Identification of Behavior Patterns Within

Graduated Students and Undergraduate Modules

at the Technical University of Cartagena, Spain

A. Molina-García

, M. Kessler

and A. Botía

Department of Electrical Eng., Universidad Politécnica de Cartagena, 30202 Cartagena, Spain

Department of Applied Mathematics and Statistics, Universidad Politécnica de Cartagena, 30202 Cartagena, Spain

Research Results Transfer Office, Universidad Politécnica de Cartagena, 30202 Cartagena, Spain

Keywords: Undergraduate Curricula, Learning Behaviour Patterns.

Abstract: As a consequence of the governmental decision to adapt the Spanish graduate and post-graduate studies to

converge to the 'European Higher Education Area', the goal of the so-called Bologna Process, committees of

experts were set up at the Technical University of Cartagena, located south of Spain, to design the new

curricula that would build up the restructured offer of courses. It was decided to provide as supporting

material to these committees statistical information about the academic behaviour and results of the students

in modules of the existing courses. In this paper the main aspects of this study are presented, discussing the

set of variables selected to characterize modules and students. Information about the structure of variability

between students on one hand and between modules on the other hand is presented, based on a principal

component analysis. Finally patterns were identified among modules and among students using a cluster

procedure. The influence of relevant factors like gender, course and marks obtained at the School Leaving

certificate on the resulting groups composition was explored as well.

1 INTRODUCTION

The Technical University of Cartagena, located

south of Spain, offers a generalist engineering

education, with emphasis in engineering

fundamentals and practices attending approximately

6000 students. Nowadays, these undergraduate

degrees usually involve five academic years and

allow the students to continue their university

education through the Doctor of Philosophy (PhD)

degree. It is possible for the students to focus on a

specific field of interest: mechanical, electrical,

chemical, civil; within the last stages. A complete

restructuration of the courses was undertaken in the

last years as a consequence of the governmental

decision to adapt the Spanish graduate and post-

graduate studies to converge to the ‘European

Higher Education Area’, the goal of the so-called

Bologna Process, the inter-governmental process

that promotes reforms in higher education with 47

countries. Consequently committees were set up on

one hand on a national level, where experts from

both academia and private sectors would establish a

list of recommendations for the design of the new

syllabuses, but also on a local level within each

university, where representatives of each department

involved in the teaching programs would concretely

decide about the modules that would build up the

curricula.

A statistical study of academic indicators

computed from data collected during the last decade

was then launched in our university. Two datasets

were built: dataset S, consisting of more than 1000

students that successfully graduated from the School

for Industrial Engineering at the Technical

University of Cartagena, and dataset M, describing

more than 200 modules along the last decade as

well. The purpose of this study was to provide

updated diagnostic regarding patterns of behaviour

within the students and, simultaneously, identify

groups of modules within the different courses that

are offered, which would present homogeneity in

terms of student behaviour. It must be emphasized

that within the Spanish system, for a given module,

each student has three opportunities to take the

associated exam along a given academic year.

582

Molina-García A., Kessler M. and Botía A..

Identiﬁcation of Behavior Patterns Within Graduated Students and Undergraduate Modules at the Technical University of Cartagena, Spain.

DOI: 10.5220/0004964305820587

In Proceedings of the 6th International Conference on Computer Supported Education (CSEDU-2014), pages 582-587

ISBN: 978-989-758-020-8

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

Moreover, it is not compulsory to pass successfully

all the modules corresponding to a given stage in

order to proceed to the next stage. As a consequence,

a significant variability is observed between the

student behaviours and strategies, resulting into

variability between their trajectories within the

university studies. Variability is also present

therefore between modules. In this paper, the main

results and conclusions of the statistical study are

presented.

The rest of the paper is structured as follows.

Section 2 gives a brief description about the most

relevant variables used to provide, on one hand,

information about the students’ patterns of academic

behaviour and, on the other hand, information that

could help discriminating between modules. Section

3 presents preliminary results of an exploratory

analysis of these variables. Multidimensional

analysis techniques were then applied, and the

results of a principal component analysis are

discussed in Section 4. Finally, relevant conclusions

are listed in Section 5.

2 VARIABLES AND FACTORS

As mentioned in Section 1, two multi-dimensional

datasets S and M (Students data and Modules data

respectively) are constructed by merging several

university records databases. The essential one is the

examination records database, but a student personal

information database, is used to recover data like

birth-date, gender or marks achieved at the School

Leaving Certificate.

2.1 Data-Set M

For each module and each academic year from

2002/2003 to 2008/2009, the following variables

have been computed:

 TOOK_EXAM: Within the students that

registered for that module that year, proportion

of students that took the exam at least in one out

of the three possible opportunities.

 PASSED_EXAM_REGISTERED: Within the

students that registered for that module that year,

proportion of students that passed the exam.

 PASSED_EXAM_TOOK_EXAM: Within the

students that took the exam for that module at

least once out of the three possible opportunities,

proportion of students that passed the exam.

 OPP_TAKE_EXAM: Within the students that

took the exam for the first time that year, average

number of opportunities they have had to take

that same exam previously. This variable may

require a little bit more explanation: since it is

not compulsory for a student that has registered

for a given module to take the exam, it happens

that some students decide eventually not to take

the exam in the first opportunity they have,

neither in the second opportunity, or even end up

not taking the exam at all that year. It is therefore

of interest in particular to assess the perception

that the students have regarding the difficulty of

passing the exam associated to the module, to

check, within the students that took the exam for

the first time, how many times have they waited

before daring to do it.

 AVG_MARK: Within the students that passed the

exam that year, the average mark (on a 0 to 10

scale).

 NUM_EXAM_PASS: Within the students that

passed the exam that year, the average number of

times they had to take the exam to actually pass

the module. It therefore amounts to the number

of times they failed plus one.

2.2 Data-Set S

For each student that successfully graduated within

the years 2001/2002 to 2008/2009 at the Industrial

Engineering School, the following variables have

been computed:

 DURATION: Relative duration of the studies, i.e.

the number of years it took for the student to

graduate divided by the number of stages in the

course.

 MARK: Weighted average mark on a 0-10 scale.

The weights are proportional to the ECTS

assigned to each module.

 OPP_TAKE_EXAM: Within all compulsory

modules, average number of opportunities that

the student used to actually take the exam for the

first time. (For more explanation, see Database

M).

 NUM_EXAM_PASS: Within all compulsory

modules, average number of times that the

student had to take the exam to pass it (see as

well Database M).

A series of additional variables or factors were also

included to check their association with the variables

of interest: gender, age at graduation, identification

of the High School of origin, mark achieved at the

School Leaving Certificate. (Called “Selectividad”

in Spanish). The dataset S contains 1087 students.

IdentificationofBehaviorPatternsWithinGraduatedStudentsandUndergraduateModulesattheTechnicalUniversityof

Cartagena,Spain

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3 FIRST DESCRIPTIVE

INDICATORS

As a first step into the data exploration, a descriptive

analysis was carried out making an intensive use of

graphics and numerical indicators. A brief summary

is presented in this Section to provide a sense of the

orders of magnitude and the variability of the

different variables.

3.1 Data-Set M

The dataset M contains the evolution of almost 200

modules over the considered academic years.

Compulsory modules were only considered in this

dataset, since optional modules present a high

homogeneity in terms of student behaviours and

performance. In Table 1, the first quartile, median,

third quartile, mean, and standard deviation of the

relevant variables are presented.

We may for example pinpoint a few figures out

of Table 1: the average number of opportunities

{OPP_TAKE_EXAM} that the students use to

actually take an exam is close to 2, and some

modules present really high values for that variable.

On average almost 80% of the students that take at

least once the exam of a module at the Industrial

Engineering School pass {PASSED_EXAM_TOOK_

EXAM}, while 70% of the registered students take

the exam at least once. The number of times the

students take an exam until they pass

{NUM_EXAM_PASS} takes typically lower values

than the number of opportunities that the students

use to take the exam for the first time, a fact that

already seems to anticipate that the perceived

difficulty of a module before taking the exam is

higher than the “real” difficulty to pass it.

From a quick check of the values of the Pearson

correlation coefficients, we can emphasize the

following:

 The highest correlation is found between the

proportion of students that pass the exam with

respect to the total number of registered students

(PASSED_EXAM_REGISTERED) and the

proportion of registered students that take the

exam at least once:

$cor(PASSED_EXAM_REGISTERED,TOOK_

EXAM)= 0.86$.

 The second highest correlation happens to be

found between the proportion of registered

students that pass the exam and the proportion of

students that pass the exam with respect to the

number of students that take the exam at least

once: $cor(PASSED_EXAM_REGISTE

RED,PASSED_EXAM_TOOK_EXAM)=0.75$.

This is of course very natural; both variables

depend directly on the number of students that

pass the exam.

 The variables PASSED_EXAM_TOOK_

EXAM and NUM_EXAM_PASS present a

correlation of 0.66, which reveals a clear (and

expected) association between the proportion of

success when taking an exam and the average

number of times the student has to take the exam

before actually passing it.

 The lowest degrees of association are found

between the variables TOOK_EXAM

and OPP_TAKE_EXAM with the variables

NUM_EXAM_PASS, PASSED_EXAM_TOOK

_EXAM and AV_MARK_10, see values of

correlations in Table 2, which tends to confirm

that there is no strong relation between the

perception of the student in terms of anticipating

his possibilities of success at an exam (measured

through his disposition to take the exam) and the

actual difficulty to pass if he takes the exam.

3.2 Data-Set S

The dataset S contains 1087 students that

successfully graduated from the Industrial

Engineering School at the Technical University of

Cartagena. 932 were male students while 155 were

female students. In Table 2, the first quartile,

median, third quartile, mean, and standard deviation

of the relevant variables are presented. It may

pointed out the high values that takes the variable

DURATION, the centre of its distribution

corresponding to an increment by 2 thirds of the

expected “theoretical” duration before graduation.

This is explained partly by the fact that the

students end their studies by a final project requiring

full time investment while they also have to take

modules until the end. They then usually begin an

extra academic year to complete and present the

project, which then adds one year to the absolute

duration even if they actually use only a few extra

months to do it.

On the other hand, half of the graduated students

present in their academic trajectory an average close

to 2 as for the number of opportunities they use

before actually taking an exam, while the average of

times they have to take the exam to pass it, is close

to 1.

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Table 1: Dataset M. Relevant variables.

NUM_REGIS

TERED

TOOK_

EXAM

OPP_TAKE_

EXAM

NUM_EXAM_

PASS

PASSED_EXAM_

REGISTERED

PASSED_EXAM_

TOOK_EXAM

AV_MARK_10

Min. 1.0 Min 0.1667 Min 0.000 Min 0.000 Min 0.1239 Min 0.2609 5.000

Qu. 50.0 1

Qu. 0.5433 1

Qu. 1.443 1

Qu. 1.250 1

Qu. 0.3647 1

Qu. 0.6581 1

Qu. 5.867

Median 82.0 Median 0.667 Median 1.969 Median 1.571 Median 0.4921 Median 0.7778 Median. 6.176

Mean 90.65 Mean 0.6678 Mean 2.204 Mean 1.605 Mean 0.5273 Mean 0.7748 Mean 6.340

Qu. 119.0 3

Qu. 0.7987 3

Qu. 2.770 3

Qu. 1.885 3

Qu. 0.6618 3

Qu. 0.9104 3

Qu. 10.00

Max. 296.0 Max. 1.000 Max. 11.33 Max. 3.091 Max. 1.000 Max. 1.000 Max. 10.00

Sd. 58.98 Sd. 0.17 Sd. 1.02 Sd. 0.43 Sd. 0.21 Sd. 0.16 Sd. 0.71

Table 2: Dataset M. Variable correlation results.

NUM_EXAM_PA

PASSED_EXAM_TOOK_EX

AV_MARK_10

TOOK_EXAM -0.3015765 0.3496622 0.2827057

OPP_TAKE_EXA

0.4034407 -0.3738091 -0.3646772

Table 3: Dataset S. Relevant variables.

AGE MARK_SLC DURATION MARK_GRAD OPP_TAKE_EXAM NUM_EXAM_PASS

Min. 21 Min 5.020 Min 1.000 Min 5.350 Min 1.000 Min 1.000

Qu. 24 1

Qu. 6.274 1

Qu. 1.500 1

Qu. 6.100 1

Qu. 1.380 1

Qu. 1.200

Median 25 Median 7.066 Median 1.670 Median 6.390 Median 1.780 Median 1.380

Mean 25.27 Mean 7.055 Mean 1.792 Mean 6.478 Mean 1.918 Mean 1.446

Qu. 26 3

Qu. 7.752 3

Qu. 2.000 3

Qu. 6.755 3

Qu. 2.310 3

Qu. 1.615

Max. 49 Max. 9.680 Max. 4.500 Max. 9.490 Max. 6.220 Max. 3.000

Sd. 3.27 Sd. 0.97 Sd. 0.54 Sd. 0.55 Sd. 0.71 Sd. 0.34

NA’s 170000

As for dataset M, a first glance at the correlation

structure (see Table 4) reveals some interesting

facts:

 The correlation between the mark achieved at the

School Leaving Certificate MARK_SLC and the

remaining variables is negative except with

MARK_GRAD for which it is close to 0.5.

 There is a rather strong negative association

between the variable NUM_EXAM_PASS and the

final mark achieved at graduation, which seems

to indicate that when the students have failed an

exam, they usually do not achieve good marks

when they finally pass.

A more complete exploratory analysis was

performed by systematically splitting the datasets

according to the levels of the considered factors,

distinguishing between courses, students gender,

high school of origin for dataset S and courses,

stage, temporal location of the module for dataset M,

and computing accordingly numeric indicators and

displaying graphs.

4 PRINCIPAL COMPONENT

ANALYSIS

Our interest was in particular in gaining

understanding about the structure of variability

between modules on one hand, and between students

on the other hand. Among the considered variables,

which ones contribute the most to discriminating

between modules or students? A principal

component analysis was then performed on the

correlation matrix in both datasets.

4.1 Data-Set M

For dataset M the six variables: TOOK_EXAM,

OPP_TAKE_EXAM, NUM_EXAM_PASS, AV_

MARK_10 PASSED_EXAM_REGISTERED,

IdentificationofBehaviorPatternsWithinGraduatedStudentsandUndergraduateModulesattheTechnicalUniversityof

Cartagena,Spain

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PASSED_EXAM_TOOK_EXAM, were considered

for the principal component analysis based on their

correlation matrix. The proportion of variability

explained by the first, the first two and the first three

components is respectively 58%, 74% and 84%, and

the expression of the first three components is the

following:

PC1= 0.40 TOOK_EXAM - 0.37OPP_TAKE_EXAM

+ (-0.39)·NUM_EXAM_PASS +

0.50•PASSED_EXAM_REGISTERED +

0.43•PASSED_EXAM_TOOK_EXAM +

0.34 AV_MARK_10 (1)

PC2= (-0.59)•TOOK_EXAM + 0.31 OPP_TAKE_

EXAM + (-0.46)•NUM_EXAM_PASS -

0.23 PASSED_EXAM_REGISTERED +

0.33 PASSED_EXAM_TOOK_EXAM +

0.42•AV_MARK_10 (2)

PC3= 0.03 TOOK_EXAM + 0.45 OPP_

TAKE_EXAM + (-0.17)•NUM_EXAM_PASS +

0.26 PASSED_EXAM_REGISTERED +

0.46 PASSED_EXAM_TOOK_EXAM -

(-0.70)•AV_MARK_10 (3)

The first component is clearly a weighted average of

the different variables, assigning positive weights for

the variables for which high values indicate good

results and negative weights for the two variables for

which low values indicate good results

OPP_TAKE_EXAM and NUM_EXAM_PASS. The

modules that score higher in this first component can

thus be considered as the most successful modules,

in terms of student behaviour and results. As for the

second component the following interpretation is

suggested: PC2 measures the difference between the

difficulty perceived by the students before the exam

and the actual difficulty to pass the module. Indeed

it can be written as the sum of two terms: (-

TOOK_EXAM - PASSED_EXAM_REGISTERED +

OPP_TAKE_EXAM) and (AV_MARK_10 +

PASSED_EXAM_TOOK_EXAM - NUM_EXAM_

PASS). The first term takes its highest values for

modules where a low proportion of students take the

exam and therefore the proportion of students that

pass the module with respect to the registered

students is low and the number of opportunities used

to actually take the exam for the first time is high.

The influence of the different factors (Stage,

temporal location in the academic year, course, and

assigned ECTS value) on the principal components

scores was explored. Differences between the

different courses at the School for Industrial

Engineering was found for the PC2, where two

courses scored typically higher: the Industrial

Management Engineer course and the Automatism

and Industrial Electronics course, where a significant

part of the students work and therefore have a higher

tendency to use several opportunities before taking

an exam. Principal components plots (PC2 versus

PC1) were also provided to follow the temporal

evolution of the module scores. As an example, the

scores obtained for the considered years by the

modules of the first stage of the Industrial

Engineering course are shown in Figure 1. This kind

of plot allows monitoring the evolution, for a given

module, of the student behaviour and results and

detecting possible difficulties.

4.2 Data-Set S

For dataset S five variables MARK_SLC,

DURATION, MARK_GRAD, OPP_TAKE_EXAM,

NUM_EXAM_PASS were considered for the

principal component analysis based on their

correlation matrix. The proportion of variability

explained by the first, the first two and the first three

components is respectively 55%, 75% and 85%, and

the expression of the first three components is:

PC1= 0.37·MARK_SLC + (-0.47)·DURATION +

+0.46·MARK_GRAD - 0.45·OPP_TAKE_EXAM-

-0.46 NUM_EXAM_PASS (4)

PC2= -0.56 MARK_SLC+ -0.48 DURATION -

0.37·MARK_GRAD -0.54·OPP_TAKE_EXAM +

0.19 NUM_EXAM_PASS (5)

PC3= 0.74 MARK_SLC - 0.06 DURATION -

0.42·MARK_GRAD -0.25 OPP_TAKE_EXAM +

0.46·NUM_EXAM_PASS (6)

As for dataset M, the first component is easy to

interpret as a global score of the graduated student’s

success: it consists of a weighted average of all

variables, with positive weights for variables that

translate positively in terms of the student’s results

and negative weights for variables for which high

values would indicate worst results. The second

component is interpreted as the sum of two terms:

MARK_SLC+MARK_GRAD - NUM_EXAM_

PASS and DURATION + OPP_TAKE_EXAM.

The weights have been omitted, which reflect on

one hand the student’s performance (their marks and

the number of times they need to take an exam to

pass the module) and on the other hand their

apprehension before taking an exam

(OPP_TAKE_EXAM) which have of course an

influence on the duration of their studies. The

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students that score most negatively on PC2 have

achieved good or very marks at the School Leaving

Certificate and during their graduate studies but have

taken a rather long time to graduate and have used

several opportunities before actually taking an exam.

Finally the third component can be seen as the

influence of two differences: MARK_SLC-

MARK_GRAD and NUM_EXAM_PASS-

OPP_TAKE_EXAM: students that score high in PC3

are students that have achieved lower marks during

their graduate studies than was expected from their

School Leaving Certificate and that, although they

usually take the first opportunities to take an exam,

frequently fail and need to repeat the exam several

times to pass the module.

As for dataset M in the previous subsection, an

exploration of the influence of the factors considered

in the dataset on the principal components was

carried out. As an example, interesting facts was the

influence of the Gender on the PC3 score. Consider

for example the Technical Industrial Engineer

course, mention Industrial Chemistry, where

approximately half of the graduated students are

female (concretely 49 out of 101 individuals in the

dataset S), consider the lower part of the PC3 scores

that contains 10 % of the students, i.e. the portion of

the dataset with PC3 scores values under the

corresponding 10% quartile, only 1 out of the 9

corresponding students is female, while if you

consider the 10% upper part, 8 out of the 9 included

students are female.

5 CONCLUSIONS

In this paper the main aspects of a statistical study

about students' academic behaviour and results at the

School for Industrial Engineering in the Technical

University of Cartagena are presented. This study

was initiated to provide supporting material to the

local committees at the university, who are in charge

of designing the new curricula and syllabuses as a

consequence of the restructuration of the courses in

the context of convergence to the 'European Higher

Education Area'. Two datasets were considered, one

focused on modules and the evolution of associated

academic indicators, and the other one focused on

graduated students.

This datasets allowed us to explore

systematically and confirm (or refute) the existing

impressions or empirically gained knowledge of the

members of the committees based on their

experience as teachers and managers at the

university. Additionally, it also allowed identifying a

few modules with atypical results and quantifying up

to which extent they behaved really differently from

the other modules in the same course, and opened

thus the door to a possible action from the

responsible of the School.

Multivariate analysis techniques like principal

component analysis and clustering have been used to

understand better the structure of the variability

between modules and between students, and

permitted to define sensible partitions of the

datasets: five groups of modules characteristics were

proposed while six profiles for the graduated

students were suggested. It is then particularly

interesting to check the association of relevant

factors with the groups' composition: for example

the differences in gender composition between the

different students' profiles, or the differences in the

groups relative size between the different courses.

ACKNOWLEDGEMENTS

The authors are very grateful to the Vice-Chancellor

for European Convergence and Quality Standards

Education, Josefina García-León, for her constant

support; and to the Chief Computing Developer,

José Sánchez-Manzanares for endless technical help

and advice.

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http://europa.eu/legislation_summaries/education_training

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http://www.educacion.es/educacion/que-estudiar-y-

donde/bachillerato/opciones-despues-

bachillerato/pau.html.

Mardia, Kantilal Varichand, Kent, John T. and Bibby,

John M; Multivariate analysis: Probability and

Mathematical Statistics: A Series of Monographs and

Textbooks; Academic Press Harcourt Brace

Jovanovich Publishers, London 1979.

Industrial Engineering Curriculum, Spanish Government

Reporter, (203), August 2000.

European Commission - Education and Training, Online.

[Available], http://ec.europa.eu.

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Cartagena,Spain

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