Educational Data Clustering in Secondary School Sensor-Based Engineering Courses Using Active Learning Approaches

Abstract

The authors investigated the impact of active learning STEM and STEAM approaches on secondary school students’ general engineering knowledge, intrinsic relevance, and creativity. Three out-of-school sensor-based courses were held successively. Every sensor-based course involved the final project development. A structured questionnaire was administered to 379 students and consisted of two critical factors: creativity and intrinsic relevance. The third factor was dedicated to the students’ engineering learning outcomes. Two factors were addressed to secondary school students, while the third factor was addressed to the tutors’ observations of the students’ general sensor-based knowledge. Clustering validation analysis quantified the obtained results and justified the significant differences in all estimated factors for different educational modes. Moreover, the study showcases the value of the arts in sensor-based learning-by-doing courses when tackling complex issues like engineering topics. The authors suggest that broader research be undertaken, involving a larger sample, a greater scale, and a diversity of factors.

1. Introduction

As we delve into the era of intelligence, the importance of sensors is becoming increasingly evident. Nowadays, sensors link multiple ICT (information and communications technology) devices and enable various machines to communicate [1]. The rapid advancement of cutting-edge ICT technologies, including virtual and augmented reality, immersive technology, artificial intelligence, the Internet of Things, and wearable technology, has turned ordinary sensors into intelligent electronics. Sensors have become incredibly compact and highly portable. Along with their expanded capacities and low-cost electronics for control and data acquisition, they can be connected to various simple and sophisticated ICT devices [2].

With the rise of inexpensive microcontrollers such as Raspberry Pi, Arduino, and NodeMCU, as well as inexpensive sensors that work with these ICT devices, there is increased interest from educators and teachers in exploring the potential of this technology in secondary school learning and teaching settings [3,4,5]. Their use in the classroom allows students to become acquainted with the elements of automated process control, data management, measurement methods, and monitoring techniques [6]. Through interactive hands-on practices, students can expand their critical and logical thinking skills, and problem-solving abilities, as well as deepen their understanding of technological and engineering subject matters [7]. This interest is also an extension of an existing movement toward integrating hands-on instrumentation as part of learning-by-doing experiences in the classroom [8,9].

The learning-by-doing educational approach involves designing systems using software and hardware that can perceive and respond to the simulated world. In real-world classroom applications, learning-by-doing mainly uses physical computing with microcontrollers and multiple sensors, such as temperature, humidity, light, sound, and movement. Moreover, it incorporates LEDs and LED bars using dimmer switches, push buttons to switch LEDs, RGB LEDs, LCDs to output text information, and actuators to convert analog inputs into a software system or to control electronic mechanical devices, such as motors, steering gears, or other hardware [10,11]. Therefore, it acts as a bridge between traditional and active forms of science education, static or lifelong learning, or as an interactive platform for handmade works of art using a collaborative process of designing, constructing, programming, and testing student-implemented projects [12]. The advent of affordable electronics and low-cost sensor-based technology in specific applications, serving as reliable and robust substitutes for expensive proprietary solutions, is creating new opportunities that are far broader and more effective than ever, which makes them significantly necessary for major breakthroughs in technology in the 21st century [13,14,15,16,17,18].

The education research community agrees that active learning pedagogies, especially STEM (Science, Technology, Engineering, and Mathematics) and STEAM (with the A standing for “the Arts”) education will drive new innovations across disciplines, making use of computational power and ICT technologies to accelerate discoveries and find creative and collaborative ways to work across disciplinary silos, solving real-world challenges. According to the 2020 report [19], “The STEM Education of the Future brings together our advanced understanding of how people learn with modern technology to create more personalized learning experiences, to inspire learning, and to foster creativity from an early age”, in recent years, in many countries, STEM-related fields (concerning teaching and learning) have become more prominent sources of innovation [20,21,22]. The integration of creativity—encompassing talent, knowledge, ability, intrinsic motivation, and personality traits—into STEM pedagogy expands the scope of hard scientific, technological, and engineering subjects, leading to interdisciplinary STEAM education that includes language arts, dance, drama, music, visual arts, design, new media, etc. [23,24]. Recently, the European Commission’s Proposal on the European Roadmap to Education 2021–2027 extended the STEM acronym to STEAM, with the A standing for “the Arts” [25].

In this context, the work aims to show how STEM and STEAM educational approaches can help secondary school students improve their learning skills through interactive, hands-on sensor-based out-of-school courses [26]. The objective of the study is to perform an overall analysis and comprehensive comparison of active learning methods with traditional ones to reveal fundamental differences in educational modes in engineering courses in Polish secondary school settings [27]. By offering specific findings and important scientific results about the necessity of integrating STEM and STEAM active learning approaches into secondary school sensor-based education, the authors emphasized that the idea of learning-by-doing is, therefore, not only topical but offers highly interdisciplinary practical subject matter, providing motivating scenarios for teaching a multitude of subjects. Moreover, in this article, the authors demonstrate the significant importance and benefits of active learning methods so that STEM and STEAM concepts can be successfully introduced to Polish secondary schools [28].

STEM and STEAM engineering courses provide students with the opportunity to learn about sensor technology through a hands-on, collaborative process of designing, constructing, and programming a sensor-based system. The research study implies a descriptive and clustering validation analysis of secondary school students’ learning outcomes, creativity, and intrinsic relevance toward the presence of active STEM and STEAM learning approaches in engineering courses. The experimental setup includes three independent groups of students: the first group acquires sensor-based knowledge via traditional learning methods, the second uses the STEM approach, and the last uses the STEAM approach. In this context, the following research questions are crucial:

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Do the STEM and STEAM active learning approaches influence secondary students’ learning outcomes, creativity, and intrinsic relevance in out-of-school extra-curriculum settings at sensor-based engineering courses?

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Does the presence of arts in the active learning STEAM approach have a crucial impact on secondary students’ learning outcomes, creativity, and intrinsic relevance in out-of-school extra-curriculum settings at sensor-based engineering courses?

The major novelty of this study compared to previous works is the cross-comparison of the tutors’ observations and secondary school students’ appreciation of educational modes toward the improvement of engineering knowledge, intrinsic relevance, and creativity at out-of-school sensor-based courses. Moreover, the present study uses innovative clustering validation methods to reveal, justify, and quantify the presence of differences in educational modes, which opens the path to cross-disciplinary research in pedagogy and machine learning.

2. A Polish Perspective beyond STEM/STEAM Approaches

In the current digital era, developing competencies in STEM and STEAM disciplines is a key goal of education systems around the world [22]. Implementing innovative approaches requires overcoming traditional “old-fashioned” teaching methods (e.g., direct instructions, seatwork, “chalk and talk”), which are often teacher-centered and fragmented, to promote “modern” (e.g., problem-based and collaborative learning, computational thinking) student-centered interdisciplinary approaches covered by high-tech ICT equipment and up-to-date knowledge. However, research shows that the successful integration of STEM and STEAM approaches into education requires an overall policy vision, organizational change, leadership, and, in particular, support for teachers [29]. In 2020, Poland received a country-specific recommendation from the Council of the European Union to “improve digital skills” [30]. In 2023, Poland obtained a National Recovery Plan entitled “Setting new directions for the development of Polish education 2021–2027”, signed the “Regulation on the teacher training standards” and announced the “Investment in Education” and “Development of the Infrastructural Potential of Institutions Supporting the Education System” programs [31,32,33]. With the progressive changes in education, Polish policymakers should exercise caution in making informed decisions to aid the transition from traditional to active STEM and STEAM forms of education as well as develop preparedness plans for future, innovative, and demanding technological and information development to meet the twenty-first-century learning and teaching expectations [34].

There is a wealth of literature on the benefits of STEM and STEAM concepts and their positive impact on students’ learning outcomes. Like many other countries, Poland has experienced an expansion of STEM and STEAM active educational approaches across different educational levels. Surma et al. (2019) have presented the results of strategic partnerships among five research teams from Italy, Ireland, Spain, and Poland in promoting the international exchange of best practices and experiences in selecting active learning environments, modern and interactive STEM-based teaching methods at the level of early childhood education [35]. An article by Zdybel et al. (2019) presented the idea of STEM education as an interdisciplinary “meta-discipline” and showed the possibilities of implementing this type of curriculum and material in a preschool environment [36]. Plebańska and Szyller explored the specifics of STEM education as a space conducive to the development of cognitive activity in preschool-aged children [37]. The authors addressed why the STEAM approach is successfully suitable for the youngest, meeting their development needs and stimulating various aspects of their growth. Other research showcased the concept of using the STEAM design in the shaping of geometric concepts in preschool-aged children [38].

In primary education, researchers have showcased the importance of creativity from the perspective of the Polish education system [39]. Other researchers described the novel interdisciplinary method of education through art [40]. Plebańska discussed the digitization of Polish schools based on the “Polish School in the Digitisation Era. The 2017 Diagnosis” survey, regarding the necessity of implementing the STEAM model of teaching [41]. Research by Łukasik et al. (2021) focused on creative competence as an integral component of competence for sustainable development [42]. Their research explored and described the level of creativity competence among Polish primary school students. Tomczyk et al. (2019) focused on the conditions related to the use of ICT in the didactic process in Polish primary schools [43]. They showed how digital media and literacy are being used by primary school students and teachers. Panskyi et al. showed how active learning methods, especially game-based learning, could bridge the gap between schools and universities [44,45]. Moreover, the authors demonstrated the significance of implementing a digital game-based learning approach in out-of-school education to stimulate the creative and innovative learning and teaching of Polish primary school students. Another creative project-based learning (PBL) approach showed active ways of teaching and learning mathematics in primary school settings [46]. Guenaga et al. (2017) presented the STEAM-based Make World online platform to promote computational thinking and active learning skills [47]. Finally, Dudel focused on practical STEAM exercises for primary school students, providing a range of information, methodological advice, and materials useful for conducting classes [48].

With respect to the secondary level, Sysło highlighted the role of problem-based active learning methods in high school [49]. Łukaszczyk and Grebski presented a comparative analysis of STEM-based subject curricula and students’ learning outcomes in Poland and the United States [50]. Kisiel focused on the use of active learning methods in informatics education, particularly for teaching spatial modeling and visualization [51]. Walat presented research on secondary school informatics education, focusing on students’ skills in perception, interpretation, and creative production of visual materials [52].

Finally, from the perspective of teachers, the research shows the significant impacts of creativity and problem-solving on the development of teachers’ skills [53]. The effect of active forms of education in the context of teaching practices was examined [54]. The problems within the contemporary education system and suggestions dedicated to the smooth and effective implementation of active teaching methods and approaches were explored [55]. The crucial roles of both prospective and active teachers in students’ education have also been explored [56]. Real ICT skills, knowledge of new media, digital competencies, and the preparedness of current teachers and future pedagogical staff for active learning and teaching models were carefully presented in several recent works [57,58,59,60,61].

Research at the university level is described in references [62,63,64], while discussions on novel active forms of education are presented in references [65,66,67]. We should also mention the difficulties and challenges of the proper integration of active learning methods and approaches (STEM, STEAM, PBL, and others) in formal and non-formal educational settings in Poland [68,69,70,71,72].

A comprehensive literature review has demonstrated that Polish researchers and educators are consistently conducting attempts to reveal and justify STEM and STEAM active education approaches at different levels of education. The authors published their scholarly works through a variety of publication outlets, including journals, books, and conference proceedings. However, research development in the field of active learning and teaching methods in secondary school education, especially in sensor-based engineering courses, is not straightforward. Unlike school-based education research with curriculum subjects, STEM and STEAM approaches are not well-defined fields. It is difficult to discuss the effectiveness of STEM and STEAM because there is still a lack of research. From an international point of view, however, efforts are still being made. Fernández-Morante et al. (2022) explored how the STEM active learning approach and project-based learning influence secondary school students’ perception of basic learning competencies [73]. Jiang et al. (2023) identified intercultural team characteristics of engineering students based on team formats, collaboration levels, learning goals, evaluation methods, and learning gains [74]. Asghar et al. (2019) studied secondary students’ creative alternative ideas about engineering design technology and technological systems [75]. Jantassova et al. described the issues of critical thinking development using the creative STEAM approach to solve professional tasks in the higher engineering education system (2022) [76]. Sukackė et al. (2022) focused on secondary school students’ learning outcomes in engineering education through active learning methods [77]. An accurate and concise synthesis of the citation list, clear methodology, and transparent reporting demonstrate the effective influence of STEM and STEAM learning and teaching approaches in formal and non-formal education settings. Therefore, the authors attempted to follow this approach and conducted a study on the learning outcomes, creativity, and intrinsic relevance of secondary school students, examining whether active learning in STEM and STEAM was present or not.

3. Methodology

3.1. Sensor-Based Course Organization

Sensor-based engineering courses conducted in traditional modes were held in secondary schools in 2022. STEM-related courses were held at the Faculty of Electrical, Electronic, Computer, and Control Engineering at the Lodz University of Technology in autumn 2022, and STEAM-based courses were performed in the Active Education Laboratory of the same university (spring 2023). Every engineering course consisted of 5 sessions, with each taking 4 lesson hours (3 clock hours). Every session was held once a week.

Despite the learning mode, two tutors were engaged in teaching one session and directing the entire class of participants. Tutors had sufficient pedagogical competencies and used different traditional and active learning approaches. Tutors held PhDs in electrical engineering and computer science, postgraduate diplomas in pedagogy, and a minimum of 5 years of teaching experience.

As identified in previous research, one important reason that may explain the significant impact of STEM and STEAM education is that student-centered and active instructional methods lead to greater achievement in terms of students’ learning outcomes when compared to traditional modes [78,79]. Traditional teaching often involves the teacher instructing from in front of the classroom. Traditional teaching is usually teacher-centered and focuses on imparting book knowledge to students. Generally, in Polish schools, traditional teaching methods are common because teachers want students to learn fixed knowledge and obtain good scores on exams. In the traditional classroom, students must obey discipline to ensure a good learning environment, and teachers are the controllers of the class. In addition to listening to course topics, other participatory activities such as small group discussions, cooperative learning, and peer questioning are not favored because of the traditional classroom design. Traditional information delivery is mostly one-way—from the teacher to the students—apart from the listeners asking the teacher questions [80].

Nevertheless, in traditional sensor-based courses, the entire class was divided into groups of 4–5 students, as strictly managed by the tutors. Tutors assigned students to small groups. Students participated in debates only within one specific group or directly asked the tutors questions by raising their hands. The tutors stood in front of the blackboard without circulating the classroom. Students were not allowed to walk during their lessons. The tutors used straightforward traditional chalk and blackboard teaching tools to teach crucial sensor-based knowledge topics.

STEM and STEAM sensor-based courses focused on instructional strategies for active learning as a whole or on specific strategies like project-based learning, creative experimental learning, interactive learning-by-doing, and team-based learning. In this sense, active learning courses are student-centered and, therefore, include questioning, discussing, writing, problem-solving, teamwork, peer learning, and hands-on experiments. In active learning sensor-based courses, tutors asked students to divide themselves into groups of 4–5 and interact in small teams in order to complete a task. Students were encouraged to work together and communicate with each other within or throughout the groups. Students were allowed to walk during their lessons. The teaching atmosphere was relaxed, and the flexible nature of the work in the classroom created a rich and diverse learning environment to meet students’ individual and group needs. The tutors intentionally used multimedia ICTs and other learning visuals to promote active learning and students’ engagement.

In both traditional and active learning STEM and STEAM sensor-based courses, the Arduino open-source platform served as the main hardware component, with several low-cost starter kits, for example, the DFRobot Mega D3 kit, the FORBOT kit, the Starter Kit K000007, and the EL-GO Edu 1, were used. Every group of secondary school students, despite their educational mode, received sensor-based Arduino starter kits for course purposes. The Arduino platform is designed to facilitate electronic learning and programming, especially for secondary school students. The sensor-based courses were taught using the Arduino boards in conjunction with the mBlock visual-based environment and C/C++ programming languages.

Every course was divided into three crucial parts. The first part (1 session) focused on the contextual problems of modern sensor-based ICT technology. This part engaged students’ prior knowledge about programming, components of electronics, physics, and mathematics. The tutors started the course with interesting questions about the subject. Thereafter, the tutor presented possible ideas, encouraging students to participate and showing solutions that could be used with the use of technology and engineering. Students learned how to solve problems, develop ideas, discuss their conceptions with their groups, and apply the most appropriate ideas they came up with. The second part of the course (2 sessions) allowed students to explore new sensor-based knowledge through collaborative learning-by-doing experiences. It involved using Arduino starter kits with different sensors, GPS modules, switches, motors, jumper cables, and other electronic components. Moreover, this part aimed to teach basic programming principles, such as loops, synchronization, variables, conditionals, operators, broadcasts, functions, and more. In the traditional learning mode, simple schematics of electronic circuits with sensors, batteries, and other electrical symbols were sketched with white chalk on the blackboard, while in active learning modes, tutors used digital ICTs, videos, artificial intelligence generators, scientific articles, image databases, etc., to promote a deeper understanding of interesting engineering topics. The third part (2 sessions) of the sensor-based courses involved the final project development. The final project focused on the development and introduction of sensor-based ICT technologies. In both the traditional and STEM courses, students created advanced electronic circuits with microcontrollers, batteries, distance light, and motion sensors, while STEAM courses required students to design a portable and low-cost smart home prototype (see Figure 1).

Smart home projects aim to encourage students to develop creativity in presenting or revealing arts and innovative thinking through a STEAM approach. The arts should be as equally important as other subjects because art-integrated STEM education could lead to the development of soft and transversal skills, enhance recognition of the significance of cultural education, and open new opportunities to satisfy and deepen students’ interest in creative work and aesthetic competencies through their natural inquisitiveness and eagerness for free-thinking (see Figure 2). Moreover, the multidisciplinary STEAM approach incorporates the arts with multiple scales of abstraction and different viewpoints.

In STEAM active learning sensor-based courses, ‘intelligence arts’, such as smart home design, construction, and operation, mainly focused on the multidimensional representation of the arts in the form of creativity and innovative thinking skills. Neglecting the arts may primarily lead to a focus on learning within the hard scientific, technological, engineering, or mathematical environments of STEM, without using its potential leverage for interdisciplinary STEAM development.

3.2. Participants and Data Collection

The data set for this study was collected using an electronic questionnaire tool by means of ‘asking questions’ in an online-based self-completion anonymous questionnaire, Q1–Q15, containing closed questions (see Table 1). The questionnaire targeted new secondary school students who had completed their primary education level. The questionnaire consisted of 15 questions related to three crucial aspects of active learning: general sensor-based knowledge (5 questions), intrinsic relevance (5 questions), and creativity (5 questions). In sensor-based student learning outcomes, four tutors evaluated student achievements, while in creativity and intrinsic relevance factors, students estimated their perceptions by themselves. For each question, both tutors and students responded to a self-referring statement on a slider scale ranging from 1—“definitely disagree” to 100—“definitely agree”. The questionnaire was distributed at the end of each course. The study sample consisted of 379 unique Polish secondary school students, divided into three distinct groups:

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A group of 126 secondary school students who acquired sensor-based knowledge via traditional education pedagogy.

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A group of 125 secondary school students who acquired sensor-based knowledge by means of a STEM active learning approach and hands-on experience.

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A group of 128 secondary school students who acquired sensor-based knowledge using the STEAM interdisciplinary approach.

Table 1. The anonymous questionnaire directed to students and tutors.

General Sensor-Based Knowledge (Directed to Tutors)	Short Name
The student is familiar with basic sensor-based knowledge, including Arduino microprocessors, digital communication, sensors, and actuators.	Q1
The student has no significant difficulty programming the basic electronic parts.	Q2
The student is able to design, test, and modify the electronic circuits with limited supervision and instructions.	Q3
The student is able to transfer knowledge and apply skills across multiple contexts for real-world challenges.	Q4
The student is able to communicate and collaborate clearly on intellectual and emotional levels to share ideas, gain main insights into the problem, and identify solutions effectively.	Q5
Intrinsic relevance (Directed to Students)
The course is interesting in its problem-solving, designing, and programming practices.	Q6
The course let me feel more related to the contents with useful skills and information.	Q7
I learned new things about communication and collaboration with my colleagues.	Q8
I improved my interest in mathematics, science, and technology.	Q9
I improved my appreciation for the arts.	Q10
Creativity (Directed to Students)
I enjoyed learning, while the hands-on work felt automatic and effortless.	Q11
If I get stuck on a problem, I look for clues in my surroundings.	Q12
The course boosted my imagination for potential solutions to a problem.	Q13
Thinking about more than one idea at the same time can lead to a new understanding.	Q14
In this course, I tried to generate as many ideas as possible.	Q15

Table 1. The anonymous questionnaire directed to students and tutors.

General Sensor-Based Knowledge (Directed to Tutors)	Short Name
The student is familiar with basic sensor-based knowledge, including Arduino microprocessors, digital communication, sensors, and actuators.	Q1
The student has no significant difficulty programming the basic electronic parts.	Q2
The student is able to design, test, and modify the electronic circuits with limited supervision and instructions.	Q3
The student is able to transfer knowledge and apply skills across multiple contexts for real-world challenges.	Q4
The student is able to communicate and collaborate clearly on intellectual and emotional levels to share ideas, gain main insights into the problem, and identify solutions effectively.	Q5
Intrinsic relevance (Directed to Students)
The course is interesting in its problem-solving, designing, and programming practices.	Q6
The course let me feel more related to the contents with useful skills and information.	Q7
I learned new things about communication and collaboration with my colleagues.	Q8
I improved my interest in mathematics, science, and technology.	Q9
I improved my appreciation for the arts.	Q10
Creativity (Directed to Students)
I enjoyed learning, while the hands-on work felt automatic and effortless.	Q11
If I get stuck on a problem, I look for clues in my surroundings.	Q12
The course boosted my imagination for potential solutions to a problem.	Q13
Thinking about more than one idea at the same time can lead to a new understanding.	Q14
In this course, I tried to generate as many ideas as possible.	Q15

All 379 secondary school students voluntarily completed the questionnaire, which focused on their perception of creativity and intrinsic relevance in different sensor-based engineering courses. It should be noted that the study sample contained 379 unique secondary school students. That is, the students who finished the traditional sensor-based course could not sign in to participate in STEM and STEAM courses, and vice versa.

3.3. Design and Procedure

For quantitative analysis, firstly, descriptive statistics were used; however, to reveal the crucial differences between groups of secondary school students in sensor-based learning outcomes, creativity, and intrinsic relevance in traditional STEM and STEAM engineering courses, clustering analysis was carefully applied [81]. Regarding questions related to students’ learning outcomes (Q1–Q5), to create the questionnaire, the authors used general sensor-based knowledge, including the Arduino ecosystem, programming and electronics fundamentals, libraries, and communication features. Moreover, the questions assessed whether secondary school students possessed the ability to think critically and logically, to clearly and concisely identify the most important elements of a problem, to develop possible solutions, and to apply new crucial sensor-based knowledge in practical and versatile real-world applications.

For the intrinsic relevance evaluation, the ARCS model of learning motivation was used and carefully modified in Q6–Q10 [82]. The ARCS model includes four factors that could effectively help to enhance students’ learning motivations and interests, namely “attention”, “relevance”, “confidence”, and “satisfaction.” The ARCS motivation model has been widely applied in the literature for a variety of quantitative evaluation works [83,84,85,86,87]. Nevertheless, previous studies mainly used the ARCS model to reveal the key factors in the learning motivations of students or the relationship between factors. The presented research only highlighted relevance as a key factor to be assessed. According to the relevance factor, a sensor-based course and its learning topics aim to enhance students’ interest in problem-solving, designing, and programming, making students immerse themselves in learning activities, especially in mathematics, science, technology, and the arts. Learning topics can help cultivate self-learning capabilities and enhance pleasant learning experiences related to the course contents with useful skills and information. Moreover, the relevance aspect was designed for this research questionnaire in order to evaluate students’ self-esteem in communication and collaboration skills and overall interest in sensor-based engineering topics.

Assessing creativity has been widely discussed for decades, particularly with regard to the number of factors required in such assessments. With respect to creativity assessments, the authors used the CPAC (cognitive processes associated with creativity) scale in Q11–Q15 [88]. The shorter CPAC scale is suitable for assessing particular dimensions of creativity, including idea manipulation, idea generation, flow, imagery/sensory perception, and metaphorical/analogical thinking. The CPAC scale is widely used in the literature to evaluate students’ creative and innovative thinking skills [89,90,91,92]. According to the creativity factor, a sensor-based course aims to improve secondary school students’ enjoyment and satisfaction in learning-by-doing engineering topics. Moreover, it emphasizes the crucial role of creative thinking in collaborative work. The self-reported questions aim to evaluate a student’s openness to experience, ambiguity tolerance, and self-confidence. Some authors insist that the definition of creativity involves sensitivity, flexibility, the ability to analyze, synthesize, evaluate, and reorganize information, and the ability to cope with complexity [93]. The CPAC scale was chosen as it met the requirements of this study for analyzing the creativity of secondary school students and was adapted for research purposes.

4. Results

4.1. Descriptive Statistics

The descriptive statistics are presented in

Table 2. Descriptive statistics broken down by educational mode.

	Sensor-Based Knowledge (Q1–Q5)	Intrinsic Relevance (Q6–Q10)	Creativity (Q11–Q15)
Traditional course
Mean	22.59	29.19	23.23
Std. Dev	17.08	16.74	18.65
Skewness	2.19	1.71	1.55
Kurtosis	5.37	3.04	1.74
STEM course
Mean	58.34	53.80	49.43
Std. Dev	12.15	13.59	12.52
Skewness	1.13	0.80	0.13
Kurtosis	1.45	1.48	0.34
STEAM course
Mean	75.10	86.09	77.93
Std. Dev	9.82	9.13	13.78
Skewness	−0.46	−0.89	−1.58
Kurtosis	−0.14	2.98	5.27

. The table includes three learning modes: traditional, STEM-based, and STEAM-based. For each educational mode, the mean, standard deviation, skewness, and kurtosis of the students’ answers and tutor estimations were calculated. The authors displayed descriptive statistics according to the educational mode without dividing the mode into particular questions. For the sake of simplicity, clarity, and integrity, statistical criteria were calculated for the educational mode to emphasize the crucial role of active learning methods and significant differences compared to the traditional one.

To avoid the appearance of anomalies in the questionnaire that could lead to confusion from subjective answers by secondary school students or tutors’ expertise, the authors use average values for the particular education mode. External factors like mood, behavior, tiredness, thermal comfort, mental agility, and the respondent’s self-perception could also influence the completeness and sufficiency of the questionnaire. Moreover, the authors acknowledge the possibility of inconsistencies in specific educational modes, which could lead to misleading and biased results and blur the overall context of the research. Overall, the authors aim to shed more light on the educational mode than on the particular questions contained.

The analysis imposes a non-normal data distribution when skewness and kurtosis are, respectively, out of the range of ±1 and ±3. Therefore, the normality assumption does not matter and is unimportant in the presented case study [94]. The normality assumption is particularly important in statistical analysis. In practice, the violation of this assumption can lead to biased, unreliable, and inaccurate results. Some statistical treatments deal with the violation of the normality assumption. One of the most common ways is to apply transformations to the data (logarithmic or square root). Another way is to use non-parametric methods that do not assume any particular distribution of the data. Finally, the outlier detection and removal procedure should be carefully applied. Outliers can significantly blur the normality of the data. Therefore, clustering validation analysis, particularly using majority-based decision fusion methods, has been chosen as the optimal and efficacious tool to lead in quantitative analysis.

The analysis of the overall questionnaire in all three educational modes revealed the highest mean score of 86.09 within the STEAM sensor-based active learning courses in the intrinsic relevance factor. The lowest overall mean score within the particular educational mode is identified in the traditional teaching/learning mode with respect to the sensor-based engineering knowledge of secondary school students in out-of-school extra-curriculum settings (22.59).

With respect to the educational mode, the pairwise analysis of the mean scores identified the dominance of the STEAM active learning method over the STEM and traditional forms of education in all factors, including learning outcomes, intrinsic relevance, and creativity. The biggest difference in mean scores (56.9) is noted in favor of the STEAM active learning method compared to the traditional one toward the intrinsic relevance factor, while the smallest (16.76) is in favor of the STEAM approach compared to STEM active learning in factors dedicated to students’ general engineering learning outcomes.

Within the traditional educational mode, the biggest difference in mean scores (6.6) is revealed between intrinsic relevance and general sensor-based knowledge factors, in favor of the second one, while the lowest (0.64) is between learning outcomes and creativity factors. The notable difference in mean scores in STEM education courses could be observed between sensor-based student outcomes and creativity (8.91), in favor of the first factor. Finally, within the STEAM form of active education, a significant difference in mean scores is shown between sensor-based knowledge and relevance (10.99), while the lowest values are between students’ knowledge and creativity (2.83), in favor of the first factor.

To summarize, the descriptive analysis shows significant differences between the mean scores toward active learning educational modes. The mean scores of all estimated factors, including general sensor-based knowledge, intrinsic relevance, and creativity, are considerably increased in favor of active learning pedagogy. Within active learning methods, STEAM-based engineering courses exhibit higher mean scores in all estimated factors.

In order to verify the reliability of the questionnaire presented in this research and to estimate the internal consistency of the factors, the Cronbach’s alpha test is used. The degree of internal consistency is represented by the reliability coefficient (Cronbach’s alpha). The reliability analysis shows that Cronbach’s alpha is 0.61, indicating the acceptable degree of internal consistency of the presented questionnaire [95]. Additionally, an intraclass correlation coefficient is used to determine if answers to the questions can be rated reliably by different raters (students and tutors). The value of an intraclass correlation coefficient is 0.78, indicating that three factors of the questionnaire can be rated with “good” reliability by different raters [96].

The descriptive analysis provides the reader with a basic foundation and essential insights and gives a potential starting point for deeper and more sophisticated data analysis. Therefore, for further comprehensive research, data clustering validation analysis is applied.

4.2. Clustering Validation Analysis

The essence of cluster analysis assumes that little or nothing is known about the grouping structure that underlies the data set. The operational objective, in this case, is to discover a data grouping structure that is frequently stated as the problem of finding natural groups or clusters. The approach to this problem and the results achieved help the investigator choose to give operational and quantitative meaning to the phrases “natural association” and “relatively distinct”. Cluster analysis remains the most relevant and robust tool to gain insight into previously unknown grouping structures and to disclose the intrinsic characteristics of data.

The cluster analysis task may have more than one solution and, thus, is recognized as “ill-posed” [97,98]. For instance, the result of the validation procedure depends on the choice of the data, clustering algorithms, dissimilarity measures, etc. [99]. Applying different clustering algorithms or the same clustering algorithm with varying input parameters on the same given data set can result in diverse partitions and, therefore, may greatly affect the goodness/quality of clustering results [100]. Such issues are related to clustering validation, which is one of the most challenging topics in data mining literature. The main objective of clustering validation is the effective evaluation of the goodness of clustering results. This involves finding not only the “true” number of clusters but also the optimal partition that best fits the underlying grouping structure of the data set.

One common practice in clustering validation procedures is to apply clustering validation indices (CVIs). However, many authors agree that there is no universal CVI that always enables the correct decision to be made. In some research, multicriteria solutions used to reach the best and most adequate results have been commonly used [101,102]. These solutions assume the adoption of several CVIs to achieve greater certainty and correctness in clustering results. For instance, when a group of CVIs takes part in the decision process, their votes, in many cases, disagree. Frequently, the CVIs have different sensitivity domains: some are heavily biased toward particular clustering algorithms and distance-based dissimilarity measures, such as the silhouette CVI; and some are sensitive to outliers, such as the Dunn validation index. Moreover, certain data characteristics, including high dimensionality, noise, types of attributes, and scales, may strongly affect clustering validation analysis [103]. In light of this fact, in the presented research, the authors used majority-based decision fusion clustering validation methods to reveal the “true” number of clusters and to justify the presence of significant differences in all estimated factors toward different educational modes.

The authors applied the combination of two novel decision-making approaches: a non-invasive majority-based decision fusion method and an invasive clustering validation method. These clustering validation methods have been carefully described in previous works [81,104], including the experimental setups, general input settings, and guidelines for benchmarking; the methods’ execution with different data sets were also showcased. The combination itself should easily evaluate the correctness of obtaining the “true” number of clusters and the goodness of the clustering results. Moreover, the majority-based clustering validation methods will help us completely and utterly answer the research questions posed at the beginning of the manuscript. Figure 3 illustrates the simplified validation scheme of a non-invasive majority-based decision fusion method and invasive clustering validation methods.

The result of the CVIs’ voting process aligns with one of the most common scenarios in majority-based decision fusion validation methods. According to previous studies [81,104], almost 99% of input benchmark data sets follow this pattern. This pattern is divided into several clear or controversial scenarios that map the CVIs’ voting process and the production of the final decision.

Scenario 0: The decision is made by the CVIs’ absolute majority. The absolute majority points to the correct “true” number of clusters. This scenario illustrates the consensus between CVIs in final decision-making. Moreover, Scenario 0 does not require additional verification by invasive methods.

Scenario 1a: The decision is made by the relative majority of CVIs, and the nearest alternative (the second largest group of CVIs) has 50% fewer votes than half of the majority. The relative majority points to the correct “true” number of clusters. The situation is clear enough; however, an absolute majority is not obtained as in Scenario 0.

Scenario 1b: The final decision is taken by the CVIs’ relative majority, and the nearest alternative is 50% more votes than half of the majority. The relative majority points to the “true” number of clusters. This scenario shows the controversial situation where there is no clear-cut grouping structure. Scenarios 1a and 1b require additional verification by means of the invasive relative majority decision fusion method.

Scenario 2: The relative majority of CVIs points to the incorrect number of clusters. The nearest alternative group of CVIs, in turn, shows the “true” number of clusters. The most critical of all the previous scenarios, it requires complete and precise verification by means of the invasive relative majority decision fusion method.

Scenario 3: The data sets for which no majority prevails. Two of the largest equal groups of CVIs vote for different numbers of clusters; however, only one group of CVIs makes the “true” decision, and the other is misleading. This scenario requires complete and precise verification by means of the invasive parity majority decision fusion method.

Figure 4 shows the study sample, which consists of 379 data points (without dividing the data into a particular educational mode) in the form of a three-dimensional scatter plot.

To provide significant insights into clustering validation procedures, the clustering operation should first be applied. Figure 5 shows the results of the clustering operation, where three clear-cut globular-form clusters are identified.

Figure 5 illustrates the result of the clustering process. The raw input data set is partitioned into three clusters. The clustering results could be extrapolated to the descriptive statistics, where the critical verdict could be made, namely, the blue cluster corresponds to the traditional educational mode, the green cluster corresponds to the STEM-based approach, and the orange cluster corresponds to the STEAM active learning approach. Even though the clustering algorithm with the dissimilarity measure identifies three clusters, the validation procedure should be applied. To verify the quality of clustering results and to justify that three is the “true” number of clusters, majority-based decision fusion methods are performed. The validation results of majority-based decision fusion methods with 24 CVIs engaged in the voting process are shown in

Table 3. The validation results of the 24 CVIs engaged in the voting process using the majority-based decision fusion methods.

		The Best Number of Clusters Based on the Critical Values of the CVIs
No	Name of the CVI	Three Clusters	Two Clusters	One Cluster
1.	Calinski–Harabasz	10.18
2.	Krzanowski and Lai	689.74
3.	Hatigan	323.57
4.	Cubic Clustering Criterion		24.54
5.	Scott	562.30
6.	Marriot	1.25 × 1015
7.	TrCovW			8.6 × 108
8.	TraceW	134,135.90
9.	Friedman	23.72
10.	Rubin	−8.91
11.	C index			0.17
12.	Davies and Bouldin		0.63
13.	Silhouette		0.60
14.	Duda	0.79
15.	PseudoT2	38.61
16.	Beale		2.01
17.	Ratkowsky		0.53
18.	Ball	102,570.40
19.	PtBiserial		0.81
20.	Frey		2.77
21.	McClain		0.23
22.	Dunn		0.12
23.	SDindex	0.08
24.	SDbw	0.29

. Critical values of CVIs are used to select the best number of clusters. This set of 24 CVIs has been chosen from the literature [105].

The majority-based decision fusion method with a non-invasive configuration reveals the absolute majority (13 CVIs) voted for three clusters to be the “true” ones. This falls into Scenario 0, and, therefore, it is not necessary to validate the results by means of the invasive relative majority decision fusion method. The second-largest group (9 CVIs) voted for two clusters, while only 2 CVIs voted for one cluster to be the “true” one. To summarize, the clustering algorithm identified three clusters, and the majority-based decision fusion method confirmed and justified this number of clusters. Moreover, the research confirms the crucial and significant differences between traditional and active learning modes. However, a moderate difference between STEM and STEAM approaches could be observed. The presence of arts in STEAM pedagogy enhances and boosts students’ general sensor-based knowledge, intrinsic relevance, and creativity more than a STEM-based approach in extracurricular learning-by-doing engineering courses in secondary school settings.

4.3. Visual Validation Analysis

Majority-based decision fusion methods clearly identify and justify three clusters as “true”. Nevertheless, for transparency reasons, the authors have attempted to analyze the clustering results using other validation concepts by means of visual clustering assessment tools.

Cluster analysis is an unsupervised and often exploratory issue without fixed, predefined expectations from the expert. Patterns in the data set that qualify to be interpreted as clusters could have very manifold shapes, configurations, and appearances. Therefore, in clustering validation assessment, there is room for the concept of visual analysis. Visible patterns in the data set may be identified as clusters. Effective plots for visual cluster validation include scatterplots, multidimensional plots, parallel coordinate plots, etc., in which the revealed clusters can be indicated by colors or shades, contour maps, dendrograms, and silhouette plots. Another broad category of visual validation methods is the visual assessment of tendency (VAT) family of algorithms, which reorders the pairwise dissimilarity matrix and then generates a cluster heat map that shows possible clusters in the data as dark blocks along the diagonal [106]. Moreover, the iVAT algorithm is an improved version of the VAT algorithm that more clearly shows the number of clusters, as well as their sizes [107]. The gap statistic can also be classified as a visual validation method. The basic idea of the gap statistics is to choose the number of clusters where the largest “jump” in within-cluster distance occurs.

Visual clustering validation methods should be used as informal graphical illustrations, as a rule of thumb. Moreover, to begin with, such methods should be used with great caution since the visual representations of clusters may significantly vary with the nature of the parameter being tuned (dissimilarity measure, clustering algorithm, etc.) and the validation indices used. Nevertheless, the visual validation concept remains crucial and valuable for cluster validation assessment. The presented visual clustering validation methods are illustrated in Figure 6.

Figure 6 clearly shows that the visual methods reveal three “true” clusters. VAT and iVAT algorithms show the number of clusters, the visual sizes of clusters, and the distances among them. Therefore, Figure 6b,d display two clusters—near each other and far from the third. Nevertheless, the number of separate “true” clusters remains at three. This only justifies the veracity of clustering validation results presented by the majority-based decision fusion methods. The concluding statement is that there are significant differences between traditional, STEM, and STEAM educational modes in sensor-based engineering out-of-school courses in secondary school settings.

5. Discussion and Conclusions

The research study applied in this article discusses the possible differences in educational modes in out-of-school sensor-based engineering courses in secondary settings. Significant differences in students’ general knowledge, creativity, and intrinsic relevance could be observed between traditional pedagogy and active learning methods. With respect to the first research question, STEM and STEAM active learning approaches highly increase students’ learning sensor-based outcomes, boost their creativity, and develop intrinsic relevance toward hard scientific and technological topics. Descriptive statistics and clustering validation analysis quantify the revealed differences and justify the presence of an educational gap between these learning methods.

The results of the presented research are in line with multiple studies provided worldwide. The authors confirm that an active learning STEM-based curriculum significantly impacted the development of students’ creative thinking compared to students who studied under a traditional curriculum method [108]. Others assume that active learning methods may contribute to the development of creativity in young people [109]. Moreover, active learning practices significantly influence the development of innovative thinking among students [110]. The researchers found that students engaged in active learning lessons outperformed expectations in terms of learning outcomes when compared to students in traditional classrooms. Moreover, research has supported the role of active learning as a superior approach compared to traditional pedagogy [111]. With respect to intrinsic relevance, students studying in active learning classrooms had significantly higher motivation and attitudes toward learning than students studying in traditional classroom layouts [112].

Active learning approaches and methods are popular in 21st-century student-centered education. Nowadays, active learning education is robust, flexible, and effective enough to outperform traditional education in all school subjects and fields of education. Nevertheless, questions arise within the context of active learning methods. Do the arts in STEAM active learning education influence students’ knowledge, creativity, and intrinsic relevance, especially in sensor-based learning-by-doing engineering topics? The results confirm the moderate difference between STEM and STEAM-based active learning approaches in students’ learning outcomes, creativity, and intrinsic relevance. Clustering validation analysis has clearly highlighted that the multidimensional representation of the arts added to STEM education could boost students’ achievements, perceptions of modern sensors, and application prospects of hard engineering topics. This is consistent with previous research, which reached similar conclusions. The arts contribute to promoting student satisfaction, interest, and different levels of artistic literacy. It becomes particularly important when students are faced with sophisticated and complex tasks [113]. Various authors have expressed the advantages of the arts in generating a favorable classroom climate for the development of student creativity [114,115]. “Art and engineering integration is a process taking place before our eyes, in a dynamically changing reality” [116]. Another statement declares that engineering education is being dubbed the new liberal arts degree for the 21st century [117]. STEAM education has broadened the STEM approach by incorporating the arts, fostering interdisciplinary collaboration, and providing students with a more holistic understanding of problems and their solutions [118]. Anne Pirrie claims the following: “Reconceptualising the interrelationship between sciences and the arts has the potential to enrich our understanding of science, revitalise our teaching and make us open to new ways to respond to environmental challenges” [119]. Finally, the presented results justify the statement: “Engineering education should be re-imagined by making the arts an essential part of the engineering curriculum to develop reflective engineers who are willing and able to navigate the “swampy lowlands” of engineering practice” [120].

To summarize, the STEAM approach has been widely generative in creating new and creative pedagogical and instrumental practices in the fields of the arts and STEM learning, particularly around new media and ICT technology. Its goal is to bridge learning between (inter-) and beyond (trans-) disciplines. Within the evolving field of sensor-based education, secondary school students have connected their engineering knowledge with basic artistic skills through the STEAM learning approach in their final smart house project, which equipped them to better “see” their ideas. This study revealed an emphasis on developing STEAM-related disciplinary knowledge in sensor-based engineering education, with a notable emphasis on the arts. Active learning approaches not only empower students’ hard skills but also improve soft skills such as creative and abstract thinking, problem-solving, and intrinsic motivation in learning. Moreover, they foster true innovation that combines the mind of a scientist, the practical knowledge of a technologist, the critical thinking of a mathematician, and the elegance of an artist or designer.

There is room to extend this work by including more dimensions of the arts, exploring the intersections with non-STEM fields, and deepening the understanding of the arts’ influence on students’ learning outcomes. In this context, motivation and self-efficacy aspects would appear to be the most interesting factors to analyze in greater depth. Moreover, broader research should be undertaken involving a larger sample of secondary school students and on a larger scale.