STEM and HASS Disciplines in Architectural Education: Readiness of FAD-STU Bachelor Students for Practice

Abstract: Since the beginning of this century, STEM education has become increasingly important in preserving prosperity and economic competitiveness. Architecture has its own specific attributes. It overarches the STEM and HASS disciplines, and it should be perceived as a cultural phenomenon rather than as a field of study. The main objective of this article is to highlight the methodology based on the statistical method evaluating the correlation rate between the Bachelor’s student performance (SP) in design studio courses and STEM and HASS categories, represented by particular subjects of various areas of study. The relationship between the admission examination procedure and the academic performance of graduates in the DESIGN category was also analyzed. Although the level of knowledge and skills required based on the study results within the curricula was more significant in the HASS category, the direct correlation between subjects in the STEM category, especially engineering, and the quality of the design studio′s outputs as the main and fundamental part of the creative architectural work, was also confirmed. The authors of the article found that STEM knowledge and STEM skills do not reach the required level and, therefore, the emphasis should be placed on changing curricula, balancing the ratio of STEM and HASS categories, adjusting the credits assigned to STEM subjects, or reviewing the classification system.


Introduction
Humanity is characterized by the acquaintance of knowledge in various disciplines, to ensure its development, preserve culture, and respond to numerous challenges associated with its activities. It is the basis and assumption for progress, productivity growth, and value/wealth creation. In general, high-quality education allows young people to develop their knowledge, skills, and competencies. It provides them with the system to learn and comprehend the global/local background, as well as the possibility to become creative, active, and responsible citizens fully integrated into society, while meeting its requirements and expectations. In addition, it gives them the option to influence and shape the future and to participate in economic activities.
In the beginning of the 21st century, there emerged a strong need to emphasize the links between prosperity, knowledge-intensive jobs dependent mainly on science and technology (S & T), and continued innovation, especially incremental technological innovation of products and services, to address societal problems and achieve economic competitiveness. Therefore, S & T and its transfer from the education system to the economy play a central role in the modern society based on knowledge and technology [1][2][3]. In this context, traditional education in science, technology, engineering, and mathematics (also known, colloquially, as STEM education) is an inter-/multi-/transdisciplinary approach to curriculum in many educational systems connecting independent disciplines and represents the primary gateway of higher education to the field of STEM work [4,5]. In fact, the symbiosis

Materials and Methods
The main data for this research study were extracted from the university-wide academic information system (AIS), which is used to monitor the course of each student's achievement across various academic subjects (their academic performance) and makes a lot of information available to the academic community, university staff, and the general public. All data have been processed anonymously, and the authors of the article, as academics, are bound by professional secrecy.

Characteristics of the Analyzed Data Set
The investigated cohort of Bachelor's graduates included the students who started their studies in the winter semester of the academic year 2014/2015. In this generation, the total number of students enrolled was 159, of which 110 successfully finished their studies, and 49 were unsuccessful. The analysis also considered those students who have repeated any of the subjects or exceeded the standard length of study. All subjects in the study program were analyzed, except one elective course completed without classified credit. A total of 64 subjects with 235 credits were analyzed out of a maximum of 240 compulsory credits to pass the 4-year Bachelor's study [26]. Since the study included only successful graduates, the evaluation of their academic performance was classified by grades, from the best to the worst, as follows: A (1.0); B (1.5); C (2.0); D (2.5); and E (3.0). The arithmetic mean (AM) of this classification scale was C (2.0), which corresponded to the intermediate level of knowledge and skills required. The data included the results of the admission examination procedure, as well as the results of particular tasks within it.

Data Processing Method
The very starting point for the analysis was the creation of individual student profiles. Each profile included their overall academic performance, where their results in individual subjects, as well as the results of the admission examination procedure, were recorded. The student profile analysis enabled to evaluate the relationships between individual subjects or groups of subjects using a comparative method. The data processing method consisted of four stages.

Stage No. 1
In this stage, as presented in Appendix A, the authors of the study established the student profile data sets (Tables A1 and A2) and the data sets of subjects (Table A3), with assigned credits and basic statistical data such as the number of graduates, the numbers and values of the grades, and their (AM). Furthermore, subjects were classified into 3 main categories, DESIGN, STEM, and HASS, including groups of subjects according to their field and the provided knowledge. The first was the DESIGN category, in which the design studio courses were included. Design studio courses colloquially form the backbone of the future architect in practice. In general, the subjects of DESIGN category simulate the real practice of an architect who simultaneously uses knowledge/skills from STEM and HASS subjects. In the second STEM category, the authors involved the MATH-mathematical, TECH-technical, and ENGI-engineering subjects. Since any subjects in the Bachelor study did not meet the characteristics of the Science group, this category was not established. Such subjects are an integral part of Master and Doctoral studies. The third HASS category covered HIST-historical, HUMA-humanities, ART-artistic, and SOCSCI social-sciences subjects. The SOCSCI group was represented only by a single-credit subject. Therefore, this group was evaluated as non-representative and excluded from the next steps of the analysis performed. Since some subjects in their syllabus covered several areas of study, they were classified according to the predominant focus.

Stage No. 2
Based on student profile data sets, student performance (SP) in individual subjects and categories/groups of DESIGN, STEM, MATH, TECH, ENGI, HASS, HIST, HUMA, ART and OVERALL was determined using a weighted arithmetic mean (WAM), weighted by the number of credits of the subject. WAM in the individual subject categories and groups was also converted to normalized values (NV), so that the student with the worst SP acquired a value of 0, while the student with the best SP received a value of 1. The SP between the best and worst was proportionally divided within the interval (0, 1). The NV conversion allowed the authors to compare the SP of classified subjects and tasks of the admission examination procedure (Section 3.10). At the same time, in Section 3.9, it enabled to minimize the differences in the middle level of the required knowledge and skills for a given category/group of subjects. Credits represented a mixed value consisting of learning outcomes that are attributed to individual educational components within the Architecture and Urbanism study program as a whole and the workload, which means that one credit corresponded to 25 to 30 h of work. In the next steps of the analysis, the sum of the credits of the subjects in particular categories and groups was not considered because the authors considered the acquired knowledge and skills important without preference for the architect in practice.

Stage No. 3
The AM of a given category of subjects was determined as the basic parameter characterizing the level of acquired knowledge/skills of the whole analyzed cohort of students. The average value of knowledge/skills in terms of the study program for a given category of subjects was 2.0 (grade C). For the STEM subject category, including the TECH, ENGI, and MATH groups, the AM value was greater than 2.0. This fact confirmed that the stu-dents did not reach the intermediate level of knowledge/skills required on average. The largest difference was recorded in the ENGI group of subjects.
For the HASS subject category and the subjects HUMA, HIST, and ART, the AM was lower than 2.0, which means that students exceeded the intermediate level of knowledge/skills required on average. The largest difference was recorded in the HUMA group of subjects.
From three main categories, the largest difference in AM was found in the DESIGN subject category, which meant that the students significantly exceeded the intermediate level of required knowledge/skills. The AM of the overall SP was below 2.0. The relatively high oscillation of the AM (lowest 1.52/highest 2.28) indicates the disproportion between the intermediate level of knowledge/skills required, the real initial knowledge/skills of the students, and the value of credits for individual subject categories/groups. This oscillation may have been caused by other factors. The reason for this oscillation was not the subject of this analysis. However, the balance between the required level of knowledge/skills and the real initial knowledge/skills of the students is a key to effective education.
Another parameter for evaluating the course of SP in the subject categories/groups was the AM of the best and worst SP in the given subject category or group (AMbw). The AMbw-AM difference determined the degree of proportionality of the achieved SP. If AMbw-AM > 0, then in the given category/group of subjects there was a higher number of worse SP than the better ones. The opposite was true if AMbw-AM < 0. The concrete data show Table 2. The SP in the individual subject categories and groups or admission examination procedure results (AR) was ranked from best to worst and compared with the modified Gaussian curve. Modification of the Gaussian curve is based on the probability density of normal distribution of real SP of given category/group of subjects or AR determined by its AM and standard deviation, cumulatively spread to the whole number of the analyzed student cohort. This comparison evaluated the suitability of the proposed assessment. In all categories and groups of subjects or admission examination procedures, the assessment in terms of normal distribution was interpreted as adequate.
The SP or AR was divided into three levels: the first level (best), the second level (moderate), and the third level (worst), which were symmetrically divided around the AM of the SP of the given category/group of subjects or AR. Values outside these three levels were marked as 'out of range'. The division into three levels resulted from the intention of the authors of the article to compare the SP of individual categories and groups of subjects at equal levels based on the real SP or AR determined by their AM.
The SP in the STEM and HASS categories were, subsequently, compared with the DESIGN category represented by the design studio courses. The correlation rate (CR) between the number of SP in levels of the STEM and HASS categories or the number of AR in levels of the admission examination procedure and the number of SP in levels of the DESIGN category of subjects was evaluated by geometric mean. Its value demonstrates the following Equation (1): The comparative analysis was performed only in one direction, which means that the influence of the SP in the STEM or HASS categories on the SP in DESIGN was examined. The analysis was not performed in the opposite direction and, therefore, it was not evaluated how the SP in the DESIGN category affects the SP in the STEM and HASS categories. The partial findings are shown in Figure 1.   Figure 1, all other interrelationships were examined. The final findings on the correlation rate between STEM, HASS categories/groups of subjects, and the DE-SIGN category calculated according to Equation (1) are shown in the following paragraphs. The correlation rate (CR) is expressed as a percentage. The darker the cell, the higher the degree of correlation rate (Table 3). In Tables 4-11 the integer represents the count of SP of a given level in category/group.

TECH vs. DESIGN
The correlation rate between the TECH and DESIGN categories was relatively low ( Table 4). The most prominent CR was on the first level of acquired knowledge. It was assumed that students with above mean SP (1st level) from TECH subjects can adequately apply these knowledge/skills in design studio work. In general, the design studio work is characterized by an effort to establish the student's ability to creatively implement the acquired knowledge/skills from theoretical subjects into the process of creation. From the comparison of the relationship between TECH and DESIGN, it is possible to assume that to be able to implement knowledge/skills from theoretical subjects into the creative processes within the design studio, it is necessary to acquire their critical mass. Table 5 confirms that SP in the ENGI and DESIGN categories correlates the most among all groups of subjects within the STEM category. Therefore, it is possible to assume that the level of knowledge acquired in the subjects of the ENGI category is directly related to the quality of design studio outputs that were included in the DESIGN category. At the same time, it is possible to conclude that the mastering of the design studio work from the engineering point of view, such as statics, the quality of project drawings, or building equipment, influences the evaluation of the works on a regular basis.

MATH vs. DESIGN
Student performance in MATH and DESIGN categories does not highly inter-correlate, respectively, MATH correlates more significantly with random levels as shown in Table 6. For example, the third level of MATH correlates with the first level of the DESIGN category. Based on this result, it can be assumed that MATH knowledge is not directly related to the quality of design studio outcomes. However, it is necessary to highlight the importance of mathematics for the study of subjects included in the TECH and ENGI categories. In this study, the relationship among MATH, TECH, and ENGI is not investigated.

STEM vs. DESIGN
According to the results shown in Table 7, student performance between STEM and DESIGN categories correlates well but less significantly than in the case between HASS and DESIGN categories. Based on the findings from the relationship among TECH, ENGI, and MATH groups of subjects and the design studio, it is possible to conclude that design studio work does not require such deep STEM knowledge and skills. However, practice through many shining examples shows that STEM knowledge and skills are irreplaceable, especially if the design is implemented. This difference was probably due to the detail level of the design studio work processing. Except for the Final Bachelor's Project, in general, the output of the design studio courses is an architectural design, in which the construction and technical solution is documented at the level of a rough concept. Admittedly, another factor that influences the position of STEM in the design studio is the evaluation method. Design studio work is evaluated at FAD-STU using the peer-to-peer review method, where the output includes qualities in the entire spectrum of STEM and HASS subjects and is rated by one grade. Table 8 shows a quite significant correlation between the HUMA group of subjects and the DESIGN category. It is assumed that the knowledge and skills required within the HUMA group of subjects were applied in the creation of the design studio works and their evaluation.

HIST vs. DESIGN
The correlation between the HIST group of subjects and the DESIGN category was present with greater variance within the evaluation, as shown in Table 9. It is assumed that the knowledge/skills from HIST subjects are a good starting point, but in relation to other evaluation criteria of design studio work, they do not have a distinctly reserved position.

ART vs. DESIGN
The correlation between ART and DESIGN was most pronounced at the lowest level (Table 10). It is assumed that the aesthetic qualities acquired within the ART group of subjects were the most significant evaluation criteria for lower-quality design studio works. With good quality design studio works, the design was evaluated in a wider range of qualities.

HASS vs. DESIGN
The correlation between HASS and DESIGN was more significant compared to the STEM and DESIGN categories (Table 11). It is assumed that the degree of correlation reflects the overall better readiness of the students in the theoretical subjects of the HASS category, which corresponds to a lower AM of SP compared to STEM. At the same time, HASS qualities are the predominant assessment criteria in the design studio work evaluation.

The Relationship Overview of STEM-HASS vs. DESIGN
Using the NV of SP, Figure 2 and Table 12 show that the SP in the design studio (DESIGN) was in direct connection with SP in theoretical subjects, represented by the cumulative value of the STEM and HASS SP (calculated as AM of STEM NV of SP and HASS NV of SP). The ratio between knowledge/skills from the STEM and HASS categories was indirectly related to the SP in the DESIGN category and the cumulative value of the STEM and HASS SP. In the case of students with a worse SP in DESIGN, STEM knowledge/skills prevailed over HASS. On the contrary, for the students with good performance in subjects of DESIGN category, HASS knowledge/skills prevailed over STEM.  It is assumed that engineering creativity, which is closely related to STEM, is a natural skill of architecture students and is deepened and supplemented by HASS competencies through the educational process. For the best students characterized with the best cumulative SP values within the STEM and HASS categories, this corresponds to the required learning outcomes of STEM and HASS subjects within the study program curriculum and their AM within the analyzed cohort of students.

Admission Examination Procedure vs. DESIGN
An integral part of education is the determination of the requirements for applicants and a strategy for the selection of future students. In the European Union, there are no single selection strategies or requirements for applicants in relation to STEM and HASS disciplines in the field of study architecture and urbanism. On one pole, there exist universities with an open or no student admission examination procedure, and the selection process is managed naturally during the studies. The other pole represents universities with selective requirements for admission to study in accredited study programs. The nature of these requirements is diverse and follows the dynamic development of society and the role of the architect within it. Therefore, the intention of the authors of the article was also to confront admission requirements with student performance in the DESIGN category.
Admission examination procedures at the FAD STU are primarily focused on the assessment of applicant s inborn talent. In the analyzed cohort of students, their STEM or HASS knowledge from secondary school was not identified during the admission procedure. Therefore, on the one hand, it is not possible to recognize a direct link between the acquired knowledge and skills from the STEM and HASS theoretical subjects and the explicit knowledge acquired from previous studies. On the other hand, it is possible to partially analyze how the degree and character of the applicant's talent affect their study results. The admission examination procedure of the analyzed cohort of students consisted of four tasks. The first task dealt with composing the volume from geometrical bodies on a specified architectural topic in a spatial perspective. In addition to the ability to capture space with a linear drawing, this task also verified the applicant's creativity and their perception 3D space. The maximum value of this assignment was 250 points. The second task tested the ability to realistically display the still-life model with a linear drawing and was assigned 250 points as well. The third task included the test of spatial imagining verifying the spatial sentience, respectively, it solved the intuitive tasks from projective and descriptive geometry. This task was evaluated with a maximum of 200 points. The fourth was the so-called SCIO test, provided by an external institution that assessed the general study prerequisites and the applicant's abilities to complete university studies. The maximum value of points for this assignment was 300. The maximum point gained from the admission examination procedure was 1000 points, while the threshold to pass this procedure was set at 510 points. The first 200 applicants were given the opportunity to start the study. The fourth task was excluded from the comparison with student performance in the DESIGN category, since it was focused on the ability to complete university studies and the analyzed cohort consisted only of successful graduates. The results of individual tasks (1st task-Composing volume from geometric bodies-COMPO; 2nd task-Still life model drawing-STILL; 3rd task-Test of spatial imagining-SPAT) and the overall results (sum of the first to third task-ADMISS) were converted to NV and examined similarly to Figure 2. The relationship between the admission process and student performance in the DESIGN category of subjects is shown in Tables 13-16 (the integer represents the count of SP of a given level in category/group).  The results of the admission examination procedure and student performance in DE-SIGN category, as shown in Tables 13-16, do not correlate or correlate very slightly in the test of spatial imagining (SPAT) and composing volume from the geometric bodies (COMPO).
In fact, these tasks are inherently creative and directly related to the design studio courses. It is assumed that creativity is a natural competence of an architect. Besides the general and artistic creativity, today's architect shall dispose with the engineering creativity, which is closely linked to flexibility, understanding of the context, and identification of the problem. The essence of engineering creativity can be perceived on the following three levels: (1) innovation in solving open-ended problems; (2) the ability to cross the boundaries of one's own field and to expose oneself to the uncertainty of the unknown; and (3) to bring solutions that can be implemented today or in the future [27]. As a result, a more detailed focus on the creativity of the applicants could be a suitable complement to the admission examination procedure.

Discussion
The total value of the European construction market of 31 European countries (Europe-31) is estimated to be worth EUR 1914 billion in 2020. The sector study conducted by the Architects' Council of Europe (ACE) on the architectural profession in Europe in 2020 also revealed that in the Europe-31 ACE member countries surveyed, there is an estimated total number of 559,070 architects contributing approximately EUR 17 billion to the economy of Europe. Of these, three-quarters of architects work full-time. As the sole principals working independently and providing a full range of architectural services to clients describe themselves as 33% of architects (more than 50% in Slovakia), making this the largest employment group in the profession. Architects working in private practice as associates or salaried architects comprise 29% of the profession, 7% describe themselves as freelance, 9% are partners and directors, and the public sector employs 13% of European architects. Architectural practices in 2020 remained strongly skewed toward the smallest size groups, as almost two-thirds are one-person practices [28]. This significant rate that reaches almost 80% in Slovakia goes hand in hand with knowledge level and great responsibility to secure the equilibrium/ultimate synthesis of three pillars of architecture introduced by Vitruvius, such as firmitas (commodity), utilitas (firmness), and venustas (delight). In addition, these requirements are nowadays broaden-ing by highly demanded and forced restituitas (sustainability), to ensure the sustainable development and mitigate climate change and human activities on the environment.
In general, graduates are able to design simple architectural or urban proposals and structures under professional supervision, work effectively as team members, and are competent to independently prepare project documentation for constructions to a reasonable extent using computer and manual techniques. These graduates have the ability to independently prepare and evaluate materials for architectural or urban design as well as present and justify them to a professional audience.
Further investigation in this field could be conducted within the Master's studies that enrich the previous studies with extensive professional knowledge, skills, and competences at the level of evaluation of theory, history of architecture and urban construction, fine arts, humanities and environmental sciences, construction, or technical problems, equipment, and technologies. Master's graduates are versatile, practical, and, theoretically, prepared for independent architectural and urban planning. The authors are also interested in doctoral studies, and they consider examining the topics of dissertation theses in accordance with the STEM and HAAS disciplines. Such research forms the basis for more comprehensive analyses to properly understand the interrelationships among the subjects of different disciplines, to improve the education provided by higher education institutions, and to increase the employment of architecture students in various professional realms.

Conclusions
The results of this study authenticated the great importance of knowledge and skills in STEM disciplines for architects to carry out their practice. Despite the insufficient intermediate level of STEM knowledge and skills of the FAD STU Bachelor's students, the direct relationship between student performance in STEM and DESIGN categories of subjects was confirmed. There is an assumption that balancing the ratio of the STEM and HASS categories should contribute, in the end, to higher quality of design studio outputs as the main and fundamental part of creative architectural work, which is primarily evaluated during the authorisation-the process of recognition of professional qualification.
Current discussions in the Slovak academic sector aim at the implementation of a compulsory upper secondary school leaving examination in mathematics, which is generally considered a starting point and a basic prerequisite for the successful study of STEM disciplines. In respect to knowledge productivity/creation of knowledge, beyond its acquisition and application, the STEM disciplines along with the HASS disciplines will enhance the expertise and will lead to success and maintaining a competitive advantage not only in architectural practice.
The conducted research by the authors of the article highlights a close link between the acquired knowledge/skills of the FAD-STU Bachelor's graduates and the curriculum of the Architecture and Urbanism field of study, which emphasizes the university's responsibility in educating architects. The sustainability of the balance between the competencies of the applicants entering higher education and the labor market and various social requirements is, indeed, a dynamic process. The statistical method applied in the analysis of the educational process, and using the student performance, proved in this study that it can be considered a suitable tool to assess the complex of interrelated factors entering the educational process. Furthermore, this analysis allows one to expand the complex of monitored parameters by the study results of the candidates before entering the higher education institution, respectively, the second or third cycle education. At the same time, the authors see a potential to supplement the student's profile with the characteristics of their tacit knowledge, the evaluation of which is not considered in the classification system. Based on this analysis, the authors are of opinion that the traditional classification system using five grades (A-E) is insufficient, which is especially relevant for subjects such as design studio, which penetrate the content of several areas of study. This strictly scaling of the student performance does not allow to effectively evaluate the synergy of subjects from related areas. Therefore, it would be appropriate to evaluate such subjects with several grades, or to introduce a points system to difference student performance in STEM and HASS disciplines.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy reasons.

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.