2010 International Conference on Educational and Network Technology (ICENT 2010)

A Software Solution for a Mathematical Model of Professor Efficacy Parameters

Haris Balta Faculty of Information Technology,

University "Dzemal Bijedic" Mostar, Bosnia and Herzegovina

haris.balta@fit.ba

Alsa Cvitkovic Interagent d.o.o.

Mostar, Bosnia and Herzegovina alsa@interagent.ba

Djenan Heric Agency Hermes

Mostar, Bosnia and Herzegovina dz _ heric@yahoo.com

Abstract-During recent years much significant progress has been made in the research of different aspects of university education. Various methods, techniques, approaches and

learning concepts related to research in this area have been developed. It is undoubtedly that in the entire educational process one of the central places is occupied by teachers. In accordance with this role, there is an implicit effect to the

quality of teachers on the quality of graduates. There are many attributes on which we could define the quality of teachers -among other things there are academic title, experience, number of courses that one professor could teach, personal

traits - charisma, etc. Bearing in mind these parameters of teachers quality, in this study we defined Professor Efficacy Parameter, which represent a numerical display of academic ability of each teacher individually. In this paper we present a

Software solution for the Mathematical Model of Professor Efficacy Parameters.

Keywords-Professor Efficacy Parameters, Education Process, Mathematical Model, Software solution.

I. INTRODUCTION

Central position in any educational process is occupied by the teachers. It is not easy to determine the degree of correlation between certain teacher's personal characteristics (such as intelligence, level of knowledge, preparation, experience, etc) and the teaching efficiency reached. Albeit complicated, the determination of these dependencies as input to the teaching process and the achievement of students as outputs of the teaching process is a possible way to analyze an individual teacher's efficiency.

In this paper we apply the mathematical method [1] for quantitative analysis of higher education on Faculty of mechanical engineering at University "Dzemal Bijedic" Mostar, create computer software for the method proposed and calculate and present Professor Efficacy Parameters.

The mathematical methodology for analysis of academic processes is based on mutual interaction among elements of the four basic education sets: courses set Cu (consisting of all

978-1-4244-7662-6/$26.00 © 2010 IEEE 518

Adil Joldic Faculty of Information Technology,

University "Dzemal Bijedic" Mostar, Bosnia and Herzegovina

adil@fit.ba

AjlaDjonko BH Telecom d.d.

Sarajevo, Bosnia and Herzegovina ajla.djonko@bhtelecom.ba

the courses), professors set Pu (involves all the teachers), periods set Hu (includes all periods available for teaching on the weekly basis) and students set Su (is the total number of students enrolled under analysis). The elements of the basic higher education sets are grouped, in accordance with different ordering criteria, into corresponding subsets/subgroups.

The mathematical model of Professor Efficacy Parameters (PEP) used in this paper was originally defmed and presented by prof. dr. Emir Humo in his book "Modeling Higher Education". In this paper we apply this model and developed appropriate prototype Software solution for calculating and visualizing PEP.

II. PROFESSOR EFFICACY PARAMETERS

Professor Efficacy Parameters [1] are parameters which represent the teachers' efficiency, don't represent the willing of the teacher to teach, nor the way he teaches the course, but only represent the academic capacitation of the professor.

This capacitation parameters introduced above improves the teaching efficiency of the professor, frees more hours for professor to work and research.

We will use some of the following parameters for determining efficiency:

• Professors. • Courses. • Number of teaching hours. • Number of hours necessary to prepare lectures. • Number of hours necessary to prepare exams. • Number of hours necessary to correct exams. • Number of hours necessary for consultation with

students. • Professor's academic title. • Professor's executive position. • Number of students.

2010 International Conference on Educational and Network Technology (ICENT 2010)

The parameters describing the efficacy of professor's capacitation usage provide a valuable insight into the functioning and nature of the academic process.

Hence, it is a question of efficacy by which a professor capacitation is used in actual lecturing.

III. MATHEMATICAL MODEL

Professor Efficacy Parameters are parameters which express numerically the real contribution of a professors teaching. In order to quantify this aspect of professors' activity (professor efficacy - professor's capacitation used in actual lecturing) we will use the traditional instruction indicator such as course's weekly hours. Since all professors' academic obligations are scheduled as department activities, this academic entity will be used for a mathematical definition of Professor Efficacy Parameters.

It is necessary to associate to binary matrix as in Figure 1. respective quantification matrix of professors course's weekly working hours in order to formulate Professor Efficacy Parameters:

qf'pDIcDI 1 1

qf'pDIcDI 2 1

qf'pfIcfI

qf'pDIcDI rI 1

qf' pfIcfI

qf'pDIcDI 2 2

qf'pfIcfI

qf'pDIcDI rI 2

qf'pDIcDI 1 I

qf'pfIcfI

qf'pDIcDI J I

qf'pDIcDI '1 I

Figure l. PEP Quantification Matrix

qf'pDIcDI 1 WI

qf'pDIcDI 2 WI

qf'pDIcDI J WI

qf'pDIcDI rj WI

where qfpOI cO

l is the number of working hours per week of J '

professor p?' at course c�'. Thus, the professor capacitation,

defmed as number of courses q pdi which professor p?l can J

teach at department 0" may be expressed in terms of working hours per week qf 01 01 in the following manner:

Pj Ci

i=qpdi

Hrpfl = IqfpOlcOI i=1 J ' (1)

In equation (l) Hrp?' represents the total capacitation for

teaching of professor p?l at department 01 expressed in

courses working hours per week or weekly courses working hours.

A university professor distributes his weekly working hours to teach, to do research and to administrate. The proportion of this distribution varies from university to university. Mostly, these weekly hours dedicated to teaching

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are about half of the weekly working hours. This time period we will call standard weekly working hours:

Hrs of professor Pj at department OJ or Hrsp�I .

Taking into account the above consideration, we can introduce parameter of capacitation ; which is the ratio of capacitation of professor in weekly working hours to standard weekly working hours of the department:

HrpDI

�= J

Hr pDI s J (2)

If I;> 1, capacitation of professor p?' in weekly working

hours is greater than standard weekly working hours of the department. Thus, professor p?l is overcapacitated. If ;=1,

capacitation of professor p?' in weekly working hours is

equal to standard weekly working hours of the department. Then is professor p?' critically capacitated. Finally, if ;<1

capacitation of professor p?' in weekly working hours is less

than standard weekly working hours of the department, in which case professor p?' is under capacitated.

Professors' weekly class working hours may be over, under, or just equal to his capacitation expressed in weekly working hours during a given academic year or semester. Also, when the weekly working hours are considered, it is possible to get the same situation. So, we can defme two professors' efficacy parameters.

Hence, if professor Pj has Hrel weekly class working hours at department OJ or Hrclp?I , we can introduce

parameter of efficacy of professor capacitation usage defmed in the following manner

£ (3)

Parameter £ quantifies the efficacy by which professor capacitation is used in actual teaching, and in most cases £<1, because only a limited number of professors actually use their capacitation in a current academic year. If a professor is overcapacitated (;> 1) this parameter will not describe the efficacy of professor's capacitation usage appropriately. Therefore, we need another parameter for measuring efficacy of professor capacitation usage with regard to standard weekly working hours of the department. This indicator we call parameter of standard efficacy of professor capacitation usage:

2010 International Conference on Educational and Network Technology (ICENT 2010)

(4)

where Hrsp�j

is a period of time defmed above. That

means that standard weekly working hours are equal for all teachers of the department, but sometimes may vary, according to the particular criteria (such as academic title or executive position).

In the preceding considerations professor efficacy parameters are formulated on the basis of weekly working hours. However, by using this approach we take into account only weekly hours dedicated for presentation of the topics and concepts of the course. Other important activities such as planning and organizing the course, preparing lectures, grading tests and exams, etc. are not involved in weekly course hours. In order to include these items when teaching the course, we introduce weekly course working hours, instead of weekly course hours.

Differences between these two quantities are result of two factors:

a) Period of time needed to prepare lectures for each of the courses which a given professor teaches in a semester Aji.

b) Period of time to execute all items connected with the number of students at the above mentioned courses Bji.

These factors may be considered as weighting factors which evaluate the professor's activities resulting from weekly course hours of lecturing. For this situation, the weekly course working hours qf

pD1c

D1 may be expressed in J '

terms of weekly course hoursqcli Dj Dj : Pj c,

Weighting factors Aji and Bji evaluate the periods of time which the professor spends in preparing and executing the lectures.

Now it is possible to express the total capacitation for teaching of professor pf I in terms of weekly hours of the

courses for which professor is capacitated. Substituting equation (5) into equation (1) we obtain:

Applying the above procedure again, the weekly working hours of the course professor lectures during a given semester or academic year may be expressed in terms of the courses weekly hours we obtain:

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i=q D clp. I

Hr,p?; = � A .. B .. q , f D D C J L J1 J1 C .1 . 1 i=' PJ c.

(7)

where q D is the total number of courses which the clPj I

professor teaches during the semester or academic year.

We can say that the standard weekly working hours may be reduced according to the particular criteria such as the academic title or the executive position of the particular professor. The corrective factors which correspond to the reduction of the standard weekly working hours with regard to the title or executive position of the professor under consideration are KJ and L], respectively. Therefore, we obtain the following equation:

This equation states that the number of working hours of the courses taught by a professor during a given semester or academic year cannot be greater than standard weekly working hours of the department corrected by the title or executive position of the mentioned professor.

IV. DATA PREPARATION

The initial data set were taken from Faculty of mechanical engineering archives: list of all the courses for all years of study, for both summer and winter semesters of 2009/10 academic year, list of all engaged professors, total capacitation for teaching of professor expressed in semester courses.

This initial data set needed to be adjusted for the calculation of PEP.

Total number of student enrolled per course was taken from initial data set. Than we calculated weighting factor B for each professor depending on number of student ( ns ) by

3n formula B = _s_ + 0.85 (for example factor B had value

1000 0.88 for 10 students and 1.15 for 100 students).

After detailed analysis of content, we awarded each course weighting factor A. Values of A depend on courses group (core, liberal, major). Result of weighting factor goes from 0.8 for core courses to 1.2 for major courses. The corrective factor L corresponds to executive position is: for non-executive position, L = 1; for Chair of Department, L =

0.5; for Associate Chair, L = 0.7; for Career Coordinator, L =0.8.

Final dataset include following set: Area, AreaCourse, Classes, Course, ExecutivePosition, GroupOnClasses, Professor, ProfessorTitle, SemesterOfArea.

2010 International Coriference on Educational and Network Technology (ICENT 2010)

V. SOFTWARE APPROACH

In order to verify the proposed mathematical model of Professor Efficacy Parameters we developed a software solution. The idea of implementing the software was to visualize the results for better reviewing and analyzing of the parameters.

As shown in Figure 2. capacitation of professor pf' in

weekly working hours is less than standard weekly working hours of the department. So, we can conclude that all professors are under capacitated.

Parameter of standard efficacy of professor capacitation usage for semestar I

Figure 2. Results of Professors Efficacy Parameters

Dataset which is used for the software was described in section 4. It was necessary to transform the original dataset into a relations data model. In the proposed software PEP was calculated in a sequence beginning from equation (1) to equation (8). Fig. 3 shows the user interface.

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Jusuf Kevelj, Van. prof.

LUNa Haznadarevit. Doc.dr.

Mehmed Behem, prof. Dr.

Men; lda ManJgo. Doc.dr.

Mirna Nofilt. Ooc.dr.

Remzo Dedic, prof. dr.

.·'M'F' Title

POSition

KLHrs

Total capacitation for teaching (Hrp)

Parameter of capacitation (�I

Weekly class working hours (Hrclj

Parameter of efficacy of professor capacitation usage (E)

Parameter of standard efficacy of professor capacitation usage (E 51

Semestar 1 Semestar 2

Parameter of standard efficacy of professor capacitation usage (reduced for K l) 0.3

Figure 3. User interface

CONCLUSION

The professor capacitation parameters are defined for professors on Faculty of mechanical engineering at. The parameters describing the efficacy of professor's capacitation usage provide a valuable insight into the functioning and nature of the academic process. We conclude that all professors are under capacited.

ACKNOWLEDGMENT

We would like in this acknowledgment to thank prof dr. Emir Humo and Haris Memic for their help and support in this research.

REFERENCES

[I] E. Humo, Modeling Higher Education, University of Mostar, 2005, pp 108-113.

[2] Archive academic data of Faculty of mechanical engineering at University "Dzemal Bijedic" Mostar.