Unobtrusive monitoring of learners interactions with educational ...

British Journal of Educational Technology doi:10.1111/bjet.12445

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Unobtrusive monitoring of learners’ interactions with educational games for measuring their working memory capacity Mohamed Ali Khenissi, Fathi Essalmi, Mohamed Jemni, Kinshuk, Ting-Wen Chang and Nian-Shing Chen Mohamed Ali Khenissi is a PhD student in computer science and member of the Research Laboratory of Technologies of Information and Communication & Electrical Engineering, LaTICE, University of Tunis, Tunisia. His research interests include: computer educational games, learner model and educational games for people with disabilities. Fathi Essalmi is a PhD in computer science since 2011. His research interests are educational games, personalized elearning, ontologies and fuzzy logic. He is also a senior member in the Research Laboratory of Technologies of Information and Communication & Electrical Engineering (LaTICE). Google scholar link: http://scholar.google.com/ citations?user=gzKgASMAAAAJ&hl=fr. Mohamed Jemni is a Professor of Computer Science and Educational Technologies at the University of Tunis, Tunisia. He is the Director of ICT at The Arab League Educational, Cultural and Scientific Organization (ALECSO). He is a Senior member IEEE and member of the Executive board of IEEE Technical Committee on Learning Technology. His Research Projects Involvements during the last 25 years are tools and environments of e-learning, Cloud and Grid computing and Accessibility of ICT to People with Disabilities. He published more than 200 papers in international journals and conferences and produced many studies for international organizations such as UNESCO, ITU and ALECSO. Kinshuk is Associate Dean of Faculty of Science and Technology, and Full Professor in the School of Computing and Information Systems at Athabasca University, Canada. He also holds the SERC/CNRL/Xerox/McGraw Hill Industrial Research Chair for Adaptivity and Personalization in Informatics. His work has been dedicated to advancing research on the innovative paradigms, architectures and implementations of online and distance learning systems for individualized and adaptive learning in increasingly global environments. Ting-Wen Chang is a researcher and the director of international cooperation office in Smart Learning Institute of Beijing Normal University (SLIBNU) for doing the research on Smart Learning as well as making many international cooperation projects. His research mainly focus on technology enhanced learning, adaptivity and personalization, user/student modelling, multimedia Learning instruction, multi-screen learning environment, and computer assisted instruction. Ting-Wen Chang is with Collaborative & Innovative Center for Educational Technology (CICET), Beijing Normal University, Beijing, China. Nian-Shing Chen is Chair Professor in the Department of Information Management at the National Sun Yat-sen University, Taiwan. He has published over 400 papers in the international referred journals, conferences and book chapters. His current research interests include assessing e-Learning course performance; online synchronous teaching & learning; mobile & ubiquitous learning; natural user interface & game-based learning. Address for correspondence: Nian-Shing Chen, National Sun Yat-sen University, Kaohsiung, Taiwan. Email: [email protected]

Abstract Working memory capacity (WMC) plays an important role in the learning process, because learners need to hold and process some information in the short-term memory while they are engaged in learning activities. Measuring learners’ WMC can be helpful to support and enhance their learning. For example, teachers can use this information to adapt their teaching strategies according to learners’ level of WMC. In addition, information about learner’s WMC can be exploited by adaptive e-learning systems for providing recommendations to support learners with low and high WMC. Furthermore, early detection of the level of individual learner’s WMC is a very important step to be able to provide appropriate intervention for the learners. In this context, a number of tools are available in the literature to explicitly measure learner’s WMC. However, most of them require considerable experience in the administration and interpretation of results. This study proposes an approach based on fuzzy logic for measuring learner’s C 2016 British Educational Research Association V

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WMC in an unobtrusive manner, from learner’s interactions with an educational game. Results of experiments proved the effectiveness of this method in measuring WMC. The educational game, used in this work, could help parents and teachers to know the WMC of their kids and learners. In addition, the proposed approach could be adapted by researchers working in this field to measure learners’ WMC using other educational games.

Practitioner Notes What is already known about this topic • •

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Working Memory Capacity plays an important role in the learning process. Current approaches in psychology to measure working memory capacity distract learners from the learning tasks and require considerable experience in the administration and interpretation of results. While there are techniques available that can detect learners’ working memory capacity through their interactions, majority of learning systems have very limited interaction possibilities for those techniques to provide meaningful results. Educational games not only provide ample opportunities for learner interactions but are also quite in tune with today’s digital native generation of learners.

What this paper adds •

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This paper proposes a novel fuzzy logic based approach for measuring learner’s working memory capacity in an unobtrusive manner from learner’s interactions with educational games. Experimental results demonstrate that the approach can be an effective tool for parents and teachers to know the working memory capacity of their kids and learners. The paper also provides a fully logic based system architecture for educational game based working memory assessment, that educational technology system developers can use to easily create similar systems.

Implications for practice and/or policy • • •

Measuring learners’ working memory capacity can be helpful to support and enhance their learning. Early detection of the level of individual learner’s working memory capacity can be instrumental for providing appropriate instruction for the learners. The approach can also help in detecting impairment of learners’ working memory capacity at early stages, hence enabling early intervention.

Introduction Working memory is the system that holds and processes information in the brain for brief periods of time (Baddeley & Hitch, 1974). Gathercole and Alloway (2008) highlighted that working memory plays a critical role in the learning process. In addition, several studies showed that learners’ different levels of WMC can affect their learning performances (Alloway & Alloway, 2010; Woehrle & Magliano, 2012). Several studies have also investigated the relations between WMC and different aspects, such as reading comprehension, comparison speed, fan effect, navigational pattern and attention control (Lin, 2007; Carretti et al., 2009). For example, Lin (2007) C 2016 British Educational Research Association V

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mentioned that learners with low WMC have poor reading comprehension, low comparison speed, greater fan effect, nonlinear navigational pattern and poor attentional control. Contrariwise, learners with high WMC have good reading comprehension, high comparison speed, lesser fan effect, linear navigational pattern and better attentional control. Having information about learners’ WMC could be helpful to support them during the learning process. For example, by providing learners personalized suggestions, appropriate materials and meaningful recommendations to support their low and high WMC. Chang et al. (2014) suggested to present an adaptive recommendation in learning system that encourage the students with low WMC to rethink or remember the key or important content after they have learnt a learning object. In fact, students with limited working memory are likely to forget the key information after a brief period of time. Once the adaptive recommendation is presented, the student could either chose to remain in the content of the current learning object or proceed to the next object. Literature survey on learner’s WMC modeling shows that there are two main methods of measuring the WMC of learners. The first one is by asking learners to use a measuring tool and inform them explicitly that this tool is for measuring their WMC. As examples of measuring tool we cite: counting span (Case et al., 1982), operation span (Turner & Engle, 1989) and reading span tasks (Daneman & Carpenter, 1980). This method could be considered as an explicit method of measuring WMC. The second method is by interpreting learners’ traces while using e-learning system. As examples, we cite the works of Chang et al. (2013a) and Lin (2007). These works proposed approaches for evaluating the learners’ WMC, in an unobtrusive manner, from the behaviors of the learners in learning systems. This method could be considered as implicit method of measuring WMC. The difference between explicit and implicit methods of learner modeling is related to the ways of extracting information about learners. An explicit method aims to use direct and obvious tools of measuring WMC and making it overt to learners. On the other hand, an implicit method aims to measure the learners’ WMC in a hidden and unobtrusive way. While the measuring tools, in the explicit method, can provide direct and precise estimation of learners’ WMC, use of these tools can also create interruptions in the study and may lead to decline in learners’ motivation. Most of these tools also require considerable experience in the administration and interpretation of results. An alternative approach is to extract learners’ WMC implicitly from their behaviors in learning systems. However, a serious obstacle for implementing such method is that learners’ interactions with traditional learning systems are very restricted. Generally, these interactions are limited to clicks, time that the learners invested in visiting a page, and so on. This information does not really inform us how the learners interacted with the content. This lack of information could negatively affect the accuracy of the interpretations obtained. One of the ways to get more valid results is by using educational games that provide ample opportunities for learner interactions with the computer. As a preliminary step for developing educational computer games to evaluate learner’s WMC, a Learning version of the Memory Match Game (LMMG) has been adapted to measure a learner’s WMC by monitoring learner’s interactions within the game (Khenissi et al., 2015). This study focuses on the relationships between various elements of the adapted LMMG and working memory components. In particular, Baddeley (2000, 2012) described four components of working memory which are central executive, phonological loop, visuo-spatial sketchpad and episodic buffer. The main objective is to analyze whether there is any relationship between the elements of LMMG and various components of the working memory that can guide us to measure WMC of the learner. The rest of this paper is structured as follows: the next section starts by presenting a definition of the concept “working memory.” In particular, it describes the main components of the working memory model. In addition this section describes the Learning version of Memory Match Game C 2016 British Educational Research Association V

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(LMMG). Section 3 proposes relationships between the elements of the adapted LMMG and different components of working memory model. Section 4 describes an approach based on fuzzy logic to assess whether the proposed relationships can guide us to measure the learner’s WMC. Section 6 describes an experiment conducted for validating the proposed approach and discusses the findings. Finally, section 7 concludes the paper with a summary of the work and future research directions. Background In order to achieve the objective of measuring learners’ WMC using educational games, this section starts with reviewing literature in relation to working memory. It is followed by the description of the LMMG adapted for the purpose of measuring learners’ WMC. Working memory Working memory is defined as the system that holds and processes several pieces of transitory information in human brain (Baddeley, 1992; Baddeley & Hitch, 1974; Becker & Morris, 1999). The term “working memory” has in fact been developed from the earlier concept of short term memory (McLeod, 2009). Short-term memory has three main characteristics: limited capacity, limited duration and encoding (translating visual information into sounds). In particular, encoding (Healy, 1975, 1977; Craik & Lockhart, 1972) is the process of coding information so that it can be placed our memory system. In fact, information needs to be changed into a form that the system can cope with, so that it can be stored. There are three types of encoding: visual, acoustic and semantic. The acoustic encoding represents the sounds we hear in memory. The visual encoding represents the images we see in memory. The semantic encoding represents the meaning of experiences or factual information in memory. The capacity of short-term memory is estimated as 7 6 2 items (Miller, 1956). Moreover, the duration of short-term memory has been assessed between 15 and 30 s (Atkinson & Shiffrin, 1971). Researchers have proposed several models regarding how working memory functions (Baddeley & Hitch, 1974; Baddeley, 2012; Cowan, 1995). One of the most well-known models is the Baddeley’s model of working memory (Baddeley, 2000, 2012). Alan Baddeley and his collaborators studied the Atkinson and Shiffrin (1968) model and believed that the model lacked details. For that, they proposed a model of working memory, in an attempt to describe a more accurate model of short-term memory. The Baddeley’s model became the dominant view in the field of working memory. The strength of Baddeley’s model is its ability to integrate a large number of findings from study on short-term and working memory. Furthermore, the Baddeley’s model of working memory has inspired a wealth of research in experimental psychology, neuropsychology and cognitive neuroscience. Esgate et al. (2005) stated that the most influence model of working memory has been developed by Alan Baddeley and his collaborators and its application in the domains of neuropsychiatry and neuropsychology has been especially beneficial. Cavallini et al. (2002) stated that the working memory developed by Baddeley and Hitch has been judged to be generally valid, because it is able to explain how the information is processed more successfully than other models. For these reasons, the Baddeley’s model of working memory was chosen for this study. Baddeley described four components of working memory, namely central executive, phonological loop, visuo-spatial sketchpad and episodic buffer. The last three components are described as storage mechanisms. In addition, they are considered as slave systems because they simply hold information. On the other hand, the central executive system is considered as master system because it is responsible for manipulating information, controlling attention and coordinating the C 2016 British Educational Research Association V


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Figure 1: Baddeley’s model of working memory

slave systems. Figure 1 illustrates the four components of working memory and the relations between them. Central executive The central executive is the most important component of the model. However, it is the least understood component of the working memory. The central executive is responsible for the following tasks: •

• •

Monitoring and coordinating the operations of the slave systems: It decides which information has the highest priority to deal with and selects the storage systems to send that information. Focusing, dividing and switching attention: It provides the overall organization and supervision of the working memory and decision making. Dealing with cognitive tasks such as mental arithmetic and problem solving.

Phonological loop The phonological loop is a component of working memory that deals with spoken and written materials. It is described as a slave system because its main function is simply to temporarily store information. According to Baddeley and Hitch (1974), the phonological loop is divided into two subcomponents: •

•

The phonological store: This subcomponent is responsible for storing information in speech-based form for short periods of time. Spoken words enter directly to the store. However, written words must first be converted into an articulatory (spoken) code before they can enter the phonological store. The articulatory process: This subcomponent is responsible for converting written material into an articulatory code and transfer it to the phonological store. In addition, this subcomponent acts like an inner voice that tries to keep information in mind by repeating it before it fades. The articulatory process recites information from the phonological store. This information will be stored again into the phonological store where it immediately starts to decay again. This operation must be repeated to prevent the very rapid decay of information stored in the phonological store.

Figure 2 presents the subcomponents of phonological loop and shows that speech input is stored directly in the phonological store whereas written input must proceed via the articulatory process. C 2016 British Educational Research Association V

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Figure 2: Subcomponents of phonological loop (Henry, 2012)

Visuo-spatial sketchpad The visuo-spatial sketchpad is the third component proposed in the Baddeley’s working memory model (2000, 2012). This component is responsible for dealing with visual and spatial information. The visuo-spatial sketchpad is described as a slave system because its main function is only to hold information for short periods of time. Like the phonological loop, information in the visuo-spatial sketchpad decays rapidly unless rehearsed. Episodic buffer The original model of working memory was updated by Baddeley (2000) after the model failed to explain several experiments. The episodic buffer is the new component that has been added to the working memory model. The episodic buffer is described as temporary storage system with limited capacity. It is capable of integrating information from a variety of sources. The episodic buffer communicates with both long term memory and the components of working memory. The next section introduces the Learning version of Memory Match Game (LMMG). In particular, it describes various types of cards used in this learning game. A learning version of memory match game Memory Match Game (Zwick & Paterson, 1993) used in this study is a card game. This game consists of several cards that have pictures on one side. The number of cards is always even. Typically, same picture is printed on two cards. All of the cards are mixed up and laid face down on a surface. The game is designed for single player, although two-player modes are also available. In each turn, player selects a card to flip it over. If the next card selected by the player matches the first card, both cards disappear from the surface. The objective of the game is to turn over pairs of matching cards with aim to get rid of all cards in the least possible trials. In the traditional version of memory match game, all cards hold only visual information. However, in the learning version of this game (Khenissi et al., 2014a), other types of information have been added. Specifically, graphics information is kept and additional sounds, words and mathematical calculations have been added alongside. Figure 3 illustrates different types of cards included in this game. As shown in Figure 3, the LMMG uses eight types of pair of cards: • •

Visual–visual: Both cards hold the same visual content. In this case, learner must memorize content of the first card and seek the identical card. Visual–word: The first card holds visual content, whilst the second card holds written information. In this case, learner must find the relationship between the visual and written

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Figure 3: Types of memory match game cards

•

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contents. In particular, he/she has to see the visual card and read written information on the second card, and then select these two cards if they have identical meaning. Visual–sound: The first card holds visual content, whilst the second card holds voice content. When a player click on the card which hold voice content, a voice will be run which will pronounce a word. In this case, learner must find the relationship between the visual and voice contents. In particular, he/she has to see the visual card and listen to the sound card, and then select these two cards if they have identical meaning. Word–word: Both cards hold the same written information. In this case, learner must read and memorize the word in the first card and then seek the second card that represents the identical meaning. Word–sound: The first card holds written information, whilst the second card holds voice content. In this case, learner must know how to read and how to pronounce words. In particular, he/she has to search for a match with identical meaning between a word and a pronunciation sound. Sound–sound: Both cards hold the same voice content. In this case, learner must listen and memorize the sound in the first card and then seek the second card with identical sound. Calculates–calculates: Both cards hold simple math problems. In this case, learner must find the result of the calculation on the first card and then compare it to the calculation on the second card. Calculates–sound: The first card holds simple math problem content, whilst the second card holds voice content. In this case, learner must find the relationship between the result of the calculation and the voice content. In particular, he/she has to complete the calculation on the first card and memorize the result. After that, he/she has to listen to the sound on the second card. If the two results are same, learner has to turn over the two cards.

Figure 4 presents the interface of the learning version of LMMG. This figure shows that learner has selected a visual card that represents a picture of chair. After that, he/she has found the matching word card that represents the same meaning as chair in written form. While the pair of cards in the traditional version of memory match game holds only visual information, such as pictures, the learning version of this game consists of cards that hold different information such as word, voice and mathematical calculations. For that, the LMMG could be adopted to learning context. In particular, the LMMG could help kids and novices to start the learning of a new language, especially vocabulary acquisition. It also could help learners to learn the names of things and memorize how to spell words. In addition, the LMMG could also be used for other purposes such as development of math skill (mathematical calculation) and C 2016 British Educational Research Association V

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Figure 4: Learning version of memory match game

improvement of the ability to recall information. The LMMG is available online at: http://www. egresearch.info/edugame/LVMMG/index.html Relationships between types of cards and components of working memory Each pair of card in the LMMG contains specific type of information, and accordingly it will be stored in a specific component of working memory. Table 1 lists the relationships between pair of cards and components of working memory. The table also provides the rationale for these relationships. Several studies assumed that humans process different information via different modalities, as well as storing this information in different cognitive systems (Baddeley, 2000; Schnotz & K€ urschner, 2008). Table 1 shows that the information of pair (visual–visual) will be stored temporarily in the visuo-spatial sketchpad, since the visuo-spatial sketchpad is responsible for dealing with visual information. The information of pair (sound–sound) will be stored temporarily in the Phonological Loop. In particular, such information will be stored directly in the phonological store. Similarly, the information of pair (word–word) will be stored temporarily in the Phonological Loop. But this type of information must pass through the articulatory process before it can be stored in the phonological store. The justifications presented in Table 1 is based on Paivio’s dualcoding theory (1991) and Baddeley’s model of working memory (Baddeley, 2000). According to these theories, the type of information received determines the channel through which it is processed in the working memory. Mayer (2003) argued that learners process visual materials via a visual channel while processing auditory materials via a verbal channel. Paivio (1991) explained that humans process spoken words and text in the verbal system, but process pictures in the nonverbal system. In this way, pictures, graphic elements and symbolic information will be presented to the eyes and processed through the visual channel of the working memory which is the visuospatial sketchpad component of working memory. However, if the information is aural, it will be perceived by the ears and its cognitive processing will take place in the aural channel of the C 2016 British Educational Research Association V


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Table 1: Relationships between types of cards and components of working memory Pair of cards Visual–visual

Target component

Justification

Visuo-spatial sketchpad

Visuo-spatial sketchpad is responsible for dealing with visual information Sound–sound Phonological loop (phonological store) Sound information will be stored directly in the phonological store Word–word Phonological loop Written information must pass (articulatory process 1 phonological store) through the articulatory process and then it will be stored in the phonological store Calculates–calculates Central executive Central executive is the responsible of manipulating information, including mathematics calculations Visual–word Episodic buffer Episodic buffer is responsible for dealing with information from a variety of sources Visual–sound Episodic buffer Episodic buffer is responsible for dealing with information from a variety of sources Word–sound Episodic buffer Episodic buffer is responsible for dealing with information from a variety of sources Calculates–sound Episodic buffer Episodic buffer is responsible for dealing with information from a variety of sources

working memory then it will be stored in the phonological store (Truman & Truman, 2006). Regarding written text, it is processed via a visual channel initially, then it will be converted into sound to be stored at verbal working memory. Table 1 also shows that the information of pair (calculates–calculates) is linked to Central Executive component as it is responsible for manipulating information, including mathematics calculations. Finally, the information of the rest of the pairs (visual–word, visual–sound, word–sound and calculates–sound) will be stored temporarily in the Episodic Buffer as it deals with information from a variety of sources. In fact, Episodic Buffer is the new component added by Baddeley (2000) into the original model. The main motivation for introducing this component was the observation that the original model failed to explain the results of various experiments (Baddeley, 2000). The new component provides temporary storage of information held in a multimodal code. Baddeley (2015) says: “. . .I came up after 25 years with the fourth component which I called the episodic buffer. . . it could store visual and verbal information and combine them. . ..” The next section proposes an approach that uses the relationships described above for measuring the WMC of the learners. Approach for measuring learner’s WMC This study introduces an approach based on fuzzy logic (Khenissi et al., 2014b) for checking whether the relationships between the elements of LMMG and the component of working C 2016 British Educational Research Association V

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memory model can guide us to measure the WMC of the learners. The foundation of fuzzy logic was laid by Zadeh (1965) which represents an extension of crisp logic (in crisp logic, such as binary logic, variables are true or false, 0 or 1). The fuzzy logic deals with approximate reasoning rather than fixed, and approaches to some degree the flexibility of human reasoning (Zadeh, 1989; Mendel, 1995; Lee, 1990; Cingolani & Alcala-Fdez, 2012). The proposed approach in this study measures the capacity of each component of learner’s working memory while the learner plays the LMMG. The capacity of each component is estimated as 7 6 2 items (Khenissi et al., 2015; Miller, 1956). After that, the whole WMC of learner is measured by calculating the average of the capacities of different components of working memory, in order to be estimated as 7 6 2 items (Khenissi et al., 2015; Miller, 1956). Learner’s WMC 5 AVERAGE (capacity of phonological loop, capacity of visuo-spatial sketchpad, capacity of episodic buffer, capacity of central executive). Specifically, each component of working memory is measured using four traces of learner while he/she interacts with corresponding pair of cards. These traces are as follows: • • • •

Discovery_duration: time that has elapsed between the first click on the first card of the pair and the first click on the second card of the same pair. Research_duration: time that has elapsed between the first seeing of the second card of the pair (time of the first click on the second card of the pair) and time of matching the pair. Number_of_clicks: number of clicks on the first card of the pair and the second card of the same pair before the matching. Remaining_cards: remaining cards at the time of matching between two cards of the pair.

Selected traces are considered as inputs for the fuzzy logic process. The value obtained from the fuzzy logic process, that describes the capacity of each component of working memory, is passed to the function AVERAGE() in order to calculate the whole WMC of the learner. Figure 5 illustrates a system based on fuzzy logic that has been implemented in order to evaluate the capacity of each component of working memory of the learner while playing the LMMG. After that, the system draws conclusion about the learner’s overall working memory capacity. As illustrated in Figure 5, a fuzzy logic system consists of four main parts: fuzzifier, inference engine, rules and defuzzifier. The process of fuzzy logic is explained as follows: Firstly, a crisp set of input data is converted into a fuzzy set using fuzzy linguistic variables (Zadeh, 1989), fuzzy linguistic terms and membership functions. This step is known as fuzzification. Thereafter, an inference is made based on a set of rules. Lastly, in the defuzzification step, the result, so called fuzzy output, is mapped to a crisp output using the membership functions. During the interactions between the learner and the LMMG, all the learner actions are stored in an interaction traces base. The interaction traces base is defined as a history of learner’s actions, collected in real time, from his/her interaction with the LMMG. After finishing the game, traces of the learner are passed through a filtering process in order to remove all useless information. In particular, information such as Learner_Name and Learner_Score, etc. are not selected to be part of the fuzzy logic system inputs; this is because they neither provide any indications for the evaluation of working memory capacity nor they present personal information of the learners. The filtering process selects only required traces, such as the number of clicks on the pair of cards before the matching, for the evaluation of working memory capacity. At the end of this process, selected traces are considered as crisp inputs (variables are true or false, 0 or 1) of Fuzzy Logic Subsystem (FLS). Finally, the value obtained from the FLS, which describes the working memory capacity of the learner, is stored in the Learner Model. C 2016 British Educational Research Association V


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Figure 5: System architecture

Fuzzification stage This stage represents linguistic description of learner’s traces, so called linguistic variables. Linguistic variables are the input variables of the system whose values are words or sentences from a natural language, instead of numerical values. In this case, “Discovery duration” is considered as the linguistic variable assigned to the trace “Discovery_duration.” Similarly, “Research duration” is assigned to “Research_duration,” “Number of clicks” is assigned to “Number_of_clicks” and “Remaining cards” is assigned to “Remaining_cards.” Linguistic variables are generally decomposed into a set of linguistic terms. For that, a set of linguistic terms have been defined for each linguistic variable. For the Discovery_duration, the corresponding term set is defined as {Short, Medium, Long}. Similarly, for the linguistic variable Research_duration, the corresponding term set is defined as {Short, Medium, Long}. In addition, the term set {Few, Some, Many} is assigned to the linguistic variable Number_of_clicks. Finally, the corresponding term set for the linguistic variable Remaining_cards is defined as {Few, Some, Many}. Furthermore, in this stage, linguistic terms have to be described by membership functions in order to convert input variables into degrees of membership. Precisely, a membership function is a function describing the degree to which an element belongs to the set. For that, a membership function is attributed to each linguistic term. As an example, Figure 6 illustrates the fuzzy logic representation for the three Remaining cards groups: Few, Some and Many, based on the number of cards of the LMMG. Each linguistic term is represented by a curve that describes the degree to which an element belongs to that term. For example, the set Few contains number of cards between 1 and 5 with a linearly decreasing degree of membership. The closer a number is to 5, the closer the degree of membership to the set of Few approaches to zero. C 2016 British Educational Research Association V

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Figure 6: Membership functions of input variable

Inference stage In this stage, a collection of linguistic rules are applied to input values in order to generate output values. In particular, a set of IF-THEN rules with condition and conclusion is performed, which represent the reasoning for the measurement of each component of working memory. In addition, the evaluations of the fuzzy rules and the combination of the results of the individual rules are performed using fuzzy set operations. In Table 2, instances of fuzzy rules for the measurement of capacities of the working memory’s components are listed. As an example of fuzzy logic rules, the first row in Table 2 heading can be read as follows: if Discovery duration is Long and Research duration is Short and Number of clicks is Few and Remaining cards is Many, then capacity of the component is High. This rule can be explained as follows: The capacity of the component is considered as High depending on the values of the four variables. On one hand, a Long discovery duration and a Short research duration can inform us that the learner has memorized the first card for a long duration, and as soon as he/she saw the second card, he/she turns over the matching card he/ she saw earlier. On the other hand, a Few numbers of clicks and Many remaining cards can inform that the learner makes a minimum number of clicks on the pair of cards on a surface filled with cards before the matching. This indicates that the learner has succeeded to find the two cards with minimal memory rehearsal. Defuzzification After the inference step, the overall result is a fuzzy value. This result should be converted from fuzzy output sets to crisp value. This is the purpose of the defuzzifier step. Defuzzification is performed according to the membership function of the output variable. Table 2: Instances of fuzzy rules Discovery duration Long Long Medium Medium Medium

Research duration

Number of clicks

Remaining cards

Capacity of the component

Short Long Medium Long Medium

Few Many Few Many Some

Many Some Many Few Some

High Low High Low Medium



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Figure 7: Membership function of output variable

In the current work, the output of the system is the capacity of each component of working memory. For that, a set of linguistic terms is assigned to the linguistic variable Capacity. The corresponding term set is defined as {Low, Medium, High}. Furthermore, the Capacity has been described by a membership function as illustrated in Figure 7. The choice of the membership function of Capacity is not arbitrary. This choice is based on Miller (1956) that estimates the capacity of working memory as 7 6 2 items. Figure 7 illustrates the fuzzy logic representation of Capacity. This figure shows that the Capacity varies between 0 and 9 (as illustrated on the abscissa axis of Figure 7). Furthermore, the capacity is considered Low with degree of membership equal to 1 if it varies between 0 and 2. The degree of membership decreases linearly if the capacity approaches to 4. On the other hand, capacity is considered High with degree of membership equal to 1 if it varies between 7 and 9. Similarly, the capacity is considered Medium with degree of membership equal to 1 if it varies between 4 and 5. Finally, values obtained after the phase of defuzzification, that describe the capacity of each component of working memory, are passed to the function AVERAGE () in order to calculate the capacity of the whole working memory of the learner. After that, the value obtained is stored in the Learner Model. Research design The aim of this study is to assess the learner’s WMC implicitly through his/her interactions within LMMG game. This experiment was conducted in order to evaluate the effectiveness of LMMG and the proposed approach in measuring learner’s WMC. The validity of the proposed approach was compared by using a validated other instrument called Web-OSPAN (Lin, 2007; Graf et al., 2006, 2007). Participants This experiment was conducted in a private students’ residence (students’ residence Moncef Bey) in Tunisia. Participants of this study were 58 students from higher schools, aged 19–27. All participants lived together in the students’ residence. Participants were asked to self-report their expertise level in gaming. Among the participants there were 16 novices, 23 intermediate and 19 expert game players. The novice players were given a short training before they used the LMMG game on their own. Instruments For measuring WMC, a psychometric tool, called Web-OSPAN (Lin, 2007; Graf et al., 2006, 2007), was used in this study. It is important to note that all measures of short-term and working C 2016 British Educational Research Association V

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memory developed to date can be divided into two subtypes which are: simple working memory tests and complex working memory tests. Simple tests primarily measure the ability to store information, while more complex tasks are also designed to measure the ability to process information. Since there is great consensus that working memory involves both storing and processing of information (Baddeley, 2000), many believe that the simple tests are insufficient to reliably measure working memory. On the other hand, Web-OSPAN is one of the well know tools (Lin, 2007; Graf et al., 2006, 2007) designed to measure working memory capacity. WebOSPAN is considered as complex working memory test because it requires effortful processing of information while trying to retain a list of items for a short interval. For these reasons, WebOSPAN was used, in this study, as a benchmark for the evaluation of the goodness of the proposed method. In this tool, learners are required to perform simple mathematical operations and answer whether this operation is true or false. After each mathematical operation, a word is presented that is to be recalled. The main purpose of the arithmetic operations is to activate the processing component of working memory and not to test the mathematical ability, just to prevent the employment of rehearsal strategy on the words. At the end, participants are asked to recall the set words presented after each operation in the correct order. A set of words may contain from 2 to 6 words. In total, there are 60 arithmetic operations and 60 words in Web-OSPAN. Each correct mathematical operation as well as each correct recalled word is stored in the database. The total number of correctly recalled words is used as a measure of WMC. Web-OSPAN comes with three languages which are English, Chinese and German. This study improved the existing version of Web-OSPAN by a French language extension so that it would fit the language preferences of the participants in Tunisia. The reason is that Tunisians are fluent in French. In addition, French is used as first language in majority of Tunisian high school curriculum. For these reasons, this study considered that French is the most appropriate language for Tunisian participants. In the French version of Web-OSPAN, the arithmetic operations are exactly the same as the English version. In addition, the list of words is a translation of the ones used in the English version. Concerning the LMMG, three levels of this game were designed and hosted on a local server. Participants used a web browser to access the learning game and play all levels of the game consecutively. At the end of the game-play, the traces of the participants were stored in a data base. Procedure Participants in this study were provided with information about the nature of the research and the goals of the evaluation. After they volunteered to participate in the research, they were instructed how to use the Web-OSPAN and the LMMG game. Participants were each given a login account to access Web-OSPAN and were asked to select their preferred language (from the available languages). After login, participants were shown the instructions page. The instructions page contained information about the nature of the task with examples of operations and words, and some advice such as not to undertake any other tasks and not to use any assistant tools during the task. After understanding the instructions, participants could then proceed to start the experiment. During the experiment, the Web-OSPAN measures four variables which are: OperationScore, OpTotal, SetSize, and Latency (Lin, 2007). OperationScore measures the total number of correct arithmetic operations. It has a range from 0 to 60 because in Web-OSPAN there are 60 arithmetic operations. OpTotal measures the total number of correctly recalled words. It has a range from 0 to 60 because Web-OSPAN used 60 words. SetSize measures maximum number of words in C 2016 British Educational Research Association V


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Figure 8: Participants using Web-OSPAN and LMMG during the experiment

any word set that was ever correctly recalled. It has a range from 0 to 6 (technically, the range should be 0, 2, 3, 4, 5, and 6 because the smallest word set is 2 and the highest is 6). Finally, Latency measures the average response time for participants when they answer arithmetic operations. OpTotal and SetSize are used as the main indexes of working memory capacity in Web-OSPAN. On the other hand, OperationScore is used to ensure that participants performed the task seriously and did not select the answers randomly. Latency is used to guard against cheating. For example, if a participant uses a calculator to assist the arithmetic operation, then the Latency will be very large. After completing the Web-OSPAN test, participants were requested to play three levels of the LMMG game that took on average 6 min of play time. Traces of participants while using this game were stored in data base. After that, traces were passed to FLS, as explained in Figure 5, in order to estimate the working memory capacity. The FLS provides as output one variable which is FLS-WMC. This variable represents the score of participant’s WMC approximated by the FLS. FLS-WMC holds a numeric value between 0 and 9 as explained in Figure 7. Figure 8 shows the participants while using Web-OSPAN and LMMG. Results and discussion Data of 7 participants out of 58 were deleted because the participant made more than 20 errors in arithmetic operations or did not complete the test. The data obtained from Web-OSPAN are first analyzed using descriptive statistics and summarized in Table 3. In particular, Table 3 Table 3: Descriptive statistics of result from Web-OSPAN

OperationScore OpTotal SetSize Latency Valid N

n

Range

Minimum

Maximum

Mean

Std. deviation

51 51 51 51 51

16 24 4 1751

40 2 2 2091

56 26 6 3842

46.53 12.12 3.63 2779.75

4.806 6.483 1.038 416.248


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Table 4: Descriptive statistics of result from FLS

FLS-WMC

n

Range

Minimum

Maximum

Mean

Std. deviation

51

5

2

7

5.59

1.283

presents the number of valid observations, Range, Minimum, Maximum, Mean and Std. Deviation of the variables obtained from the Web-OSPAN (presented in the rows of the table). Table 3 shows that mean of the number of correct operations (OprationScore) is equal to 46.53. This means that the participants were taking the Web-OSPAN task seriously. They were not just selecting answers randomly. Furthermore, the mean response latency (time taken to solve each operation) is 2779.75 ms which is equal to 2.7 s and its standard deviation is 416.248 ms which is equal to 0.4 s. The latency variable is used to guard against cheating. For example, if a participant uses calculator to assist the arithmetic operation, then the Latency will be very high. However, the table shows that the participants had followed the instructions quite well and had devoted their time to complete the task and not doing other tasks. The data obtained from FLS are analyzed using descriptive statistics and summarized in Table 4. Especially, Table 4 presents the number of valid observations, Range, Minimum, Maximum, Mean and Std. Deviation of the working memory capacities obtained from the FLS. Table 4 shows that the mean of working memory capacity values, obtained from FLS, is equal to 5. This value is very close to the interval given by Miller (1956) which is 7 6 2 items. However, the table also shows that the minimum value of FLS-WMC is equal to 2 which is very far from the interval given by Miller (1956). To explain that, it is important to outline that 7 6 2 presents the number of objects that an average human can hold in his/her working memory. The number could be less than 5 when a human have a poor WMC or working memory impairment. After analyzing data obtained from Web-OSPAN and FLS, this study conducted a Pearson correlation analysis between the two main indices of performance in Web-OSPAN (OpTotal and SetSize) and FLS-WMC. Results of the Pearson correlation are summarized in Table 5. Table 5 has a list of the variables (OpTotal and SetSize and FLS-WMC) across the top, and the same list down the side. Each row of the table contains values for PearsonCorrelation, Sig. (two-tailed) values and a number (N) value. The diagonal is always all 1, because that is the correlation between each variable and itself. This table could be either read across (row name correlated with column name) or down (column name correlated with row name) and getting the same answer. In Table 5, the variable FLS-WMC represents the score of working memory capacity approximated by the FLS. On the other hand, the variables OpTotal and SetSize represent the two main Table 5: Pearson correlation of variables

OpTotal

SetSize

FLS-WMC

PearsonCorrelation Sig. (two-tailed) N PearsonCorrelation Sig. (two-tailed) N PearsonCorrelation Sig. (two-tailed) N


OpTotal

SetSize

FLS-WMC

1

0.850 0.000 51 1

0.528 0.000 51 0.603 0.000 51 1

51 0.850 0.000 51 0.528 0.000 51

51 0.603 0.000 51

51


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indices of performance in Web-OSPAN. The OpTotal variable represents the total number of correctly recalled words in the Web-OSPAN task. Concerning the SetSize variable, it represents the maximum number of words (from 2 to 6) that a participant had correctly recalled. Table 5 shows a significant correlation between the approximations of FLS-WMC obtained from the FLS and the scores obtained from the psychometric tool Web-OSPAN. Especially, Table 5 shows that the correlation coefficient between FLS-WMC and OpTotal is equal to 0.528 and the correlation coefficient between FLS-WMC and SetSize is equal to 0.603. These two correlations coefficients are quite high and are statistically significant. In addition, Table 5 shows that the results are based on n 5 51 cases. Since this corresponds to the sample size, we conclude that there are no missing values in our data. Furthermore, the p value is low (p 5 0.000 (two-sided)), therefore the correlations are statistically significant. These correlations provide a practical validation to the FLS and educational game as well as prove the effectiveness of the current method of measuring WMC. Although that correlations between and SetSize, OpTotal and FLS-WMC are statistically significant, the relationship is not linear. Therefore, we will improve, in future works, the system architecture for getting strong linear correlation between these variables. In particular, we will adopt machine learning (Alpaydin, 2014; Domingos, 2012) for the automatic generation of fuzzy rules component which considered the most critical component in this work. This method of measuring WMC provides a convenient way for learners to measure their WMC compared to explicit measuring instruments of WMC that require considerable experience in the administration, training and interpretation of results. Using educational games for implicitly measuring WMC does not require any training or administration. This will allow learners to concentrate on the game when playing. In parallel, the system measures the WMC in unobtrusive way. Conclusion The research reported a preliminary step for developing educational computer games to measure learner’s WMC. In particular, this paper proposed an approach based on fuzzy logic for measuring learner’s WMC from his/her interactions with an educational Game. The results show a significant correlation between the approximations of WMC obtained from the FLS and the scores obtained from the psychometric tool Web-OSPAN. The correlation provides a practical validation to the FLS and educational game as well as proves the effectiveness of this method of measuring WMC. This method of measuring WMC provides a convenient way for learners to detect early impairment in their WMC. The limitations of working memory should be taken into account in the design and the presentation of the instructional material in order for this material to be effective for learning. In fact, according to cognitive load theory (Sweller, 1988, 1994), there is a certain amount of information that can be processed in working memory at one time without overloading processing capacity. Thus, when cognitive load is increased beyond our working memory capacity, learning is depressed. For that, cognitive load theory provides guidelines and instructional strategies intended to assist the presentation of information and to design learning environment in accordance with working memory capacity (Paas & Sweller, 2014; Paas, Van Gog, and Sweller, 2010; Chang et al., 2012). These guidelines and instructional strategies should be taken into account for providing learners with an effective learning experience. In addition, this method helps parents to known and support the WMC deficiency of their kids at early stages. Furthermore, teachers could benefit from the information about their learners’ WMC by adapting their teaching strategies for learners with WM difficulties. As an example of strategy, Gathercole and Alloway (2008) advise teachers to break down tasks and instructions C 2016 British Educational Research Association V

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into smaller components; also to prompt learners with regular reminders of what they need to do next to finish a task. Information about learner’s WMC can be used in adaptive e-learning systems for providing learners with individualized materials and personalized recommendations. For example, Chang et al. (2013b, 2014) proposed a recommendation mechanism that provides teachers and learners with meaningful recommendations and suggestions based on different levels of learners’ WMC in learning systems. Particularly, students are provided with appropriate number of learning objects that they have learnt earlier, based on different degrees of WMC in order to remind them about and help them concentrate on learning certain types of learning objects. As a concrete instance, Chang et al. (2014) suggested to provide a student who has Moderate LOW WMC a 70% of learning objects that he/she has learnt in the previous week/section, in order to remind her/him and to support her/his low WMC. The proposed approach can improve the accuracy of learner model and can subsequently enable the fine grained personalization and adaptive recommendations that positively affect the learners’ learning process. However, the limitation of this approach is that it requires expert experience in fuzzy logic system for defining membership functions for inputs and outputs, and for creating the linguistic rules. Future works will extend the current study by detecting the responsible component of working memory impairment. In fact, some learners may have a poor central executive component, making it difficult for them to deal with subjects such as mathematics. Others may have low auditory working memory, so they may find difficulty with spoken instructions. For that, finding the responsible component for working memory impairment and recommending solutions to improve that component will be a promising future work. Statements on open data, ethics, and conflict of interest a) All data obtained from the current empirical research are available online, for all researchers, at http://www.egresearch.info/experiment/data/data.html b) Participants of this empirical research were students from higher schools, aged 19 to 27. They participated voluntarily in the experimentation without any duress. All participants were informed, in advance, about the goal and the different steps of the experiment. Participants were also informed that they have the right to withdraw from the experiment for any or no reason and at any time. Moreover, all participants’ personal information were excluded from the final results presented in the paper. c) The authors declare that they have no conflict of interest. References Alloway, T. P., & Alloway, R. G. (2010). Investigating the predictive roles of working memory and IQ in academic attainment, Journal of Experimental Child Psychology, 106, 20–29. Alpaydin, E. (2014). Introduction to machine learning. MIT Press. Atkinson, R. C., & Shiffrin, R. M. (1968). Human memory: a proposed system and its control processes. The Psychology of Learning and Motivation, 2, 89–195. Atkinson, R. C., & Shiffrin, R. M. (1971). The control processes of short-term memory. Stanford, CA: Institute for Mathematical Studies in the Social Sciences, Stanford University. Baddeley, A. (2015). Introduction of the episodic buffer. Interview. 2.29 Minutes. Available online at: http://gocognitive.net/interviews/introduction-episodic-buffer. Baddeley, A. D. (1992). Working memory. Science Magazine, 255(5044), 556–559. Baddeley, A. D. (2000). The episodic buffer: a new component of working memory?. Trends in Cognitive Sciences 4, 417–423. Baddeley, A. D. (2012). Working memory: theories, models, and controversies. Annual Review of Psychology, 63, 1–29. C 2016 British Educational Research Association V


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Baddeley, A. D., & Hitch, G. J. (1974). Working memory. In: G. H. Bower (Ed.). The Psychology of learning and motivation: Advances in research and theory (Vol. 8, pp. 47–89). New York: Academic Press. Becker, J. T., & Morris, R. G. (1999). Working memory(s). Brain and Cognition 41, 1–8. Carretti, B., Borella, E., Cornoldi, C., & Beni, R. D. (2009). Role of working memory in explaining the performance of individuals with specific reading comprehension difficulties: a meta-analysis, Learning and Individual Differences, 19(2), 246–251. Case, R., Kurland, M., & Goldberg, J. (1982). Operational efficiency and the growth of short-term memory span. Journal of Experimental Child Psychology, 33, 386–404. Cavallini, E., Fastame, M. C., Cattaneo, Z., Palladino, P., & Vecchi, T. (2002). Theoretical and practical aspects of working memory. Perspectives on Cognitive Psychology, 31–49. Chang, T. W., Kinshuk, Chen, N. S., & Yu, P. T. (2012). The effects of presentation method and information density on visual search ability and working memory load. Computers & Education, 58(2), 721–731. Chang, T. W., El-Bishouty, M. M., Graf, S., & Kinshuk (2013a). An Approach for detecting students’ working memory capacity from their behavior in learning systems. In 13th IEEE International Conference on Advanced Learning Technologies (ICALT) (pp. 82–86). Beijing: IEEE. Chang, T. W., El-Bishouty, M. M., Graf, S., & Kinshuk (2013b). Recommendation mechanism based on students’ working memory capacity in learning systems. In Proceedings of the International Conference on Advanced Learning Technologies (ICALT 2013), IEEE Computer Society, July 2013, Beijing, China (pp. 333–335). Chang, T. W., Kurcz, J., El-Bishouty, M. M., Graf, S., & Kinshuk (2014). Adaptive recommendations to students based on working memory capacity. In Proceedings of the International Conference on Advanced Learning Technologies (ICALT 2014), IEEE Computer Society, July 2014, Athens, Greece (pp. 57–61). Cingolani, P., & Alcala-Fdez, J. (2012). jFuzzyLogic: a robust and flexible fuzzy logic inference system language implementation. In IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) (pp. 1–8). IEEE. Cowan, N. (1995). Attention and memory: an integrated framework. Oxford psychology series Vol. 26. New York: Oxford University Press. Craik, F. I., & Lockhart, R. S. (1972). Levels of processing: a framework for memory research. Journal of Verbal Learning and Verbal Behavior, 11(6), 671–684. Daneman, M., & Carpenter, P. A. (1980). Individual differences in working memory and reading. Journal of Verbal Learning and Verbal Behavior, 19, 450–466. Domingos, P. (2012). A few useful things to know about machine learning. Communications of the ACM, 55(10), 78–87. Esgate, A., Groome, D., & Baker, K. (2005). An introduction to applied cognitive psychology. Hove, United Kingdom: Psychology Press. Gathercole, S. E., & Alloway, T. P. (2008). Working memory and learning: a practical guide for teachers. London: Sage Press. Graf, S., Lin, T., Jeffrey, L., & Kinshuk (2006). An exploratory study of the relationship between learning styles and cognitive traits (pp. 470–475). Berlin Heidelberg: Springer. Graf, S., Lin, T., & Kinshuk (2007). Analysing the relationship between learning styles and cognitive traits. In Proceedings of the Seventh IEEE International Conference on Advanced Learning Technologies, ICALT (pp. 235–239). Niigata: IEEE. Healy, A. F. (1975). Coding of temporal-spatial patterns in short-term memory. Journal of Verbal Learning and Verbal Behavior, 14(5), 481–495. Healy, A. F. (1977). Pattern coding of spatial order information in short-term memory. Journal of Verbal Learning and Verbal Behavior, 16(4), 419–437. Henry, L. (2012). The development of working memory in children. London: SAGE Publications. Khenissi, M. A., Essalmi, F., Jemni, M., & Kinshuk (2014a). A learning version of memory match game, In Proceedings of the 14th IEEE International Conference on Advanced Learning Technologies (ICALT2014), July 7–9, 2014, Athens, Greece (pp. 209–210). Khenissi, M. A., Essalmi, F., Jemni, M., & Kinshuk (2014b). Learners’ working memory capacity modeling based on fuzzy logic, In Proceedings of the 14th IEEE International Conference on Advanced Learning Technologies (ICALT2014), July 7–9, 2014, Athens, Greece (pp. 520–521). C 2016 British Educational Research Association V

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Khenissi, M. A., Essalmi, F., Jemni, M., Kinshuk & Chang, T. W. (2015). Measuring learners’ working memory capacity from their interactions within educational game. In Emerging Issues in Smart Learning (pp. 233–237). Berlin/Heidelberg: Springer. Lee, C. (1990). Fuzzy logic in control systems: fuzzy logic controller parts i and ii. IEEE Transactions on Systems, Man, and Cybernetics, 20, 404–435. Lin, T. Y. (2007). Cognitive trait model for adaptive learning environments (PhD thesis, Massey University Palmerston North, New Zealand). Mayer, R. E. (2003). Cognitive theory of multimedia learning. The Cambridge handbook of multimedia learning. New York: Cambridge University Press. McLeod, S. A. (2009). Short term memory—simply psychology. Retrieved from http://www.simplypsychology.org/short-term-memory.html Mendel, J. M. (1995). Fuzzy logic systems for engineering: a tutorial. Proceedings of the IEEE, 83(3), 345– 377. Miller, G. A. (1956). The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychological Review, 63(2), 81–97. Paas, F., & Sweller, J. (2014). Implications of cognitive load theory for multimedia learning. In The Cambridge handbook of multimedia learning (Vol. 27, pp. 27–42). Cambridge: Cambridge University Press. Paas, F., Van Gog, T., & Sweller, J. (2010). Cognitive load theory: new conceptualizations, specifications, and integrated research perspectives. Educational Psychology Review, 22(2), 115–121. Paivio, A. (1991). Dual coding theory: retrospect and current status. Canadian Journal of Psychology, 45(3), 255–287. Schnotz, W., & K€ urschner, C. (2008). External and internal representations in the acquisition and use of knowledge: visualization effects on mental model construction. Instructional Science, 36(3), 175–190. Sweller, J. (1988). Cognitive load during problem solving: effects on learning. Cognitive Science, 12(2), 257–285. Sweller, J. (1994). Cognitive load theory, learning difficulty, and instructional design. Learning and Instruction, 4(4), 295–312. Truman, S. M., & Truman, P. J. (2006). An investigation of the situated learnability effects of single-and dual-modal systems in education: a report of music-oriented learning environment and science computer-assisted teaching studies. British Journal of Educational Technology, 37(1), 131–142. Turner, M. L., & Engle, R. W. (1989). Is working memory capacity task dependent? Journal of Memory and Language, 28, 127–154. Woehrle, J. L., & Magliano, J. P. (2012). Time flies faster if a person has a high working-memory capacity, Acta Psychologica, 139(2), 314–319. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353. Zedeh, L. A. (1989). Knowledge representation in fuzzy logic. IEEE Transactions on Knowledge and Data Engineering, 1(1), 89–100. Zwick, U., & Paterson, M. S. (1993). The memory game. Theoretical Computer Science, 110, 169–196.

Appendix This study dealt with four linguistic variables. Each linguistic variable was decomposed into three linguistic terms. 1. 2. 3. 4.

Discovery_duration {Short, Medium, Long}; Research_duration {Short, Medium, Long}; Number_of_clicks {Few, Some, Many}; Remaining_cards {Few, Some, Many}.

All the possible combinations used in determining the high and low WMC will be calculated as follow: 3^4 5 81. In total, there is a 81 fuzzy rules. These rules were identified based on discussion with researchers. Table 6 presents all fuzzy rules for the measurement of the capacities of the working memory’s components are listed. C 2016 British Educational Research Association V


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Table 6: Fuzzy rules for the measurement of the capacities of the working memory’s components Discovery duration

Research duration

Number of clicks

Remaining cards


Long Long Long Long Long Long Long Long Long Long Long Long Long Long Long Long Long Long Long Long Long Long Long Long Long Long Long Medium Medium Medium Medium Medium Medium Medium Medium Medium Medium Medium Medium Medium Medium Medium Medium Medium Medium Medium Medium Medium Medium

Long Long Long Long Long Long Long Long Long Medium Medium Medium Medium Medium Medium Medium Medium Medium Short Short Short Short Short Short Short Short Short Long Long Long Long Long Long Long Long Long Medium Medium Medium Medium Medium Medium Medium Medium Medium Short Short Short Short

Many Many Many Some Some Some Few Few Few Many Many Many Some Some Some Few Few Few Many Many Many Some Some Some Few Few Few Many Many Many Some Some Some Few Few Few Many Many Many Some Some Some Few Few Few Many Many Many Some

Many Some Few Many Some Few Many Some Few Many Some Few Many Some Few Many Some Few Many Some Few Many Some Few Many Some Few Many Some Few Many Some Few Many Some Few Many Some Few Many Some Few Many Some Few Many Some Few Many

Low Low Low Medium Medium Low High High Medium Medium Medium Low High Medium Low High High Medium Not possible Not possible Not possible Not possible Not possible Not possible High High High Medium Low Low High Medium Medium High High Medium Medium Low Low Medium Medium High High High Medium Not possible Not possible Not possible Not possible


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Table 6: Continued Discovery duration

Research duration

Number of clicks

Remaining cards


Medium Medium Medium Medium Medium Short Short Short Short Short Short Short Short Short Short Short Short Short Short Short Short Short Short Short Short Short Short Short Short Short Short Short

Short Short Short Short Short Long Long Long Long Long Long Long Long Long Medium Medium Medium Medium Medium Medium Medium Medium Medium Short Short Short Short Short Short Short Short Short

Some Some Few Few Few Many Many Many Some Some Some Few Few Few Many Many Many Some Some Some Few Few Few Many Many Many Some Some Some Few Few Few

Some Few Many Some Few Many Some Few Many Some Few Many Some Few Many Some Few Many Some Few Many Some Few Many Some Few Many Some Few Many Some Few

Not possible Not possible High Medium Medium Medium Low Low Medium Low Low High High Medium Medium Low Low Medium Medium Low Medium Medium Low Not possible Not possible Not possible Low Low Low Luck Luck Luck
