MODELLING A FUZZY SYSTEM FOR TEACHERS’ TRAINING

DESIGN

Eliza Stefanova

and Svetla Boytcheva

Faculty of Mathematics and Informatics, Sofia University, St. Kl. Ohridski, 5, James Bourchier, 1164 Sofia, Bulgaria

Department of Computer Science, State University of Library Studies and Information Technologies

119, Tzarigradsko Shosse, 1784 Sofia, Bulgaria

Keywords: Adaptive teachers training design, Fuzzy logic, Design of fuzzy controller.

Abstract: This paper presents a model, based on fuzzy logic, aiming to support teachers’ training design. The

complexity of the task of technology utilisation in education, leads the authors to decision to base its

adaptive system on fuzzy controller. We shortly describe the system architecture and its functionality. The

presentation includes also fuzzy model implemented in the kernel of the system, its components, linguistic

variables and values. Further steps for improvement of the system performance are sketched as well.

1 INTRODUCTION

Many researchers and politicians hope that

Information and Communication Technologies

(ICT) itself will dramatically change the education.

But it seems just ICT to be present in the schools is

not enough. They are not effectively used, in some

cases not used at all. One of the conclusions of the

Institute of Prospective Technological Studies report

(Cachia et al., 2010) is “it is necessary teachers to

be trained appropriately in order to have effective

use of technology in the school”. Although in many

countries massive teachers training on ICT were

done in recent years (Bulgaria, Romania, etc.), in

other (UK) - teacher professional development is

embedded in the systems, the expected changes still

are not visible. One of the reasons for

ineffectiveness is related to the design for teachers

training in field of integration of technology in

education. In this paper we will focus on the

problem and will discuss some possible solutions.

Teacher training is one of the four forms of the

professional development. In-service courses format

is appropriate and very effective when some

innovations are introduced and small number of

people are well informed about them (Guskey,

2010). Exactly this is the case with teachers training

in field of integration of technology across curricula.

Designing training, the characteristics of

professional developments of adult should be kept in

mind. It is not enough to build the knowledge for a

technology per se. The knowledge about technology

is context-dependable. The effective teaching of

technology requires an understanding how

technology relates to the pedagogy and content. As

consequence, the designers of teachers training

should aim to build Technological Pedagogical

Subject Knowledge (Mishra and Koehler, 2006).

More over, it is crucial to respect personal models

because personal values (as expressions of personal

priorities and positions) are inextricable from

making decisions by training designers (Pratt et al.,

in press). The characteristics of teachers training,

which design we would like to support, makes the

model very complex. In addition, the model should

be adaptable to different technologies, users and

their objectives.

In Section 1 we argue our decision to choose the

fuzzy logic as base of the approach to cope with the

problems. Second section is devoted to the design of

fuzzy logic controller. Finally, the aggregation done

by the system is presented. The conclusion sketches

some further steps in the research and the

improvement of the system prototype as well as

possible future use of the model and system itself.

2 FUZZY SYSTEM DESIGN

The field, we try to model, is too complex. The

505

Stefanova E. and Boytcheva S..

MODELLING A FUZZY SYSTEM FOR TEACHERS’ TRAINING DESIGN.

DOI: 10.5220/0003674505050508

In Proceedings of the International Conference on Evolutionary Computation Theory and Applications (FCTA-2011), pages 505-508

ISBN: 978-989-8425-83-6

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

formal modelling in similar cases is appropriate to

be developed through Fuzzy Logic (Zadeh, 1965;

Zadeh, 1973) integrated in Expert System. Such

model promises to support successfully designers of

training. We start the design of the model from

‘catching’ reality in the education: collecting

experts’ knowledge, converting it into the

conceptual abstract model, deriving the conclusions

based model and using it to support designers.

2.1 Components Identification

The identification of the components is based on

collecting experts’ understanding on importance of

the factors related to teachers training in digital

technologies for education. There were chosen

mainly components that affect to great degree

effective use of ICT in their school practice.

In this phase 23 experts from Bulgaria was

involved. Fifteen experts were most active

participants. They are experts in field of training

teachers for effective integration of ICT in

education.

Methodology used to collect experts opinion

follows the structured participative approach called

Group Concept Mapping, applied successfully in

solving similar problems (Stoyanov and Kirschner,

2004; Trochim, 1989; Wopereis et al., 2005). The

approach is very powerful combining both

qualitative and quantitative methods, but it is useless

without expert ideas and opinions. The Group

Concept Mapping procedure consists of four steps.

At first step the experts were asked to brainstorm

which are most important factor during the teachers

training, reflecting on effective use of the ICT in

school practice. Then, they send back the generated

by them list. The lists were collected and joint.

During the second step the list of all generated

factors was sent to the experts. They were asked: to

group the factors; to rank factors into each group

(according to their importance to relation with future

effective application of ICT in teachers practice); to

name the groups; to rank the groups (according to

their importance to relation with future effective

application of ICT in teachers practice).

After detailed analysis of the focus group

brainstorming, sorting and rating main components

of the model, a triangulation with parallel analysis

with two experts was then made. Four top factors,

rated by participants, are concluded to be main

components of the model namely: Methodology,

Technology, User, Objectives.

2.2 Defining Linguistic Variable

The participants of Group Concept Mapping listed

main properties related with each of the factors

detected as important characteristic of the

component. On their base variables of each

component are created (Stefanova and Boytcheva,

2010). Table 1 presents methodology component

linguistic variables and values.

Table 1: Methodology linguistic variables and values.

Variable Values

Learner activity (LA)

Very Low, Low, Average, High,

Very High

Learners style

correspondence (LSC)

Fully, Almost, Slightly, None

Practice orientation

(PO)

Very Low, Low, Average, High,

Very High

Technology

Integration (TI)

Fully, Almost, Slightly, None

Technology present

(TP)

Very Abstract, Abstract,

Concrete, Very Concrete

The Objectives component has linguistic

variables Skills (S), Knowledge (K), Competence

(Cp) and Educational Level (EL). The User

component has following variables: Qualification

(Q), Motivation (M), Personal Reasons (PR), and

Professional Factors (PF). The Technology

component variables are Complexity (Cx), Cost (C),

Functionality (F), and Utilization (TU). Our main

goal is to make an inference about Technology

Utilization variable, based on the model and rules.

2.3 Defining Rules

The relations between components and their

linguistic variables are defined on based on experts’

opinion. They are presented on Figure 1.

Figure 1: Relations between linguistic variables.

FCTA 2011 - International Conference on Fuzzy Computation Theory and Applications

506

In order to make the inference about technology

utilization it is necessary to choose in advance the

components priorities: how the user orders by

importance the component in the design of training.

Thus we can have methodology, technology or

objective centred training approaches. On the Figure

2 the methodology centred approach dependences

are presented. In this case for different combinations

of the linguistic variables values for Methodology

component we can infer different combinations of

values for Objectives component.

Figure 2: Methodology Centric Approach: Inferred values

for Objectives.

On such base rules were generated using

Methodology variables values combinations for

prerequisites and setting values for objective

component variables as conclusion. However most

of the rules use not only single component variables

as prerequisites. About 75 rules were developed by

experts in the current stage of the project.

Triangular versions membership functions were

used to represent variables values. In inference

engine centroid technique is used.

3 AGGREGATION OF TRAINING

DESIGN MODELS

The designed model is used to build the fuzzy

system (Stefanova and Boytcheva, 2011) supporting

design of training models. One of its important

functionality is to compare users’ profiles in the

training group. This task can’t be performed as a

simple production of average values, due different

Training models and complex interrelations between

linguistic variables. The comparison procedure

includes usage of priorities for different linguistic

variables. These priorities are defined explicitly and

implicitly. The explicit priorities are settled during

the user registration in his/her profile, choosing

preferences for training method – methodology,

technology or objective centred. The implicit

priorities are based on user’s performance history.

Depending on linguistic variables priorities we

associate to each linguistic variable corresponding

weight.

We are comparing separately values of each

component Methodology, Technology, User,

Objectives (Figure 3).

Figure 3: Distances between values of linguistic variables

for each of the components of the model for six training

design models.

The comparison of multiple users’ models is quite

complex task. That is why we are comparing rather

individual values than the sum effect of them,

because the data are too disperses (Figure 4).

Figure 4: Comparison betwen total vatiables for each

component for six training design models.

Using the weight for each different variable in the

component we are calculating the total value of each

component. For instance for methodology we have

equation (1).

iiiiii

tpmwtimwpomwlscmwlamwM _._._._._.

54321

++++=

(1)

Similarly we calculate the total effect of

Technology (T), Objectives (O) and User (U). Then

we find the average values of totals for each

MODELLING A FUZZY SYSTEM FOR TEACHERS' TRAINING DESIGN

507

component and the deviations for Training design

models from it (2) and (3).

avg

∑

(2)

iavg

MMM −=

(3)

The final evaluation of models is the sum of

deviations of each model totals from the average (4).

UOTME +++=

(4)

Setting in advance the thresholds (t) the final

scores for two models E

and E

are considered the

same if their difference is bellow threshold.

tEE

<− ||

(5)

The final result of comparison of multiple user

training design models is clustered of similar models

depending on thresholds neighbourhood (Figure 5).

There are two cases:

 One of the clusters dominates – in this case we

choose its aggregated training model for the

whole learning group.

 None of the clusters is dominant – then we split

the group on subgroups corresponding to

clusters and perform aggregated training model

for each cluster individually.

Figure 5: Clustered space to four training design models.

4 CONCLUSIONS

In this paper we present work in progress. On the

current stage of the project we need to tune the

linguistic variables values and to test different

membership functions and inference engine

techniques for generating output values. The final

decision which of them fits best to our domain

representation would be made on the testing results

base. Further research steps will be followed by

testing and validating the model with available data

for already passed teachers’ trainings. On the results

base, the model will be refined. In order to approve

the proposed approach applicability into practice, the

prototype of the build fuzzy system will be tested

with teachers and instructional designers of teachers’

trainings.

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