1 Introduction

We live in a world where technologies continue to develop at a rapid pace, dynamically changing our way of life with each passing day. The progressive increase in production, the demand for services, and the need to achieve a balance between quality and economic benefit find a solution in the advantages offered by 3D printing technology. The printing process is done in layers, as thinly sliced horizontal sections are layered on top of each other. Various printing technologies can be applied in the object design process with the usage of a wide variety of materials [1].

The additive process of the three-dimensional printing technology is fundamentally opposite to the traditional manufacturing, which is subtractive, involving cutting away a block of material to produce the desired object [2]. Special tools and equipment are not required during the three-dimensional printing process, apart from the presence of a 3D printer [3]. Therefore, the initial setup costs are low, and moreover, the types of materials that can be used in production are numerous and vary depending on the 3D printing technology—plastics, resins, rubber, metals, sand/ceramics, alloys, etc. Thanks to these advantages, 3D printing is widely used in various fields for prototype development, contributing to the integration of new technologies during the manufacturing process [4].

The development of 3D printers began in the 1980s, with the advent of FDM (Fused Deposition Modeling), as one of the first additive manufacturing technologies. It is a 3D printing technology that operates on the principle of material extrusion, using thermoplastic filaments to build strong, durable, and dimensionally stable parts with the highest precision and repeatability. Three-dimensional printing has reached a stage where it can be used for the production of detailed and high-quality objects [5]. Also 3D printing is a valuable tool for problem-solving and a key competency for the future workforce. Integrating this technology into educational courses enables learners to create their own 3D models, use the necessary equipment, and conduct research on their own printed objects. It provides an opportunity to relate education to the real work environment that happens at the design and manufacturing companies, where the application of 3D printing technology becomes an inseverable part of the product design and visualization processes.

In recent years, there has been a rapid development in technologies, with education focused on the close connection and interrelation between many different disciplines in the learning process. From this perspective, 3D technologies are emerging as an important element in the key competencies development among learners. The article presents an analyzation process of the application of 3D modeling in STEAM (Science, Technology, Engineering, Arts, and Mathematics) learning approach, with a sequential execution of the following three phases of the research, titled “3D Technologies in STEAM Education”:

  1. 1.

    Preparation for designing a 3D model by the teacher and analysis of process difficulties, encountered in the object usage in workplace;

  2. 2.

    Giving students and lecturers the opportunity to perform a 3D modeling task;

  3. 3.

    Questionnaire to analyze and evaluate the skills and knowledge of the participants in the field of 3D modeling.

Before we conducted the research, focused on the integration of 3D technologies in STEAM education, a 3D steam locomotive model was designed, using Autodesk 3ds Max. The creation process of the complex object is examined in detail, and the FDM technology is presented as one of the most widely used 3D printing technologies. The research aims to assess the skills and competencies of the participants in the 3D modeling field by challenging them to perform a simple task, using unfamiliar 3D modeling software, within a limited time. The participants were assigned a 3D modeling task for creating a steam locomotive object, using basic primitives from solid geometry with the help of Blender, as free 3D modeling software. In this way, 3D technologies reveal opportunities for their integration in real workplace with application of the designed objects in various fields, during prototype development, and the specific technologies also contribute to the usage of new methods in the production process [6]. In educational environments, learners can be acquainted with the 3D modeling and 3D printing technologies and experiment with printing more complex models through the STEAM approach [7].

2 Materials and methods

2.1 3D model creation process

In order to print a specific three-dimensional object, it is necessary to create the model with the help of 3D modeling software [8]. The process involves creating a computer-generated representation of a three-dimensional object or shape through 3D computer graphics software. The designed object is called a 3D model, and these three-dimensional models are used in various industries such as film, television, video games, architecture, construction, product development, science, medicine, etc. The application of 3D modeling encompasses visualization, simulation, and rendering of objects. Some well-known programs for 3D modeling are Autodesk 3ds Max, Blender, ZBrush, while specialized software in the field of industrial and product design includes Autodesk 123D Design, Autodesk Inventor, and Autodesk Fusion 360.

The realization of a three-dimensional product in a printed object form involves several distinct stages, chronologically organized as follows:

  1. 1.

    Conceptual design and study of product characteristics;

  2. 2.

    Design the 3D model, using three-dimensional modeling software;

  3. 3.

    Export the model as a .stl file;

  4. 4.

    Research on 3D printing technologies;

  5. 5.

    Import the .stl model into slicing software and determine the necessary printing settings of the 3D printer, as well as the available printing material, based on the selected technology;

  6. 6.

    Slice the model with the help of slicing software and review the layers;

  7. 7.

    Generate G-code, which is transmitted to the printer by the slicing software. The G-code translates the CAD language of the project into a code, recognizable by all 3D printers;

  8. 8.

    Application of the printed object.

Before we carried out the research, we decided to create a three-dimensional model of a steam locomotive for educational purposes as part of the preparation process, using Autodesk 3ds Max. The steam locomotive object is a combination of various locomotive models, which ensures its uniqueness. Prior to starting the object construction, references of different locomotives were prepared, and a study of the model’s components was done to achieve an accurate visualization of the object in the three-dimensional space. Modeling can begin from any side of the object, but a standard primitive should be selected as a base. In the steam locomotive project, the process started with the body of the model, for which the Cylinder primitive was chosen, as the closest object in the program that resembles this component. Then the 3D object was converted into an Editable Poly, and various modifiers, tools, and functionalities were used during the modeling process in accordance with the individual elements manipulation [9]. While designing the 3D steam locomotive model, manipulation of the object from different viewports in the three-dimensional space was done in order to achieve the correct visualization of the object, as shown in Fig. 1.

Fig. 1
figure 1

Steam locomotive 3D modeling project, Autodesk 3ds Max

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After designing the 3D object in a digital environment, using 3D modeling software, the steam locomotive model was exported as a .stl file, so that it can be used in the next 3D printing stage. The extension name itself is an acronym that stands for stereolithography, a popular 3D printing technology.

Before we moved on to the slicing stage of the object, a study was conducted on the 3D printing technologies for the general purpose of this research. Nowadays, one of the most widely used 3D printing technologies is FDM (Fused Deposition Modeling), which is based on the principle of material extrusion. Specialized 3D printers and thermoplastic filaments are used to build strong, durable, and dimensionally stable parts with the best accuracy and repeatability, compared to other 3D printing technologies. FDM technology was invented and patented by Scott Crump, the founder of Stratasys, in 1989, and since then, Stratasys has been leading the revolution in 3D printing [10]. 3D printers create objects by heating and extruding the thermoplastic filament layer by layer, from the base upwards. The slicing software divides the CAD model into layers, after that the 3D printer heats the thermoplastic materials above the melting point and extrudes them through the nozzle in the printing area, along the calculated path, as shown in Fig. 2. The printer converts the dimensions of the given object, loaded from the computer into X, Y, and Z coordinates, and prints it along the calculated path. When each individual layer is completed, the base is lowered (or the nozzle is lifted) in order to start building the next layer. The FDM technology allows usage of a variety of filaments, such as PLA, ABS, PVA, and FLEX, enabling the creation of complex geometries and details of the three-dimensional object, which are typically challenging areas [11].

Fig. 2
figure 2

Fused deposition modeling (FDM)

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We continued with the stage of importing the model into the slicing software. The slicing process of the 3D object effectively translates the 3D image into a code, understandable by the printer. The software creates paths for the 3D printer to follow during the printing process. One of the widely used slicing software is Ultimaker Cura, which has the ability to establish a connection between the 3D model and the 3D printer [12]. The printing strategy is developed for the model, and in addition to the default parameters, specific settings for fast printing with optimized printing profiles can be set. Among the commonly used settings are determining the printing strategy, the overall strength of the model, automatically generated support structures with the available extruders in order to achieve reliable and successful prints, setting adhesion type, etc. Once the printer type, configuration, and printing settings are reviewed, the model is sliced into layers. When the slicing process of the model is completed, a preview of the print can be seen with the layer slider and the simulation view, which are used in order to check important elements of the 3D printed fragment structure.

The overall build process of the steam locomotive printed object, including the stages of modeling in Autodesk 3ds Max software, exporting as a .stl file, importing the file into Ultimaker Cura slicing software, forming the layers and generating support structures, and visualizing the print, is demonstrated step by step in Fig. 3.

Fig. 3
figure 3

Steam locomotive 3D printed project process

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The slicing software generates the G-code that is sent to the connected 3D printer. Therefore, the 3D printer reads the paths, provided by the software, in order to execute the printing process correctly. These paths consist of geometric instructions, as well as of instructions for the print speed and temperature analysis. The firmware is the software that controls the motors and heaters, and processes the motion and control commands from an online software and G-code [13]. Loaded onto the microprocessor board of the 3D printer and stored within the device, it controls the motors, the display screen, the brightness of the lights, and the temperatures of the hot end, during the 3D printing process. Marlin Firmware is well-known firmware for 3D printing that provides excellent print quality and full control over the whole process, as it coordinates the heaters, steppers, sensors, lights, LCD display, buttons, etc.

The presented project has a wide field of development in the STEAM education, based on the idea of focused learning across five disciplines—science, technology, engineering, arts, and mathematics, in an interdisciplinary and applied approach [14]. Projects and programs can be created with the idea of integrating academic subjects, such as mathematics, computer graphics, and physics. In this case, the goal of the transdisciplinary level of integration is to demonstrate to students the interaction between the three disciplines through topics related to the study of mathematical models in the field of solid geometry and their wide application in 3D computer graphics, with the execution of a real task for creating a three-dimensional model of a steam locomotive, and studying the functionalities of its individual components [15]. By integrating STEAM activities into academic domains, students are given an opportunity to develop skills necessary for their adaptation in the dynamically evolving technological environment, such as creative thinking, critical analysis, teamwork, and initiative, which provide them with a solid foundation for success, both in school and in real life [16,17,18].

3D printing becomes a valuable technology, not only for achieving faster production with minimal costs and high quality, but also for problem-solving and acquiring a key competence for the future workforce. From this perspective, integrating the technology into training courses allows learners to create 3D models, use the necessary equipment, and do research on their own printed objects [19]. It reveals an opportunity to combine education with the real work environment that takes place within design and manufacturing companies, where the usage of 3D printing technology becomes an inseverable part of designing and visualizing specific products in the workflow [20]. Figure 4 shows the 3D printed object of a steam locomotive. The idea is to be applied in the creation of a comprehensive railway modeling project, with additional components, such as a tender, wagons, railway stations, tracks, mountain landscapes, and other elements that recreate the appearance of railway layouts. Therefore, the project is suitable for both children and enthusiasts, and the created models can be printed in an economical and innovative way, using 3D printing technology [21].

Fig. 4
figure 4

Steam locomotive 3D printed project, ABS

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In the context of STEAM education, there can be done an in-depth study of the build process of a steam locomotive printed object, along with the stages of creating the model and working with the necessary software for 3D modeling and slicing, examining the characteristics of material extrusion technology, conducting a comparative analysis of the advantages and disadvantages of the technology, experimenting with printing more complex and detailed models, etc.

2.2 Research “3D technologies in STEAM education”

In February 2023, the scientific research “3D Technologies in STEAM Education” was carried out with a 3D modeling task to be performed and a questionnaire to be completed by the involved participants. The target audience of the study included students and lecturers from the Faculty of Mathematics and Informatics at the Paisii Hilendarski University of Plovdiv, as well as students and teachers from the Academician Kiril Popov High School of Mathematics in Plovdiv, Bulgaria.

The conducted research has a scientific purpose to highlight the importance of the integration of 3D technologies in STEAM education. The study is based on the idea of providing focused learning across five disciplines—science, technology, engineering, arts, and mathematics, and its objectives could be summarized as follows:

  1. 1.

    Giving participants to perform a task to design a 3D model of a steam locomotive, using basic primitives from solid geometry with Blender, as unfamiliar 3D modeling software;

  2. 2.

    Assessment of participants’ skills and competencies in the field of 3D modeling through a questionnaire to analyze their knowledge and self-assessment of the assigned task.

The participants were challenged to create a three-dimensional model, using previously unfamiliar computer graphics software, within a limited time, by completing the task “Create a 3D steam locomotive model with Blender”. They were provided references of the object and information about the program, as well as guidelines for designing the model. The questionnaire consisted of 23 closed-ended questions, categorized into 7 sections, forming the concept of TPACK (Technological Pedagogical Content Knowledge). Topics in the field of education, science and art, STEAM, and 3D modeling, were covered with the aim to assess the respondents’ knowledge and self-evaluation in the research. The total number of participants who completed the task is 10, while the number of participants who responded to the questionnaire is 115. Male respondents are 31, and female respondents are 84, which indicates a significant difference in the number of participants based on gender, at first glance. However, using the statistical software IBM SPSS Statistics with a conducted Independent-Samples T-test on independent samples with gender, as a dichotomous grouping variable, we concluded that there is no statistically significant difference in the opinions of both groups, regarding individual questions.

3 Results

3.1 Correlation analysis

Through this analysis, we aim to study the correlations between the variables. We compare the correlation coefficients between one or more pairs of variables to establish statistical dependencies between them. For the purposes of the research, we conducted a correlation analysis of the sample data, using IBM SPSS Statistics, as we selected to investigate the presence of relationships between seven questions from the questionnaire [22]. The correlation matrix, shown on Table 1, displays the values for Pearson Correlation and Sig. (2-tailed) for all indicators, for which we looked for relationships. The results showed that 3 pairs of variables have a negative sign – \({X}_{1}, {X}_{6}\); \({X}_{3}, {X}_{5}\) and \({X}_{4}, {X}_{5}\), when determining the correlation relationship between them.

Table 1 Correlation analysis
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In the remaining pairs, the increase in one variable is associated with an increase in the other, based on the positive sign of the coefficient. The absolute value of the coefficient was also taken into account. The greater it is, the stronger the correlation relationship is between the two variables. The highest degree of correlation, based on its absolute value, was observed in the relationship between the variables in the pair \({X}_{3},{ X}_{4}\), where \(\left|{R}\right| = 0.645\). For the rest, we concluded a weak or no degree of dependence, as the following scale was used to determine the degree of correlation relationship:

\(\left|{R}\right| \, \ge \, 0.6\) (strong correlation)

\(0.6> \, \left|{R}\right| \, \ge \, 0.45\) (medium correlation)

\(0.45 > \left|{R}\right| \, \ge \, 0.3\) (weak correlation)

\(0.3 > \left|{R}\right|\) (no correlation)

A significance test for the coefficient was conducted by examining the null and alternative hypotheses, regarding the value of the population coefficient and concerning the correlation relationship between the variables:

\({H}_{0}: \rho = 0 \) (no correlation)

\({H}_{1}: \rho \ne 0\) (significant correlation)

We determined the level of significance as \(\alpha= 0.05\) and searched for statistically significant and statistically non-significant indicators, taking into account the result of \(Sig. \, < \alpha\). The pairs of variables for which the inequality \(Sig. \, < 0.05\) is true, showed statistical significance between them. The remaining indicators were considered statistically non-significant, as we had no basis to reject the null hypothesis \({H}_{0}\). Therefore, they do not have a particularly strong influence in determining the dependencies. Out of all 12 significant variables, in 10 of them, the correlation, besides being significant, could be reduced to a 0.01 level (**) or to a 1% error, as \(Sig. < 0.01\), based on testing the null and alternative hypotheses, regarding the value of the population coefficient \(\rho\).

First of all, after deriving the statistically significant results in descending order according to the degree of correlation, the results showed that variables \({X}_{3}\) and \({X}_{4}\) have the highest degree of correlation between them, as \(\left|{R}\right| = 0.645\), and they are statistically significant in their relationship. Therefore, the surveyed participants strongly agree with the stated opinion, regarding the answer to the questions—“In 3D modeling, I find the application of mathematical models in 3D art: primitives, curves, symmetry, etc.” and “According to me, 3D modeling can be applied in math classes to visualize simple and complex solid geometry objects.”. The respondents perceive the dependencies between mathematical models and the process of 3D modeling and find real integration of three-dimensional modeling in math classes as a key approach to explaining objects in solid geometry.

Second of all, we found that variables \({X}_{6}\) and \({X}_{7}\) are statistically significant, despite having a weak degree of correlation between them due to \(\left|{R}\right| = 0.436\). The given responses to the questions—“In my future work, I will be delighted to integrate 3D modeling tasks into the educational process.” and “In my opinion, education should focus now and in the future on the STEAM approach.”, showed that both opinions are related to each other. We can interpret that in the future education should not only focus on the STEAM approach, but also include the implementation of 3D modeling in the educational process. The same conclusion can be drawn from the relationship between variables \({X}_{4}\) and \({X}_{7}\), concerning the answers to the questions—“According to me, 3D modeling can be applied in math classes to visualize simple and complex solid geometry objects.” and “In my opinion, education should focus now and in the future on the STEAM approach.”.

An interesting aspect for the purposes of the research was also considering the opinions of the participants based on age groups. In the case of Fig. 5, a Clustered Bar diagram is shown with a selected question—“In 3D modeling, I find the application of mathematical models in 3D art: primitives, curves, symmetry, etc.”. The number of surveyed participants in each age group was as follows: 97 (16–21 years old), 6 (22–27 years old), and 12 (28+ years old). The results demonstrated a visibly positive opinion among the respondents, regarding the given question. In all age groups, the dominant responses were “Strongly agree” and “Agree”, indicating that the participants perceive the application of mathematical models in three-dimensional art.

Fig. 5
figure 5

Clustered bar diagram

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The result is further confirmed by examining the correlation between variables \({X}_{1}\) and \({X}_{3}\) in Table 1. We observed a relationship between age and the specific question, where the correlation, although with a coefficient value of \(\left|{R}\right| = 0.245\), showed statistical significance, based on the value of \({Sig.} = 0.008\), satisfying the condition \(Sig. < \alpha\).

3.2 Cluster analysis

Cluster analysis is a concept in computer science and mathematical modeling that refers to the grouping of a diverse set of objects in such a way that objects within the same group (cluster) are more similar to each other (based on a given attribute) compared to objects in other clusters. For the purposes of the study, we conducted several types of cluster analysis on the data from the sample, using IBM SPSS Statistics:

  • Hierarchical cluster analysis;

  • K-means cluster analysis;

  • Two-step cluster analysis.

We decided to examine the presence of dependencies and perform data grouping, based on similarity, among the selected seven questions from the administered questionnaire.

3.2.1 Hierarchical cluster analysis

At the core of the hierarchical cluster analysis lies the process of constructing and analyzing a dendrogram. It is a tree-like structure that explains the relationship between all data points in the system. In the dendrogram, the horizontal axis represents the distance between clusters in a specific metric. With each successive descent further to the left along the branches of the dendrogram, clusters are divided into smaller and smaller units until the level of detail reaches the individual data points. Conversely, when moving to the right at each level, smaller clusters are merged into larger ones until the entire data system is formed. Figure 6 displays a dendrogram, created to determine the number of clusters in the sample using Ward’s Method for clustering to create more evenly distributed clusters. Then, the structure is vertically sliced, and all resulting daughter branches formed below the vertical cut represent distinct clusters at the highest level in the system, with the option to increase or decrease the level of detail [23].

Fig. 6
figure 6

Dendrogram

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In this context, the result of the dendrogram is interpreted to identify a reasonable number of clusters, and therefore, the number of clusters is three, as indicated by the position of the red vertical line that determines the distribution of clusters in the sample data.

3.2.2 K-means cluster analysis

In the K-means method, the distance of each data point to the centers of individual clusters is taken into account, and the closest distance determines the membership of the data point to the corresponding cluster. The method requires determining the number of clusters in advance. This information can be derived from the generated dendrogram in Fig. 6, where the number three was chosen as the initial number of clusters. The centers of the clusters will be calculated after all the objects are assigned to a specific cluster, and additional information about the membership of each object to the corresponding cluster, as well as the distance to the cluster centers for each object, will be retained.

The ANOVA table was generated, showing the variance analysis, which is important for determining the extent to which the variables, included in the model, are significant for the differentiation process among the individual clusters. We concluded that all variables are statistically significant because the condition \(Sig.< \alpha\) is satisfied. As a result, there is a difference among the individual clusters for the selected questions and all variables play a key role in the data differentiation, so that each cluster contains similar elements, but the groups themselves differ to a certain extent. Three clusters are formed with elements being distributed as follows—39, 61 and 15. There is also a difference in the mean value among the three clusters and all variables have an influence on the clusters’ formation.

3.2.3 Two-step cluster analysis

The advantages of the Two-Step Cluster Analysis over other cluster analyses are that it provides the option for automatic determination of the number of clusters within the data and the ability to choose between Continuous or Categorical variable types. It is important to determine the “quality” of the formed clusters, i.e., to determine the extent to which individual objects within the cluster are close to each other and how different each cluster is from the others. The average value of “quality” is interpreted as acceptable for well-formed clusters based on the specified formation criteria. The sizes of the generated clusters are as follows: 36, 58, and 21 for each specific cluster, and these values are at some extent similar to those generated by the K-means cluster analysis. Taking into account the information about the significance of individual questions from the conducted two-step cluster analysis, we could draw the conclusion that age has the greatest influence in the cluster formation, followed by the other questions, as shown in Table 2.

Table 2 Predictor importance (Pr. Imp.)
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The integration of 3D technologies in STEAM education, specifically 3D modeling and 3D printing, aligns well with the Technological Pedagogical Content Knowledge framework, emphasizing the interconnected nature of Technological Knowledge (TK), Pedagogical Knowledge (PK), and Content Knowledge (CK). Therefore, we have used TPACK theoretical framework to construct the study’s questionnaire, which encompassed 23 closed-ended questions categorized into seven sections. It covered various topics related to education, science, art, STEAM, and 3D modeling, with the aim of assessing the respondents’ knowledge and self-evaluation in the research. TPACK played an essential part in the creation of the questions, addressed to the partcipants, as it revealed the interconnectivity between technology, pedagogy and content knowledge with focus on key features as hardware and software, digital literacy, instructional strategies, assessment techniques, subject integration, curriculum alignment, effective integration, adaptability, digital content creation, content enhancement, content delivery, and problem-solving approaches.

4 Conclusion

The importance of this paper lies in its focus on the role of integrating three-dimensional technologies in STEAM education. By conducting a scientific research, we presented 3D modeling and 3D printing as an innovative approach in achieving an interdisciplinary learning model. The study included the following stages: preparation for designing a detailed 3D steam locomotive model; analysis of process difficulties; giving students and lecturers the opportunity to perform a specific modeling task, using basic primitives from solid geometry, and a questionnaire to analyze and assess the skills and knowledge of the participants in the 3D modeling field.

The article discusses step-by-step the entire process of a 3D steam locomotive model creation for educational purposes, using Autodesk 3ds Max, as professional computer graphics software, and presents FDM technology, as one of the most widely used 3D printing technologies nowadays. The aim of the research is to challenge participants to complete a non-complex object modeling design task, using unfamiliar software for 3D modeling Blender, within a limited time.

Questionnaire’s content is related to the concept of TPACK (Technological Pedagogical Content Knowledge), covering topics in the field of education, science, art, STEAM, and 3D modeling, and focusing on the self-assessment by the involved participants. Data from the conducted research were analyzed, using the statistical software IBM SPSS Statistics, and the results showed that participants find a close connection between mathematical models and the process of 3D modeling with real integration of three-dimensional modeling in math classes as a key approach to explaining objects in solid geometry. Moreover, education should not only focus on the STEAM approach, but also include the integration of 3D modeling in the learning process.

In this way, in educational environments, learners will become acquainted with 3D modeling and 3D printing technologies and experiment with printing more complex and detailed models through the STEAM approach, with the aim to develop key knowledge and skills through an interdisciplinary learning model. Modeling and printing as 3D technologies offer possibilities for their integration into a real work environment, with prospects for applying the created object prototypes in various fields during model development. The specific technologies contribute to the implementation of new methods during the production process. Prospects for future development of the presented project include experimenting with model printing using different 3D printing technologies and materials, as well as conducting a comparative analysis of the obtained results.