Toward A Unified Modeling of Learner's Growth Process and Flow ...

Challco, G. C., Andrade, F. R. H., Borges, S. S., Bittencourt, I. I., & Isotani, S. (2016). Toward A Unified Modeling of Learner’s Growth Process and Flow Theory. Educational Technology & Society, 19 (2), 215–227.

Toward A Unified Modeling of Learner’s Growth Process and Flow Theory Geiser C. Challco1*, Fernando R. H. Andrade1, Simone S. Borges1, Ig I. Bittencourt2 and Seiji Isotani1 1

University of São Paulo, ICMC, Brazil // 2Federal University of Alagoas, Brazil // [email protected] // [email protected] // [email protected] // [email protected] // [email protected] * Corresponding author (Submitted December 3, 2014; Revised May 18, 2015; Accepted August 2, 2015) ABSTRACT Flow is the affective state in which a learner is so engaged and involved in an activity that nothing else seems to matter. In this sense, to help students in the skill development and knowledge acquisition (referred to as learners’ growth process) under optimal conditions, the instructional designers should create learning scenarios that favor the learner’s flow. One-way to obtain these scenarios is to incorporate the conditions postulated by the Flow Theory in the context of the instructional design process. However, little attention has been drawn to this integration, and how to apply the Flow Theory based on learning theories that provide theoretical justifications during the instructional design process. Thus, in this paper, we propose a framework to integrate the learner’s growth process and the Flow Theory. It provides adequate support for the instructional design of learning scenarios that lead and maintain learners in flow state. We demonstrate the usefulness of this framework by presenting an application that helps designers to search and select learning objects that have the potential to maintain the learner’s flow in a learning scenario.

Keywords Learning theories, Flow theory, Learner’s growth model, Instructional design, Learning objects

Introduction In the learning process, the learner’s affective state plays an essential role that influences several mechanisms of rational thinking and learning (D’Mello, 2012; Picard, 1997; Duque Reis et al., 2015). Learners citing negative affective states (e.g., boredom) during learning activities are, in general, significantly more likely to show inadequate learning outcomes, because they often are not motivated and are not engaged in learning (Craig, Graesser, Sullins, & Gholson, 2004; Shernoff, Vandell, & Bolt, 2008). To motivate a student so that he/she performs learning activities with complete immersion, it is necessary that his/her affective state provide an optimal experience. This affective state is denominated flow, and it is a mental state of operation characterized by a feeling of energized focus, full involvement, and success in the task being performed (Csikszentmihalyi, 2013). One condition for attaining and maintaining the flow state is a good balance between the perceived challenges of a task and the participant’s own perceived abilities to solve it (Csikszentmihalyi, 2014). A task that is too challenging or one that is not challenging enough may lead to frustration or boredom, hence demotivating learners. Thus, to define a learning scenario with specific learning objects that favors and maintains the learner’s flow during educational activities, instructional designers need to have some understanding about the influence of these activities/objects in the affective state of a leaner. For example, one factor that affects the perceived challenge of a given activity is the difficulty levels of learning objects. In this case, if the difficulty level of a learning object (or sequence of learning objects) is not adequately connected with the learning goals and the current knowledge and skills of a student, the learning scenario will be perceived as too hard and frustrating, or as too easy and boring. In a collaborative learning scenario, the challenge of designing adequate activities and selecting learning objects is even harder. If the instructional designer selects problems and learning objects that are too difficult (or too easy) for students, it will hinder students’ interactions, demotivate students, and lead students to not want to work in groups over time (Challco, Moreira, Mizoguchi, & Isotani, 2014; Isotani, Inaba, Ikeda, & Mizoguchi, 2009). For instance, consider a scenario where a student (the tutor) interacts with another student (the tutee) to solve a given problem (i.e., a selected learning object). In this situation, the tutor will learn by using his knowledge/skills to demonstrate how to solve a problem and the tutee will learn by following the tutor’s guidance. If the problem is too hard or the sequence of activities is not created to help students to collaborate, the tutor will not have the sufficient skill level or ISSN 1436-4522 (online) and 1176-3647 (print). This article of the Journal of Educational Technology & Society is available under Creative Commons CC-BY-ND-NC 3.0 license (https://creativecommons.org/licenses/by-nc-nd/3.0/). For further queries, please contact Journal Editors at [email protected].

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knowledge to solve and guide the tutee in the resolution of the problem. As a result, the learning scenario will cause emotional distress in both tutor and tutee, and the desired learning outcomes will not be achieved. To support the design of better learning scenarios that are pedagogically sound and can keep learners in a flow state, it is essential during the instructional design process to take into account the level of difficulty of learning objects and to link learning objects with theories that describe leaners’ growth. Unfortunately, this task requires specialized knowledge about instructional/learning theories, Flow Theory, and Affect Theory, and the skills to apply this knowledge in an integrated manner in order to select adequate learning objects and design effective learning scenarios that match students’ abilities. To support the design of authoring tools that help instructional designers with the proper selection of levels of difficulty that keep the learners in flow, in this paper we propose a framework to integrate the learner’s growth process and Flow Theory through a new theory-based model, named GMIF: Learner’s Growth Model Improved by Flow Theory. This model explains and describes the necessary conditions under which learners are able to learn more effectively based on learning theories, while keeping the ability-challenge balance of tasks defined in the Flow Theory. In particular, the GMIF has been used to create algorithms that help to automatize the selection of proper learning objects for specific learning situations. This paper is organized as follows: The next section provides details about the Learner’s Growth Model (LGM) and Flow Theory. Then we present related works on the application of Flow Theory in educational settings. Following that, we present the GMIF, offering a detailed description of our framework that integrates the LGM and Flow Theory. Next, to demonstrate the usefulness of our framework, we illustrate how the GMIF can be used to design learning activities and select learning objects. Finally, we present the conclusion of our work and recommendations for future research.

Theoretical background Learner’s Growth Model Based on learning theories, the Learners Growth Model (LGM) is a graph that represents the learning process of a student as stages of skill development and knowledge acquisition in a simplified way (Inaba, Ikeda, & Mizoguchi, 2003; Isotani & Mizoguchi, 2006). The learner’s growth process is represented as paths on the graph that allow for the representation of the relationships between learning strategies and their educational benefits. As shown in Figure 1, the LGM has twenty states that are the result of the number of stages related to skill development multiplied by the number of stages related to knowledge acquisition. In the graph, the stages of skill development (nothing, rough cognitive, explanatory cognitive, associative, and autonomous) are represented in the lower-left triangle, while the stages of knowledge acquisition (nothing, accretion, tuning, and restructuring) are represented in the upper-right triangle. In skill development, the cognitive stage (rough and explanatory) involves an initial encoding of a target skill that allows the learner to present the desired behavior or, at least, some rough approximation thereof; the associative stage is the improvement of the desired skill through practice; and the autonomous stage involves gradual continued improvement in the performance of the skill (Anderson, 1982). During knowledge acquisition, the accretion stage incorporates the addition and interpretation of new information in terms of pre-existent knowledge; the tuning stage involves coming to understand the knowledge through its application in a specific situation; and the restructuring stage comprises a process in which the relationship of the acquired knowledge is considered and the existent knowledge structure is rebuilt (Rumelhart & Norman, 1976). The arrows in the LGM shown in Figure 1 represent possible transitions between stages, and the form s(x,y) on the top of each vertex is the simplified form of representing a stage, where x represents the current stage of skill development and y represents the current stage of knowledge acquisition. For instance, the transition s(0,0) s(2,0) means the possible transition from stage s(0,0) where a learner does not have any knowledge or skills to the associative stage s(2,0) of skill development.

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Figure 1. Learner’s Growth Model (LGM) One of the most interesting uses of this model is the representation of learning strategies based on the benefits that different learning theories offer. Figure 2 shows two examples of this representation based on Cognitive Apprenticeship Theory (Collins, 1991), in which each black arrow implies the application of a learning strategy that facilitates the learner’s growth process. Figure 2 (a) shows the application of the apprenticeship learning strategy, where a student grows his/her cognitive skill from nothing s(0,y) into the associative stage s(3,y) through the rough cognitive stage s(1,y) and the explanatory cognitive stage s(2,y). Figure 2 (b) shows the application teaching learning strategy, where a student grows his/her cognitive skill from the associative stage s(3,y) into the autonomous stage s(4,y). With the use of the LGM, any learning strategy or educational best practice can be explicitly described as a path on the graph, facilitating the understanding, visualization and utilization of the model (Isotani, Mizoguchi, Inaba, & Ikeda, 2010).

Figure 2. Examples of LGMs based on Cognitive Apprenticeship

Flow Theory Csikszentmihalyi’s Flow Theory constitutes an important theory regarding the study of affective states during activities that require active work from participants, such as discussions, exercises, and group activities (Csikszentmihalyi, 2014; Snyder, Lopez, & Pedrotti, 2010). This theory has been applied in several fields, including 217

game design, commerce, and education. The key concept of this theory is the definition and description of “The Zone” (i.e., flow state) as a situation where a person is so engaged and focused on a particular task that he/she is completely immersed in it (Csikszentmihalyi, 2013). According to Flow Theory, the following conditions must be satisfied to achieve flow:  Clear goals in which the expectations and rules are clearly discernable  Direct and immediate feedback in which the successes and failures of the task are apparent, so that behavior can be adjusted as needed  Good balance between ability level and challenge One of the conditions given above is that the flow state only occurs if there is a good balance between the perceived challenges of the task at hand and the learner’s own perceived ability to solve it. This means that the definition of an appropriate challenge (i.e., level of difficulty) is fundamental to the design of situations that promote a flow state (Linehan, Bellord, Kirman, Morford, & Roche, 2014). Thus, Csikszentmihalyi proposes the three-channel model of Flow Theory (Csikszentmihalyi, 2013) shown in Figure 3, in which both anxiety and boredom drive persons to frustration. When a task is too difficult to be solved, it causes anxiety because it is perceived as too challenging or because the person’s skill level is not sufficient to solve the task. In the same way, when a task is too easy it causes boredom because it is not challenging enough, or because the person’s skill level is too high for the task.

Figure 3. Affective state in terms of ability level and challenge level, according to the Flow Theory model In the context of education, learners in the flow state frequently experience positive affect and better scores/performances compared with other learners who are in a similar situation but not in flow (Baydas et al., 2015; Ibáñez, Di Serio, Villarán, & Delgado Kloos, 2014; Shernoff, Csikszentmihalyi, Schneider, & Shernoff, 2003). For example, several empirical studies conducted by D’Mello and Graesser, using intelligent tutoring systems (e.g., AutoTutor) have shown strong positive correlations between learning gains, confusion, and flow (D’Mello & Graesser, 2012). Another example is the study of Choi et al., (2007), where participants used a web-based e-learning system in a program on Enterprise Resource Planning. The data of this study revealed that flow experiences were directly linked with learning outcomes and leaners’ attitude towards e-learning.

Related works The Flow Theory and the three-channel model proposed in Csikszentmihalyi (2013) have been frequently used for building instruments and tools for detection of the flow state (Kort, Reilly, & Picard, 2001; Pearce, Ainley, & Howard, 2005; Vanlehn, 2006; Shernoff et al., 2008; Esteban-Millat, Martínez-López, Huertas-García, Meseguer, & Rodríguez-Ardura, 2014). More recently, studies have attempted to analyze and model students’ flow experiences in order to (a) evaluate students’ interactions with learning objects; (b) personalize educational activities (e.g., lessons); and (c) develop better content. In this arena, the study of Del Blanco et al. (2012) proposes a framework to support the integration of games in learning activities. To do so, authors identified key aspects about the mechanisms that facilitate the use of pedagogical approaches with games to keep students in flow state. Then they proposed a 218

workflow for integrating games into learning designs. As a result, it is possible to create guidelines to help educators use (and reuse) sequences of games in the learning process. Although this work provides some initial support for creating better learning experiences, if the games themselves do not have the qualities and attributes necessary to maintain student engagement, flow experiences will not occur. Considering this problem, Kiili et al. (2014) presented a framework for analyzing and designing educational games based on Flow Theory. This framework describes several dimensions of flow experience as well as meaning factors that affect the design of game-based learning activities. Still, it is limited to specific parts of the game design process. The related work and frameworks presented in the previous paragraph are important for guiding educators and game designers to create better learning situations. Nevertheless, they were not created to automate the process of learning design and do not have the necessary formalization to be implemented and included as a feature in a learning design authoring tool. This means that if an instructional designer wants to support flow, he/she will need to do so manually, without any computational support. Such a manual approach is infeasible to be carried out when there is a need to plan personalized sequences of activities for a class of students with different needs, using a database with multiple learning objects (e.g., games, texts, videos, images) and taking into consideration several pedagogical approaches to support flow experiences. Toward the automation of detecting and using flow state to create better learning experiences, Lee and colleagues provide adaptive learning contents by selecting appropriate problems based on Flow Theory (Lee, Jheng, & Hsiao, 2014). They propose an automatic flow detector where the three-channel model of flow is built based on features related to affective dimensions (i.e., valence and arousal) and interactions (i.e., mouse click duration, keystroke duration) with learning software. As we can observe, despite the broad use of Flow Theory in educational contexts, to the best of our knowledge, there is not a computational model/framework based on Flow Theory that provides support for instructional designers to create learning scenarios that maintain the flow experience while offering theoretical justifications regarding the learner’s growth. In particular, there is no computational help to define appropriate challenges for leaners and to select adequate learning objects as needed to promote a flow state. Thus, our approach aims to fill this gap by proposing a computational framework that connects Flow Theory and the learner’s growth process. It allows for identifying a proper balance between ability and challenge according to the learner’s state of knowledge acquisition and skill development. It can also be used to create algorithms to equip authoring tools with intelligent features to automatize the design of learning scenarios that increase the chances of students reaching and staying in flow state.

Framework to integrate the learner’s growth process with Flow Theory The tasks that will be performed by a student in a pedagogical scenario are learning activities. The ability-challenge balance defined in Flow Theory should be determined by the current stage of the learner’s growth process and the difficulty level to maintain the learner’s flow. Therefore, our framework integrates the learner’s growth process and Flow Theory by labeling each arrow s(x,y)s(x,y) of the LGM with the form (zmin;zmax), indicating the minimum level (zmin) and the maximum level (zmax) of difficulty that are necessary to maintain the learner’s flow. This LGM with labels is called the GMIF: Learner’s Growth Model Improved by Flow Theory. In this section, we first show how a scale of five levels of difficulty is obtained with the GMIF. Next, we present our framework as a pseudo-algorithm that can be used to create a GMIF of any scale (n-scale GMIFs).

Five-point scale GMIF As we see in the three-channel model of Flow Theory, the perceived ability and challenge are indicators used to identify a person’s affective states. These two indicators are represented in the model of Flow Theory as an axis without scales and labels to depict situations where a learner can be anxious, bored or in a flow state. Thus, first we divide the axis into five parts to obtain a five-point scale. Next, the transitions in the skill development or knowledge acquisitions defined by the LGM model are set for the ability axis as the scales of space using a uniform distribution. Figure 4 shows the five-point scale of skill-difficulty that is defined by employing the five levels of difficulty [0:very-easy, 1:easy, 2:medium, 3:difficult, 4:very-difficult], and the transitions in skill development [s(0,y)s(1,y): from nothing to the rough-cognitive stage; s(1,y)s(2,y): from the rough-cognitive to the explanatory-cognitive 219

stage; s(2,y)s(3,y): from the explanatory-cognitive to the associative stage; s(3,y)s(4,y): from the associative to the autonomous stage]. According to this five-point scale, the label sequence for maintaining the learner’s flow is s1={[0;0],[1;2],[2;3],[4;4]}, in which each position represents a transition in skill development. The first element means that, during the transition s(0,y)s(1,y), the proper level of difficulty to maintain the learner’s flow is 0:veryeasy. The second element means that, during the transition s(1,y)s(2,y), the proper level of difficulty to maintain the learner’s flow is 1:easy or 2:medium. The third element means that, during the transition s(2,y)s(3,y), the proper level of difficulty to maintain the learner’s flow is 2:medium or 3:difficult. Finally, the fourth element means that, during the transition s(3,y)s(4,y), the proper level of difficulty is 4:very-difficult.

Figure 4. The five-point scale of skill-difficulty By employing the transitions for knowledge acquisition (s(x,0)s(x,1): from nothing to the accretion stage; s(x,1)s(x,2): from the accretion to the tuning stage; s(x,2)s(x,3): from the tuning to the restructuring stage), we obtained the five-point scale of knowledge-difficulty as shown in Figure 5. In this space, the label sequence s2 = {[0;0],[1;3],[4;4]} means that, during the transition s(x,0)s(x,1), the level of difficulty should be 0:easy to maintain the learner’s flow. The second element in the sequence means that, during the transition s(x,1)s(x,2), the proper level of difficulty to maintain the learner’s flow is 1:easy, 2:medium, or 3:difficult. Finally, the proper level of difficulty during the transition s(x,2)s(x,3) is 4:very-difficult. To obtain the five-point scale GMIF, we need to understand the relationship between the student’s growth state (i.e., perceived ability) and the difficulty level of learning materials (i.e., challenge). With this knowledge it is possible to design learning scenarios that (i) favor the maintenance of a flow state for students; and (ii) help them to achieve desired educational goals (i.e., acquisition of knowledge or development of skills). To accomplish our objective we used the analysis presented in Figures 4 and 5, which enables us to understand when students are in flow state (by making the correlation between knowledge and skills with a five-point difficulty level scale), to adequately label each transition (i.e., s(x,y)s(x’,y’)) between states in the LGM with a tuple [zmin; zmax], where zmin refers to the minimum difficulty level necessary for a learning material (or sequence of materials) to be considered interesting and not too easy for a student, and zmax refers to the maximum difficulty level possible for the same material to be considered challenging but not too difficult. According to previous findings, such an explicit formalization is one of the key features needed to promote more effective and robust learning in e-learning environments (Esteban-Millat et al., 2014; Fulmer, D’Mello, Strain, & Graesser, 2015; Linehan et al., 2014). To define the values of each label [zmin; zmax] for each transition s(x,y)s(x’,y’), we used the sequences s1 and s2 that define the proper levels of difficulty for each transition related to skill development and knowledge acquisition, respectively. Thus, when a transition is related to skill development, we used sequence s1 and Figure 4. For example, to develop skills from the explanatorycognitive stage to the associate stage, we label the transition s(2,y)s(3,y) in the LGM graph as [2;3] by looking at 220

where this transition is located in the flow area presented in Figure 4. In this particular situation, [2;3] means that to maintain the learner’s flow, learning materials should be selected to challenge students by offering moderate levels of complexity to solve a task. Following the same procedure, the transitions related to knowledge acquisition use sequence s2 and Figure 5 to define the values of the labels. Figure 6, then, shows the five-point scale GMIF that results from labeling the LGM with a scale of five levels of difficulty.

Figure 5. The five-point scale of knowledge-difficulty levels

Figure 6. Five-point scale Learner’s Growth Model Improved by Flow Theory 221

There are several theoretical and practical applications of the proposed framework. One of them is helping instructional designers and educators to adequately select learning strategies (Figure 2) and challenges to create sequences of activities that have the potential to support the learner’s growth (based on learning theories) and at the same time provide a learning environment suitable for getting students into a flow state. It is also possible to use this framework for selecting learning objects that offer the right amount of challenge to students. We will further discuss the benefits of this framework in the following sections. It is also important to note that although in this work we use a five-point scale of difficulty level, there are other scales of difficulty that can be considered during the design of learning scenarios. Thus, in the next section we will present how our framework can be mapped and used with any desired scale of difficulty.

Pseudo-algorithm for n-scale GMIFs Figure 7 shows the pseudo-algorithm of our framework that can be used to build a GMIF for any difficulty level scale (n-scale GMIF), where the expected difference for levels of difficulty in the flow area is passed as a second argument (delta that has the default value zero). In the pseudo-algorithm, the symbol GMIF((x,y),(x’,y’)) represents a label for the transition from s(x,y) to s(x’,y’) of the LGM, and each label is represented as the form (zmin;zmax), which indicates the minimum (zmin) and maximum (zmax) levels of difficulty for maintaining the learner’s flow. The flow region in the pseudo-algorithm for the two areas of skill-difficulty and knowledge-difficulty are obtained by the function get_flow_region (lines 2-3), where the first parameter is the number of transitions (for skill development or knowledge acquisition), the second parameter is the scale of space, and the third parameter is the expected difference for levels of difficulty.

Figure 7. A pseudo-algorithm to build the n-scale GMIF In the pseudo-algorithm shown in Figure 7, because the transition of skill development includes a flexibility that allows for increasing the skill stage without following all the transitions between stages, transition s(x,y)s(x’,y) (lines 4-5) is labeled by all levels of difficulty that are defined in intermediate transitions. For example, it is possible to go from 0:nothing to 3:associative stage without moving through 1:rough-cognitive stage and 2:explanatorycognitive stage; thus, the transition s(0,y)s(3,y) is labeled with the union of levels of difficulty defined in the transitions s(0,y)s(1,y), s(1,y)s(2,y) and s(2,y)s(3,y). In the case of knowledge acquisition, the transition of stages is completed step-by-step without skipping any of the stages; thus the transition s(x,y)s(x,y’) (lines 6-7) is labeled by setting the corresponding levels of difficulty knowledge-difficulty. Figure 8 details the pseudo-algorithm for the function get_flow_region. This function calculates the flow region for skill-difficulty and knowledge-difficulty, where the flow region is represented as an array of size m (number of transitions for skill development or for knowledge acquisition) in which each i-th element contains the levels of difficulty for the transition from the i-th stage to the next stage (i+1 stage). For an instance of five levels of difficulty and three transitions of knowledge acquisition (shown in Figure 5), the flow region as a result of the pseudoalgorithm is a sequence s = {(0;0),(1;3),(4;4)}, where the first element (0;0) indicates the level of difficulty as 0:very-easy for the transition s(x,0)s(x,1). The pseudo-algorithm to obtain the flow region shown in Figure 8 can be summarized in a narrative form as follows: Calculates the number of levels that should be distributed for each transition of stage (lines 3-12). These values are calculated through a uniform distribution that tries to maintain the same number of levels in all stages. The stages located in the same distance of mean stage should have the same number of levels. For example, the distribution of 222

eight levels of difficulty in five transitions is defined as the array s = {1,2,2,2,1}, where the second, third, and fourth transitions are set with two levels (s(1) = s(2) = s(3) = 2), while the first and fifth transitions are set with one (s(0) = s(4) = 1). The transition located in the third transition is set with two levels (s(2) = 2). The steps that calculate these levels are as follows:  The normalization for the number of levels of difficulty. This is done to avoid the non-uniform distribution that happens when this number is odd and it is greater than the number of transitions. For example, the distribution of nine levels among four transitions only can be done by setting one transition with three levels, and setting the rest of transitions with two levels. Therefore, the normalization of level of difficulty is done by reducing the number of levels by one (lines 2-5). In the previous example, the distribution of nine levels into four transitions can be defined as the array s = {2,2,3,2} before the normalization, while the distribution of these nine levels after the normalization is defined as the array s = {2,2,2,2}.  After the normalization, the minimum number of levels of difficulty for each stage is defined by the function initialize_array (line 7), which initializes an array of size m with the value n/m. The remaining levels of difficulty (line 8) are distributed according to the position inv_sigma (lines 11-12). The value of inv_sigma is the result of dividing the number of free spaces after the distribution of the remining levels of difficulty by two (line 12).

Figure 8. A pseudo-algorithm to obtain a flow region in m transitions with n difficulty levels After determining the number of levels of difficulty that will be distributed for each transition (distr), the next step is the setting of labels for the flow region that has no expected difference in the levels of difficulty (lines 14-24). Thus, the process to define these labels consists of:  Setting of flow region for the first transition through the definition of minimum level with the value zero (line 14) and the definition of maximum level with the number of level of difficulty decreased by one (line 15).  Setting of flow region for the rest of the transitions (lines 16-24). The minimum level of difficulty is defined as the maximum level of the previous transition increased by one (line 17), and the maximum level of difficulty is defined as the maximum level of difficulty of the previous transition increased by the number of levels (line 18). For cases in which the normalization of levels has been done, the following two rules must be applied:

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 

If the number of transitions is odd, then the maximum level of difficulty is increased by one in the mid-transition (lines 20-21). Thus, the flow region for nine levels of difficulty in five transitions is defined as the array s = {(0;0),(1;2),(3;5),(6;7),(8;8)}. If the number of transitions is even, then there are two mid-transitions: the first mid-transition is located in the position m/2-1, and the second mid-transition is located in the position m/2. Next, the maximum level of difficulty is increased by one in the first mid-transition (line 23). Finally, the minimum level of difficulty is decreased by one for the second mid-transition (line 24). Thus, the flow region for nine difficulty levels in four transitions is defined as the array s ={(0;1),(2;4),(4;6),(7;8)}.

Finally, the expected difference in level of difficulty, defined as the parameter delta, is used to decrease and increase the minimum and maximum levels of difficulty for each transition in the flow region (lines 25-29).

Benefits and application of GMIF in learning design Several factors must be considered during the learning design process, such as learning goals, pedagogical preferences, intervention timing, type of feedback, students’ needs, available resources, and so on. The work of Koedinger et al. (2013) estimates that there is a poll of 330 (205 trillion) instructional choices that could be considered when designing a learning activity. Unfortunately, most designers and educators do not have enough knowledge/skills to cope with this huge number of instructional choices and select those choices that are the best fit for a particular situation. To help in this process, our framework offers an appropriate integration of instructional design with learning theories, models of learner’s growth, and theories related to people’s experiences and engagement, namely Flow Theory, in order to reduce the complexity of the learning design task. Specifically, this section presents two concrete scenarios where designers can use GMIF to create optimal learning scenarios.

Foster flow experiences in theory-based learning scenarios To get students into the flow state and produce optimal learning experiences, one should initially consider:  The learner’s initial state and learning objectives in terms of knowledge acquisition and skills development (Anderson, 1982; Rumelhart & Norman, 1976);  The learning path based on theoretical justifications (Isotani et al., 2010; Romiszowki, 1984); and  The definition of the challenge. Here it is necessary to select the difficulty of the activities to keep students motivated and engaged (Csikszentmihalyi, 2013; D’Mello & Graesser, 2012). We have developed the GMIF to support each of these steps. In the first step, the GMIF provide a standard to describe and represent learning objectives as well as the learner’s state. Thus, the problem of sharing learning designs among people (and computers) is reduced. Accordingly, an instructional designer can indicate the initial state of the learner and select his/her learning objectives. Both correspond to a state in the GMIF. After that, the designer can check manually or automatically (using learning design authoring tools) which learning theory (or theories) provides an adequate sequence of learning activities (i.e., learning path) that supports a learner in achieving the desired goals. In this situation, the GMIF offers visual representation (as a path on the LGM graph) of the theories and how they support the learner’s growth. Finally, to create flow experiences, the designer needs to define the difficulty of the challenge that the learner will work on. In this regard, the GMIF will indicate the level(s) of difficulty that should be considered when creating tasks to alter the state of the learner while keeping him/her motivated and engaged.

Develop flow-aware authoring tools to automate search and selection of learning objects With the GMIF detailed in this paper, we can develop different functions for authoring tools for learning scenarios. A useful function is searching for proper learning objects that will favor and maintain the learner’s flow in a learning scenario. Thus, an instructional designer should first set the initial and goal stages of a student in a learning scenario using the graphical representation of the GMIF. Next, each label for a difficulty level in the transition from the initial 224

stage to the goal stage can be used as a constraint search. Finally, this constraint can be employed through a search process of different learning object repositories. Ideally, the repositories should be able to search learning objects by the level of difficulty related to skill development or knowledge acquisition separately. However, the current repositories, following the standard for Learning Objects Metadata (LOM) ( Thropp & McKell, 2001), only provide the field “educational.difficulty” in the metadata to define the levels of difficulty for learning objects. Thus, in this example application, we assume that this field (educational.difficulty) is related to both levels of difficulty (skill development and knowledge acquisition). For the instance shown in Figure 9, where the application employs a five-point scale GMIF, if the instructional designer set the initial stage of a student as s(0,0)—nothing for skill and nothing for knowledge—and the goal stage as s(3,0—associative stage for skill development—the proper levels of difficulty that will favor and maintain the learner’s flow are first, level 0:very-easy for the transition s(0,0)s(1,0). Next, for the transition s(1,0)s(2,0), the proper levels of difficulty for learning objects that will maintain the learner’s flow are 1:easy, or 2:medium. Finally, for the transition s(2,0)s(3,0), the proper levels of difficulty for learning objects that will maintain the learner’s flow are 2:medium, or 3:difficult.

Figure 9. Screenshot of applications for the GMIF showing the Cognitive Apprenticeship Theory The solution shown in Figure 9 was obtained for a learning scenario based on the Cognitive Apprenticeship Theory (Collins, 1991), where a student without knowledge or cognitive skill should follow the strategy of learning by apprenticeship to reach the associative stage of cognitive skills. In this theory, a student using the strategy learning by apprenticeship will slowly improve his/her skills from nothing s(0,y) to associative stage s(3,y), moving through the rough cognitive stage s(1,y) and the explanatory cognitive stage s(2,y). In other words, this learning strategy is defined by the sequence s(0,y)s(1,y)s(2,y)s(3,y); more about the representation of this theory is presented in the works of Isotani and colleagues (Isotani et al., 2010; Isotani & Mizoguchi, 2006). Thus, when an instructional designer selects a transition in the graphical representation of the GMIF, the application automatically show a list of adequate learning objects (shown in Figure 9, left-bottom) that can be selected to maintain the learner’s flow during the selected transition. In Figure 9, a list of adequate learning objects that can be selected to maintain the learner’s flow during the transition from the rough cognitive stage s(1,0) to the explanatory cognitive stage s(2,0) is shown at the bottom of the graphical representation of the GMIF. The left portion of Figure 9 also shows the five-point scale of skill-difficulty that was used for the generation of the GMIF, where the label for the transition s(1,0)s(2,0) is emphasized by a double blue line. Furthermore, each dashed arrow from the five-point scale to the graphical representation of GMIF points to the corresponding label of levels of difficulty. 225

Conclusions and future research Employing Flow Theory in the instructional design of learning scenarios is a way to favor the learner’s flow state in those scenarios. To incorporate Flow Theory in the design instructional process, a theory-based model that integrates the learner’s growth process and Flow Theory was proposed in this paper. This new model, called GMIF (Learners Growth Model Improved by Flow Theory) was developed by integrating the LGM (Learner’s Growth Model) and Flow Theory. To demonstrate the utility of the current version of our model, we illustrated in this paper how an application can provide support to help instructional designers in the proper selection of learning objects that help to keep the learner in flow. We believe that the results shown in this paper can be used in theory-aware authoring systems, such as CHOCOLATO (Isotani et al., 2013), to improve the development of collaborative learning scenarios that favor the learner’s flow. In addition, we believe that introducing cognitive skills and knowledge level complexity into the LOM of the repositories would facilitate the use of the GMIF and even the LGM. In future work, our model should include others conditions of Flow Theory to provide better learning scenarios. Furthermore, we will develop empirical studies to validate our proposed model.

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