LEARNING STYLE ESTIMATION USING BAYESIAN

NETWORKS

S. Botsios, D. A. Georgiou and N. F. Safouris

Department of Electrical & Computer Engineering, School of Engineering

Democritu University of Thrace, GR 67100 Xanthi, Greece

Keywords: Learning style estimation, Adaptive Educational Hypermedia Systems, Bayesian Networks, expert systems.

Abstract: In order to improve the efficiency of Learning Style estimation, we propose an easily, applicable, Web

based, expert system founded on Bayesian networks. The proposed system takes under consideration

learners’ answers to a certain questionnaire, as well as classification of learners who have been examined

before. As a result, factors such as cultural environment will add value to the learning style estimation.

Moreover, the influence of wrong answers, caused by various reasons, is expected to be reduced.

1 INTRODUCTION

The development of artificial intelligence

methodology has been recognized as an important

requirement in complex asynchronous e-learning

situations. Cognitive Style (CS) estimation is a

particularly good example, because of the

complexity of the learner behaviour and style as well

as of our limited and vague knowledge of how these

interact to each other. This estimation is also

influenced by the teacher’s expertise. Such

difficulties mean that a degree of uncertainty is

involved in Learning Style (LS) estimation.

Moreover, acquisition of Learning Objects (LO) in

Adaptive Educational Hypermedia Systems (AEHS)

requires analysis of the learner’s CS. The link

between LS estimation and LO retrieval thus

produces large numbers of cause-effect relations at

many interacting levels of both description and

function. The relations are necessarily poor

approximations of complex dynamic systems, and

some allowance must be made for uncertainty at this

level of description.

There exists a great variety of models and

theories in the literature regarding LS and CS.

Although some authors do not distinguish between

LS and CS (Kaltz, Rezaei, 2004), there are others

who clearly do (Smith, 2001). In any case, both of

them are considered relevant for the adaptation

process in the user model, and have been used as a

basis for adaptation in AEHS (Georgiou, Makry,

2004). Related models have been proposed by Kolb

(Kolb, 1984), Honey and Mumford, Dunn R. and

Dunn K. (Dunn, Dunn 1985 & Dunn, Dunn 1992),

Felder and Silverman (Felder, Silverman, 1988),

Murray (Murray, 1999) and others. Most of the

authors categorize LS and/or CS into groups and

propose certain inventories and methodologies

capable of classifying learners accordingly.

Such procedures can be influenced by a wide

variety of errors which may be caused by reasons

such as diverse as misconception, false use of the

space that has been alloted for the answer or bad

formulation of the questionnaire. Learners may also

respond to the questions in a wrong way, as slippery

answers or lucky guesses due to misconceptions

appear (VanLehn, Martin, 1995 & Reye, 2004).

Another significant source of poor LS estimation can

be deficiencies in the formulation of the

questionnaire itself. Barros et al (Baros, Verdejo,

Read, Mizoguchi, 2002) address the issue of cultural

environment influence on learners’ behavior. A

review of the vast literature shows that such factors

lead to controversial comments on the model’s

applicability and efficiency (Murray 1999). Despite

the bottleneck caused by such reasons, it is

worthwhile developing LS estimation techniques.

In order to improve the efficiency of LS

estimation, we propose an expert system based on

Bayesian Networks (BN). The proposed system

takes under consideration learners’ answers to a

certain questionnaire, as well as classification of

learners who have been examined before. BNs, and

their close cousins, influence diagrams, have been

proved to be both a natural representation of

probabilistic information and the basis for inference

415

Botsios S., A. Georgiou D. and F. Safouris N. (2007).

LEARNING STYLE ESTIMATION USING BAYESIAN NETWORKS.

In Proceedings of the Third International Conference on Web Information Systems and Technologies - Society, e-Business and e-Government /

e-Learning, pages 415-418

DOI: 10.5220/0001275704150418

 SciTePress

mechanisms that are suitably efficient in practice. A

BN is a direct, acyclic graph that consists of nodes

and arcs (Pearl 1988). Nodes represent random

variables and arcs qualitatively denote direct

dependence relationships between the connected

nodes (Milan, de la Cruz, Suarez, 2000). A BN

indirectly specifies the joint probability distribution

of the random variables, so we can compute any

conditional probabilities that involve variables in the

network. Edges in the graph represent causal

relationships between random variables, and thus

such networks are sometimes called causal

networks. In fact, degrees of relation are conditional

probabilities adapted as weights to the Bayesian

network’s edges.

In this paper we introduce a BN capable of

classifying learners in a predefined set of classes. It

is expected that our method, which takes advantages

of previously accumulated knowledge, will be more

accurate than LS direct estimation, i.e. an estimation

based only on single user responses. Since such

knowledge is based on the responses to the given

questionnaire made by antecedent users, their

classification in LS classes provides information that

contributes to the random variables’ degree of

relation. It is noted that the use of the proposed BN

restricts the LS grey areas, i.e. the areas where the

estimation does not provide a clear output.

In order to implement the BN we propose, we

made use of the Kolb’s Learning Style Inventory

(LSI) (Kolb, 1999).

2 RELATED WORK

Work has been published that accords with LS

recognition via BN. Bund et al. (Bunt, Conati,

2003), address this problem by building a BN

capable of detecting when the learner is having

difficulty exploring, and of providing the types of

assessments that the environment needs to guide and

improve the learner’s exploration of, the available

material. In Garcia et al. (Garcia, Amandi, Sciaffino,

Campo, 2005), a BN that detects the student’s LS is

evaluated. The BN’s input is the student’s

interactions with the Web-based educational system.

They used the Felder – Silverman classification

method. Zapata-Rivera et al. (Zapata-Rivera, Greer,

2004), present SModel, a BN student-modeling

server used in a distributed multi agent environment.

They implemented their Bayesian student models on

a modified version of the belief net backbone

structure for student models proposed by Reye

(1996).

The above-mentioned work applies BN as the

learning process is in progress. It bases LS

estimation on the learner’s behaviour, avoiding the

use of inventories proposed by cognitive science

specialists.

3 THE MODEL

Let LS={C

,…,C

} be the set of LSs. A learner is

recognized being as of class C

, (i=1,2,…,v)

according to his/her responses to a given set of m

questions. Each question can be answered by yes or

not. Let M={Q

(k)

, Q

(k)

,…,Q

(k)

} be the set of

answers where k is a Boolean operator taking the

values TRUE or FALSE whenever Q

(k)

represents

the answer YES or NOT respectively. There are 2

different sets of such responses to the questionnaire.

Let us consider the index j, where j

∈

{1,2,…,2

}. A

learner’s responses to the set of questions formulates

an element

where r

∈

M. Obviously, r

≠

for any pair r

∈

with i

≠

j. Let n be the number of learners who made

use of the system, and n

be the number of them

who responded to the questionnaire with an r

. The a

priori probability that the (n+1)

user responded to

the questionnaire with an element r

In this case, the BN in use is a weighted and

oriented K

m graph, i.e. a weighted and oriented

complete bipartite graph on n and 2

nodes. Figure 1

represents the proposed BN.

()

(1)

()

(

)

(2)

−

(

)

()

⎛⎞

⎜⎟

⎝⎠

ure 1: The

osed BN.

WEBIST 2007 - International Conference on Web Information Systems and Technologies

416

Concrete

Experience

Active

Experimentation

Reflective

Observation

Abstract

Conceptualization

Accommodating Diverging

Converging Assimilating

At each edge of the network’s graph we adjust

the conditional probability P(r

(n)

). This

probability expresses the ratio of users who

responded to the questionnaire with the element r

and were finally classified to C

, in terms of the total

number of r

responses. Thus, the measure P(C

(n+1)

)

is the probability that the LS of the (n+1)

learner

belongs to C

. This probability is given by the

relation

where

Finally, the learner’s dominant LS is given by

Where P(C

(n+1)

) = P(C

(n+1)

) for i≠j, the learner can

be classified either in class C

or in class C

. Since

this conflicts with the procedure, the system, in

order to avoid such a situation, redirects the

programme flow to a subsystem where the whole

procedure is repeated on a BN which has only the

dominated classes C

and C

In what follows, the proposed model is applied

using the Kolb’s Adaptive Style Inventory (Kolb,

1999).

4 THE IMPLEMENTATION

Kolb's learning theory sets out four distinct learning

styles (or preferences), which are based on a four-

stage learning cycle (figure 2), which might also be

interpreted as a ‘training cycle’.

Based on Kolb’s Learning Cycle, the set LS has

four elements which represent the four LSs as they

appear in table 1.

Let us consider LS={CE,RO,AC,AE} the set of

four classes. The set M has card(M)=2

which

indicates all the possible elements, i.e. the arrays of

answers to Kolb’s inventory. It follows that the BN

is a weighted and oriented K

48 graph having as

weights at its edges the conditional probabilities

P(r

(n)

To start with, we define the initial conditional

probabilities. The BN is therefore trained by a direct

classification via Kolb’s inventory. Special attention

has been paid to avoiding an initial uniform joint

distribution that results in the system’s inability to

detect the user’s LS. To this end, further direct

classification via Kolb’s inventory is made, skipping

the use of BN. The data produced enrich the

system’s database and modulates the conditional

probabilities. Practically, such implications are not

expected to occur after the initial system’s training.

Figure 2: Kolb’s Learning Cycle.

In the proposed algorithm one recognizes the

following steps:

Table 1: Kolb’s Learning Cycle.

D As C Ac

Diverging

(Feel and Watch)

Assimilating

(Think & Watch)

Converging

(Think & Do)

Accommodating

(Feel & Do)

Concrete

Experience

(CE - Feeling)

Reflective

Observation

(RO – Observing)

Generalization and

Abstract

Conceptualization

(AC – Thinking)

Active

Experimentation

(AE - Doing)

Concrete

Experience

(CE - Feeling)

()

() ()

()

∑

rPrCPCP

(3)

() ()

()

() ()

(

)

()

(

)

() ()

()

(){ }

{}

, 1,2,..., 1,2,...,2

nn n

ij j

nn n

ik k

Pr C PC

PC r

Pr C PC

ij n

∀∈ ×

∑

(4)

()

(

)

()

(

)

max

PC PC

≤≤

(5)

LEARNING STYLE ESTIMATION USING BAYESIAN NETWORKS

417

1. The system’s training. This is necessary at the

beginning, as there are no stored data. So, as the

system recognizes a certain response r

(n)

, having

no other identical match stored in the database, it

skips the BN part of the algorithm and simply

stores the response r

(n)

and the ratios, as they

appear in the Kolb’s calculations, in the data

base.

2. The BN application. This part of the algorithm

makes use of the stored data to calculate

conditional probabilities P(r

(n)

). In this step,

formulas (3) and (4), the program calculates

probabilities of the elements in LS. The system

therefore, returns an LSs hierarchy. According to

Kolb’s learning cycle, the two leading LSs

characterize the learner as D, As, C, or Ac. As

soon as a response r

(n)

(different from the stored

responses) appears, step 1 is activated.

5 CONCLUSION AND FUTURE

WORK

Using collected data from various test groups, we

shall compare LS direct diagnoses to the diagnoses

that are outcomes of the proposed algorithm. We

expect to have explicit diagnoses even in cases

where the direct application of Kolb’s inventory

leads to equal LS scores.

ACKNOWLEDGEMENTS

This work is supported through The European Social

Fund and the Hellenic Ministry for

Development/General Secretariat for Research and

Technology, under contract 03ED552.

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