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Home > Vol 14, No 3 (2024) > Weingärtner Junior

SELF ORGANIZING MAPS (SOM) AND STATISTICAL METHODS FOR DESCRIBING THE PHYSICOLOGICAL PROFILE OF UNDERGRADUATES STUDENTS OF ENGINEERING

Escola Politécnica. Universidade de São Paulo (USP) (Brazil)

Received March 2023

Accepted December 2023

Abstract

To meet a Brazilian guideline for engineering courses, which advocates the use of active learning in applied disciplines, this research studies new students entering an Engineering course at an important university in Brazil. It was applied to them a traditional MTBI (Myers–Briggs Type Indicator) questionary with the aim of finding out if there is recurrence of psychological profiles and to understand the characteristics of the freshmen to learning. This information was subjected to statistical analysis to observe the recurrence of the psychological characteristics of freshmen over the years (2017 to 2021). The data was also subjected to the Self Organizing Maps (SOM) machine learning technique, to delineate and group the psychological profiles observed in the students, enabling the analysis of the psychological characteristics and the comparison with the results obtained via statistics. After that, the results from the MBTI Traditional and the SOM clustering were submitted to comparison methods through multivariate statistics and Multiple Correspondence Analysis (MCA). It was found that there is recurrence of psychological characteristics between the years of collection, what were the psychological profiles of these freshmen as to how they learned. It was found that the freshmen surveyed mostly belong to Generation Z (or iGen) and characteristics pertinent to this group were observed. A scenario is obtained to point out the best active learning techniques for these students with the verification of recurrence of profiles and other correlated psychological characteristics, aiming to provide the most effective teaching in the engineering course.

 

Keywords – Descriptive statistics; SOM clustering; Correspondence analysis; Generation Z; Psychological profile of students.

To cite this article:

Weingärtner-Junior, P.R., Piedemonte-Antoniassi, N., Ferreira-Bindo, V., & Bernardo-Lenz e Silva, G.F. (2024). Self Organizing Maps (SOM) and statistical methods for describing the physicological profile of undergraduates students of engineering. Journal of Technology and Science Education, 14(3), 664-682. https://doi.org/10.3926/jotse.2164

 

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1. 1. 1. Introduction

The techniques derived from active learning allow the teacher to use different and innovative resources in the classroom, changing the axis of traditional teaching, where the teacher is the center of academic dialectics, into attitudes of experimentation and actions of students before the theoretical concepts, constituting skills for these entrants to higher education. The change of this academic paradigm implies in the evolution of the educational methods used, leading the student to compose his education in a hands-on mode.

Particularly in Brazil, engineering education is going through moments of reflection and reinvention. There is resistance from professors to change teaching techniques (Neves, Lima & Mesquita, 2021). There is also indication that academic curricula may be outdated and rigid (Oliveira, 2022). However, the Brazilian Ministry of Education (MEC) applied directive aiming to favor the application of the active learning concept in engineering courses (MEC-CNE/CES resolution #2 of 04/24/2019), and to adjust academic curricula being more attractive & actual to higher education level. There is also, in this regulatory document, the attribution of responsibility to the higher education institution to apply learning improvements with governance of the process. The directive has driven discussions at engineering education conferences and in academic articles, where numerous techniques are tested and presented as alternatives to encourage engineering students to obtain skills needed for what the future labor market requires (Oliveira, 2022).

A reflection should be made by the teacher: What is the tool that will be most effective for the learning of my group of students? After this reflection, the teacher can categorize some teaching tools and can test them in his/her classes, however without the guarantee that the technique will work the same way it worked in the literature, because the use of the techniques presented cannot not be validated with the class to which it was applied (Felder, Woods, Stice & Rugarcia, 2000).

There are several factors that influence teaching: gender, ethnicities, nationalities, number of students in the class, among other class characteristics, etc. However, a very incisive characteristic is the psychological factor (Weissberg, Durlak, Domitrovich & Gullotta, 2015). Still in the sense of understanding the factors that influence teaching, Light (2001) mentions in his work that two factors stand out in students´ reports of how small classes make an especially strong impact. First, such classes enable a professor to get to know each student reasonably well, second, a professor can use certain teaching techniques that are hard to implement in large classes.

Thus, there is the importance of analyzing which is the way that a certain group of students feel more comfortable to learn and develop new skills. This pushes the teacher to analyze the way of learning presented by his class, knowing who his students are and their ways of learning, there is higher possibility that his teaching will be more effective and remarkable (Felder et al., 2000).

This study seeks to present a form of psychological delineation of student learning by obtaining information through the self-report technique Myers-Briggs Type Indicator (MBTI), which is indicated one of best-known instrument user to assess learning styles (Felder, Felder & Dietz, 2002). Besides this resource, in this study, statistical analysis techniques were associated with the objective of indicating whether there are differences between the recurrences of the profiles found in the observations made in the years of collection. Part of the data was subjected to a SOM (Self Organizing Maps) an unsupervised machine learning technique, which favors a graphic observation producing a low-dimensional representation of a higher dimensional data set for analysis and findings, in a simple and objective way. In addition, it has been used to characterize personality profiles by data affinity and minimizing biases related to the tie between psychological types.

In this way, by analyzing the collective characteristics of undergraduate students and using a personality profiling technique, the research aims to obtain a model for decision making as to the most appropriate way of teaching that meets the students’ needs and seeks to improve learning in the field of engineering.

1.1. A brief Description of the MBTI

The Myers-Briggs Type Indicator (MBTI) methodology is widely used in several areas such as jobs and human resource corporations (Cohen, Ornoy & Deren, 2013), relationships, problem solving (Myers, 1998) and learning (Felder et al., 2002), because this resource is simple to apply and very efficient in its results.

The MBTI test is based on concepts from Carl G. Jung’s theory of psychological personality types. These types are obtained from two forms of interaction of the individual with his or her environment: World Orientation, where the person chooses Introversion (I) or Extraversion (E); and Basic Mental Processes, where the person chooses to gather information from the world with Perception (P) or Judgment (J) (Higgs, 2001).

Perception (P) can be divided into two ways of obtaining information by the individual, which are Sensation (S) and Intuition (N); the same goes for Judgment (J), where the individual chooses to use either Thinking (T) or Feeling (F) to deal with information around him (Myers, 1998). For better understanding, these psychological types presented are shown in Table 1.

Other characteristics can be provided through the combination of MBTI psychological types, which allow for a deeper understanding of the individual’s way of acting. Table 2 was prepared according to Myers (1998), which shows that associations between psychological types present other characteristics for personal preferences.

		Basic mental processes
		Perception (P)		Judgment (J)
World Orientation	Introversion (I)	Sensation(S)	Intuition(N)	Thinking(T)	Feeling(F)
	Extroversion (E)	Sensation(S)	Intuition(N)	Thinking(T)	Feeling(F)

Table 1. Combination of Carl G. Jung’s theory - World Orientation of the Individual with the Basic Mental Processes (Myers, 1998)

Psychological association	MBTI type
Learning Styles / Career Interests	SF/NF/ST/NT
Use of information	ES/IS/EN/IN
Leading/Following Styles	EP/IP/EJ/IJ
Temperaments	SJ/SP/NF/NT
Dealing with Change	IJ/IP/EP/EJ

Table 2. Association of psychological characteristics (Myers, 1998)

Some characteristics of the main and associated psychological functions were discussed by Myers (1998) are shown in Table 3 and will assist in the analysis of this study. According to the model for the learning profile proposed by Jung, the individual learns best if the information comes from the psychological area in which there is effective control over their dominant function (Myers, 1998). The most significant channels for learning are Sensation (S) and Intuition (N), with the supporting participation of other psychological functions. Individuals related to Sensation (S) find it easy to receive information objectively, while metaphors or symbolism hinder the learning process. For individuals related to intuition (N), they lose patience with the well-developed and profound constructions of reasoning practiced by their sensory colleagues.

For Culp and Smith (2009), people with a preference for Sensation (S) are attentive to the practical, like real, tangible information presented in a logical way, while Intuitive (N) individuals don’t like details and look at the overall context of things. With regard to the psychological types that support learning, Myers (1998) shows that extroverts (E) learn by talking, while introverts (I) need time, silence and space. People with Judgmental characteristics (J) require structure, dedicated time, a stipulated deadline, and those related to Perception (P) require flexibility to explore.

The Judgment-Perception dichotomy may be the most controllable pair of preferences for a student; students who are of Perception (P) type tend to develop better organization and time management skills (Schurr & Ruble, 1986).

	Function		Characteristics and preferences
Dichotomy	Sensing (S)		Receive real and tangible information; Observers of the specifics; Prefer practical realities; Factual and concrete; Build carefully and thoroughly toward conclusions; Understand theories through practical applications; Trust experience
	Intuition (N)		Has an overview of everything to receive information; They like to grasp patterns; Oriented to future possibilities; Imaginative and verbally creative; Draw conclusions quickly, follow hunches; Needs clarify theories before putting them into practice; Trust inspiration
Learning Style / Career Interests	ST	Learning	Facts about real things; Useful, practical information about everyday activities; Learn best by doing, hands-on activities; Need Precise, step-by-step instructions; Logical, practical reasons for doing something; Want from teacher to be treated fairly
		Career	Factual; Objective analysis and experience; Practical and analytical; Technical skills
	SF	Learning	Useful, practical; Information about; People, and a friendly environment; Doing, hands-on; good with activities with others; Precise, step-by-step; instructions; needs frequent friendly interaction and approval; Sympathy, support, needs individual recognition
		Career	Factual; Personal warmth, concern for others; Sympathetic and friendly; Practical help and services for people
	NF	Learning	New ideas about how to understand people; Symbolic and metaphorical; activities; lmagining, creating with others, writing; General Direction with freedom to do it their own creative way; Needs frequent positive feedback; Warmth, enthusiasm, humor, needs individual recognition
		Career	Sees possibilities; Perspective to people’s potentials; Insightful and enthusiastic; Understanding and encouraging people
	NT	Learning	Theories and global explanations about why the world works the way it does; Learn Categorizing, analyzing, applying logic; To be given a big problem to solve, needs an intellectual challenge, and then to be allowed to work it out; Needs to be treated with respect, to respect the teacher’s
		Career	Sees possibilities; Theoretical concepts; Logical and analytical; Theoretical and technical frameworks
Use of Information	IS	Thoughtful Realists	Knowledge is important to establish what is true
	IN	Thoughtful Innovators	Knowledge is important for its own sake
	ES	Action-Oriented Realists	Knowledge is important for its practical uses
	EN	Action-Oriented Innovators	Knowledge is important for changing reality
Leading/Following Styles	TJ	Logical Decision Makers	Analytical, decisive leaders; Make decisions based on principles and systems; Overall impacts, and rational assessment outcomes, and can be tough-minded in implementing those decisions; Effective implementers of policies, if they respect the leader
	TP	Adaptable Problem Solvers	Lead by example; Value and display technical expertise, and create consistent and orderly frameworks for working; Objective, skeptical, and curious; Will change course as new information comes in; Effective problem solvers, if interested
	FP	Supportive Coaches	Warm, flexible, and encouraging leaders; Support individual work styles and like to involve others in decisions; Prefer collegial relationships, shared rewards, and consensus in decisions; Energetic followers if treated with respect
	FJ	Values-Based Decision Makers	Warm, decisive leaders; Make decisions based on their personal values and empathy with others; Strive for harmony, consensus, and a supportive environment, are expressive and often inspiring; Loyal followers if the leader honors their values
Temperaments	NF	ldealists	Search for unique identity and meaning; Value empathic, meaningful relationships; Generally enthusiastic; Want to make the world a better place; Trust their intuition and imagination; Think in terms of integration and similarities; Focus on developing potential in others, finding a purpose in life, and bridging differences; Want to be authentic
	NT	Rationals	Theory oriented; Seek to understand the principles on which the world and things in it world; Trust logic and reason; Skeptical and precise; Think in terms of differences, categories, definitions, and structures; Focus on strategies and designs that achieve long-range goals and lead to progress; Want competence and thorough knowledge;
	SP	Artisans	Action and impact oriented; Hunger for spontaneity; Optimistic; Trust luck and ability to handle whatever comes up; Absorbed in the moment; Read people and situations and adapt to changes to get the job done; Seek adventure and experiences; Think in terms of variations; Focus on tactics to help others and get desired results; Want freedom to choose their next action;
	SJ	Guardians	Hunger for responsibility and predictability; Like standard operating procedures to protect and preserve; Serious and concerned; Trust the past, tradition, and authority; Think in terms of comparisons, sequences, and associations; Focus on logistics to support people, maintain organizations, and achieve objectives; Want security, stability, and to belong;

Table 3. Main and associated MBTI roles (Myers, 1998)

2. Methodology

The MBTI test is initiated by filling out a self-report form, which is the data input for obtaining the individual profile configuration. For this purpose, the form for the test was obtained from the American Psychological Association (APA), drawn up in accordance with The Myers-Briggs Type Indicator: Manual (1962) (Myers, 1962) and contains 70 questions. Each of the questions on this form involves choices between two opposite options within a psychological dichotomy, and the answers obtained are grouped and framed within characteristic type profiles. A simple sum of answers of a given dichotomy of psychological characteristics will determine the psychological profile frame.

The traditional collection methodology may allow the result of the individual’s choices to be in a region of hesitation, that is, in a region of a tie between two dichotomies, which will result in indeterminacy between the two terms, requiring observation of other characteristics of the individual’s choice after the test.

For the research, the MBTI questionnaire was applied to entering students in the Department of Metallurgical Engineering and Materials of the Polytechnic School of the University of São Paulo between the years 2017 and 2021. There was a total of 252 forms, with 55, 38, 47, 60 and 52 respondents in the years of 2017, 2018, 2019, 2020 and 2021 respectively. The information collected followed the flow demonstrated by Figure 1.

The students themselves, under orientation, filled out the tabulation of points, summed up the questions on a tabulation form, and obtained their psychological type by defining the MBTI profile. In case of blurring between two psychological characteristics, the respondent was instructed to indicate the characteristic he/she best identifies itself within the tied dichotomy. Later these forms were collected, and the data obtained were grouped in electronic spreadsheets, which consolidated the basis of results for the elaboration of basic statistics.

In order to verify whether there was a recurrence of personality patterns , the data was submitted to multivariate statistical analysis to verify the existence of differences between the groups, according to conditions for the execution of this analysis. Next, the SOM computational method was applied to the data with the objective of observing patterns of psychological profiles and to observe the clustering of these profiles, because this method groups personality patterns by data affinity, which favors the accuracy of the profiles obtained as output data. In this way, the statistical method and the computational method will complement each other in their results.

Figure 1. Flow of data and analysis methods used in this study

The psychological patterns found were then analyzed as to the way the students learn, according to the precepts of learning MBTI profiles, providing a basis for indicating the best teaching strategies for this group of students.

Finally, then the information was submitted to two comparative methods, the KRUSKAL-WALLIS statistic and the Multiple Correspondence Analysis (MCA), in order to verify differences between the results from traditional MBTI pattern and the SOM clustering.

3. Results

3.1 Statistical Method

The data collected with the MBTI profiles is shown in Table 4. It is observed that the MBTI ISTJ profile was represented by 21.83% of students in all years of collection. Another profile that prevailed in the tabulation was ESTJ, represented by 19.44% of freshmen. On the other hand, the least recurrent profiles were ESFP, ISFP, and ESTP.

	2017	2018	2019	2020	2021		Legend
ESTJ	10.9%	23.7%	25.5%	21.7%	17.3%		E	Extroversion
ESTP	3.6%	2.6%	2.1%	-	1.9%		I	Introversion
ESFJ	7.3%	-	4.3%	3.3%	1.9%		S	Sensation
ESFP	1.8%	-	2.1%	-	3.8%		N	Intuition
ISTJ	18.2%	15.8%	19.1%	28.3%	25.0%		T	Thinking
ISTP	10.9%	-	-	1.7%	-		F	Feeling
ISFJ	1.8%	2.6%	10.6%	3.3%	1.9%		J	Judgment
ISFP	1.8%	-	-	-	1.9%		P	Perception
ENTJ	3.6%	10.5%	6.4%	10.0%	13.5%
ENTP	3.6%	-	2.1%	1.7%	3.8%
ENFJ	-	7.9%	2.1%	-	3.8%
ENFP	1.8%	2.6%	4.3%	6.7%	3.8%
INTJ	12.7%	15.8%	8.5%	13.3%	11.5%
INTP	5.5%	5.3%	6.4%	1.7%	5.8%
INFJ	9.1%	13.2%	6.4%	6.7%	3.8%
INFP	7.3%	-	-	1.7%	-
	100%	100%	100%	100%	100%

Table 4. Percentage values of psychological type observed in entering students

Figure 2. MBTI types of characteristics of students entering
the Engineering School between the years 2017 to 2021

This data was consolidated, and a radar chart was made. It was observed that the psychological characteristics are hypothetically recurrent over the years (Figure 2), given the symmetry between the lines generated by each year of data collection.

To verify whether there are recurrences of psychological profiles over the years, it was decided to choose a multivariate statistical method in which the data collected would be suitable. This data come from choice dichotomies, that is, the person only had one or another option to answer the questions and, therefore, there are only two classes and the data do not present a normal distribution (Larson & Farber, 2010). Naturally this type of tabulation generates non-parametric data, which will directly implicate the technique for evaluating this information.

The data was separated by year and each year was subjected to analyses according to the MBTI Types and psychological type of preference of the individual (Introversion/Extroversion, Sensation/Intuition, Thinking/Feeling, Judgment/Perception).

The multivariate statistical analysis was preceded by the Fligner-Killeen test of homogeneity of variance. According to Niu (2004), this methodology performs median centering on each sample and is more robust against normality deviation. The equation (1) used for the test is:

(1)

where:

The results obtained from the Fligner-Killeen test are available in Table 5 and indicate that there is homogeneity in the variance of the data under study.

	χ²	df	p-value
General	1.3572	4	0.8516
Extroversion	2.236		0.692
Introversion	0.913		0.923
Sensation	1.488		0.829
Intuition	3.894		0.421
Thinking	2.524		0.640
Feeling	5.326		0.255
Judgment	2.128		0.712
Perception	1.963		0.743

Table 5. Fligner-Killeen homogeneity of variance test for all grouped data
and for each of the eight preference types observed in MBTI tests

Another analysis performed was the verification of the existence of Outliers in the data. The existence of this anomaly among the data directly implies the choice of the statistical method to be used. The Outlier detection method foresees two levels of incidence of the statistical phenomenon, according to equations (2) and (3):

(2)

(3)

Where:

Q1 and Q3 are the first and third quartile of data, and;

IQR is the interquartile range, given by IQR = Q3 – Q1.

The results from this analysis indicate the existence of Outliers in all data scenarios (general data and the data separated by psychological type - Table 6). Attempts were made to transform the data, either to a base modeled in square roots or logarithmic modeling and exclude the Outliers but were unsuccessful in excluding these anomalies for the analyses.

2017

2018

2019

2020

2021

Preference type

E Extroversion

Outliers

ESTJ

ESTJ

ESTJ

ESTJ

ESTJ

ENTJ

Extreme

I Introversion

Outliers

ISTJ

ISTJ

Extreme

S Sensation

Outliers

ESTJ

ISTJ

ESTJ

ISTJ

ESTJ

ISTJ

Extreme

N Intuition

Outliers

ENTJ

Extreme

T Thinking

Outliers

ENTJ

Extreme

F Feeling

Outliers

INFJ

ISFJ

Extreme

J Judgment

Outliers

ESTJ

Extreme

P Perception

Outliers

ENFP

Extreme

General

Outliers

ESTJ

ISTJ

ESTJ

ISTJ

ESTJ

ISTJ

Extreme

Table 6. Identification of Anomalies or Outliers in the data population

The MBTI profiles ESTJ and ISTJ appear several times as OUTLIERS, since these two profiles greatly exceed the dimensions of the other profiles presented, therefore they are anomalous when compared to the other profiles.

Given this scenario where the original data comes from dichotomies and the existence of outliers in all models submitted to analysis, there are restrictions for applying this data in parametric statistical modeling. Thus, the option is to choose a non-parametric method that meets a universe of multivariate data and that accepts the observed characteristics. The method used for the analysis was the Kruskal-Wallis, which presents as null hypothesis assuming that samples come from the same population or from identical populations with the same median (μ). This method is defined by means of the equation (Fávero & Belfiore, 2017):

(4)

Where:

k: number of samples or groups;

nj: number of observations in the sample or group j;

N: number of observations in the overall sample;

Rj: sum of positions in the sample or group j;

The result of this Kruskal-Wallis statistical analysis is presented in Table 7. It was found that the null hypothesis of the method was satisfied for all scenarios evaluated, that is, there are no significant differences between the models compared.

		χ²	df	p-value
E	Extroversion	1.925	4	0.750
I	Introversion	1.594		0.810
S	Sensation	1.757		0.780
N	Intuition	0.566		0.967
T	Thinking	0.349		0.986
F	Feeling	1.551		0.818
J	Judgment	0.712		0.950
P	Perception	7.778		0.100
General		1.352		0.853

Table 7. Kruskal-Wallis multivariate evaluation application
for the preference types and for the total data

The authors gave a more in-depth demonstration of this statistical treatment in another publication (Weingärtner-Junior, Piedemonte-Antoniassi, Ferreira-Bindo & Bernardo-Lenz e Silva, 2022).

3.2. SOM Clustering

Self-Organizing Maps (SOM), or Kohonen Maps, is an Artificial Intelligence (AI) tool. It provides an examination of high dimensional data in discrete low dimension maps (two dimension) for analysis, while preserving the data’s topology (Asan & Ercan. 2012).

For this analysis. a neural network is used for three processes: competition, cooperation, and synaptic adaptation. The neurons in this type of network are hierarchical, as a discriminant function performs the competition between them. The neuron with the lowest value obtained by the discriminant function is selected. The position of the selected neuron is determined in the network and the neurons in the direct vicinity are adjusted with the selected neurons value, creating an affinity neighborhood and cooperating for allocates (Haykin. 2009). The groups, or clusters, are formed from the feature affinity of these neighborhoods.

In this research. the MBTI profile data is organized by intensity of the characteristic type (E/I, S/N, T/F and J/P) in the allocation of the neighboring neuron formed. It is important to note that the data continues between the vertical and horizontal borders, as it was organized in the form of a pseudo-toroid map, with the radial axis in the horizontal orientation. This project was set up with 136 cells and 16 clusters to insert the process data from the SOM analysis.

The results of de SOM analysis are shown in Figure 3, the types of dichotomies are described in the rows, and the columns indicate the way the individual interacts with the world.

World orientation of the individual	E (Extroversion)	I (Introversion)
Basic mental processes	S (Sensation)	N (Intuition)
	T (Thinking)	F (Feeling)
Mental mode of action	J (Judgment)	P (Perception)

Figure 3. SOM analysis for the characteristic psychological types in the group
of entering students in the years 2019 to 2021

The result obtained by grouping of psychological profiles by affinity obtained clusters with the profiles ISTJ, ESTJ, INTJ, ENFP, ENTJ, INFJ, INTP, INFP, ENFJ and ISFJ (Figure 4). It was observed that in the input data there were some incoming student profiles that showed undefined dichotomies in at least 1 dichotomous pair and therefore the artificial intelligence did not fit them into a particular group. Other less critical indistinctiveness was fit by AI with other profiles according to their affinity, as the traditional MBTI tabulation has no power to fit a particular blurred type to a particular group.