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Computers & Education 48 (2007) 618–641

Computer support for learning mathematics: A learningenvironment based on recreational learning objects

Gabriel Lopez-Morteo, Gilberto Lopez *

Computer Science Department, CICESE, Km. 107, Carretera Tijuana-Ensenada, 22860 Ensenada,

Baja California, Mexico

Received 24 February 2004; accepted 21 April 2005

Abstract

In this paper, we introduce an electronic collaborative learning environment based on Interactive

Instructors of Recreational Mathematics (IIRM), establishing an alternative approach for motivating

students towards mathematics. The IIRM are educational software components, specializing in math-

ematical concepts, presented through recreational mathematics, conceived as interactive, recreation-

oriented learning objects, integrated within the environment. We present the architecture of the learn-ing environment which integrates communication services that support the interaction processes of the

learning community, through instant messaging, chat rooms, and multi-player math games. Through

the environment�s interface of their personal workspace, students have access to several easy-to-use

mechanisms that allows them to customize its content, its layout, and its appearance. At internal lev-

els, the functionality of IIRM is enhanced with features supported by the environment infrastructure.

We evaluated different aspects of the learning environment in three short, motivation-oriented math

courses given to Mexican high-school students. The results indicate that the use of the IIRM-based

electronic learning environment, positively affects student attitudes towards mathematics. We believethat this approach has the potential to promote the mathematics learning process, basically on its

motivational aspects.

� 2005 Elsevier Ltd. All rights reserved.

0360-1315/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compedu.2005.04.014

* Corresponding author. Tel.: +52 646 175 05 93x25500; fax: +52 646 175 05 93.

E-mail addresses: [email protected] (G. Lopez-Morteo), [email protected] (G. Lopez).

URL: http://supersabios.cicese.mx (G. Lopez-Morteo, G. Lopez).

mailto:[email protected]

mailto:[email protected]

http://supersabios.cicese.mx

G. Lopez-Morteo, G. Lopez / Computers & Education 48 (2007) 618–641 619

Keywords: Interactive learning environments; Architectures for educational technology system; Distributed learning

environments; Multimedia/hypermedia systems; Cooperative/collaborative learning

1. Introduction

Many efforts have been made to explore alternative ways of teaching mathematics by creatingcurricula and didactic material that incorporate new tools, pedagogical approaches, and modelsor methods, which engage learners in a more pleasant, mathematical learning process (Szendrei,1996).

Through the use of new technologies in the classroom, there is promising evidence of a relation-ship among computer-supported recreational activities, positive attitudes towards mathematics,improvement in mathematical learning, and student performance (Kenneth, 1996; Rosas et al.,2003). As noted by Jonanssen and Carr (2000), technology is used as a mindtool that ‘‘can be usedto support the deep reflective thinking that is necessary for meaningful learning.’’

According to Brandt (1997), the use of computers in education can be utilized as a new tech-nological support for the visualization of abstract concepts through computer-generated virtualrepresentations, allowing for the generation of mental models of the concept. With computer soft-ware, students can interact with educational material designed to develop the skills necessary tosolve everyday situations by using their mathematical background. Nevertheless, the ludic com-ponent in the instruction of mathematics has acquired relevance due to its ability to engage learn-ers in mathematics, either through ludic learning environments (Sanchez, 1998) or introducingmathematical games into the classroom (CIMT, 1999, 2000; Gros et al., 1998).

The use of a recreational context, where students are presented with a problem as part of aplayful situation, represents one approach in the design of educational software. One of themost relevant works is Papert�s LEGO-based Microworlds (Papert, 1996), in which childrenare encouraged to build their own videogames, as a strategy to understand that learningcan be done in a natural way through the derivation of new knowledge from mental structuresalready acquired. Therefore, learning can be improved if the student builds his/her own learn-ing environment, as Gros (2002) pointed out. However, this approach requires a strong com-mitment on the part of the student in order to acquire and develop the required skillsnecessary to become a Microworld-specialized computer programmer, reducing the numberof potentially successful students.

Another approach is the one used by the Colombian Ludomatica project (Galvis-Panqueva,1998, available at http://lidie.uniandes.edu.co/ludomatica/principalesp.html), which is based onthe exploration of fantasy and magical worlds in which students are presented with problem-solving situations as they progress in their own adventure. In order to gain access to new scenes,students have to solve puzzles, riddles, and crosswords. The activities that students must performin the learning environment focus on the psychological and motivational aspects of learning, inorder to reinforce cognitive skills rather than acquire specific mathematical knowledge, as sug-gested by Quinn (1997). The Ludomatica project is also intended to prepare teachers to adoptthe model and develop playful activities, such as collaborative problem-solving and computer-supported activities using multimedia software, Internet services, games, building sets (such asMecano), and books (Galvis-Panqueva, 2000).

http://lidie.uniandes.edu.co/ludomatica/principalesp.html

620 G. Lopez-Morteo, G. Lopez / Computers & Education 48 (2007) 618–641

The usefulness of designing computer games to teach mathematics can be found in the project,Electronic Games for Education in Math and Sciences, E-GEMS (http://www.cs.ubc.ca/nest/egems/index.html) of the Canadian University of British Columbia. E-GEMS is intended to moti-vate students to learn math and science through the use of computer games. The project analyzesthe ways in which interface design affects learning, game preferences by gender (Gorriz & Medina,2000), and the use of multi-player games for collaborative learning (Dai, Wu, Wu, & Cohen,2002). Members of the project consequently developed several independent educational computergames, some of which are available commercially.

In the work by Henderson and Landesman (1992) a significant importance is given to themotivational components in the learning experience in mathematics. Equivalently, Chacon(2000) relates a negative attitude towards mathematics, with the difficulties of applying mathe-matical concepts. These works agree with the results given in the Trends in International andMathematics and Science Study (TIMMS, 1999), that clearly show that students that have apositive attitude towards mathematics, tend to perform better than those with a negativeattitude.

In this paper, we present an approach to motivate students towards mathematics by using anelectronic collaborative learning environment. Our development is based on self-existent softwarecomponents called Interactive Instructors of Recreational Mathematics (IIRM) (Ibarra-Esquer,Lopez-Mariscal, & Lopez-Morteo, 2001; Lopez-Morteo & Lopez-Mariscal, 2000, 2003). Theseinteractive, recreation-oriented learning objects are integrated within a collaborative electroniclearning environment. Our proposal represents a unified platform that can be used as a personalworkspace by members of a collaborative learning community, providing a space wherein instruc-tors can publish their educational content and allowing developers to create interactive educa-tional content with features aggregated from the container. In order to support it, a detaileddescription of the IIRM architecture is presented. Descriptions of all of its elements are explainedin the IIRM context. In addition, the conceptual and technological model for the electronic envi-ronment is described. The foundation for its development is not only to create a respository forthe IIRM, but to have an integrated virtual workspace with a strong support to collaborativelearning. We present the results of the evaluation of the attitudes towards mathematics after stu-dents use the IIRM and the learning environment in different groups of high school students.A general platform for our study was established by a series of questions directed to determinetheir general sentiment towards mathematics and their previous experience of using software inthis process. We analyzed the usability and functionality of the learning environment, and also,the level in which the students perceived the recreational approach inherent in the IIRM. Theseresponses were mingled with the input we received from the students about their experience ofusing the learning environment, in order to analyze the motivational impact of the approachfor learning mathematics in the context presented in this paper.

2. The interactive instructor of recreational mathematics

For some time, we have been creating computer-based instructional material to contribute tothe process of learning mathematics. The main objective has been to enhance mathematical skillsand to help develop mathematical thought among users. For this purpose, we have been

http://www.cs.ubc.ca/nest/egems/index.html

http://www.cs.ubc.ca/nest/egems/index.html


developing educational software components, specializing in mathematical concepts presentedthrough recreational mathematics, called IIRM (Lopez-Morteo & Lopez-Mariscal, 2000).

We build the IIRM from self-contained educational content, designed to provide a ludic prob-lem-solving approach for learning mathematical concepts and promoting a positive attitudetowards mathematics. We call these basic elements Instructors of Recreational Mathematics(IRM). Basically, an IIRM can be viewed as an extension of the IRM, in which we add com-puter-based interactive elements to a specific IRM. Conceptually, an IIRM represents an educa-tional unit, composed of several elements – digital and rationale – with an instructional purposeon a well-defined mathematical topic. The IIRM, therefore, can be virtual laboratories, animateddemonstrations, and simulation tools that represent different metaphors of computer-aidedinstruction such as the computer as a tutor, a pupil, a simulation engine, and as a tool, asdescribed by Crook (1994).

The IIRM conceptual architecture (Fig. 1) consists of several elements that maintain a relationwith the central element, in order to add some of their features to the main mathematical topic.These elements are: pedagogical support, ludic context, interactivity support, the telematic sup-port, and the metadata element.

Pedagogical support. The IIRM model considers the fundamental issue of adopting a construc-tivist problem-oriented approach, as represented by the two rhombus in Fig. 1, with specialemphasis given to the generation of mathematical foundations. Central pedagogical issues relatedto curriculum design, the topics covered, and the appropriate use of technology to enhance learn-ing, as established and articulated in the Principles and Standards for School Mathematics of theNational Council of Teachers of Mathematics (NCTM, 2002), are considered. The actual imple-mentation is complemented by the research of several authors. We adopt the problem-solvingheuristic method of Polya (1973) as a step-by-step approach to analyze and solve a mathematicalproblem. The instructional content design is well implemented by the non-algorithmic approachfor teaching mathematics, as described by Szendrei (1996) and well-illustrated by examples bySteen (1999). In addition we use multiple representations of mathematical concepts, as recom-mended by Heuvelen (2001). In order to organize the on-line content, we use the model proposedby Chan-Nunez (1999). The latter is based on the five dimensions of learning developed byMarzano, Pickering, and McTighe (1993).

Telematicsupport

Interactivitysupport

Ludiccontext Metadata

Mathematicaltopic

Pedagogicalsupport

CognitiveLearningTheory

ProblemSolving

Orientation

Fig. 1. Conceptual model of the interactive instructors of recreational mathematics.


The Ludic context. In the development of the IIRM, the ludic context is shown as an independentelement. The importance of using a ludic approach to teach mathematical concepts is well docu-mented. It has the advantage of engaging learners with the content (Szendrei, 1996), and providesseveral alternative mechanisms to explore the concepts to be learned, either through fictitioussituations or recreational problems (Averbach & Chein, 2000; Sanchez, 1998; Szendrei, 1996). Thisludic approach has been tested successfully in the classroom to teach mathematics (CIMT, 1999;Gorriz & Medina, 2000; Rosas et al., 2003), science, geography, and history (Gros et al., 1998).Nevertheless, we do not use a specific mathematical recreation just because of its ludic nature.Its pedagogical value is essential too. The criterion is fundamentally that described by Papert(2000) in the sense that if specific mathematical recreation is going to be used to transmit mathe-matical knowledge, it should be chosen for the mathematical concept covered and its potential useas educational material with a direct pedagogical value. In this sense, the mathematical recreationsshould not represent isolated mathematical knowledge or be easy to master.

Interactivity support. Interaction is a major component in our development. We consider uni-directional and bidirectional interaction between learner and computer software in order to re-trieve rich multimedia content (e.g. video, audio or animations). In addition, we contemplatesupport for social interactions between learners through the use of interactive tools like chatrooms, instant messaging systems, and multi-player games.

Telematic support. This element contemplates the manner in which media and software aredelivered, as well as how learners can reach the IIRM and other computational resources. Sincewe have worked mainly with the WWW service, our approach uses several Internet services tocommunicate learners, to store and retrieve IIRM, to deliver IIRM content, and to synchronizemulti-player games.

Metadata element. The inclusion of the metadata element responds to the necessity of incorpo-rating a categorized description layer, which contains information about the IIRM and identifiesit as a learning object. Metadata acts as a bridge between the content and the context, where theIIRM is being used educationally or functionally. In an educational context, metadata can beused by the learner to identify properties of the learning object – valuable in a particular educa-tional situation – in such a way that the user can retrieve it from a catalog if needed. In a func-tional context, metadata is used to search, load, and exchange IIRM with other systems.

The IIRM model is designed to include elements from several areas of computer science andinstructional design in a single entity. Thus, the resulting instructional content incorporates fea-tures that make it more attractive to the students, compared to its static, digital or non-digitalcounterparts.

3. The electronic learning environment

Since each IIRM is an independent element, it can exist by itself without specialized computersystem support or awareness of the environment. The IIRM can be presented as web pages con-taining text, images, video, interactive dynamic elements, or Java-embedded applications. There-fore, we can distribute IIRM on-line, in CD-ROM or in any other storage media. The IIRM canalso be delivered via WEB site repositories. However, this does not fulfill our goal of an integratedvirtual workspace. In order to do so, we extended our model from isolated elements, contained on


a WWW-technology system, to a set of fully interconnected elements, interacting among them-selves, with the user, and with the container. With this in mind, we developed an architecturefor a virtual learning environment. Our first prototype, called ‘‘Los Supersabios’’ (http://azul.cice-se.mx/supersabios/), in honor of the Mexican science fiction comic strip of the same name (pub-lished by German Butze in 1936), has been running since the Spring of 2001.

Our electronic learning environment is defined as a collaborative workspace for the generationof mathematical knowledge through the use of playful learning objects. It has been designed toprovide support for learner–learning object interaction, learner–learner interaction, as well aslearner–workspace interaction. The environment model is organized with fully independent lay-ers. This allows us to extend the functionality of the system without affecting the entire model,in the sense that new elements can be added or modified to a specific layer when new pedagogicalor technological elements become available. In this way, each layer provides the learning environ-ment with specific functions that are then incorporated into the final outcome (Fig. 2).

First layer. The support for the Interactive Instructor of Recreational Mathematics. This layerprovides the mechanisms that support the information exchange between the IIRM and the sys-tem, in such a way that the IIRM can use the system resources through its container.

Second layer. Collaboration Mechanisms. Here, the learning environment is enhanced with thecapability of supporting interaction between learners through collaborative tools such as an in-stant messaging client. This layer provides mechanisms, like the invitation process to engage ina multi-player math game among users, in order to automate the process of interaction.

Third layer. Interfaces. In this layer, we find the elements that form the link between the envi-ronment and the user, acting as Duchastel�s learning interfaces (Duchastel, 1996), in the sense thatthe interfaces are situated between the learner and the knowledge that he/she intends to acquire,thereby acting as facilitators that offer access to the content, its structure, and the mechanisms tomanipulate it. This layer is divided into two parts: application to application interfaces and userinterfaces. The first one is related to the mechanisms that interconnect applications through the

Third Layer. Interfaces

Application toApplication Interfaces

User Interfaces

Second Layer. Collaboration Mechanisms.

First Layer. The Interactive Instructor of RecreationalMathematics.

Fourth Layer.Learning andPedagogical

Model.

SimulationsVirtual

LaboratoriesGames Math Tools

Collaborative Learning Interaction Tools

ProblemSolving

CognitiveLearning

Fig. 2. Conceptual model of the electronic learning environment.

http://azul.cicese.mx/supersabios/

http://azul.cicese.mx/supersabios/


environment. The second corresponds to the final appearance and layout of the user workspace,as well as the mechanisms to customize it. Also we find the mechanisms that an IIRM uses tointeract with the learning environment services in this layer.

Fourth layer. Learning and Pedagogical Model. This layer consists of the learning models usedby the other layers. Since all of the layers can implement different learning models, this verticallayer represents the contribution of each of the horizontal layers to the learning processes.

3.1. Developing the electronic learning environment

In accordance with the learning environment model described above, the system should provideseveral services that are able to support both the system and the IIRM requirements. The archi-tecture proposal should be capable of allowing maintenance of the system without imposing arigid framework for future development. Therefore, we developed a model architecture composedof modules. The modular architecture provides a well-defined separation of the different elementsthat constitute the system, wherein each module holds isolated services in order to avoid functionoverlapping. Hence the modules and their associated services can interact with each other throughinterfaces. This results in a design that allows for communication between components, whichoffer information only to client applications.

The architecture consists of four modules: the Session Management Module, the WorkspaceManagement Module, the Content Management Module, and the Messaging Management Mod-ule. All of these are available through a larger module that provides WEB application support.Fig. 3 demonstrates the relationship between the modules and the services. As mentioned above,each of these four modules provides at least one system service, which will be described below.

Membership service. This provides an interface to create, store, edit, and access personal infor-mation about the user, including their username and password, e-mail address, and session activ-ity. User session information is utilized by the interaction tools and the interactive learning objectsduring their execution. This layer manages user groups and introduces roles associated with mech-anisms that control access to the content, according to access control lists.

Customize service. Through this feature, users can customize their workspace, according to theirinterests. Users can change the color scheme of their personal workspace, the layout of the learn-ing objects, and then add or delete selected learning objects from their workspace.

Interaction service. The learning environment provides synchronous (instant messaging) andasynchronous (e-mail) interaction tools that allow interaction between users within the work-space. This interaction is intended to promote collaborative learning processes among members.Because these tools are fully integrated into the environment, embedded applications within learn-ing objects are able to use their interaction capabilities, in conjunction with a membership layer,to connect learners or applications and to facilitate the exchange of data.

Catalog service. The catalog provides a single interface to browse and retrieve learning objectsin the workspace. Through this service, the user has access to a list of learning objects, which aresorted by title. In order to assist the selection process, the interface shows a brief description ofeach object and explains the objectives and activities to be developed.

Interoperability service. The environment includes mechanisms that permit the incorporation ofexternal learning content into the catalog, making them available locally. Therefore, it is able tomanage a centralized registry of local and remote learning objects.

WEB Application Support

Session Management Module Content Management Module

Workspace Management Module Messaging Management Module

Membership Service

Membership information

Session tracking

Autentication mechanism

Access control

Interoperability Service

Import content mechanism

Export content mechanism

Registry of portal elements

Customize Service

Customization mechanism

Personal workspace management

Catalog Service

Catalog management

Presentation management

Interaction Service

Instant Messaging System

Chat Rooms Support

e-mail support

Applications state delivery

Fig. 3. Elements of the architecture of the electronic learning environment. Each element inside modules represents a

service available to the system, the user, and the applications.


3.2. Technologies

The electronic learning environment is an Internet portal composed of portlets (portal ele-ments), each containing a single learning object. We have adopted the definition of an Internetportal as a system composed of several applications available through a single interface. The sys-tem displays several learning objects at once, along with the mechanisms to manage the interfacelayout and the content.

We developed our first prototype based on the Jetspeed project of the Apache Software Foun-dation (http://portals.apache.org/jetspeed-1/). Jetspeed provides a Java-based platform to buildInternet portals. In addition to the basic portal functionality, this platform provides computerprogrammers with an Application Program Interface (API), which can be used to extend portalfunctionality. The API allows us to build portal elements that will operate as native portal appli-cations, providing access to the internal mechanisms of the system; a feature that we use to buildthe portlets, providing dynamic behavior or the user information to the applications embedded inthe learning objects.

For the web platform support, we used the Apache WEB server (http://httpd.apache.org/) todeliver static content, such as auxiliary pages and multimedia files. Also, this web server acts asa front end to the Tomcat application server (http://jakarta.apache.org/tomcat/), when the portalsystem is running. As a permanent storage engine, we used the relational database managementsystem, MySQL (http://www.mysql.com/products/mysql/index.html), because of its reliability andwell-tested robustness.

http://portals.apache.org/jetspeed-1/

http://httpd.apache.org/

http://jakarta.apache.org/tomcat/

http://www.mysql.com/products/mysql/index.html


For the messaging module, we used the Jabber instant messaging server (http://www.jabber.org/about/), which provides learner–learner communication through instant messaging and chatrooms. The open protocol specification based on XML, as well as its robustness, represent themost interesting and useful features of the Jabber project. With these features, it is possible tobuild Jabber clients easily, as we did for multi-player games; an example of which will be shownin detail in the next section. In addition, we used the Exim mail server (http://www.exim.org/exim-html-4.50/doc/html/spec.html) and the Cyrus IMAP server (http://asg.web.cmu.edu/cyrus/imapd/index.html) to manage electronic mail and deliver messages, respectively. These applications runsimultaneously in a single Linux box. It is important to mention that we have tested successfullyusing other platforms, such as the Microsoft Windows NT and Sun Solaris operative system.

3.3. User session and information management

Special care is taken in regards to user information integrity in the system and in the interactiontools. For this purpose, we consolidated the user information in shared tables in the MySQL data-base. Therefore, embedded applications either have direct access to it or through the learningenvironment membership service. Hence, when a user authenticates himself within the environ-ment, he/she automatically acquires access to all of the content and services, without having toretype their authentication information in order to use a specific service. For example, when a userlogs into the learning environment, the instant messaging client automatically initiates a sessionwith the Jabber server, allowing the user to receive messages from partners. These can be simpletext messages or invitations to start a multi-player game. In this case, the game requests user infor-mation from its portlet container to create an instance for the shared game session.

The environment builds the learner portal home page from several sources: HTML static pages,dynamic server-side processing HTML pages, HTML client-side dynamic pages (with Javascript,Java applets, and Macromedia Flash objects), XML to HTML transformed pages, syndicationcontent through XML applications, and other WEB-based applications. The electronic environ-ment provides two different ways of presenting itself. The first one is a folder-like interface thatprovides access to a variety of content, while maintaining the structure of the site visible to thestudent as it browses the content. This interface is intended to be accessible in the public sectionof the environment. The second one resembles a layout similar to the front page of a newspaper(Fig. 4). In this way, students have access to several learning objects at the same time.

The customization mechanisms of the learning environment permit the workspace owner tomodify the layout of the web page, the color scheme, or the arrangement of each portal element,each of which contains a single learning object. The user can browse a catalog of learning objects,selecting those that will be added to the workspace. When a learning object becomes part of theuser workspace, it becomes an active portal element. The user can also remove single portal ele-ments from the workspace directly or through a special web page designed for this purpose. Thefeature gives the learner full control over the active learning objects at a given time, creating anadequate atmosphere for self-conducted learning and special types of courses. However, teachersenjoy different levels of control over the content that is presented in the learner workspace.

When a user logs on for the first time, he/she will be presented with a pre-configured homepage by the system administrator. It will contain a collection of learning objects, arranged ina pre-defined layout. In a tutor-driven context, this feature allows teachers to provide a unified

http://www.jabber.org/about/

http://www.jabber.org/about/

http://www.exim.org/exim-html-4.50/doc/html/spec.html

http://www.exim.org/exim-html-4.50/doc/html/spec.html

http://asg.web.cmu.edu/cyrus/imapd/index.html

http://asg.web.cmu.edu/cyrus/imapd/index.html

Fig. 4. Example of a student�s workspace with references to the type of content that the learning environment can handle.


content to the learning community by revealing a learner workspace with the layout that theyconsider most adequate for their group and their educational objectives.

At the same time, the system provides auxiliary mechanisms to retain non-removable content,including visible long-term information such as course objectives, references, and external URL.This can be achieved by providing fixed sections of content within the public area of the environ-ment, or by limiting the access to portal element controls to deny their removal from the work-space. Teachers can also maintain contact with learners through e-mail messages and bybroadcasting instant messages through the embedded instant messaging client.

Fig. 4 shows an example of the workspace. The IIRM shown is the well-known Hanoi Towersproblem viewed as a learning object. This IIRM is intended to show the recursive process associatedwith some properties of the integer numbers, such as the counting process, cardinality, and infinity.This is done while the user tries to find the minimum number of moves needed to solve the problemwith a given number of plates. As shown in the figure, the user has an open chatting session providedby the instant messaging client. Other active IIRM, like the ArithMem multi-player game, text show-ing a riddle, and the instant messaging client, are located in the workspace. As we can see, the learn-ing environment offers many mechanisms for learner interaction via interaction tools or by means ofmulti-player math games, these latter constitute important elements of our development.

3.4. Collaborative learning

In order for a learner to establish relationships with other learners, the environment providesseveral communication tools as well as support for multi-player math games. To support the


entire interaction process, we first consolidated authentication information for the learning envi-ronment and the messaging services (instant messaging, chat rooms, and e-mail). We designed anddeveloped an IIRM communication interface based on the Jabber messaging server. The Jabberserver is capable of detecting on-line users for sending and receiving invitations to initiateinteraction sessions as well as communicating the parameters and actions between IIRM in theform of XML strings, which are sent within the fields of a Jabber message with the same structureas an e-mail message.

To test this methodology, we developed a math game, named Arithmetic Memory Game or‘‘ArithMem’’ (Ibarra-Esquer et al., 2001); a Java applet in which the players try to find pairsof matching cards laying face down on a board. In each matching pair, one of the cards will havean arithmetic expression, chosen by the user at the beginning of the game. The result will be foundon the other. Users alternate turns. In each turn, a player selects two cards. If both cards make amatch, those cards will be removed, the player scores a point, and the turn continues. The gameconcludes when all of the pairs have been found. For this, the system provides a turn controlmechanism. During the execution, players can see, in real time, the actions performed by theplayer in turn. We have also embedded a chat area, where players can send messages to each otherwhile playing the game interface. For this game, we adopt the flashcards approach with univocalrelationships between the questions and their answers in the form of an epistemic game. This is inaccordance with the ideas established by Sherry and Trigg (1996), who argue that such relation-ships help to develop mental models (epistemic forms), promoting reflection, analytical thought,and inquisitive learning.

For player interaction, we considered several processes, including interaction between users, usersession management, user to user communication, data synchronization between applications,concurrence management for delivering messages, floor control, and collaboration awareness.The information exchanged between game instances follows the relationship showed in Fig. 5.

Fig. 5. Relation between mathematical data, their XML representation, and the document type definition that defines

the structure of the XML document. Note that the iirm.dtd file is referenced at the top of the XML document.


The events related to the card selection are codified in a XML document, which is distributed to thegame instances as an application event. When the remote instance of the game receives the messageevent wrapped in a Jabber message, the remote game unwraps the event, decodes it, and parses theXML document in accordance with the document structure, as defined by the Document TypeDefinition file (DTD). The information is sent then to the presentation module of the game, so thatthe interface is updated to reflect the last move of the remote player. In this prototype, we haveimplemented a paired user interaction scheme, wherein floor control is defined by turns and undera non-optimistic blocking concurrence control scheme, as suggested by Greenberg and Marwood(1994).

4. Evaluation and results

After the development and deployment of the learning environment, we tested the overall func-tionality of the system. This was done while looking for evidence of the influence of using thelearning environment in the attitude of the students towards mathematics. We analyzed the moti-vational effect of using the IIRM and the environment by using them in three short, motivation-oriented courses for Mexican high school students, where they used ‘‘Los Supersabios’’environment.

The first course held in the summer of 2001, constituted part the ‘‘First Scientific Workshop forYouth’’ (Primer Taller de Ciencia para Jovenes, http://www.cicese.mx/tallerjovenes/) held inEnsenada, Baja California, Mexico. A total of 30 students (hereafter, Group A), attended a fourhour session course in groups of seven or eight students at a time. In the fall of 2001, six students –winners of a national high school science contest (hereafter, Group B) – participated in a similarfour hour session course. In the summer of 2002, eleven students (Group C), participating in the‘‘Second Scientific Workshop for Youth’’, attended a longer course divided in four two hour dailysessions for four consecutive days.

The courses were conducted in Internet-ready computer labs. Each student logged onto thecourse website, while the teacher presented the lesson, projecting it into the wall. In the website,students interacted freely with the material, computer programs, spreadsheets, animations, andinteraction tools. At some point, the students were asked to log onto the learning environment,thereby gaining access to their own electronic workspace. The topics covered in the courses were,in principle, familiar to the students. Nevertheless, they worked on non-trivial mathematical con-structions while exploring the topics.

At the conclusion of each course, the students completed a survey, consisting of fourteen ques-tions (shown in Table 1), distributed in five sections. Each question could be answered with one offive options on an ordinal scale: completely disagree, disagree, neutral, agree, and completelyagree. In the first section (Q1–Q3), feedback was intended to capture student attitudes towardmathematics. Since this represents a major issue in our work, we complemented the results of thissection by conducting a four-question survey (shown in Table 5) using 77 students at a local highschool (Group D). In addition, we explored the possible relationship between their future careergoals and their attitudes toward mathematics (question Q4cb). Questions Q4–Q7 examined theprevious experience of students with computer-based educational games, both local and distrib-uted. Questions Q8 and Q9 addressed the usability of the learning environment. The next three

http://www.cicese.mx/tallerjovenes/

Table 1

Questionnaire applied to Groups A, B, and C

Q1 Mathematics are very useful in daily life.

Q2 Do you think that mathematics are easy to learn?

Q3 Is it possible to learn mathematics in a fun way?

Q4 Do you like to use computer games?

Q5 Do you know of any programs that can help you learn or practice mathematics?

Q6 Have you used these programs?

Q7 Do you use games, in which you compete against other users on the Internet?

Q8 Did the learning environment of Los Supersabios seem easy to use?

Q9 Did you experience any problems while using the site?

Q10 Did the use of Los Supersabios motivate you to learn mathematics?

Q11 Did the use of Los Supersabios help you learn mathematics?

Q12 Did the games and activities of Los Supersabios amuse you?

Q13 Were the games and activities of Los Supersabios easy to use?

Q14 Would you play the Arithmetic Memorama again?


questions, Q10–Q12, inspected the relation between the use of the environment and student atti-tudes toward mathematics. The last two questions addressed their attitudes in relation to the useof games in the environment.

Table 2

Percentage results of the questionnaire for Groups A, B, and C

Options Section 1 Section 2 Section 3 Section 4 Section 5

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14

Completely

disagree

0.0 6.7 3.3 0.0 30.0 40.0 33.3 0.0 23.3 3.3 0.0 0.0 0.0 6.7 Group A N = 30

Disagree 6.7 13.3 10.0 16.7 16.7 26.7 40.0 6.7 33.3 3.3 10.0 0.0 6.7 3.3

Neutral 6.7 43.3 13.3 3.3 16.7 10.0 3.3 30.0 20.0 23.3 20.0 10.0 16.7 6.7

Agree 23.3 20.0 36.7 20.0 20.0 6.7 6.7 20.0 20.0 40.0 43.3 33.3 33.3 16.7

Completely

agree

63.3 16.7 36.7 60.0 16.7 16.7 16.7 43.3 3.3 30.0 26.7 56.7 43.3 66.7

Completely

disagree

0.0 0.0 0.0 0.0 16.7 33.3 33.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Group B N = 6

Disagree 0.0 16.7 0.0 0.0 50.0 16.7 0.0 16.7 0.0 0.0 0.0 0.0 0.0 0.0

Neutral 0.0 16.7 16.7 16.7 16.7 50.0 0.0 16.7 50.0 0.0 16.7 0.0 16.7 0.0

Agree 33.3 16.7 16.7 33.3 16.7 0.0 33.3 16.7 16.7 50.0 33.3 16.7 16.7 0.0

Completely

agree

66.7 50.0 66.7 50.0 0.0 0.0 16.7 66.7 16.7 50.0 50.0 83.3 66.7 100.0

Completely

disagree

0.0 0.0 0.0 0.0 18.2 27.3 36.4 0.0 54.5 0.0 9.1 0.0 9.1 9.1 Group C N = 11

Disagree 0.0 0.0 0.0 9.1 27.3 45.5 27.3 0.0 36.4 0.0 0.0 0.0 0.0 0.0

Neutral 9.1 9.1 0.0 9.1 36.4 0.0 36.4 9.1 9.1 0.0 0.0 0.0 9.1 0.0

Agree 36.4 63.6 54.5 18.2 9.1 9.1 0.0 27.3 0.0 45.5 63.6 45.5 36.4 45.5

Completely

agree

54.5 27.3 45.5 63.6 9.1 18.2 0.0 63.6 0.0 54.5 27.3 54.5 45.5 45.5

The options column represents the five possible responses for each of the fourteen questions (Q1,Q2, . . . ,Q14), which

are completely disagree, disagree, neutral, agree, and completely agree, with a value ranging from 1 to 5, respectively.

Table 3

Likert-scale assertions and their answers mode from Group C

Dimension of the attitude towards mathematics Mode

I understand how mathematical concepts, which I learn in school, are related to one another 3

I do not understand how mathematics are used in daily life 3

I avoid activities related to mathematics 4

I do not know how mathematics are used 4

Dimension of the usefulness of recreational mathematics in learning mathematics

The games and recreational activities, which I use, do not relate to the mathematics that are used in daily life 4

I understand how to relate recreational mathematics, based on games and activities, to the mathematics that

I learn in school

3

I can use computer programs like Los Supersabios to better understand mathematics 4

If I can solve recreational problems, I can solve problems given to me in school 4

I prefer the didactic material used in school more than computer programs like Los Supersabios 4

The games and recreational activities that I used in the course do not relate to the mathematics that I learn

in school

4

Each option has a value from 1 to 4 for positive attitude, and 4 to 1 otherwise.

Each question has four options, ranging from completely disagree, disagree, agree, and completely agree.


In order to acquire more information about the population in the survey, we conducted a Kol-mogorov–Smirnov (KS) test on the data (Siegel, 1979). This test is commonly used to determinewhether samples of a population tend to share specific values, or whether the sample�s values arehomogeneously distributed among all of the possible values. The null hypothesis denoted by H0indicates that there is no difference between the expected number of choices for each option.Moreover, the observed differences are casual variations of a random sample of a rectangularpopulation, where f1 = f2 = � � � = fn are the sample values. In order to determine a possible ten-dency on the part of the individuals in the population to choose a specific option in each question,we applied the KS test to each survey question answered by Groups A, B and C, with a signifi-cance level of p = 0.01. The results of the test, indicating when the null hypothesis can be acceptedor rejected, are presented in Table 4 and organized by groups of values calculated for each ques-tion. These results, as well as the results from the first and second surveys (Tables 2 and 5, respec-tively), will be analyzed in detail in the following section.

4.1. Students feelings toward mathematics

Based on our analysis, there is good agreement among the participants in regards to the useful-ness of mathematics in daily life (Q1, average of 92.5%). In Table 4, the value of the KS test forGroup B indicates that we cannot reject the null hypothesis with p = 0.01, as in the other cases.This result indicates that students in this group did not select a specific answer. This was an unex-pected behavior for the group, because it was composed of winners of a science contest. Never-theless, a closer look at the percentage data in Table 2 indicates the opposite. To clarify thesituation, we raised the value of the significance level to p = 0.05 for this group. By doing so,we were able to reject the null hypothesis.

Table 4

Data for the Kolmogorov–Smirnov test evaluated at p = 0.01

Question Group D H0 N P

1 A 0.5667 Rejected 30 0.01

B 0.6000 Accepted 6

C 0.8000 Rejected 11 0.01

2 A 0.8276 Rejected 29 0.01

B 0.6333 Rejected 6 0.01

C 0.8966 Rejected 11 0.01

3 A 0.6333 Rejected 30 0.01

B 0.6333 Rejected 6 0.01

C 0.8333 Rejected 11 0.01

4 A 0.6000 Rejected 30 0.01

B 0.5000 Accepted 6

C 0.7667 Rejected 11 0.01

5 A 0.8333 Rejected 30 0.01

B 1.0000 Rejected 6 0.01

C 0.9667 Rejected 11 0.01

6 A 0.8333 Rejected 30 0.01

B 1.0000 Rejected 6 0.01

C 0.9333 Rejected 11 0.01

7 A 0.8333 Rejected 30 0.01

B 0.8333 Rejected 6 0.01

C 1.0000 Rejected 11 0.01

8 A 0.6000 Rejected 30 0.01

B 0.6333 Rejected 6 0.01

C 0.7667 Rejected 11 0.01

9 A 0.9667 Rejected 30 0.01

B 0.8333 Rejected 6 0.01

C 1.0000 Rejected 11 0.01

10 A 0.7000 Rejected 30 0.01

B 0.6000 Accepted 6

C 0.8000 Rejected 11 0.01

11 A 0.7333 Rejected 30 0.01

B 0.5000 Accepted 6

C 0.9000 Rejected 11 0.01

12 A 0.5000 Rejected 30 0.01

B 0.6333 Rejected 6 0.01

C 0.8000 Rejected 11 0.01(continued on next page)


Table 4 (continued)

Question Group D H0 N P

13 A 0.5667 Rejected 30 0.01

B 0.6333 Rejected 6 0.01

C 0.8333 Rejected 11 0.01

14 A 0.6276 Rejected 29 0.01

B 0.8000 Rejected 6 0.01

C 0.8276 Rejected 11 0.01

The null hypothesis denoted by H0 indicates that there is no difference between the expected number of choices for each

option and that the observed differences are casual variations of a random sample of a rectangular population where

f1 = f2 = � � � = fn, and fn are the sample values.

Table 5

Questionnaire and percentage results applied to Group D (N = 77)

Options Q1cb (%) Q2cb (%) Q3cb (%)

Completely disagree 1.3 22.1 9.1 Group D N = 77

Disagree 0.0 16.9 14.3

Neutral 5.2 41.6 27.3

Agree 14.3 5.2 10.4

Completely agree 79.2 14.3 39.0

Qcb4 %

Careers with strong mathematical background 56.3

Careers without strong mathematical background 43.7

The options column represents the five possible responses for each of the three questions (Q1cb, Q2cb and Q3cb), which

are completely disagree, disagree, neutral, agree, and completely agree, with a value ranging from 1 to 5, respectively.

Results for the fourth question (Q4cb), were obtained after grouping the student�s answers in two classes: those who

expect to study careers with and without strong mathematical background.

Q1cb Do you think that it is important to learn mathematics?

Q2cb It is difficult to learn mathematics?

Q3cb Do you like mathematics?

Q4cb What are you going to study in the university?


The results from the questionnaire applied to Group D are shown in Table 5 under the Q1cb toQ4cb columns. Again, the behavior of the answers in regards to the importance of mathematics(Q1cb) shows a notable trend toward the positive answers. In addition, student answers to ques-tion 2 (Q2cb) demonstrate that more than 80% possess some level of confidence in their abilities tolearn mathematics. The third question shows that more than 20% of the students view their atti-tudes toward mathematics positively, whereas 27% of the students choose the neutral option andnearly 50% (49.4%) of the tested group do not like mathematics.

The answer to the second question (Q2), relating to the appreciation of the difficulty of learningmathematics, exhibits a wider distribution among the students. The answers from Group A showan homogeneous distribution with 43% of neutral answers. In the other two groups, more than


60% of the answers fall into the affirmative area, as defined by options 4 and 5. A similar behavioris shown by students when asked if they thought that mathematics could be learned in an enter-taining manner, with a tendency towards the affirmative side.

The results obtained emphasize an important issue regarding mathematical education in ourschools. The results from international evaluations, such as the one developed by the Organiza-tion for Economic Cooperation and Development (OCDE, 2000, 2001) to measure students� abil-ity to apply mathematical knowledge, show that the value of the scale of aptitude for mathematicsfor Mexican students (387 points) is located well below the international average of 500 points.The results also indicate that students realize the importance of learning mathematics and its sig-nificance in daily life activities, although a considerable portion (23.4% or 18 students) expressnegative feelings toward it, even when they express confidence in their abilities to learn it. Thesebehaviors reflect those already reported in the literature (Suraweera, 2002). Moreover, the per-centage values coincide well with those reported in the Trends in International Mathematicsand Science Study (TIMMS, 1999). In the latter, the international average value of studentswho expressed an inability to perform mathematics operations is 15%, compared with the14.3% that we found in Group D. The international average value of students with the highestself-confidence in regards to mathematical aptitude is 18%, and in our work the average valueis 22%. The importance of the motivational aspect of learning mathematics is stressed by theTIMMS findings in which students who have a positive attitude towards mathematics, tend toperform better. As Henderson and Landesman (1992) found, motivational variables contributesignificantly to the prediction of learning outcomes for concepts and applications in mathematics.

Another interesting characteristic about this group is related to the distribution among the stu-dents� career goals (question Q4cb in Table 5). Based on the answers to question Q4cb, we wereable to classify the responses into two groups, one corresponding to careers with heavy mathemat-ical content (e.g. engineering, economics or physics) and the other corresponding to careers with-out heavy mathematical content. The distribution in the responses was balanced at 56.3% and43.7%, respectively.

4.2. Previous experience of students with educational and entertainment software

Results from question 4, as shown in Table 2, demonstrate that students like to play computergames; about 80% of the responses from Groups A and C were on the positive side. Answers toquestion 4 from Group B indicates that the group does not express a propensity for the use ofcomputer games. Note that the null hypothesis of the KS test is rejected. Nevertheless, we ob-served a very enthusiastic overall behavior among these students when they were introduced toon-line mathematical games, especially those with the multi-user arithmetic memory game.

Analyzing the results from question 5 for Group A, we found that only 53% of the students arefamiliar with computer programs for learning mathematics. For Group B, the result was 33%,while 54% of Group C demonstrates some knowledge of mathematical learning software. The an-swers to question 6 for the three groups show that an average of 63% of the students do not usethis kind of software.

Based on the responses to question 7, we can conclude that students prefer to play games thatdo not support on-line interaction: only ten of forty-seven students (21.7%) play these types ofgames. When we inquired into the student�s Internet working habits, we found that they did


not have many opportunities to work on the Internet due to the lack of computer hardware intheir homes. In addition computers were not always available in their school labs due to high stu-dent demand. Consequently, the distribution of the answers did not surprise us.

4.3. Usability of the learning environment

Answers from the three groups show that the usability of the system is adequate. No less than60% of the responses to question 8 are on the positive side. As a web system, the learning envi-ronment has the advantage of presenting an interface with text, graphics, web links, and form wid-gets, all which are familiar to regular Internet users. These factors contributed to the students�positive answers regarding the use of the system. On the other hand, computer performanceand computer reliability are very important variables, affecting student experience significantly.Our prototype showed a stable behavior when used by the students. Also, the mathematical com-puter games embedded in the learning object work well, especially when certain requirements ofhardware and software are achieved. The responses to question 9 demonstrate that roughly 23%and 33% of the students in Groups A and B, respectively, experienced negative feelings whenusing the environment, whereas no negative answers were found for Group C. A series of failuresin the computer hardware, the installed software, and installation facilities accounted for the neg-ative answers. We found a simple correlation between the hardware used in the courses and theanswers we obtained. During Group A�s course, several electrical blackouts resulted in a signifi-cant loss of power during two of the four sessions. We also experienced hardware problems in thecomputer lab. These problems affected the group responses. When the course was given to GroupB, we experienced less dramatic problems, although some of the workstations still experiencedhardware problems, which were proportional to the number of negative responses we receivedfrom the group. For the third course, we used a better computer lab with new computers, resultingin more positive feedback.

4.4. Motivation to learn mathematics and learning awareness

Motivating students to learn mathematics represents the most important objective in ourwork. Consequently, the results are very encouraging, given that more than 70% of the answersto question 10 were positive and only 30% of the answers were negative or neutral. The answersto question 11 show that students feel that they are learning mathematics while using LosSupersabios. Nevertheless, the results do not demonstrate a strong correlation, because the an-swers fall within the lowest part of the positive range. That is, students seem to have a positivenotion about what they have learned, although they are not quite certain about what theylearned. If we consider the results from the KS test for Group B, where the null hypothesis can-not be rejected, we can conclude that students in this group did not select specific options forquestions 10 and 11. Since this group had already expressed a predisposition toward science, wedid not expect this behavior. Nevertheless, this group was especially enthusiastic about the con-tent, the playful orientation of the course, the interaction tools, and the multi-player game. Itseems that all of the participants in the three courses enjoyed the experience of using ‘‘LosSupersabios’’. This observation is confirmed by question 12, in which all student answers arelocated in the positive area.


4.5. About the usability of the learning objects

In general, students felt comfortable using the games and activities of the learning environment,with more than 70% of the answers located in the positive region for question 13. Positive answerswere also given to question 14; answers vary from 83% to 100%, all in the positive region. Thisbehavior agrees with the observations we made in class, in that the multiuser game, combined withthe instant messaging tool, served as a trigger for user participation in classroom activities.

4.6. Attitude measurement

After the first two experiences with Groups A and B, we decided to use the same questionnaire,as well as an assertion-based, Likert-scale survey, to measure attitudes towards mathematics(dimension 1) and the use of the learning environment and its content (dimension 2) with GroupC. Students answered the Likert-scale assertions at the end of the course. For this survey, eachassertion had four options, ranging from completely agree, agree, disagree, and completely dis-agree. We intentionally disregarded the undefined option to force an answer, either positive ornegative. The values for each option vary from 1 to 4, respectively, if the assertion orientationis positive. Otherwise, the values of each option were reversed, in order to maintain the same valuerelationship between assertions.

Table 3 shows the assertions of the Likert-scale and their mode values for the two dimen-sions evaluated. As in the previous results, the results for dimension 1 indicate a positive atti-tude towards mathematics. It is significant that all of the mode values fall along the positiveregion of the scale. According to the answers to dimension 2, the students understood the va-lue of using the learning environment as well as the value of the content for learningmathematics.

In general, students expressed excitement about using the computer games and interactiontools. Also, the students appreciated the fact that the content was presented through recrea-tional learning objects, which was viewed as an innovative approach to learning mathematicsand very different from that used in the classroom. At the conclusion of the course, studentsexpressed their feelings about it. Examples of typical observations given by Group A are ex-pressed below:

‘‘. . .the course used a fun approach to understand different problems and theorems and adifferent way of looking at mathematics.’’‘‘The approach to teaching mathematics was better than that used to teach (mathematics) inschool.’’‘‘We interacted in a playful manner. The material and the instructors were perfect for me.They showed us that mathematics are more than counting numbers, besides which they madeit fun.’’

Videotaped interviews with five students from Group C provided another source of informa-tion. During the interviews, we asked their opinion about the relationship between the mathemat-ical topics covered in the course and the material presented at school. Four of the respondentsexpressed the opinion that the two were related. However, two of the students believed that thematerial presented in the course was more advanced than the topics covered at school. A couple


of students expressed the belief that the most important element in this relation was the problem-solving orientation provided in the course, perhaps not directly, but as a methodology or strategyfor solving mathematical problems.

Most of the material covered in the course, especially the arithmetic involved like number sets,scientific notation, exponents, arithmetic and geometric series, was not really new in the sense thatthe topics are covered in secondary school (grades 7–9). Nevertheless, these mathematical skillshad to be used to solve different problems, which were presented in an innovative, playful context.So, the perception that the material presented in this course was more difficult than those coveredin school came as a surprise. It seems that the algorithmic orientation, which they are most accus-tomed to, becomes an obstacle when applying basic mathematical skills in certain contexts and forproposing solutions to a given problem. Unfortunately, in an algorithmic-oriented mathematicscourse, students must learn the procedure to solve a trivial problem, in order to analyze and elab-orate a plan to solve it, using isolated mathematical knowledge as the building blocks of morecomplex solutions (Szendrei, 1996).

5. How students use the learning environment

The electronic learning environment is intended to provide learners with a personalized work-space, in which they enjoy the freedom to explore and customize it, according to their own needs.Therefore, the electronic learning environment is designed so that learners can adapt the learningenvironment interface in accordance with their different learning styles. We observed that whenthe teacher asked students to browse the catalog for retrieving an IIDM, they used the custom-ization mechanisms to accommodate it within their home page in several ways. Some of themchose to maximize the IIRM, which the entire class was using, in order to eliminate distractionswhen they felt the need to concentrate all of their attention on the current activity, especially whenthey worked with embedded applications.

As we have seen, some students divided their attention between academic and social activities,chatting while they worked yet maintaining their attention on teacher-led activities. For example,in the middle of an exercise with the Hanoi Towers problem, a student repeatedly switched backand forth from the application that simulates the problem to the instant messaging client, sendingto and receiving messages from a friend located at another terminal in the laboratory. Neverthe-less, this student continued to work satisfactorily until the practice ended.

After receiving basic instruction on how to use the learning environment, the students workedwith it and mastered it within a short period of time. We believe that the catalog service simplifiedthe process of locating educational content in the electronic learning environment. The contentwas retrieved from a single interface, referred to by title and/or description. It is also importantto note that the students never realized that they were using several IIRM from different sourcesand authors. They used HTML files, XML files transformed automatically by the system intoHTML code, syndicated content from RSS files transformed again into HTML code, and webapplications. It also seems that the integrated instant messaging client was introduced very gentlyinto the learning process, because the course activities were not centered on the use of the com-munication tools. The tools were used as alternative communication channels between students,who were engaged primarily in social activities. It seems that this type of learning environment can


help establish virtual learning communities. Even if used as a workspace, it supports social inter-actions that contribute to a relaxed and amiable learning situation.

6. Conclusions

This work seeks to facilitate the process by which mathematical knowledge is acquired by moti-vating students towards mathematics. For this purpose, we created the IIRM. As we have shownhere, the different elements that comprise these learning objects define its objective and reveal itsoperation.

The electronic learning environment presented in this paper is an integrated, collaborativelearning workspace designed to heighten the functionality of the IIRM. Its architectural designwas conceived to provide a basis for the existence and subsistence of the IIRM. Through accessto the different services of the system, the IIRM is enhanced with features supported by the envi-ronment infrastructure.

When used in a tutor-oriented scenario, its design has several features that are useful to allparticipants. For the student, the learning environment provides a rich learning experiencethrough an appealing and easy-to-use workspace, an important consideration for the success-ful use of this kind of instructional technology, as stressed by Stefanov, Dicheva, Nikolov, andDjakova (1998). Students can customize their workspace within an uniform layout by focusingon the content rather than on the web design. The system provides a series of mechanismswith which the teacher can publish and manage the educational content, especially throughthe use of the catalog service. The system also provides different and valuable services fordevelopers of the learning objects, allowing direct interaction with the repository, session dataexchange, and automatic access to the interaction services. Computer-supported interaction isa significant process supported by the electronic learning environment. It is important toemphasize that the system architecture includes features for the development and implementa-tion of multi-player math games. We also have shown that, in the context presented here,interaction between members of the learning community plays an important role in the acqui-sition of knowledge, as well as on a social and motivational level by promoting group coher-ence (Sherry, 2000).

In addition, we studied the use of the learning environment in short, motivation-oriented mathcourses for high school students. First, we measured the participants� attitudes toward mathemat-ics. We found that there was a generalized feeling among the participants in regards to the impor-tance of learning mathematics and its significance in daily life activities. At the same time,however, an important portion (23.4%) of the students expressed negative feelings towardmathematics.

The fact that students expressed a preference for computer games was not all that surprising.Nevertheless, they rarely engage in computer games on-line. The results show that their experiencewith software for learning mathematics was very limited. The students� experience using the learn-ing environment was a pleasant one, especially when the hardware was suitable. We were pleas-antly surprised to learn that the use of collaboration tools and the multi-player game promotesgreater interaction among students. Most of the students viewed the learning environment asan aid in learning mathematics and as a motivational tool.


Based on an evaluation and a careful appraisal of the attitude of the participants in the course,we believe that the use of the electronic learning environment, as well as the approach imposed bythe IIRM model, positively affected the students� attitudes towards mathematics and the educa-tional value of the ludic, problem-oriented approach. Therefore, the use of our approach in for-mal education could possibly improve the student�s mathematical learning outcome, by providingthe motivational dimension in the relationship between motivational elements and mathematicalperformance (Henderson & Landesman, 1992; TIMMS, 1999).

From our point of view, another element achieved in this study is that the architecture fills thegap between the educational content and its container. We believe that it is necessary to break theisolation of the content from the learning workspace, in order to offer the student the best possiblelearning experience. This can be accomplished through a closer content-container relationshipthat results in more complex and interesting didactic material. In this way, students can interactwith learning objects that use several services of the system in an unintrusive manner.

We can conclude, therefore, that in the context defined in this paper, the approach shown herehas the potential to contribute to the mathematics learning process, basically on the motivationalaspects of learning mathematics. Also, through the ‘‘Los Supersabios’’ electronic learning envi-ronment, the approach provides the three dimensions associated with technology-based educa-tional environments, as suggested by Nachmias, Mioduser, Lavah, and Oren (2000): the socialdimension associated with the learning community interaction processes; the technological dimen-sion provided by the system architecture; and the educational dimension associated with theIIRM model.

The full educational potential of using the IIRM-based, electronic learning environment withinthe model presented here, is yet to be determined. Nevertheless, the results from this initial studyindicate a genuine benefit, especially in relation to the motivational aspect of the process in whichmathematical knowledge is acquired in accordance with the established objectives. Our research iscurrently directed at performing further evaluations, not only in short, motivationally-orientedcourses, but also in other educational settings, like distance learning workshops and regularschool courses. Technologically, the process of developing IIRM continues; its generation followsthe model we have developed. Conceptually, the objective is to establish them within the currentlearning objects framework (AACE, 2003).

Acknowledgements

This work was sponsored, in part, by the Consejo Nacional de Ciencia y Tecnologıa (registrationnumber 69532). The authors would like to thank Andrea Spears for her valuable comments on thepaper.

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