Possibilities of Modelling Web-Based Education Using IF-THEN Rules

Possibilities of Modelling Web-Based Education Using IF-THEN Rules and Fuzzy Petri Nets in LMS Zoltán Balogh and Milan Turčáni Department of Informatics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra Tr. A. Hlinku 1, 949 74 Nitra, Slovakia {zbalogh,mturcani}@ukf.sk Abstract. Basic requirements, which are imposed on LMS (Learning Management System) from the point of view of the needs of a teacher, are to present the contents of instruction, manage the instruction, communicate with students, motivate them to study, observe their progress and evaluate them. The article deals with an opportunity to implement fuzzy logic into web-based education using the created IF-THEN rules and modelling in Petri nets. By an application of fuzzy logic into Petri nets there arises a strong tool for modelling teaching processes, mainly thanks to the easy understandability and sophisticated mathematical setup, supporting a rather simple design of educational activities managed by LMS, for the compendious modularity of solution and robustness of the design. Keywords: Learning Management System (LMS), Fuzzy logic, Petri nets, IF-THEN rules, Model, Web Based Education, E-learning.

1

Introduction

Static structure of information on the web, the task of which is to provide information, has long been overcome. More and more web software systems, which are more complex than ever before, originate. From the point of view of application of these systems, there is a more and more frequent necessity to enrich the information space of heterogenous sources, managed by the mentioned systems, with elements of adaptation to the user and/or the environment, in which the user operates. The aim is to present the user personalized information, if possible only such that are relevant for the user, and in such a way, which suits the given user most [1]. Education was always the most popular application area for adaptive hypermedia systems. A number of interesting methods and techniques of adaptive hypermedia were originally developed for in various adaptive educational hypermedia systems. In turn, most of the early research on adaptive educational hypermedia were inspired by the area of intelligent tutoring systems [2],[3] and were born in a trial to combine an intelligent tutoring system (ITS) and educational hypermedia. With the rapid advance of the Internet, e-learning systems have become more and more popular [4],[5]. An e-learning system provides the following functions: (1) A. Abd Manaf et al. (Eds.): ICIEIS 2011, Part I, CCIS 251, pp. 93–106, 2011. © Springer-Verlag Berlin Heidelberg 2011

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delivery of learning content for students via the Internet; (2) record of learning progress and portfolio; (3) management of learning content, assessment and course; and so on [6]. The Internet and related web technologies do offer great solutions for presenting, publishing and sharing learning content and information, as is the case in many other areas. Special software called Learning Management System (LMS) (Fig.1.) is generally used in most institutions providing web-based learning [7]. The most of universities combine form of learning using one of a number of commercial or free LMS. They decided to use products such as Claroline, Fle3, ILIAS, MS Class Server, WebCT, Eden, Enterprise Knowledge Platform, LearningSpace, eAmos, eDoceo, Uniforms, uLern, Aspen, Oracle iLearnin, NETOPIL School and Moodle [8].

Fig. 1. Structure of the Learning Management System (LMS) [7]

Now that the Internet is recognized as the main platform for education, web-based applications are preferred when it comes to educational activities, channels for communications and systems to access knowledge. LMS are often viewed as the starting point of any web-based learning program [9]. Many pedagogues were introducing their models of electronic education in the early 20th century, but they had no sufficient tools to their effective implementation at that time [10]. Nowadays electronic learning systems provide possibility to save all information about student’s activities in one place. Teacher could monitor student’s activities after his login into system. Systems offer submitting the file, testing manage the communication and cooperation too. LMSs facilitates teacher to keep his methodical portfolio dynamic and offer electronic students´ portfolio in every moment [11]. An LMS provides the platform for the web-based learning environment. Because of the huge number of e-learning systems, and the availability of a large number of LMSs, one needs a systematic way, or a tool to evaluate the quality, efficiency, and the performance of LMSs and make a choice that will satisfy most or

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all of the requirements [12]. LMS systems usually have large number of features and it becomes a tedious task to make a manual selection. One possibility is to automate this evaluation process using computer aided techniques [7]. The target function of LMS managing the instruction is the direction of communication as to the student´s knowledge and abilities, thus changing the amount and demandingness of the materials submitted to the student. In the theory of management there is an obvious transition from combination procedures to sequence chains and optimized processes (the strategy of continuous assessment of the student instruction reflection, and based on that, adaptation of the following instruction, is comparable with the dual principle of identification and adaptive management). For the description of the communication of a man with a computer it is suitable to use graphic tools [13], allowing for suitably describing and expressing the interaction. The teaching interaction between a student and an information system managing the instruction is a complex process, for which Petri nets should be applied. Another attitude to the description of true and real teaching procedures is an application of fuzzy modelling [14]. Most frequently, the personalization of e-learning courses is realized based on extracted knowledge of usage data by means of the web log mining techniques [15], [16], [17], however, we focus on the personalization using fuzzy Petri nets.

2

Modelling Teaching Processes in Fuzzy Petri Nets

For the description of the behaviour of teaching processes the so called serial machines, which, however, have several limitations, e.g. in the number of statuses when modelling complex processes, are suitably used. That is why Petri nets are used for the given purposes, which have originated just on the ground of expanding modelling possibilities of serial machines. One of the advantages of modelling teaching processes using Petri nets is their formal description, which is complemented by visual graphic depiction. This allows for a precise and exact specification of the teaching process being designed and removal of ambiguity, vagueness and contradiction upon designing. Besides the visual graphic manifestation, Petri nets have also square defined mathematical bases, which can be suitably used in various software tools for the specification and analysis of computer-solved teaching processes [18], [19]. Fuzzy logic allows for using vague requirements either directly, or can simply represent them [20]. Incorporating the fuzzy logic into the classical Petri nets can be realized in this way: We draw from the definition of the fuzzy logic Petri nets. FLPN = (P,T,F,M0,D,h,a, θ ,l) where P = {p1, …, pn} is the finite set of places, T = {t1, …, tm} is the finite set of transitions, F ⊆ (P x T) ∪ (T x P) is the flow relation, where ∀t ∈ T ∃p, q ∈ P : ( p, t ) ∨ (t , q) ∈ F , M0: P → {0,1} is the initial marking,

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D is the finite set of statements – P ∩ D = T ∩ D = ∅, P = D , h: P → D is the associated function, representing the bijection from the place to the statement, a: P → [0,1] is the associated function representing the value in the place out of the set of real numbers 0 through 1, θ ,l: T → [0,1] is the associated function representing the transition through the value out of the set 0 through 1. For ∀p ∈ P , the following marking applies: M ' ( p ) = M ( p ) + 1, if p ∈ t • − • t ;

M ' ( p) = M ( p) − 1, if p∈• t − t • ; M ' ( p) = M ( p), otherwise,

α ( p) = λtα ( p' ) if α 1 ≥ θ t ∧ p ∈ t • ∧ p '∈• t . For t ∈ T AND α ( p ) = λt min α ( p ' ) applies, if min {α ( p ' )} ≥ θ t ∧ p ∈ t • ∀p '∈• t

and for t ∈ T

OR

∀p '∈• t

α ( p) = λt maxα ( p' ) applies, if max{α ( p' )} ≥ θ t ∧ p ∈ t • . ∀p '∈• t

∀p '∈• t

Now, let us express, by means of Petri nets, the rules of the IF-THEN type and their transformation into the fuzzy logic: The rule IF P1 THEN P2 will be expressed as

P1

P2

and in the fuzzy logic α 2 = λtα 1 if α1 ≥ θ t . The rule IF P1 AND P2 THEN P3 will be expressed as

P1 P3 P2 and in the fuzzy logic α 3 = λt min {α 1α 2 } for i=1 ∧ 2. α i ≥θ

t AND

The rule IF P1 OR P2 THEN P3 will be expressed using inhibition edges as

P1 P3 P2 and in the fuzzy logic α 3 = λt max {α1α 2 } for i=1 ∨ 2. OR

α i ≥θ

t OR

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The rule IF P1 XOR P2 THEN P3 will be expressed using inhibition edges as

P1 P3 P2 and in the fuzzy logic α 3 = λt α 1 if α 1 ≥ θ t XOR

α 3 = λt α 2 if α 2 ≥ θ t XOR

XOR

XOR

∧ α2 = 0 ,

∧ α1 = 0 .

Such definition of FPN comes out of the definitions of the transfer of the classical logic into the fuzzy logic. In the following table the survey of basic functions will be described. Table 1. An outline of basic functions of logical rules of Petri nets [21] No. Rules

Logical Petri Nets

Fuzzy Computing

t 1.

IF d 1 THEN d 2

2.

IF d 1 AND d 2 THEN d3

P1

P2

P1

tAND

P3

α 2 = λt α 1 ifα 1 ≥ θ t

α 3 = λt OR

P1

3.

tOR

α 3 = λt OR P3

t OR

i =1∧ 2

P2

IF d 1 OR d 2 THEN d 3

min{α1, α 2}

α i ;θ

max{α1,α 2}

α i ;θ

t OR

i =1∨ 2

P2 P1

4.

IF d 1 XOR d 2 THEN d 3

tXOR P2

3

P3

⎧ λt XOR α1ifα1 ≥ θ t XOR ⎪ ∧α2 = 0 ⎪ α3 = ⎨ λ α ⎪ t XOR 2 ifα 2 ≥ θ t XOR ⎪⎩ ∧ α1 = 0

Model of Adaptation of Teaching Using IF - THEN Rules

For the specification of a concrete model of adaptation of teaching we have to define model inputs first. Let us assume that we are able to name these input information:

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Motivation to teaching Motivation to teaching is defined by the answers to four basic questions: if I want to teach and how much I care, if I show interest in teaching, if I like the way I am successful. motivation = {low, average, high} Concentration Concentration means focusing on the contents and not taking a note of external or internal perturbing influences, which reduce efficiency of teaching/learning. Among the internal influences belong visualization and thoughts, or recollections of what does not belong to the given object. Among the outer negative influences belong for example noise, music or speech, overheating or cold, etc. concentration = {low, average, high} Memory Memory is a capability to receive, process, store and find where necessary various contents in the memory. memory = {very good, good, average, poor} Time of learning It is necessary to find suitable time for studying. There exist people, who prefer early morning hours, while others belong among „night students“- owls. The time of studying should correspond to the biorhythms of human organism. Time of learning = {improper, proper} Length of learning The length of learning depends on age, experience and habits. In the course of learning there are periods of attenuation caused by fatigue. It is inevitable to arrange short breaks (5 minutes) for the recovery of attention and concentration. Length of learning = {very short, adequate, very long} Time The overall time spent by studying. time = {very short, short, adequate, long, very long} Access/entry The number of accesses of the student to the educational activity (e-course). Access/entry = {low, average, high} Number of entries = {low, average, high} Environment Learning process is influenced by the environment – light, size and colour of the bench, shape and firmness of the chair, room temperature, ventilation, surroundings of the work table.

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Educational environment • external – surroundings (of the school, family, workplace) with economical, social and cultural, demographic, ethnical characteristics, • internal o physical – ergonomic parameters (lighting, spatial arrangement, application of colours, furniture structure, etc.), o psycho-social  static – more permanent relationships among the participants of the educational process (among parents and children, teachers and pupils) – teaching atmosphere  changeable – short-term influences having an impact on the contents and character of communication among the participants of educational processes environment = {very bad, bad, good, very good} Way of living Proper way of living can be defined as regular sleep, proper nutrition and physical and mental hygiene. Way of living = {very good, good, wrong} Studying the text – effective reading The process of reading includes deliberate bearing on the text to be decoded, transfer of graphic codes into the brain, their decoding, arrangement into words, storing in a short-term memory, assigning the meaning and allocating it within the relationships, including deeper comprehension or forecasting. From the point of view of an average reader we can differentiate roughly five types of speed [22]: • easy reading – 250 words/min, e.g. unpretentious middle article, simple newspaper article, advertising, • normal reading – 180 words/min, long newspaper articles, business correspondence, majority of working papers, • thorough reading – 135 words/min, texts from less known scientific branches or topics, we are not acquainted with, • difficult reading – 75 words/min, texts from data, numbers, formulas, technical text, foreign-language texts, • extraordinary reading – texts with formulas, difficult foreign texts reading = {simple, normal, thorough, difficult, extraordinary} Teaching materials - theory Theory – amount of theory contained in the e-learning course. theory = {very little, little, adequately, much, very much}

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Teaching materials - examples Examples – amount of specimen and examples contained in the e-learning course. examples = {very few, few, adequately, many, great many}

If we were able to define also other inputs, we would certainly improve the adaptation process quality. Other inputs include: Intelligence Intelligent people have retentive memory, which is, however, very often only selective one (i.e. the ability to remember only some area). Besides that, they use a better style of learning and acquire new knowledge much faster than people of lower rational level. There exist several types of intelligence. The speed of acquisition of the knowledge from the given area studied depends on the type of intelligence. Emotional intelligence Emotional intelligence includes the ability to perceive one´s own emotions, to allow for manipulating with these emotions, to use them in favour of a certain thing, to be able to find motivation, or the ability to empathize (empathy). Emotional intelligence is defined as part of social intelligence, which includes the ability to follow one´s or outside emotions and feelings, to differentiate them and use these pieces of information in one´s own thinking and behaviour. Specific learning disorders Specific disorders of learning are often light brain dysfunction (LMD). It is often related to children with almost average, average or above average general intelligence with certain disorders or behavioural disturbances, which are connected with deviations of the CNS system. The following rating represents the output of adaptation: Knowledge – it is an ability to recollect or remember facts knowledge = {perfect, very good, good, poor, very poor}

Comprehension – it is an ability to comprehend and interpreted the acquired information. comprehension = {perfect, very good, good, poor, very poor} Applicability – it is an ability to use the acquired material in new situations, i.e. to implement thoughts and principles into the problem being solved. applicability = {perfect, very good, good, poor, very poor} 3.1

Definition of the Model of Adaptation

Inputs environs = {very bad, bad, good, very good} motivation = {low, average, high} memory = {very good, good, average, bad}

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concentration = {low, average, high} regime = {very good, good, bad} time of teaching = {improper, suitable} length of learning = {very short, adequate, very long} time = {very short, short, average, long, very long} reading = {easy, normal, thorough, difficult, extraordinary} attitude = {low, average, high} theory = {very little, little, average, a lot of, very much} examples = {very few, few, average, a lot of, very many} Outputs knowledge = {excellent, very good, good, poor, very poor} understanding = {excellent, very good, good, poor, very poor} application = {excellent, very good, good, poor, very poor} Rules IF (environs = very bad AND concentration = low) THEN knowledge = very poor IF (motivation = low AND time of teaching = improper) THEN understanding = very poor IF (memory = bad AND regime = bad) THEN application = very poor IF (environs = bad AND length of learning = very long) THEN knowledge = poor IF (environs = good AND reading = extraordinary AND attitude = low) THEN knowledge = poor IF (motivation = average AND time = very short) THEN understanding = poor IF (memory = average AND theory = very little) THEN application = very poor IF (concentration = average AND examples = very few AND) THEN comprehension = bad IF (regime = good AND time of learning = suitable AND reading = extraordinary) THEN understanding = bad IF (time of teaching = suitable AND reading = thorough AND theory = very much) THEN knowledge = good IF (memory = very good AND length of learning = adequate AND examples = very few) THEN understanding = poor IF (reading = difficult AND theory= a lot of AND attitude = average) THEN knowledge = poor IF (regime = very good AND time of teaching = suitable AND examples = few) THEN understanding = poor IF (memory = bad AND time of teaching = improper AND attitude = low) THEN application = very poor IF (memory = good AND length of learning = adequate AND theory = adequate) THEN knowledge = good IF (reading = normal AND time = average AND examples = adequate) THEN understanding = good IF (environs = very good AND theory = adequate AND examples = adequate) THEN application = good

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Fig. 2. Example of application of IF - THEN rules into Petri nets. Output: Knowledge.

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IF (time of teaching = suitable AND memory = good AND theory = adequate) THEN knowledge = very good IF (memory = very good AND reading = easy AND examples = adequate) THEN understanding = very good IF (motivation = high AND time = long AND examples = many) THEN application = very good IF (time of teaching = very short AND reading = difficult) THEN knowledge = very poor IF (time = short AND attitude = high) THEN application = very poor IF (time = very long AND reading = difficult AND examples = few) THEN understanding = poor IF (concentration = high AND examples = a lot of AND time of teaching = suitable) THEN understanding = excellent IF (environs = very good AND memory = very good AND theory = adequate) THEN understanding = excellent IF (motivation = high AND memory = very good AND time of teaching = suitable) THEN knowledge = excellent IF (reading = thorough AND attitude = adequate AND theory = adequate) THEN knowledge = excellent IF (concentration = high AND time of teaching = suitable AND examples = a lot of) THEN application = excellent IF (reading = normal AND regimen = fair AND concentration = high) THEN application = excellent 3.2

Application of IF - THEN Rules Using Petri Nets

By an application of IF - THEN rules into Petri nets there originates a strong tool for modelling teaching processes, and mainly for their easy comprehensibility and sophisticated mathematical setup, a rather simple design, for the comprendious modularity of solution (it is possible to add or remove individual modules without any necessity to fully rework the whole system) and for the robustness of the design (the system need not be modified in case of a change in parameters of solution of the task within a certain environment). In fig. 2 we can see the draft of the model of adaptation of teaching process created by means of Petri nets for one of the outputs – knowledge.

4

Discussion

If we want to describe all teaching processes in details, it would lead to an enormous number of detailed information, which nobody could be able to read. If so, then a natural language would be needed in order to understand the essence of what is described in them; however, it will result in an inaccurate characteristics. If it be to the contrary, it would inescapably be lost in exact details, since human psychic has only limited possibilities. It turns out that accuracy is only an illusion, since, on principle, it is unreachable. All these facts stand in the background of considerations

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of the founders of fuzzy logic [23]. Nevertheless, fuzzy logic arises from the theory of fuzzy aggregates and is focused on vagueness, which it mathematically describes. In this context, fuzzy aggregate is a set, which, besides a full or null membership, allows also for a partial membership. The function, which assigns the degree of adherence to each element of the universe, is called adherence function. Fuzzy theory tries to cover reality in its inaccurateness and vagueness, and during its almost 40-year-long existence it has earned a good reputation in terms of solving several technical problems, which could not have been handled in the practice by means of other means. It is possible to gradually assign each element the so-called degree of adherence, which expresses the rate of adherence of the given element to the fuzzy aggregate. In classical determination, in this case, it is rather difficult to define the limit of what is still allowed and what is already not allowed. It can be done by allocation of a number from the interval, which expresses the measure of our confidence. The task of the fuzzy theory is to catch the vaguely specified requirements in the query and adequately calculate the degree of adherence to it. Let us solve the following task: to create an educational activity using the know LMS and use for the draft the above mentioned modelling setup, which will allow us to realize the personalization of education using Web Based systems. What and how do we intend to model using Petri nets? A student, who will require study materials necessary for learning a certain sphere, enters the teaching process managed by a suitable LMS. The entering student will enter input information according to the requirements of LMS on his knowledge, time for learning, etc. – it is not possible to exactly define whether he has/or has not any knowledge and how much time he should devote to learning. The following input information will arise: I have little knowledge, I have sound knowledge, I am busy, I have a lot of time, etc. Based on this input information LMS defines the process of learning of the student. For a faster definition of the learning process we can use a Petri net prepared in advance, which will describe individual statuses, which could occur in the student. We shall implement certain IF – THEN rules, according to which the net will be built. E.g.: IF he has little knowledge AND much time THEN all chapters of the study material will be used. Having setup this net we have to define in a certain way importance of individual transitions from one status into another. This significance will be set in Petri nets using the value from Fuzzy aggregate (0,1) upon transitions. At the moment we set up such Fuzzy Petri net, we enter tokens into initial statuses, which will take the values of the Fuzzy aggregate (0,1) again. These tokens will define with their values just the sound, small, medium knowledge, etc. After the simulation of the Fuzzy Petri net using the rules to be written out, LMS will receive the learning procedure. Before we start to enter the initial tokens, it is suitable to define terminology of input data and assign the particular values. For example: small = 0.3, a little = 0.4, much = 0.8 etc. By the application of fuzzy logic into Petri nets originates a strong tool for the modelling of educational processes, mainly thanks to: − understandability and sophisticated mathematical mechanism, − rather simple design, − modularity of solution, − it is possible to ad and remove individual module without the necessary complete re-working of the whole system.

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Conclusion

A common feature of various adaptive Web systems is the application of user models (also known as profiles) to adapt the systems’ behaviour to individual users. User models represent the information about users that is essential to support the adaptation functionality of the systems. Adaptive Web systems have investigated a range of approaches to user modelling, exploring how to organize the storage for user information, how to populate it with user data, and how to maintain the current state of the user. The majority of modern adaptive Web systems use feature-based approach to represent and model information about the users. The competing stereotype-based approach, once popular in the pre-Web area of adaptive interfaces, has lost dominance but is still applied, especially in combination with the featurebased approaches [24]. One of the main advantages of using a formal method for student modelling is its robustness. Once this model behaves in a stable and theoretically-correct fashion, the evaluation of a system can be focused on other components (such as quality of the learning material, learning strategies used, or adaptation capabilities). The future adaptation learning algorithm would then be able to process each user’s interactive behaviour information and simultaneously update the structure of the model [24]. Basic requirements, which are imposed on LMS from the point of view of the needs of a teacher, are to present the contents of instruction, manage the instruction, communicate with students, motivate them to study, observe their progress and evaluate them. The bottleneck of the description of all these processes realized within LMS is the formalization of the description of obligation of individual operations and management of individual activities. Therefore, for the provision of a good quality management of elearning education it is suitable to integrate the classical LMS with the process system. This integration will allow for changing the way through the study of teaching materials and other compulsory activities of a student. Individual parts of teaching materials are automatically activated by means of the process system, i.e. that LMS provides for the advancement of functions for students, thus passing messages to the process system, which assesses it and makes advancement in the process map [19]. Acknowledgments. This publication is published thanks to the financial support of the project KEGA 368-043UKF-4/2010 named: Implementation of elements of interactivity in the contentual transformation of professional informatics subjects.

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