Utilising a collaborative macro-script to enhance student engagement: A mixed method study in a 3D virtual environment

Computers & Education 58 (2012) 501–517

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Utilising a collaborative macro-script to enhance student engagement: A mixed method study in a 3D virtual environment Hara Bouta*, Symeon Retalis, Fotini Paraskeva University of Piraeus, Department of Technology Education and Digital Systems, 80 Karaoli & Dimitriou, 185 34 Piraeus, Greece

a r t i c l e i n f o

a b s t r a c t

Article history: Received 13 March 2011 Received in revised form 18 August 2011 Accepted 30 August 2011

This study examines the effect of using an online 3D virtual environment in teaching Mathematics in Primary Education. In particular, it explores the extent to which student engagement - behavioral, affective and cognitive - is fostered by such tools in order to enhance collaborative learning. For the study we used a purpose-created 3D virtual environment and a macro-script incorporating learning tasks related to basic fractions. The study itself took place during four teaching sessions in a primary school classroom. The data collected and analyzed included chat logs, classroom observation notes and the results of pre- and post-tests. The findings indicate that the 3D virtual environment actively engages the students’ interest and leads to richer interaction between them. This in turn results in a higher level of student engagement in the collaborative learning process. We believe that 3D virtual environments provide novel learning opportunities. However careful design is necessary in order to use their full potential. Ó 2011 Elsevier Ltd. All rights reserved.

Keywords: 3D virtual environments Online collaborative learning K-12 education Script Student engagement

1. Introduction In recent years the use of online 3D virtual environments in K-12 (primary and secondary) has been the subject of an ever increasing number of studies (Barab, Thomas, Dodge, Carteaux, & Tuzan, 2005; Choi & Baek, 2011; Garzotto & Forfori, 2006; Merchant, 2010; Nelson, Ketelhut, Clarke, Bowman, & Dede, 2005; Urban, Murty, & Twidale, 2007). Such studies have shown that these environments can yield positive results. They are currently utilized in the teaching of a range of subjects (history, sociology, languages) in an attempt to promote the cognitive aspects of learning (scientific knowledge, cognitive and metacognitive skills etc.) as well as the affective ones (attitudes, motivation, interest, curiosity, etc.) (Barab et al., 2008; Brom, Preuss, & Klement, 2011; Chen, Yang, Shen, & Jeng, 2007; Di Blas, Poggi, & Reeves, 2006; Dieterle & Clarke, 2007; Garzotto & Forfori, 2006; Urban et al., 2007). In all these contexts, studies stress the need for well–structured activities for these environments to be effective as teaching aids (Di Blas, Paolini, & Poggi, 2005a,b; Di Blas et al., 2006; Lucey-Roper, 2006). They also stress the need for further research on these environments, so they can be utilized effectively for both individual and collaborative learning (Chen, Yang, Shen, & Jeng M-, 2007; Di Blas et al., 2006; Konstantinidis, Tsiatsos, Terzidou, & Pomportsis, 2010). For this reason, research points to the need to carefully consider instructional design decisions (pedagogic strategies and appropriate activities) (Dalgarno & Lee, 2010; Lee, 2009). In addition, we need to explore a variety of factors which may affect collaborative learning in a 3D virtual environment, such as the interactivity, the representational fidelity and the embodied actions and communication facilitated by 3D virtual environments (Dalgarno & Lee, 2010). More specifically, in using 3D virtual environments to support collaborative learning, the focus should be on the construction and regulation of interactions within collaborating groups. Researchers believe that effective collaborative learning depends on the richness and intensity of interactions which group members engage in during collaboration (Dillenbourg & Hong, 2008). These interactions are the key to successful collaborative learning (Dillenbourg & Fischer, 2007; Jermann, Soller, & Mahlenbrock, 2001). In the literature, student engagement in the learning process is most commonly studied through three interdependent dimensions (Coates, 2007; Fredricks, Blumenfeld, & Paris,

* Corresponding author. Tel.: þ30 210 414 2765; fax: þ30 210 414 2753. E-mail addresses: [email protected] (H. Bouta), [email protected] (S. Retalis), [email protected] (F. Paraskeva). 0360-1315/$ – see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compedu.2011.08.031

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2004): a) behavioral engagement b) affective engagement and c) cognitive engagement. These dimensions can be seen as one of the factors which determine the effectiveness of Computer-Supported Collaborative Learning (CSCL). We believe that the need for both effective collaborative learning and well–structured activities in online 3D virtual environments at K12 level can be met by a carefully designed collaborative macro-script. According to Dillenbourg (2002), a macro-script is a computer-based pedagogical model for collaborative learning, which determines the way teams are formed and which involves specific stages, roles and activities. If carefully used, such a script provides the potential for the development of a wide range of interactions (Hernández-Leo et al., 2006). In the present study we designed a CSCL macro-script in order to investigate students’ engagement in a collaborative learning process within a 3D virtual environment called CoSy_World. CoSy_World is created on the Active Worlds 3D platform, in order to support the teaching of Mathematics in Primary Education. In particular, we selected the area of basic fractions, since this is traditionally a demanding concept for primary students to understand. The proposed macro-script utilizes the Simulation (Hernández-Leo et al., 2006; Linser, ReeLinstad, & Vold, 2007) and Jigsaw pedagogical strategies (Aronson & Bridgeman, 1979; Aronson & Thibodeau, 1992; Hernández-Leo et al., 2006). The reason we chose the jigsaw strategy is that it supports the interdependence of group members, it promotes interaction and cognitive elaboration and it fosters the construction of common knowledge (Dillenbourg, 2002; Hinze, Bischoff, & Blakowski, 2002). In addition, we took into consideration the view of a number of researchers who have advocated the use of jigsaw activities within the online context (Gallardo, Guerrero, Collazos, Pino, & Ochoa, 2003; Kordaki, Siempos, & Daradoumis, 2009). Jigsaw activities are used within the context of a simulation. The reason we used the simulation strategy was because it gives participants the opportunity to adopt roles which resemble real life. One or more participants are represented by an avatar in a realistic situation. Thus, simulation fosters a team spirit and a feeling that each member needs the others in order to achieve success (positive interdepence) (Hernández-Leo et al., 2006; Linser, Ree-Lindstad, & Vold, 2007). We believe that the use of these two strategies promotes collaborative learning enhancing student engagement (Coates, 2007; Fredricks et al., 2004). The students’ behavioral engagement refers to the degree of their active participation in discussions in order to a) solve mathematical problems (Coates, 2007; Fin, Pannozzo, & Voelkl, 1995) and b) communicate and share information found at various points in Cosy_World (extracurricular activities) (Coates, 2007; Finn & Rock, 1997). The students’ affective engagement is linked to the actions which develop when students view themselves as part of a group as they participate in collaborative learning processes. In our research this dimension is linked with the extent to which a) students are focused on their goal (achievement orientation) (Kong, Wong, & Lam, 2003), b) they demonstrate interest (Connell cited in Kong et al., 2003), c) they demonstrate boredom (an off-topic contribution) (Connell cited in Kong et al., 2003) d) they express values and feelings regarding the learning process they experience (Coates, 2007; Fin et al., 1995). The students’ cognitive engagement in the learning process is related to learning itself, to the way the individuals think and to the strategies they use in order to solve a problem or understand a concept (Coates, 2007; Kong et al., 2003). In this study this means that the students collaborate within the group, they discuss the activities and they collectively construct knowledge by comprehending basic fractional concepts and developing them (Janvier, 1987; Lesh, Post, & Behr, 1987; Seeger, 1998). Thus they acquire a) the ability to recognize the concept of a fraction in a variety of representations, b) the capacity to flexibly manipulate the concept within a system of representation and c) the ability to translate the concept from one form of representation to another. The structure of the paper is as follows: Section 1 contains the theoretical background for using online 3D virtual environments and CSCL in primary Mathematics Education. In the following section we describe the CSCL script in CoSy_World. Next, we describe the research design and evaluation methodology. Finally, there follows a discussion of the findings together with some recommendations for further study. 2. The use of CSCL and online 3D virtual environments in math education 2.1. CSCL in mathematics education Research in learning has traditionally focused on how knowledge is acquired. In recent years, the social dimensions of learning Mathematics have attracted considerable attention. In this context, Sfard (1998) talks about two main metaphors of learning: acquisition and participation. The first metaphor sees knowledge in terms of accretion/accumulation of facts, and acquisition in terms of the internal processes within the learner’s mind which ultimately lead to learning. Conversely, the second approach deals with learning through participation in an ongoing process and as the outcome of practice, discourse and activity. Sfard stresses that both approaches are needed in collaborative learning and by extension we argue that both are needed in CSCL. Faggiano, Pertichino, and Roselli (2005) claim that in the field of Mathematics, collaborative learning: a) can provide a social support mechanism and an opportunity for all students to succeed b) can promote the discovery and use of higher quality reasoning powers and the generation of new ideas and solutions c) can facilitate the transfer of mathematical strategies learned within the group to problems later encountered in individual mode. At the same time, Information and Communication Technology (ICT) can provide versatile environments in which the collaborative learning experience is greatly facilitated and enhanced. For these reasons, CSCL allows students to learn to work productively and efficiently with others and could be said to promote both acquisition and participation. CSCL offers many opportunities for innovation in education (Stahl, 2006). In the context of CSCL, students have the chance to collaboratively analyze knowledge, to make representations and to develop explanations (Scardamalia & Bereiter, 1994). Important aspects of CSCL environments are communication, reflection and inquiry among all the participants (De Lucia, Francese, Passero, & Tortora, 2009). It should be noted that CSCL practices need to be implemented within appropriate pedagogical approaches so that technology supports the learning process (Edelson, Gordin, & Pea, 1999). The importance of such practices has been amply demonstrated by research (NCTM, 2000; Sfard, 2002). Studies show how rapidly changing technology can give rise to new models for CSCL indicating that virtual learning spaces have great potential to support highly

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motivating collaborative learning experiences (Holmes, Lin, & Brandsford, 2001). The 3D environments can become an integral part of the learning experience (Jensen, 2001). 2.2. On line 3D virtual environments in math education On line 3D virtual environments have been utilized in education in such diverse fields as Biology and Epidemiology (Dieterle & Clarke, 2007), Religion, History and Sociology (Di Blas et al., 2005a,b; Di Blas et al., 2006), Language (Garzotto & Forfori, 2006; Petrakou, 2010), Science inquiry (Barab et al., 2008; Barab, Pettyjohn, Gresalfi, Volk, & Solomou, in press), and Astronomy (Chen et al., 2007). Compared to text-based and two-dimensional virtual environments, 3D virtual environments (Active Worlds, Second Life, There, etc) offer the following advantages: a) They can achieve optimal simulation of the real world or create a totally new fantasy world (De Lucia et al., 2009). b) They enhance representational fidelity through the realistic display of the environment, the smooth display of view changes and object motion, the consistency of object behavior, user representation, spatial audio, as well as kinesthetic and tactile force feedback (Chitaro & Ranon, 2007; Dalgarno & Lee, 2010). c) They enhance the feeling of immersion and the feeling of presence in their space. As a result they provide new ways to experience and view information (McLellan, 2004; Schmeil & Eppler, 2008). d) They guarantee high interactivity as well as smooth temporal changes in relation to other virtual learning environments such as Blackboard or Moodle (Dalgarno & Lee, 2010). e) They enhance learner interactions as they offer embodied actions including view control, navigation and object manipulation, embodied verbal and non-verbal communication, control of environment attributes and behavior, construction of objects and scripting of object behaviors (Chitaro & Ranon, 2007; Dalgarno & Lee, 2010). f) They offer a wide range of applications giving the user the option of constantly redefining his/her objectives. By contrast, other environments such as that of a game generally offer a single and strictly defined aim (The New Media Consortium and the EdUCAUSE Learning Initiative, 2007). These characteristics of 3D virtual environments have a great deal to contribute to the teaching of Maths since they can facilitate both collaborative learning and the learning of mathematical concepts. According to Gravemeijer (2004) there are four levels through which students progress in the study of Mathematics: the situational, the referential, the general and the formal. Assigning the task to the students is the point of departure (situational level). The task has a particular setting. Comprehension and solutions depend on the students understanding how to act in that particular setting. These settings often relate to out-of-school experiences. In order to simulate the latter in the classroom context a situation-specific model may be needed (referential level). Little by little, and with the teacher’s support, the students’ attention may shift towards the mathematical relations involved (general level). Lastly, the students may attain the final level of formal mathematical perception (formal level). 3D virtual environments can provide considerable support towards the meaningful understanding of Maths, since the construction of fundamental mathematical concepts begins with the students’ situational activity (Gravemeijer, 2004). At this point, 3D virtual environments offer a high interactivity framework suitable for action and learning. In particular, they optimally simulate the real world (De Lucia et al., 2009) and ensure representational fidelity (Chitaro & Ranon, 2007; Dalgarno & Lee, 2010). Consequently, they provide the opportunity for people and information to be organized in a realistic way in three dimensions (Schmeil & Eppler, 2008). Furthermore, the mathematical concepts can be represented in many ways which reflects what happens in real life. Research also stresses the considerable role representations play in Math education. In order to comprehend the concept of mathematical concepts, children must develop: a) competence in recognizing the concept through various representations (pictorial, symbolic, verbal), b) competence in flexibly handling representations of different qualities, and c) competence in translating the concept from one type of representation to the other (Janvier, 1987; Lesh et al., 1987; Seeger, 1998). In addition, 3D virtual environments can foster collaborative learning in Math education as they enhance the feeling of deep immersion and presence (McLellan, 2004; Schmeil & Eppler, 2008) as well as the learner interactions (Chitaro & Ranon, 2007; Dalgarno & Lee, 2010). Students interact simultaneously engaging in higher level participation. This fact makes such environments particularly appropriate for problem solving in an authentic context. By extension, these environments provide a deeper student engagement in the learning process. They provide the students with the opportunity to explore, to construct and to manipulate a range of representations regarding objects, constructions and ideas (Dalgarno & Lee, 2010). As a result, they allow students to work efficiently with others and they promote both acquisition and participation (Sfard, 1998). In this context students collaborate and argue in order to simulate the particular situation (referential level). Thereafter, they generate their conclusions concerning mathematical relations or problem solving (general level). In the last stage, they try to use mathematics at a more formal level (Gravemeijer, 2004). What is more, students make sense of complex data. This can help them develop a common understanding and it also engages them by means of enjoyable and memorable experiences. Such experiences can lead to increased involvement and provide a good basis for creativity (Schmeil & Eppler, 2008). Finally, their broad range of applications and the option for the user to constantly redefine his/her targets makes for a dynamic and flexible teaching environment which readily adapts to the students’ needs and the challenges of the learning process. Taking all the above into consideration we feel that the use of on line 3D virtual environments in Math education is amply justified (see Table 1). In this study, we attempted to make use of the advantages that 3D virtual environments and collaborative learning offer in the everyday teaching practice of Mathematics. To this end, we created a CSCL macro-script and integrated it into the 3D CoSy_World in order to develop better conditions for effective collaborative learning. The next section describes this CSCL macro-script in detail.

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Table 1 Aligning the Characteristics of 3D virtual environments with Collaborative learning and Math education. Characteristics of 3D virtual environments

Advantages for collaborative learning and math education Collaborative learning

Math education

Optimal simulation of the real world

It fosters the social dimension of learning maths It provides ‘real life settings’ for problem solving It provides optimal conditions for situated learning Students act as members of groups through enjoyable and memorable experiences It provides optimal conditions for situated learning Students experience higher levels of active participation Students become deeply engaged in the learning process It promotes knowledge acquisition and participation Students experience higher levels of active participation Students become deeply engaged in the learning process They enhance the social dimension of learning maths Students experience higher levels of active participation Students become deeply engaged in the learning process They promote knowledge acquisition and participation They promote innovative and effective ways in the collaborative learning process They offer students the option of constantly redefining their objectives

It helps students at the Situational level It allows students to use various representations

Representational fidelity

Feeling of immersion and feeling of presence High interactivity

Learner interactions

A wide range of applications

It helps students at the situational level It allows students to use various representations It helps students at the situational level It helps students at the situational level It allows students to use various representations They help students at the referential, general and formal levels They facilitate the recognition, flexible handling and translation of the concept They promote new ways of raising the level of learning They promote new ways of representing math concepts

3. A CSCL script in CoSy_World Our CSCL macro script is based on a combination of the Jigsaw and the Simulation pedagogical strategies. These two strategies foster collaborative learning creating the preconditions for a whole range of interactions. In particular, Simulation is a strategy where participants engage in role-playing experiences and learning becomes experiential (Hernández-Leo et al., 2006; Linser et al., 2007). Jigsaw is a strategy where students are given different information which they then have to pool when they get together in pairs or groups in order to collectively solve a particular problem. At the same time, the Jigsaw strategy regulates the formation and interaction of groups to ensure the smooth flow of activities and to optimize diversified participation. The learning goals of the script involve problem solving and the comprehension of fractional numbers which is a difficult concept for primary school children to master (Brousseau, Brousseau, & Warfield, 2004; Streefland, 1993). In trying to deal with situational activities, students engage in effective collaborative learning as they connect Mathematics with their daily life. Our script is supported by the CoSy_World online 3D virtual environment (see Fig. 1). CoSy_World consists of two basic areas: a travel agency and a part of ancient Cairo, where children travel together and interact in groups. Represented by avatars, they visit the travel agency to arrange a trip. The first series of tasks negotiated determines that Cairo is their travel destination and they are guided around through various stops following our script. In order to complete their trip, they engage in a number of activities and they have to interact at various levels – among initial group members (face-to-face), among groups represented in the virtual environment by avatars (through chat) and

Fig. 1. Screenshots from the CoSy_World experience.

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Fig. 2. A CSCL macro-script in 3D virtual CoSy_World.

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Fig. 3. Stage 1: Introduction to CoSy_World – initial briefing.

with the coordinator/teacher/travel agent (through chat). The mathematical activities are on the Web. Students communicate among themselves as well as with the teacher within the chat room provided by the Active Worlds platform. Our script comprises 4 stages (i.e., 4 on line sessions). The children play roles, interact with learning resources and collaborate in order to perform the learning tasks (see Fig. 2). During the first stage, the teacher briefs the children about what is to follow and they have their first experience of CoSy_World, represented by eight avatars. Each avatar has a name (Member 1A, 2A. 4B) and it represents a group of 3 children sitting in front of each P/C (initial groups). The avatars engage in a preliminary acquaintance with the environment and with each other. The eight avatars form two groups (A and B). Each group elects a leader to represent it and to coordinate its activities. The teacher is also represented by an avatar and acts as a coordinator and (travel) guide (see Fig. 3). Each avatar is instructed about its role and the route it has to follow within CoSy_World. Each route presents avatars with mathematical tasks (sub-problems) which they have to solve. Two avatars are directed to follow a particular route and they have to cooperate in order to solve the same activities. At the end of it all avatars exchange views about the World itself and about the activities they encountered and they have to pool their knowledge to solve an additional problem. Through this process avatars get to know CoSy_World while at the same time developing their understanding of basic mathematical concepts. During the second stage (see Fig. 4), the two groups (A and B) visit the travel agency, where they collaborate in solving mathematical problems in order to decide which of the trips on offer is the cheapest. Then avatars from group A get together with their group B counterparts to form pairs (‘sim groups’). The avatars engage in collaborative activities collecting information and then selecting the most economical trip. Each pair collects information about one possible trip and thus they become an ‘expert sim group’ in the section of the problem given to them (one of the three possible trips). Then the pairs report their findings to the other avatars through chat and together they all decide upon the most economical option. The avatar that represents the teacher is the travel agent acting as a coordinator, guide and expert. During the third stage, the trip which the children have selected takes place. Now the avatars collaborate again in pairs (expert sim groups), stopping at various places and carrying out a number of tasks related to fractions before they can proceed to the next part of their tour (see Fig. 5). For example at the Café station, each expert group has to solve activities which have to do with a particular fraction (e.g. expert group comprising avatars 1A and 1B have to work with the fraction 1/5; the expert group comprising avatars 2A and 2B have to work with the fraction 1/2 etc.). The activities have to do with the quantities of pizza, cheese pie and Turkish delight that the Café sells on certain days. The avatars engage in collaborative activities aiming first at: a) the comprehension of the concept of the fraction as part of a total area (Café station- see Fig. 6) and b) the comprehension of the concept of the equivalence of the fraction as part of a set of objects (Nile station), through various representational systems such as circles, rectangles, straight lines and sets of pebbles. This represents the first step towards comprehending the concept of the fraction, according to Janvier (1987). The next set of activities (Library station), aims at developing competence in the flexible handling of the concept of the fraction as part of a total and of the concept of the equivalence within a system of

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Fig. 4. Stage 2: At the travel agency – expert sim groups.

representation (2nd step, Janvier, 1987). Lastly at the Pyramid station the avatars engage in activities designed to develop the skill of translating the concept from one system of representation into another (children are asked to complete a symbolic, graphic or verbal representation of a fractional concept (3rd step, Janvier, 1987). Finally, during the fourth stage, groups A and B (jigsaw sim groups) discuss their experience (see Fig. 7). Each avatar engages in a discussion among the members of their group (A and B - jigsaw sim groups). During this discussion, the jigsaw sim group members have to pool their knowledge together in order to solve additional problems. For example, with regard to the Café station, they have to decide on which day the owner has the most leftovers (of pizza, cheese pie and Turkish delight) so that they can advise him to adjust his orders accordingly. Following this, the avatars take part in a general discussion. In this discussion they exchange views about CoSy_World and they inform their teammates (the members of jigsaw sim groups) about what they have learned by solving problems and engaging in collaborative activities related to fractions. The teacher acts as coordinator. 4. Research methodology This mixed methods study aims to examine the promotion of student engagement in collaborative learning via activities that were executed in an online 3D environment, namely, CoSy_World. In the field of social sciences such as education, mixed methods research has become popular and is considered a legitimate, stand-alone research design (Creswell, 2002, 2003; Creswell, Clark, Gutmann, & Hanson, 2003; Greene & Caracelli, 1997; Tashakkori & Teddlie, 1998, 2003). A mixed methods study is a “collection or analysis of both quantitative and qualitative data in a single study in which the data are collected concurrently or sequentially and they are prioritized. A mixed methods study involves the integration of the data at one or more stages in the process of research (Creswell et al., 2003). The reason for combining quantitative and qualitative data is to bring together the strengths of both forms of research to validate results. When both quantitative and qualitative data are included in a study, researchers may enrich their results in ways that one form of data does not allow (Brewer & Hunter, 1989; Tashakkori & Teddlie, 1998). This triangulation employed by the mixed methods design will be used to combine different but complementary data to “uncover some unique variance which otherwise may have been neglected by a single method” (Jick, 1979, p. 603). 4.1. The research questions Our macro-script aimed to promote student engagement in collaborative learning via activities that were executed in an online 3D virtual environment, namely, CoSy_World. Specifically, in the present exploratory study we tried to answer the following questions:

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Fig. 5. Stage 3: The trip – expert sim groups.

a) Does this CSCL macro-script promote students’ behavioral engagement? b) Does this CSCL macro-script enhance students’ affective engagement? c) Does this CSCL macro-script support students’ cognitive engagement?

4.2. Evaluation of the CSCL script in the CoSy_world: a case study For the students’ behavioral engagement, we evaluated the students’ active participation (AP) in the collaborative activities in order to solve mathematical problems by means of indicators describing the questions, answers, announcement of results, or expressions of attitudes of an avatar towards: a) another avatar of its group or b) an avatar of the other group or the teacher. We also evaluated the participation of avatars in activities showing their interaction with the online CoSy_World (extracurricular activities) (for example, the avatars read information provided by the 3D virtual environment on signposts). Thus we looked at the log files once again in order to extract qualitative criteria and quantitative indicators about the students’ behavioral engagement (see Table 2) in the learning process. The affective engagement dimension is associated with the degree to which students: a) focus on the goal (achievement orientation linked to the completion of the script phases). This is expressed through group collaboration, role taking and problem solving. In particular these indicators describe leadership skills (e.g. the avatar-leader guides the group), decision making skills (e.g. avatars engage in leader-selection) and trust building skills (e.g. requests for consent), b) demonstrate interest in the rest of the group and its activities. These indicators describe coordination skills (e.g., seeking other avatars), good relationship maintenance skills among group members (e.g. contributions aimed at the smooth cooperation of the group) and skills about topics outside the scenario (GU3) (e.g. general chatting).

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Fig. 6. Screenshot showing an example activity at the café station – comprehension of fraction as part of total area.

Fig. 7. Stage 4: Discussion – 2 jigsaw sim groups.

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Table 2 Qualitative criteria and quantitative indicators related to students’ behavioral engagement. Students’ behavioral engagement Qualitative evaluation criteria

Quantitative indicators

Data gathering process

Data process

The students’ active participation in the discussions in order to solve math problems

The number of times avatars ask, answer, express views addressing an avatar of their own team or the teacher (API) The number of times avatars ask, answer, express views addressing an avatar of another team (APC) The number of times avatars engage in extracurricular activities (ECA)

Videotaping each online session Reading chat messages from log files Videotaping each online session Reading chat messages from log files Videotaping each online session

Qualitative analysis: Taking observation notes and codifying chat messages Statistical process: Friedman’s non-parametric criterion Qualitative analysis: Taking observation notes Statistical process: Friedman’s non-parametric criterion

Student participation in extracurricular activities

c) demonstrate boredom (through off-topic contributions) (e.g. "Member3B": OTTRRFFF!!!!!!). In this case contributions are often irrelevant or incoherent. d) express the way they feel about the learning experience itself. They also get the opportunity to exchange views on this later on, during the 4th phase. To assess the degree of students’ affective engagement, we looked at the log files in order to extract qualitative criteria and quantitative indicators. This can be seen in Table 3. The cognitive engagement dimension is linked to the students’ comprehension of the basic fractional concepts 1/2, 1/3 and 1/5 and their multiples and the relationships between them. In our research comprehension is related to the extent to which avatars get involved in discussions negotiating and constructing knowledge (Janvier, 1987; Lesh et al., 1987; Seeger, 1998) (see Table 4) and acquiring: a) the ability to recognize the concept of a fraction through a range of pictorial representations b) the ability to flexibly handle the concept of a fraction within a system of symbolic representation and above all c) the ability to translate the concept of a fraction from one form of representation to another (pictorial, symbolic, verbal). Analyzing the context of chat log files we focus in the following qualitative criteria (see Table 4). Given that the ability to translate a mathematical concept from one system to another is particularly important to the learning of mathematical concepts (Gagatsis & Shiakalli, 2004; Janvier, 1987) quantitative indicators were extracted from the pre-tests and post-tests given to the students. These were assessed on the basis of how far the students comprehend basic fractions and give answers using pictorial, symbolic and verbal representations in their argumentation. These indicators (see Table 5) are the following: Indicator C (comprehension) refers to the extent to which the children understand the common fractions 1/2, 1/3 and 1/5 and their multiples. Similarly, indicator R (relationship) refers to the extent to which the children understand the relationship between 1/2 and 1/8, 1/3 and 1/6 and between 1/10 and

Table 3 Qualitative criteria and quantitative indicators related to students’ affective engagement. Students’ affective engagement Qualitative evaluation criteria

Quantitative indicators

Data gathering process

Data process

Students are focused on their goal (achievement orientation)

Leadership skills (SU1) Decision making skills (SU2) Trust-building among group members (SU3)

Videotaping each online session Reading chat messages from log files

Students demonstrate interest

Group coordination (GU1) Maintaining good relations among group members (GU2) Communication on topics outside the scenario (GU3)

Videotaping each online session Reading chat messages from log files

Students demonstrate boredom (through off-topic contributions)

Boredom (OTC)

Videotaping each online session Reading chat messages from log files

Students express values and feelings

Values and feelings (Only qualitative analysis)

Videotaping each online session Reading chat messages from log files

Qualitative analysis: Taking observation notes and codifying chat messages Statistical process: Friedman’s non-parametric criterion Qualitative analysis: Taking observation notes and codifying chat messages Statistical process: Friedman’s non-parametric criterion Qualitative analysis: Taking observation notes and codifying chat messages Statistical process: Friedman’s non-parametric criterion Qualitative analysis: Taking observation notes and codifying chat messages

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Table 4 Indicators related to results about students’ cognitive engagement in CoSy_World. Students’ cognitive engagement Qualitative evaluation criteria

Data gathering process

Activities in CoSy_World

Data process

The ability to recognize the concept through a variety of pictorial representations

Videotaping each online session Reading chat messages from log files

Activity: café station – pictorial representations

The ability to flexibly handle the concept of a fraction within a system of symbolic representation

Videotaping each online session Reading chat messages from log files

Activity: library station – symbolic representations

The ability to translate the concept of a fraction from one form of representation to another (pictorial, symbolic, verbal).

Videotaping each online session Reading chat messages from log files

Activity: Pyramid station – translating the concept pictorial-symbolic-verbal representations

Qualitative analysis: Taking observation notes and codifying chat messages Qualitative analysis: Taking observation notes and codifying chat messages Qualitative analysis: Taking observation notes and codifying chat messages

1/5 while indicator RC (relationship-comparison) refers to the extent to which the children understand the relationships between 3/4 and 1/ 2, 2/5 and 3/5, 1/3 and 1/4, as well as between 2/5 and 1/2.

4.3. Participants The participants in the pilot study were 24 children (15 boys and 9 girls), all 5th grade Primary School students. The study lasted for 2 weeks and the children had to meet 4 times (4 sessions), each time for two teaching hours in the Mathematics class. The experiment took place in an urban school in Athens. The conditions were far from perfect since there was no IT lab and we had to create one for the sake of our research. In addition, the children were unfamiliar with 3D learning environments. However they did have an elementary knowledge of how to use a P/C (use of the keyboard, MS Office Word and the Internet). For a period of two weeks before the commencement of our study, the children were exposed to other Active World environments in order to familiarize themselves with the software and to get some practice in learning how to operate within the latter (e.g. how to select an avatar, how to get about, how to communicate through chat, etc.). It is clear that they had no previous knowledge of CoSy World. During the experiment, the children solved mathematical problems and engaged in activities related to the comprehension of basic fractional concepts. The children had previously been taught similar concepts as part of the syllabus however the pre-tests clearly demonstrated the existence of numerous misconceptions.

4.4. Data collection The data were collected from the analysis of the students’ chat messages (obtained from the logfiles of ActiveWorlds). In particular, we used qualitative analysis, descriptive statistics and non-parametric techniques. In addition, there was systematic observation of the video-recorded sessions. The data referring to the comprehension of common fractional concepts were also collected though a two-stage assessment (pre-test and post-test) given to the students before and after our collaborative learning intervention sessions.

Table 5 Qualitative criteria and Quantitative indicators related to the comprehension of basic fractions as a result of students' cognitive engagement in CoSy_World. Evaluation relating to students' cognitive engagement Qualitative criteria

Quantitative indicators

Indicative test questions

C: Comprehension of - fractions 3/4 and 2/8 - fractions 2/3 and 4/6 - fractions 3/5 and 6/10

arguments illustrated - by pictorial (p) - by symbolic (s) - by verbal (v) representations. Also, - complete answer (c) - no answer (n) arguments illustrated - by pictorial (p) - by symbolic (s) - by verbal (v) representations. Also, - complete answer (c) - no answer (n) arguments illustrated - by pictorial (p) - by symbolic (s) - by verbal (v) representations. Also, - complete answer (c) - no answer (n)

Question: Give me an example to illustrate the fraction 2/8 Demosthenes: Today I will fill the swimming pool by 8/8. How much will remain if I reduce it by 6/8? (he also draws it – both pictorial and verbal representation)

R: Comprehension of relationships - between 1/2 and 1/8 - between 1/3 and 1/6 - between 1/10 and 1/5

RC: Comprehension of relationships - between 3/4 and 1/2 - between 2/5 and 3/5 - between 1/3 and 1/4 as well as 2/5 and 1/2

Question: How does 1/5 relate to 1/10? Yannis: 1/5 is twice 1/10, because 10 are twice 5. (verbal and symbolic representation)

Question: Which fraction, 2/5 or 3/5, is bigger and by how much? Eugenia: 3/5 > 2/5 by 1/5 (She also draws - a circle, divides it in 5 parts and colours 2 parts, - a circle, divides it in 5 parts and colours 3 parts (verbal, symbolic and pictorial representation)

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Table 6 Non-parametric analysis of the indicators of behavioral and affective engagement in collaborative learning. Indicators

API APC ECA SU1 SU2 SU3 GU1 GU2 GU3 OTC *

Friendman’s chi-square or c2 criterion

MR-Means Ranks

c2 ¼ 8.28* c2 ¼ 8.00* c2 ¼ 16.0**

1.25 1.25 1.00 Statistically 2.44 1.44 1.25 Statistically Statistically Statistically

c2 ¼ 14.30** c2 ¼ 7.38* c2 ¼ 13.00*

Stage 1

Stage 2 2.13 2.25 2.00 insignificant 2.56 2.69 1.75 insignificant insignificant insignificant

Means

Medians

Stage 3

Stage 1

Stage 2

Stage 3

Stage 1

Stage 2

Stage 3

2.63 2.5 3.00

2.63 0.88 3.00

4.88 3.88 4.50

6.50 4.75 19.0

2.00 0.50 0.00

6.00 3.00 4.50

6.50 5.00 0.00

1.00 1.88 3.00

1.12 3.63 3.63

1.75 6.75 4.25

0.00 5.25 8.00

1.00 4.00 3.00

1.00 7.00 4.00

0.00 5.00 6.50

p < 0.05. p < 0.001.

**

5. Results and discussion In order to investigate the development of factors for the engagement in collaborative learning, we used Friedman’s non-parametric criterion for the three consecutive measuring phases (Corder & Foreman, 2009) (see Table 6). We used this criterion because of the small size of our sample (9 avatars). 5.1. Behavioral engagement and collaborative learning in CoSy_World Studying the results, we notice that the indicators linked to students’ behavioral engagement in the learning process are statistically significant. This means that the macro-script and the 3D virtual environment provided the opportunity and the motivation for each avatar/ student group to develop behaviors allowing them to participate actively in collaborative problem solving activities. More specifically, it appears that students engage in the learning process by asking and answering questions, and expressing opinions as much to avatars of their initial group (A or B) (API) as to avatars of the other group (APC) since the script indicates such cooperation. The table medians (see Table 6) show that the number of exchanges observed during the second and third online sessions is quite high. This might be due partly to the structure of the script and partly to the activities incorporated in CoSy_World. During these sessions the avatars needed to cooperate in pairs so the interaction between them seems to increase. Also the avatars seek out the members of their initial group to discuss and report their performance or difficulties. The above findings are also confirmed through a qualitative analysis of the chat messages exchanged during the three stages. As students collaborate, messages are exchanged in order for an avatar to express its opinion to the group, to ask or answer a question, or to express a concern or a wish (expression of feelings). Examples of such exchanges are given below (e.g. the symbol 2B / 4B means that avatar 2B responded to avatar 4B): "Member3B": Do you need help? B / 3A "Member3A": We are still at the café; I have a question about this activity A / 3B "Member3B": Is it about Mr Michalis’ pie? How much is there left on the pan? 3B / 3A The indicator ECA (extracurricular activities) is also statistically significant. The students learn about ancient Egypt, e.g. the significance of the floods of the Nile by studying the information signposts they encounter along the way. Interestingly, this is not directly required for their progress in the journey. Therefore we might infer that they do so either because they hope it might help them with the problems they will have to solve further along the way or because they are fulfilling their roles as travelers. Their interest appears to increase during the third route where they encounter more information signposts and at more frequent intervals. Though it is not obvious to them, however, this information subtly complements the selected study area in order to render the learning process more meaningful by highlighting the real life application of Mathematics. For example, they learn that the need to redefine field boundaries after the floods led the ancient Egyptians to invent fractions. 5.2. Affective engagement and collaborative learning in CoSy_World As regards the items relating to students’ affective engagement, we observe (see Table 6) that some of them are statistically significant while others are not. More specifically, Table 6 and the medians indicate that during the 1st and 2nd online sessions the macro-script provides more opportunities for jointly taken decisions (decision making skills) (SU2) among the avatars, who often discuss the activities in order to decide how to proceed. "Member2B": Cairo is the cheapest option, right? 2B / 2A "Member2A": Yeah, that’s what we found also A / 2B

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(2A and 2B belong to the same team but arrived at the solution independently through working in pairs with members of the other team). Moreover, the indicator describing trust building skills among group members (SU3) appears to be considerably supported. This is probably due to the fact that the script requires effective cooperation in order to follow the development of the activity, which in turn entails interdependence and effective communication, which are difficult without trust. Trust is also directly linked to the roles of each avatar: qualitative analysis demonstrates that group leaders are followed and consulted when there is uncertainty. Group members also exhibit behaviors that indicate mutual trust, e.g. an avatar will follow a fellow group member when it moves onto the next stage of the journey. "Member3A": How do we get to the Nile?; A / 3B "Member3B": Follow me B / 3A The leadership skills indicator is not statistically significant, probably because the script does not provide the leader with important responsibilities or a particularly marked role in comparison with the other members. The indicator describing the avatars’ interest to coordinate their activities (coordination skills) (GU1) is statistically significant. Results show an ascending process of the value of GU1 from one stage to the next. This means that the avatars are not lost in the world; they increasingly seek each other out, gather in groups when the script requires them to and participate directly in the execution of the activities. The indicator is particularly high during the third session, where the increasing number of activities requires greater coordination for better results. "Member3A": Where are you? A / 3B "Member3B ": Coming B / 3A In Table 6 the remaining indicators which relate to avatar interest in the group are not statistically significant. For example the indicator GU2 (good relationships maintenance skills among group members) is quite low. However, by watching the videos we observe that there are few instances of friction that would require an effort on the part of other group members to restore harmony and cooperation. This is probably because the students are absorbed in their tasks and their interdependence creates an atmosphere of collective responsibility which restricts willful or selfish behavior. It might also have to do with the fact that in CoSy_World they are enacting roles, which they undertake seriously enough to transcend any tendencies towards obstinate or selfish reactions which are frequently noticed in group work of the traditional kind. Alternatively, it may have to do with the structured nature of the intervention. There are also few instances of students communicating about topics outside the scenario (GU3). They appear to be focused on the activities and neither the teacher nor group leaders need to recall them to the task in hand. This is also confirmed by the indicator OTC (offtopic contributions) which indicates boredom and is statistically insignificant. The fact that the indicators pertaining to interest and boredom have reached such high levels may be due to the novelty of the experience since our intervention was conducted with students who are accustomed to a traditional teaching model. Finally, during the 4th stage, avatars have a discussion on their shared experience in CoSy_World. As a result, we collected data relating to how the students saw this learning experience in CoSy_World (‘values’). In their chat log files there appears to be great participation among avatars expressing various opinions. It should be noted that students were uniformly enthusiastic about this teaching intervention. Member1A": We liked this world very much because we had a lot of adventures. "Member1A": I felt as though I really was somewhere else. "Member1B": I liked the civilizations and their buildings. They also liked the opportunity for communication that was offered: "Member1A": Also because we collaborated and communicated with the other group. "Member2A": Wasn’t it wonderful that we communicated with the other kids? "Member2B": We could also communicate in writing through the computer. It is interesting to note some attitudes which show how children experienced their involvement in Maths through CoSy_World: "Member2A": I liked that we used Maths as we moved on the stages. "Member3A": .that we practiced Maths in a playful way. "Member3B": We solved problems and made decisions by ourselves. Of particular interest are the messages which describe the children’s wish to repeat such an experience through CoSy_World

Table 7 Non-parametric analysis of variance (Wilcoxon z), for the indicators of comprehension of fractional concepts.

*

Indicators

Criterion Wilcoxon (z)

C R RC

z ¼ 4.29* z ¼ 4.30* z ¼ 4.30*

p < 0.001.

Means Pre-test

Post-test

6.33 5.04 12.91

12.92 27.96 21.63

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Fig. 8. Example regarding the comprehension of basic fractional concepts (from pre-tests and post-tests).

"Member1B": It was great! Only I would like us to be in that world every day! "Member3A": Why do we have to go? "Member3A": It was fantastic! We must come again! 5.3. Cognitive engagement and collaborative learning in CoSy_World In this study we used an on line 3D virtual environment and CSCL in real classroom practice to investigate (among other things) how students, through interacting with each other, negotiate, share knowledge and regulate their thinking as they try to comprehend basic fractions. The interpretation of the students’ cognitive engagement in the process of fraction comprehension was done through analyzing the content of chat log files. During the first set of activities (cafe station) avatars use arguments related to their identification of the concept of the fraction as part of a whole area and then as part of a set of objects (Nile station), through various systems of representation (circles, rectangles, straight lines, sets of pebbles) [1st stage, Janvier, 1987]. They also recognize the concept of the equivalence of the fraction through various systems of representation (circles, rectangles, straight lines, sets of pebbles) [1st stage, Janvier, 1987]. Member1A: You’re wrong, there are 5 out of 15 pieces of cheese pie remaining – you can see it in the chart. A / 1B Member1B: Yeah, I can see it now. B / 1A In the second set of activities (Library station) the goal is the flexible manipulation of the concept of the fraction as part of a whole as well as of the concept of equivalence within the same system of representation (symbolic representation – matching tasks) [2nd stage, Janvier, 1987]. Here too avatars offer arguments in their discussion in order to comprehend the concepts. Member3B: 2/4 equals 1/2. Think what we did before. B / 3A Member3A: Pies and Pans? A / 3B Member3B: Yeah. B / 3A Finally, in the third set of activities (Pyramid station) the goal is to acquire the ability to translate the concept of the fraction as part of a whole and that of the equivalence from one system of representation to another. Students are given a worksheet and asked to provide symbolic, graphic or verbal representations of a fraction) [3rd stage, Janvier, 1987]. The answer shows that the students’ experience of CoSy_World is repeatedly utilized in the representations they provide. Member2B: What did you write in the first? B / 2A Member2A: 1/2 is more than 1/4. A /2B Member2B: How did you show it? B / 2A Member2A: Circle. A / 2B With regard to the communication between the avatars it was observed that in all three stages they focused on tasks individually first and appealed to their colleagues in the pair or other group members mostly to confirm results, or when they encountered problems. It is not clear whether this was done out of force of habit (because students are accustomed to competition rather than collaboration) or whether the complexity of such communication through chat discouraged them from attempting it. As far as the learning outcomes are concerned, in order to analyze and interpret the data referring to basic fraction comprehension as a result of students’ cognitive engagement in CoSy_World, we used the Wilcoxon z non-parametric criterion for two related samples (Corder & Foreman, 2009). The reason we used Wilcoxon’s non-parametric criterion was because of the small size of the sample (24 students) and because measurements were taken on two separate occasions before and after the teaching intervention (pre-test and post-test). As we can see from the Table above (see Table 7), it seems that the results of this intervention with regard to comprehension of basic fractions are also encouraging. As can be seen from all three criteria, following the intervention the children seem to give more complete and convincing answers related to the comprehension of fractional concepts. This means that students come up with convincing arguments

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when they have to answer questions related to the comprehension of basic fractional concepts. In their arguments they make use of a range of pictorial, symbolic and verbal representations. The following example (see Fig. 8), taken from the qualitative analysis, confirms this. Nick seems to have understood the concept of the relationship between 1/2 and 3/4 since his arguments demonstrate that he can identify the concept in a pictorial representation (circle), manipulate it flexibly in a system of symbolic representation and translate it from one system to the other (pictorial, symbolic, verbal). Generally speaking the students’ improvement in comprehension and ability to express it was impressive in comparison with the corresponding results after the same number of teaching sessions in a traditional class. Again however, it is not clear whether cognitive or affective factors were more important in shaping these results, since they might be due to the novelty of the experience and the children’s consequent absorption in it. 6. Conclusion and recommendations In this study we attempted to investigate whether the teaching of Maths in Primary education can be effectively supported by Computer Supported Collaborative Learning (CSCL). More specifically, we attempted to investigate whether student engagement in the learning process is promoted and enhanced in its three dimensions (behavioral, affective and cognitive) through the use of CSCL. To this end, we created an online 3D virtual learning environment which we named CoSy_World and a macro-script which regulates the roles and activities of learner-users in this environment and fosters the development of a rich variety of interactions since, according to researchers, these are the key to successful collaborative learning (Dillenbourg & Fischer, 2007; Jerman, Soller, & Mahlenbrock, 2001). We also took into account the social dimension of learning and that learning is the result both of an internal process and of the constant participation within the group (Sfard, 1998). Finally, we incorporated mathematical activities intended to promote students’ comprehension of basic fractions and structured them in such a way as to follow specific stages of learning as described by research (Janvier, 1987; Lesh et al., 1987; Seeger, 1998). CoSy_World along with the macro-script was used in a teaching intervention with a class of fifth graders in a typical primary school. The qualitative analysis of the students’ behavior and communication in the environment as well as the learning outcomes as shown in the pre- and post-tests indicate that the intervention supports learner engagement to a considerable extent. This is evident from the fact that most indicators reach statistical significance which in turn shows a more profound and global comprehension of the concepts than that attained through the traditional model of teaching. Student interest remained at high levels throughout the four sessions. They negotiated knowledge through interacting with each other and with the environment. In this way they participated in a constant learning process and they developed an understanding of basic fractions as their ability to demonstrate it in various representations shows. This suggests that the proposed intervention facilitates constant feedback between the two main metaphors of learning, acquisition and participation, which leads to a more secure and confident grasp of the concepts (Sfard, 1998). It is also worth noting that the results corroborate findings from studies which claim that on line 3D virtual environments can be put to effective use in the teaching of various subjects (Chen et al., 2007; Dieterle & Clarke, 2007). In other words, such environments, in addition to teaching other subjects can also support the teaching of Mathematics which is related to different thinking and knowledge construction mechanisms. However, there are also a number of factors at play that may have influenced our results and should be considered while using the 3D virtual environment as a teaching tool:  As we have seen, the students’ increased interest may be due to the novelty of the medium rather than the intrinsic qualities of the macroscript. Therefore it would be advisable to replicate the study with students who are more familiar with learning in such environments.  It is still not clear whether the smooth cooperation between avatars can be attributed to the role-playing which discourages selfish behavior or merely to the clearly structured nature of the intervention. Further research would help clarify this point.  Similarly, as mentioned above the tendency of avatars to try to solve problems individually rather than through collaboration may be due to force of habit or to the complex nature of communication in the virtual world. We therefore intend to explore ways of facilitating interaction at the level of actual problem solving by modifying the activities and introducing new elements.  With regards to the students’ exceptional perceived improvement, it is once again unclear whether this can be attributed to cognitive or affective factors (the novelty of the experience and the students’ absorption in it). Therefore, we believe further research is needed before we can come to reliable conclusions concerning the value of 3D virtual environments as teaching aids. In this we agree with a number of researchers who have come to similar conclusions (Faggiano et al., 2005; Stahl, 2006). More generally, we have the following suggestions to make for future research on the usefulness of 3D virtual environments:  We need to determine which cognitive aspects are particularly enhanced by the use of 3D virtual environments. To this end we believe that it is essential to conduct parallel studies with students from different educational systems employing different teaching methodologies and evaluate the results by taking account of the variation both across and within groups.  In our intervention the avatars operated in a 3D World, but they performed the tasks in a 2D interface. It would be worth investigating whether the inclusion of the tasks in the 3D environment has a beneficial impact as it would enhance the experiential learning dimension.  As in the teaching of fractions we relied heavily on representations (pictorial, verbal and symbolic) which benefit from a 3D environment, it would be interesting to look into the effectiveness of such environments for the teaching of other subjects such as Language, History or Philosophy where this might not be the case. References Aronson, E., & Bridgeman, D. L. (1979). Jigsaw groups and the desegregated classroom: in pursuit of common goals. Personality and Social Psychology Bulletin, 5(4), 438–466. Aronson, E., & Thibodeau, R. (1992). The Jigsaw classroom: a cooperative strategy for an educational psychology course. In J. Lynch, C. Modgil, & S. Modgil (Eds.), Cultural diversity and the schools (pp. 231–256). Washington, USA: Palmer.

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