts to more specific ones according to the principles of Ausubel´s Meaningful Learning Theory [11][30][32].

For a better understanding of the application operation, a video was recorded with a demonstration of the use of M-Queops in a mobile phone (Nokia E61), which is available at

YouTube in the link:

http://www.youtube.com/watch?v=EPhBe7sRpb0.

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Fig.4. Screen shot of the Mobile Authoring Tool (caption and labels in Portuguese since the potential users are Brazilian teachers). The rectangular region positioned on the left side contains the mobile application structure (in Portuguese, “Estrutura”). The panel “preview” shows a glance of the current screen. The rectangular region positioned on the right contains a wizard, which helps the teacher in the elaboration of the questionnaires. Teachers can indicate the question (“pergunta”), the correct answer (“resposta correta”) and the messages to be presented in case of success (“mensagem acerto”) or failure (“mensagem erro”). The panel “Componentes” describes the options for each question.

Fig.5. Splash screen of M-Queops Application. It presents the lecture theme: Basic Elements of Pyramids.

B. M-Pythagoras

The application M-Pythagoras, as is shown in Figure 6, addresses concepts related to plane geometry triangles, more specifically about Pythagoras’s Theorem. In this educational application the concepts of the hypotenuse, catheti and right

angles are presented. As the concepts are transferred over the application, students should answer questions about them.

Fig. 6. Screen shot of M-Pythagoras Application. The text presents the digital Geoboard (in Portuguese, “Geoplano”) and it introduces the first concepts of the Pythagoras theorem: a right triangle (“Triângulo retângulo”) with two red sides forming a right angle.

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C. M-Prism

Similarly to the M-Queops, this application – see screen in Figure 7 - also works concepts of spatial geometry, but in this case, the studied picture is the Prism. The application works several concepts such as bases, faces, vertices, edges and a method of calculating the volume. Images and animations of milk and tomato paste boxes were used to build the context of the prism geometric picture.

Fig. 7. Screen shot of the M-Prism Application. The screen text introduces a Prism polyhedron. It enunciates that Prism has two base faces located in parallel planes and joining faces in rectangular form.

VI.APPLYING THE IDENTIFIED REQUIREMENTS

Several of the requirements described in this section were included in the developed applications presented in Section V. In general, we used the same solutions for all three applications that can, therefore, be adopted in new m-learning software for Mathematics. Moreover, some of the implementation decisions are included in the proposed Mobile Authoring Tool.

The five tables listed in this section present a mapping between the elicited requirements and the solutions designed and implemented. Table I shows the solutions to meet the economic requirements. Table II describes the socio-cultural requirement implemented. Table III and Table IV list the solutions implemented to meet, respectively, the pedagogical and technical related requirements. Finally, Table V describes the specific requirements of m-learning in the area of mathematics.

TABLE I ECONOMIC REQUIREMENTS

Economic Requirements

Requirements Expenses for application usage, cost-benefit relation, and the types of required contracts

Implemented Solution: One of the economic requirements that we chose

was to reduce the financial burden on the students, since the target audience was students from public schools. To do this, applications were implemented to avoid connections to the Internet. The student could then use the application as many times as he/she wished, without the need of a contract with the manufacturer or the mobile operator.

TABLE II

SOCIO-CULTURAL REQUIREMENTS

Socio-Cultural Requirements Requirements Attitude

Implemented Solution: The applications were developed to enable the

students to gradually develop their self-efficacy in learning the content, starting from the more specific concepts to more general concepts.

TABLE III PEDAGOGICAL REQUIREMENTS

Pedagogical Requirements

Requirements Learning Theory

Implemented Solution: Pedagogical proposal employed in a collaborative

learning approach and based on constructivist elements. Such reasoning is based on the possibility of cooperative interaction between students and the machine, which must always encourage discussions that foster teamwork and the building of new knowledge [7].

Requirements Content Presentation and Quality

Implemented Solutions: The content provided in the applications makes

use of text, questioning, different images, animations and video with good picture quality and sound. Moreover, there is a concern about minimizing the use of the scroll bar and making the most use of the screen space. The animations are presented in a loop for students to have continuous access to the construction of geometric shapes.

Requirements Content Organization

Implemented Solution: For the application M-Queops, the content is

organized from the most general to the most specific, following the assumptions of Ausubel et al. (1980). First, a video with narration about the pyramids of Egypt is presented, followed by an animation that conceptualizes a pyramid from a mathematical point of view. Later, basic elements of a pyramid are presented.

Requirements Support and Feedback to the student

Implemented Solutions: In all applications, messages tell students of

success and error situations. In case of error, the application returns to the theoretical content providing access to the theory of the studied geometric figures. Thus, students can reflect with colleagues about the problems faced during the tasks.

TABLE IV TECHNICAL REQUIREMENTS

Technical Requirements

Requirements User Interface

Implemented Solution: The developed applications require minimal user

clicks (usually only one), most of the screens have no scroll bar and their contents are basically composed of texts, images and animations, features that make use and browsing in the application easier.

Requirements Functionality

Implemented Solution: Both videos and images were constructed aiming to

combine the best viewing quality with the smallest size. On the content screens, the user interacts browsing (back and forth) between them and the screens of questions. The interaction occurs by choosing a response option and its confirmation.

Requirements Perception

Implemented Solution: The applications were developed for the context of

the student in the classroom. The compatible mobile devices with the applications have a limited scope: they must support JME and video execution.

Requirements Adaptation

Implemented Solution: The developed applications, which were written in

JME, adapt to mobile devices from different manufacturers and different operating systems, transparently to the user and maintaining their consistency.

Requirements Reliability

Implemented Solutions: In all three applications, the user does not enter

data, but just selects the commands available, which reduces operating errors. During the design of the applications, test cases (unit testing and

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integration) were built and were executed after the end of implementation. Once installed, each application will always be available to the user without depending on external data. Nor is there any need to configure the application after installation.

Requirements Efficiency

Implemented Solutions: The developed applications neither access any

database nor special hardware features of the equipment. It does not make any transmission of information, avoiding performance drop caused by the use of these resources. The entry of information is minimized and the user does not need to enter any data, but just select from the available commands. Requirements Connectivity

Implemented Solutions: Applications do not need to send or receive data

and are portable to mobile devices that support JME and 3GP video. There is no need for any additional hardware or software, which provides a good degree of autonomy to the applications, because they are not dependent on other hardware features (like GPS, digital camera, etc.) or software.

TABLE V

REQUIREMENTS OF M-LEARNING APPLICATIONS IN MATHEMATICS

Requirements of m-learning Applications in Mathematics

Requirements Support to text and images in a linear layout

Implemented Solution: In all three applications, the provision of content

happens in a linear layout, with screens in sequence, and composed of texts and images.

Requirements Use of questionnaires

Implemented Solution: Screens were presented with questions, and

students can practice the knowledge acquired by selection of multiple choices.

Requirements Use of simulations

Implemented Solution: In M-Queops, the application displays video with

three-dimensional simulations of the properties of the pyramids, and with their plans.

Requirements Creation of Guided Exercises

Implemented Solution: In all three applications, in case of error in

answering the question, the application returns to the content related to the question.

VII.METHODOLOGY FOR EXPLORATORY STUDY

Given the proposed objectives of this work, we used an initial exploratory research in the classroom to understand the impact of the use of three applications that we developed. The difficulties presented by the students in their application handling, considering both technological and pedagogical points of view as well as the ease of learning the mathematics concepts by the student, were also analyzed.

The target public of the research is composed of 10 high school students, chosen randomly in a public school in Fortaleza city, located at Ceará State, Brazil. The choice of this educational level is because the level of complexity of the developed applications that deal with matters directly related to the Geometry content is understood by students of this age group.

The research is based on the investigation of the integration of the pedagogical and technological resources. Thus, one of the goals to be achieved is the investigation of meaningful learning of the student when using the mobile device to learn mathematical concepts. Hence, a traditional education will do little for the recognition of the cognitive processes used by students in the process of assimilation of concepts. Ausubel's theory, however, contributes with our proposal that helps in the investigation of the learning process through the use of

constant self-evaluation when using the digital tool, based on prior knowledge of students.

This research is divided into four phases: planning, preliminary evaluation, intervention, and subsequent evaluation.

In the planning phase, the public schools are contacted. The presentation of the research is conducted so that the mathematics teachers of the schools are invited to participate in the planning of lessons and, together with their students, in the data collection. Teachers, therefore, are aware of the knowledge proposal and have contact with mobile devices and their applications in advance, and so develop the planning of a class, along with the researchers, that includes the use of the application.

In their preliminary evaluation, a questionnaire is applied to the students so that their previous knowledge of mathematical concepts is investigated. Responses are tabulated to serve as material for comparison at the end of the last phase of the research. In addition, students have an initial contact with the use of mobile devices in a different context. In this project, the proposal is that students use them as calculators in problem-solving situations.

In the intervention phase, the teacher introduces students to all concepts to be addressed in the application in order to prepare them for using the mobile device, through the use of previous organizers. In that way, their subsumers are triggered for the new knowledge. From a motivational form presented by their own teacher, students, in pairs, begin using the application installed on the mobile device. At the end, each group must meet the challenge of the teacher explaining its thoughts on a protocol of problem-solving. Data collection is realised based mainly on observations of the groups in the use of digital material and in the solution of the problems.

In the subsequent evaluation phase, students answer a form containing questions regarding the content of mathematics and the difficulties encountered in using the devices.

Another data collection, therefore, is made based on the lesson plan, questionnaires, procedures, troubleshooting, and scouting reports. This new data is tabulated in such a way as to demonstrate the development process of each student learning in chronological and sequential layouts.

Data analyses are performed by comparing the results of each phase, and inferences from the use of the Ausubel’s Meaningful Learning Theory. These first results provide a basis for developing a survey of more subjects and in different school contexts.

According to Ausubel et al. [32], it is important for the teacher to know which are the students’ subsumers regarding the specific content to be addressed in the classroom. In this research proposal, the previous knowledge of students concerning mathematical concepts is collected from the initial questionnaire. Once the teacher has not worked out the specific content in the classroom, we believe in the possibility of collecting the basic concepts that students have about the mathematical concepts in study.

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each student, when he/she receives his/her initial questionnaire, should find his initial conceptions about the mathematical concepts addressed, and, in a process of self-assessment, understand the conceptual transformations experienced with the use of the application.

Another aspect highlighted by Ausubel is the importance of using previous organizers before the learning of new knowledge begins. From their presentation, nonexistent subsumers, which are essential for learning to be meaningful, can be built. In addition, obliterated subsumers can be reactivated to serve as anchor of the new knowledge.

These organizers are used in this research on two different occasions. The first is with the help of the teacher, in addressing all mathematical content to be studied in one class, exploring curiosities, and contextualized situations. The second is inside the application when the student is presented to an initial video about the maths subject tackled.

The results of the exploratory study will show, from a pedagogical point of view, how the methodological approach used in the mobile device assists the student in the assimilation process of presented mathematical concepts. This fact is relevant for the adaptation and development of educational content focused on the use of mobile devices in the classroom, in different areas from knowledge.

Currently, the exploratory study is in the initial stage: selection of which school will be used as a laboratory for experiments with the developed applications.

VIII.CONCLUDING REMARKS

Due to its popularity the use of mobile devices is considered an interesting tool to support teaching and learning. Note, however, that teaching and learning of mathematical concepts using m-learning have some peculiarities, which may require adaptation from the content on small screens until the adoption of specific learning techniques.

This paper proposed guidelines for the development and use of m-learning software in Mathematics. First, we presented a set of requirements needed to develop this type of application based on research in the area, highlighting the main needs and implications. Then, from this study, we established guidelines that can serve as a handy reference for creating software in this area and may evolve towards a way of re-using artifacts for m-learning in mathematics as a future work. In addition, an existing methodology was adopted and extended to support the elicited requirements. A Mobile Learning Content Authoring Tool was also implemented to accelerate the development phase of these applications. From this tool, three applications related to the teaching of mathematics were developed and the meaningful learning concepts were applied. Furthermore, our proposal described a mapping between the elicited requirements and solutions used in the applications.

In the implementation, we chose to use resources that, although simple, because of the relatively low processing capacity of mobile devices, can be well used for the

presentation of ideas and the construction of new concepts. Among these resources, we should stress the use of questionnaires with feedback that can help students to find solutions when necessary.

In order to better evaluate the implementation of the requirements and the actual impact of the use of the developed applications, an exploratory study was planned and started. It is expected thus to contribute to the definition of specific standards that facilitate the learning of mathematics, based on the individual student-computer interaction, which does not make education something isolated, but rather can support rich discussion groups. It is also intended, from this study, to improve the features of the Mobile Authoring Tool and evaluate the use of mobile devices in the meaningful learning of mathematics.

ACKNOWLEDGMENTS

Authors thank SoftBuilder Informática and FUNCAP (Fundação Cearense de Apoio ao Desenvolvimento Científico e Tecnológico) for providing resources to the development of the Mobile Authoring Tool used in this work .

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Luciana de Lima received her M.Sc. in Education at Universidade Estadual

do Ceará, Fortaleza, Brazil (2008). She has been working as a professor at Universidade Federal do Ceará since 2009. She has experience in Teaching Mathematics and Science, working mainly with the following themes: Ausubel´s Meaningful Learning, Teacher Education, and Blended Education. She is currently a doctoral student at FACED (Faculdade de Educação), Universidade Federal do Ceará.

Edgar Marçal de Barros Filho obtained his M.Sc. in Computer Science at

Universidade Federal do Ceará, Fortaleza, Brazil (2005). He has been working as a professor at Universidade Federal do Ceará since 2009. He has experience in Computer Science, working mainly with the following themes: Requirements analysis, Mobile Computing, and Mobile Learning.

Júlio Wilson Ribeiro received his undergraduate degree in

aeronautical-mechanical engineering at Instituto Tecnológico de Aeronáutica, ITA, in São José dos Campos, SP, Brazil (1978), the M.Sc. in mechanical engineering at Federal University of Paraíba, PB, Brasil (1984), his D.Sc. in mechanical engineering at ITA, in São José dos Campos, SP, Brazil (1992) and a postdoctoral stage in education curriculum at Pontifícia Universidade Católica de São Paulo, SP, Brazil (2010). He worked as aeroespatial engineering designer and researcher at Centro Técnico Aeroespacial and Instituto Nacional de Atividades Espaciais, SP, Brazil. His publications appeared in The International Journal of Heat and Mass Transfer, The International Journal for Numerical Methods in Engineering as well as International Communications in Heat and Mass Transfer. He is currently Ph.D. advisor of the graduate program in education at Universidade Federal do Ceará, Brazil. Prof. Ribeiro is a member of the scientific council of the Brazilian Association for Distance Education.

Rossana M. C. Andrade received her Ph.D in Computer Science from the

School of Information Technology and Engineering (SITE) of the University of Ottawa, Ottawa, Canada, in May 2001. Her PhD thesis focused on the capture, reuse and validation of software patterns for mobile systems. Nowadays, she does research in the areas of computer networks and software engineering, specifically, she is looking at ubiquitous computing and software reuse. Alternative solutions to increase systems security as well as the application of formal and semi-formal techniques to specify and validate systems are also her research interests. She has been a Professor at Federal University of Ceará, Fortaleza, Ceará, Brazil, in the Department of Computer Science, since 1994, and coordinator of the Research Group of Computer Networks, Software Engineering, and Systems since 2002. Dr. Andrade is a member of ACM and SBC - Brazilian Computer Society.

Windson Viana obtained his Ph.D. degree in February 2010 from the

University Joseph Fourier (Université de Grenoble) in Grenoble, France. He received his B.Sc. degree (2002) and his M.Sc. degree (2005) in Computer Science from the Federal University of Ceará, Brazil. Nowadays, he is a Professor of the Federal University of Ceará, Brazil. His research interests include context-awareness, mobile computing, multimedia management, and mobile-learning.

Antonio José Melo Leite Júnior received his M.Sc. in Computer Science at

Universidade Federal do Ceará, Fortaleza, Brazil (2001). He has been working as a professor at Universidade Federal do Ceará since 2009. He has experience in Computer Science, working mainly with the following themes: Multimedia, Interaction Design and Serious Games Development.