Pre-Service Physics Teachers’ Perceptions of Interdisciplinary Teaching: Confidence, Challenges, and Institutional Influences

Abstract

Interdisciplinary teaching plays an important role in modern physics education by improving students’ understanding, problem-solving skills, and engagement through the integration of multiple disciplines. This study examines pre-service physics teachers’ perceptions of interdisciplinary teaching, focusing on their confidence in implementing interdisciplinary approaches, perceived benefits, and the challenges they expect. A Likert-scale survey was administered to 292 pre-service teachers from two universities in Kazakhstan. Findings indicate that students’ confidence in interdisciplinary teaching increases over time, while their recognition of its benefits remains consistently high across all academic years. However, barriers such as lack of training and feeling unprepared persist, even at the master’s level, indicating the need for structured interdisciplinary training. Institutional differences significantly impact students’ perceptions, with students from one university showing higher confidence levels than those from another, showing variations in curriculum and support systems. Gender differences in confidence were minimal. Additionally, perceptions of interdisciplinary teaching do not follow a linear trajectory, as students in their second and third years experienced a temporary decline in confidence before recovering in later years. Our findings indicate the need for structured interdisciplinary training in teacher education programs, institutional support to reduce disparities in confidence levels, targeted interventions during academic transitions, and ongoing professional development to address persistent barriers.

1. Introduction

In today’s rapidly evolving educational developments, the integration of interdisciplinary communication within education has become increasingly important. By bridging the relationships between sciences, interdisciplinary dialogue displays real-world applications and shapes critical thinking and problem-solving skills (Winowiecki et al., 2011).

Interdisciplinary communication in science education is essential for improving a comprehensive understanding of the natural world. Physics, as a fundamental science, intersects with many disciplines such as mathematics, biology, chemistry, and philosophy (Orazov et al., 2025). Integrating these disciplines can help students develop a broader scientific worldview and improve their problem-solving skills (Dyachenko et al., 2024). Research suggests that interdisciplinary approaches in physics education lead to improved conceptual understanding and retention of knowledge (Czerniak & Johnson, 2014).

Understanding the perspectives of future physics teachers on interdisciplinary communication is important for improving physics education. Studies have shown that interdisciplinary teaching increases student engagement, raises deeper understanding, and improves problem-solving abilities (Munier & Merle, 2009; Papaioannou et al., 2019). Moreover, interdisciplinary approaches align with 21st-century educational frameworks that point out cross-disciplinary learning and critical thinking (Yager et al., 1981).

Despite the growing emphasis on interdisciplinary approaches in education, particularly in STEM fields, there remains a notable gap in understanding how future physics teachers perceive and engage with these methods. Scientifically, this study contributes to the body of knowledge by examining how interdisciplinary teaching intersects with teacher development, curriculum design, and instructional confidence. From a practical perspective, understanding pre-service teachers’ perceptions is essential (Berkheimer & Lott, 1984; McIntosh & Zeidler, 1988; Tsakeni, 2023), as their beliefs and self-efficacy strongly influence classroom implementation (Kozhabekova et al., 2024; Laius & Presmann, 2024). However, without adequate training and institutional support, future teachers may struggle to translate theoretical benefits into practical applications.

This study aims to investigate how pre-service physics teachers perceive interdisciplinary communication, their confidence in implementing it, and the challenges they expect in using it in the classroom.

2. Literature Review

2.1. Theoretical Framework and Key Concepts

Interdisciplinary communication in education refers to the integration of knowledge, methods, and perspectives from multiple disciplines to enhance learning and problem-solving. This approach encourages students to draw connections between different fields, improving a more comprehensive understanding of complex concepts (Karppinen et al., 2013). In physics education, interdisciplinary communication is particularly important as it allows students to apply physics principles in broader scientific and real-world contexts, such as engineering, medicine, and environmental science (Dyachenko et al., 2024).

Several educational theories support the effectiveness of interdisciplinary learning. Constructivism, as proposed by Piaget (1972), says that learners actively construct knowledge by integrating new information with their existing cognitive structures. In interdisciplinary education, constructivist principles enable students to build connections between physics and other disciplines, enhancing their conceptual understanding. Inquiry-Based Learning (Dewey, 1938) further supports interdisciplinary education by increasing active exploration and problem-solving, encouraging students to apply physics principles in different contexts. Socio-cultural theory, developed by Vygotsky (1978), emphasizes the role of social interaction in learning. In interdisciplinary education, collaborative learning experiences allow students to engage with different perspectives, leading to a better understanding of physics concepts (Dreyfus et al., 2014).

Interdisciplinary approaches align with physics education by reinforcing real-world applications and improving higher-order thinking skills. Physics often intersects with fields like mathematics, where algebra and calculus provide essential tools for solving physical problems (Ellermeijer & Heck, 2002). Biology and chemistry are also deeply connected to physics, particularly in areas like biophysics and thermodynamics (Yavoruk, 2022). Additionally, recent advancements in technology and engineering have indicated the need for interdisciplinary physics education, as modern scientific challenges require knowledge from multiple domains (Bao & Koenig, 2019; Bybee & Bonnstetter, 1987; Ngozwana, 2025).

By integrating interdisciplinary communication into physics education, students develop a more holistic scientific worldview. This approach not only improves content knowledge but also increases critical thinking, adaptability, and problem-solving skills, which are essential for success in STEM fields (Bao & Koenig, 2019; Shim & Yoon, 2024; Yermekova et al., 2024). Understanding how interdisciplinary methods can be effectively incorporated into physics curricula is important for preparing future educators to meet the demands of modern science education (Descamps et al., 2020).

Interdisciplinary approaches in physics education help students develop a deeper and more interconnected understanding of scientific concepts. Research shows that linking physics with mathematics allows students to better grasp abstract theories, as mathematical models provide a structural foundation for physical laws (Gleichmann et al., 2025; Sherin, 2001). The connection between physics and biology is particularly evident in fields such as biophysics, where principles of mechanics, thermodynamics, and electromagnetism explain biological phenomena (Yavoruk, 2022). Additionally, integrating philosophical perspectives into physics discussions enables students to engage with the historical and epistemological foundations of scientific knowledge, improving a broader appreciation of the subject (Matthews, 2014).

Studies have shown that interdisciplinary learning improves retention and comprehension, as students are more likely to remember and apply concepts when they see their relevance in multiple domains (Ivanitskaya et al., 2002). The ability to integrate knowledge across disciplines also aligns with real-world problem-solving, where scientific challenges rarely exist in isolation but require a combination of different fields (Dreyfus et al., 2014).

Interdisciplinary education improves critical thinking by encouraging students to analyze problems from multiple perspectives and develop innovative solutions. Inquiry-based and problem-solving approaches, which draw on knowledge from different scientific disciplines, have been shown to improve students’ cognitive flexibility and reasoning abilities (Descamps et al., 2020). For example, incorporating engineering principles into physics coursework allows students to design and test real-world applications, improving their ability to apply theoretical concepts practically (Shaw, 2016).

Research also suggests that interdisciplinary teaching can promote higher-order thinking skills, as students must synthesize information from multiple fields and consider different perspectives when solving complex problems (Spelt et al., 2009). This approach aligns with 21st-century education models, which stress adaptability and creativity as essential competencies for success in STEM careers (Buick, 2016; Bojulaia & Pleasants, 2021).

Interdisciplinary teaching improves student engagement by making physics more relevant and applicable to everyday life. Studies indicate that students are more motivated to learn when they perceive a subject as meaningful and connected to their interests (Ernazarov & Abduqodirov, 2022). For example, integrating environmental science with physics allows students to explore topics like climate change and renewable energy, which are directly related to global challenges and sustainability efforts (Kimori, 2017).

Moreover, interdisciplinary approaches encourage active learning strategies, such as project-based learning and collaborative problem-solving, which have been shown to increase student participation and curiosity (Brassler & Dettmers, 2017). When students see how physics connects to other disciplines, they develop a stronger intrinsic motivation to explore the subject further and apply their knowledge creatively (Bøe et al., 2024).

2.2. Teacher Perceptions of Interdisciplinary Teaching

Research indicates that teachers generally hold positive views toward interdisciplinary teaching, recognizing its potential to increase student engagement and learning outcomes. A study by Laius and Presmann (2024) found that pre-service science teachers valued integrated teaching approaches, stating that such methods could make learning more relevant and engaging for students. Similarly, a meta-analysis by Becker and Park (2011) revealed that teachers believe interdisciplinary strategies can improve deeper understanding and retention of scientific concepts. However, some educators express concerns about the challenges associated with interdisciplinary instruction, including potential difficulties in curriculum alignment and the need for adequate resources to effectively integrate multiple subjects. A study by Brand and Triplett (2012) indicated that while teachers appreciate the benefits of interdisciplinary teaching, they often feel constrained by standardized curricula and testing requirements.

Several factors impact a teacher’s decision to implement interdisciplinary approaches. Educational background plays a significant role, as teachers with different academic training or exposure to multiple disciplines during their education are more inclined to adopt interdisciplinary methods. Laius and Presmann (2024) observed that pre-service teachers with backgrounds in different science subjects were more enthusiastic about integrated teaching. Teachers’ beliefs and attitudes also influence their willingness to adopt interdisciplinary instruction. Educators who prioritize student-centered learning and recognize the interconnectedness of knowledge are more likely to do interdisciplinary methods, as noted by Becker and Park (2011), who found that teachers who value holistic education approaches tend to support interdisciplinary strategies.

A teacher’s confidence and competence significantly influence their willingness to implement new teaching methods. Nadelson et al. (2013) stated that teachers confident in their ability to integrate subjects effectively are more likely to adopt STEM approaches. Institutional support also plays an important role, as supportive school environments that encourage collaboration and provide necessary resources facilitate the adoption of interdisciplinary teaching.

Differences exist between pre-service and in-service teachers regarding interdisciplinary teaching. Pre-service teachers often exhibit enthusiasm for interdisciplinary methods, viewing them as innovative ways to enhance student learning. Laius and Presmann (2024) found that pre-service teachers are generally open to integrated teaching approaches, though they may lack practical experience. In contrast, while recognizing the benefits, practicing teachers may be more cautious due to practical constraints such as time limitations, curriculum demands, and standardized testing pressures.

2.3. Challenges and Barriers to Implementing Interdisciplinary Teaching

A significant obstacle to interdisciplinary teaching is the lack of training and professional development opportunities for educators (Reyes, 2025). Many teachers have not received adequate preparation in interdisciplinary instructional methods during their formal education, leaving them uncertain about how to design and implement interdisciplinary lessons effectively. Research by Summers et al. (2005) found that many teachers felt unprepared to integrate multiple disciplines into their teaching due to a lack of structured training programs. Becker and Park (2011) indicated that professional development initiatives focusing on interdisciplinary approaches could help teachers build confidence and competence in applying these methods. Without proper training, even teachers who recognize the value of interdisciplinary teaching may struggle to incorporate it into their classrooms (Gouvea et al., 2013).

Curriculum restrictions and time constraints also pose significant challenges to interdisciplinary instruction. Standardized curricula often prioritize discipline-specific content, limiting opportunities for integrating knowledge across subjects. Teachers must adhere to rigid course structures and standardized testing requirements, which can leave little room for creative, interdisciplinary lesson planning (Bhatnagar, 2018; Laius & Presmann, 2024; Mutseekwa, 2025). Additionally, time constraints related to covering required physics content within a school year further discourage educators from implementing interdisciplinary approaches. Czerniak and Johnson (2014) stated that teachers who attempted interdisciplinary teaching often felt pressured to revert to traditional methods due to time limitations.

The availability of resources and instructional materials presents another barrier to interdisciplinary teaching. Many schools lack sufficient interdisciplinary teaching materials, including textbooks, laboratory equipment, and digital resources tailored to integrative approaches (Becker & Park, 2011). Additionally, interdisciplinary teaching often requires collaboration among educators from different disciplines, which may be difficult to achieve without administrative support and structured planning time. Hall and Weaver (2001) suggested that without institutional commitment to interdisciplinary teaching, educators face difficulties in accessing the necessary resources and support to implement such approaches effectively.

Another concern among educators is the perceived difficulty in maintaining content depth when integrating multiple disciplines. Some teachers worry that interdisciplinary teaching might weaken the precision of instruction by shifting the focus away from fundamental principles (You, 2017). Teachers accustomed to traditional discipline-specific instruction may fear that students will develop a fragmented understanding of physics concepts if lessons emphasize connections with other subjects rather than core physics theories (Vieyra & Himmelsbach, 2022).

2.4. Existing Models and Best Practices in Interdisciplinary Physics Education

One effective strategy is project-based learning (PBL), which involves students engaging in projects that require the application of physics concepts to real-world problems. This method encourages active learning and collaboration, allowing students to see the relevance of physics in everyday life. Research by Guo et al. (2020) and Ospankulova et al. (2025) stated the effectiveness of PBL in science education, indicating its role in promoting deeper understanding and retention of scientific concepts.

Another successful approach is the integration of case studies into the physics curriculum. By analyzing real-life scenarios, students can connect theoretical physics principles to practical applications, increasing their critical thinking and problem-solving skills. According to Rahman (2024), the use of case studies in physics courses improves student engagement and comprehension by encouraging analytical thinking and collaborative problem-solving.

Several educational institutions have successfully implemented interdisciplinary approaches in their physics programs. Amherst Middle School developed a two-day interdisciplinary lesson where seventh-grade students used coding to program mini-robots, integrating computer science and physics concepts. This initiative not only reinforced physics principles but also increased students’ computational thinking skills (New York State Education Department, 2023). Another example is the Technology-Enhanced Active Learning (TEAL) project at the Massachusetts Institute of Technology. TEAL combines lectures, simulations, and hands-on experiments in a collaborative setting, effectively integrating technology and physics education. This approach has led to improved student understanding and retention of physics concepts (Dori & Belcher, 2005).

Technology plays an important role in facilitating interdisciplinary learning in physics education (Aldazharova et al., 2024). Digital tools such as PhET Interactive Simulations provide students with interactive environments to explore and visualize complex physics phenomena, bridging the gap between abstract concepts and real-world applications (Wieman et al., 2008).

Additionally, the use of storytelling and theatrical techniques, supported by digital media, has been explored as a method to teach complex physics topics like gravitational waves. This approach not only makes the content more accessible but also engages students’ creativity and imagination, increasing a deeper interest in the subject matter (Tuveri et al., 2024).

2.5. Conclusion and Link to Current Study

The review of literature shows the importance and benefits of interdisciplinary teaching in physics education, demonstrating that integrating multiple disciplines increases conceptual understanding, critical thinking, and student engagement (Bao & Koenig, 2019; Rahman, 2024; Kaltakci-Gurel, 2021; Winowiecki et al., 2011). Different studies have shown that interdisciplinary approaches improve problem-solving skills and make physics more relevant to real-world applications (Dreyfus et al., 2014; Dyachenko et al., 2024; Shaw, 2016; Wieman et al., 2008). However, despite the recognized advantages, there are significant challenges in implementing interdisciplinary teaching, including insufficient teacher training, curriculum restrictions, resource limitations, and concerns about content depth (Brand & Triplett, 2012; Czerniak & Johnson, 2014; Laius & Presmann, 2024). These gaps lead to the following research questions: (1) How do students’ perceptions of the benefits of interdisciplinary teaching change as they progress through academic years? (2) How do students’ confidence and preparedness for interdisciplinary teaching change across academic years? (3) What are the key challenges and barriers that prevent students from adopting interdisciplinary teaching, and how do these barriers change over time? (4) How do interdisciplinary teaching perceptions vary between universities, and what institutional factors contribute to these differences? (5) To what extent does prior training impact students’ confidence and reduce barriers in interdisciplinary teaching?

3. Methods

This study employed a quantitative, cross-sectional survey design (Creswell, 2015) to examine pre-service physics teachers’ perceptions of interdisciplinary teaching. The research is grounded in a positivist paradigm (Cohen et al., 2018), which assumes that reality can be objectively measured through empirical observation and statistical analysis.

3.1. Sample and Context

This study examines pre-service teachers’ self-perceived competencies and challenges regarding interdisciplinary teaching in physics education. The research was conducted at two universities in Kazakhstan: South Kazakhstan Pedagogical University named after Özbäkali Jänibekov (OKPU) in Shymkent and L.N. Gumilyov Eurasian National University (ENU) in Astana. These institutions were selected to provide different perspectives on interdisciplinary teaching, as they differ in curriculum structures, faculty expertise, and interdisciplinary exposure.

The sample consists of 292 pre-service teachers aged 17 to 23 years, ensuring representation across different academic levels. Gender distribution shows that 52.7% of the participants are female, while 47.3% are male. Students were distributed across academic years, with 25.0% in their first year, 19.9% in their second year, 22.9% in their third year, 17.1% in their fourth year, and 15.1% at the master’s level. Regarding institutional representation, 64.0% of the participants are from OKPU, while 36.0% are from ENU.

The final sample consisted of 292 pre-service physics teachers, which represents a robust sample size for survey-based educational research. According to guidelines by Comrey and Lee (2013) a sample size of 200–300 is considered “good” for factor analysis and other multivariate techniques. While the findings are likely to be indicative of trends within similar institutional contexts, generalizability to all teacher education programs should be approached with caution.

OKPU specializes in teacher education and has a history of 85 years. The university serves over 7100 students, including 6047 undergraduate students, 518 master’s students, and 33 doctoral students. It collaborates with more than 50 international universities and consists of six faculties, including the Faculty of Physics and Mathematics, where the participants of this study were enrolled. Detailed information about these programs can be found on the university’s official website: https://okmpu.edu.kz/en (accessed on 22 May 2025).

The goal of the 7M01502—“Physics Teacher Training” educational program at the South Kazakhstan Pedagogical University named after Özbekali Jänibekov is to train competitive scientific and pedagogical specialists in physics who possess general cultural and professional competencies that meet the requirements of the National Qualification System and the labor market in the fields of science and professional activity. According to the curriculum of the educational program, a total of 120 credits (3600 h) are offered. The program spans four semesters, with 30 credits allocated per semester. Instructional formats include lectures, practical classes, laboratory work, independent student work, and guided independent work with instructors.

Interdisciplinary teaching is actively integrated into the curriculum at South Kazakhstan Pedagogical University. Since the introduction of interdisciplinary approaches in physics education, the course “Methods of Teaching Physics through Integration” has been included in the 7M01502—Physics Teacher Training educational program. Undergraduate courses such as Mechanics and Molecular Physics for first-year students, as well as Methods of Teaching Physics for second- and third-year students, incorporate interdisciplinary connections with chemistry, biology, geography, visual arts, history, and music. These connections are designed to help students understand key physics concepts such as velocity, sound waves, fluids, density, temperature, molar mass, and capillary phenomena through real-world applications, enhancing engagement and deepening their scientific understanding.

ENU is one of the top-ranked universities in Kazakhstan, ranked among the top 300 universities globally. It has 460+ international partner universities and consists of 13 faculties, including the Physics-Technical Faculty, where the participants in this study were enrolled. More information is available at: https://www.enu.kz/en (accessed on 24 May 2025).

At ENU, interdisciplinary connections are emphasized in the Department of Theoretical Physics through courses such as “Methods of Teaching Physics” and “Integration of Natural Sciences”, which are taught to first- and fourth-year undergraduate students. These courses are designed to increase interdisciplinary understanding by integrating concepts from multiple scientific disciplines. The university’s educational programs aim to equip future physics teachers with the knowledge and skills necessary to apply interdisciplinary methods effectively in their professional practice.

3.2. Instrument

To investigate pre-service physics teachers’ perceptions of interdisciplinary teaching, a structured survey was developed and administered. The instrument aimed to measure students’ views across three core dimensions: perceived benefits, confidence and preparedness, and challenges and barriers related to interdisciplinary teaching in physics.

Each dimension of the survey instrument was directly aligned with one or more of the study’s research questions. Items in the perceived benefits dimension correspond to RQ1, the confidence and preparedness items relate to RQ2, the challenges and barriers items address RQ3, and RQ4 and RQ5 are explored through comparative analyses of responses across demographic variables.

The survey included 17 items (Appendix A), each rated on a five-point Likert scale (Boone & Boone, 2012) (1 = strongly disagree to 5 = strongly agree). The reliability of the overall scale was high (Cronbach’s α = 0.92), with strong internal consistency across the three dimensions: perceived benefits (PB) α = 0.95, confidence and preparedness (CP) α = 0.94, and challenges and barriers (CB) α = 0.93. The Cronbach’s alpha values, while indicating excellent internal consistency, may also suggest potential redundancy among some items (Tavakol & Dennick, 2011). However, expert reviews and the authors’ re-evaluation of the survey did not identify any redundancy among the items.

To establish content validity, the survey instrument underwent an expert review process. Three university faculty members with expertise in physics education and interdisciplinary teaching were invited to evaluate the instrument. Each expert was asked to assess the clarity, relevance, and alignment of the items with the intended constructs and research questions. To further validate the instrument, cognitive interviews were conducted with three pre-service physics teachers. These students were purposefully selected to reflect variation in academic year (first-year, third-year, and master’s level) and gender. Participants were asked to complete the survey while thinking aloud, and follow-up probing questions were used to clarify how they interpreted each item. The goal was to ensure that the language was clear, culturally appropriate, and aligned with the intended constructs. Based on their feedback, minor revisions, such as rephrasing technical terms and simplifying complex sentence structures, were made.

Each item was grouped into its respective dimension based on theoretical constructs and expert judgment. To ensure the construct validity of the instrument, an Exploratory Factor Analysis (Fabrigar et al., 1999) was conducted using the maximum likelihood extraction method with oblimin rotation. The results supported a three-factor model (

Table 1. Exploratory factor analysis: factor loadings.

Items	1	2	3
PB1	0.45	0.45
PB2	0.35	0.58
PB3		0.73
PB4		0.96
PB5		0.84
PB6		0.91
CP1	0.74
CP2	0.82
CP3	0.84
CP4	0.88
CP5	0.6
CB5	0.6		0.36
CB4	0.52		0.44
CB3			0.98
CB2			0.94
CB1			0.98
CB6			0.96

) corresponding to the conceptual dimensions.

The results revealed a clear three-factor structure (see Table 1), aligning with the intended dimensions: Items CP1 through CP5 loaded strongly on Factor 1 (0.60 to 0.88), confirming a cohesive confidence and preparedness dimension. Items PB3 to PB6 demonstrated high loadings on Factor 2 (0.73 to 0.96), supporting the perceived benefits factor, while PB1 and PB2 showed moderate cross-loadings on both Factor 1 and Factor 2, indicating some conceptual overlap. After consulting with experts, we chose to retain these items in the perceived benefits dimension due to their theoretical relevance and contribution to the overall reliability of the scale. Items CB1 to CB6 loaded strongly on Factor 3 (0.94 to 0.98), establishing a well-defined challenges and barriers dimension.

3.3. Data Collection

The data for this study were collected through the survey administered to students during their coursework. The survey was designed using Google Forms, and the link was distributed to participants for completion. Students were given 9–12 min to respond, and they completed the survey using their personal mobile devices. Given the widespread accessibility of digital technology, the survey process was conducted smoothly without any technical difficulties. For senior students, including fourth-year undergraduates and master’s students, the survey was distributed remotely to accommodate their academic commitments. Fourth-year students were engaged in pedagogical internships in schools, while master’s students were participating in research internships, making an online format the most effective means of data collection for these groups. The survey was launched on 13 February 2025, and remained open for one week. A total of 302 students completed the survey; however, responses of 10 students were removed during data cleaning process.

To ensure that only the intended participants, that is, pre-service physics teachers enrolled in the specified programs, completed the survey, specific measures were implemented. The survey link was distributed directly by course instructors during scheduled class time, and students completed the questionnaire using their personal devices under supervision. For students at the master’s level and those engaged in internships, the survey was shared via institutional communication channels.

3.4. Data Analyses

To analyze the collected data, a combination of descriptive statistics, clustering techniques, and comparative analyses was employed. The dataset was first examined for missing values, outliers, and inconsistencies. Of the 302 responses, 10 were removed due to incompleteness or selecting the same choice for all items. Missing values were replaced with mean replacement to maintain data integrity while ensuring all responses were included in the analyses. A K-means clustering technique (Jain, 2010) was applied to identify distinct student groups based on their responses. The optimal number of clusters was determined using the Elbow Method and Silhouette Score. Five clusters were identified, representing varying levels of confidence, perceived benefits, and barriers to interdisciplinary teaching. The resulting clusters were analyzed in relation to demographic factors such as age, gender, academic year, and university affiliation to understand differences in student perceptions.

3.5. Ethical Considerations

This study was conducted in accordance with established ethical standards for research involving human participants. Prior to data collection, ethical approval was obtained from the research ethics committee of OKPU (#=3, 13 February 2025). During online data collection, the principles of anonymity and informed consent were carefully upheld. Participants accessed the survey via a secure Google Forms link, which included an introductory section explaining the purpose of the study, the voluntary nature of participation, and their right to withdraw at any time. Before proceeding to the survey items, participants were required to read the consent statement and indicate their agreement by checking a box labeled “I voluntarily agree to participate.” No personal identifiers (e.g., names, email addresses, or IP addresses) were collected.

4. Findings

The elbow method plot (Figure 1) visualizes the within-cluster sum of squares (WCSS) for different numbers of clusters in the K-means algorithm. As the number of clusters increases, WCSS decreases because smaller clusters are able to fit the data better. However, after a certain point, the rate of decrease slows down, forming an elbow shape in the plot.

In Figure 1, the elbow appears at k = 5, meaning that adding more clusters beyond this point results in only a minor reduction in WCSS while increasing model complexity. This shows that five clusters provide an optimal balance between minimizing within-cluster variation and avoiding excessive fragmentation of the data.

The Silhouette Score plot (Figure 2) shows the quality of clustering by measuring how well separated and cohesive the clusters are. The Silhouette Score ranges from −1 to 1, where values closer to 1 indicate well-defined clusters, values around 0 suggest overlapping clusters, and negative values indicate potential misclassification.

As seen in Figure 2, for k = 5, the overall silhouette score is 0.59, showing a well-structured clustering.

The stacked area plot in Figure 3 shows how the three survey dimensions change across different clusters.

As indicated in Figure 3, Cluster 1 has the highest scores across all dimensions. Cluster 0 shows high scores in perceived benefits and confidence and preparedness, but lower challenges and barriers. Cluster 2 has moderate scores in perceived benefits and confidence and preparedness but the lowest challenges and barriers score. Cluster 3 shows relatively low scores in all dimensions. Cluster 4 has moderate scores in all dimensions.

Students’ responses are distributed to the clusters, and it is visualized in Figure 4.

Cluster 0 consists of students who generally have a strong understanding of interdisciplinary teaching and feel confident in integrating physics with other disciplines. They tend to agree that interdisciplinary connections enhance students’ understanding and problem-solving skills. Their responses indicate a lower perception of barriers, indicating they are more open to adopting interdisciplinary approaches without feeling hindered by a lack of training or resources. Cluster 0 consists of students who are, on average, around 20 years old and predominantly male. They are typically in their third or fourth year of study and mostly attend University OKPU. A significant portion of them have some prior teaching experience, but not overwhelmingly so. Their familiarity with interdisciplinary teaching is relatively high compared to other clusters.

Cluster 1 represents a more balanced group with moderate agreement on the benefits of interdisciplinary teaching but also some reservations. While they acknowledge the advantages of integrating physics with other subjects, they do not exhibit the same level of confidence as Cluster 0. Their responses suggest they might require additional training or exposure to interdisciplinary teaching methods to feel more comfortable applying them. They do not strongly perceive a lack of resources or curriculum constraints as major obstacles. Cluster 1 is similar in age to Cluster 0, averaging around 20 years old, and also has a male majority. Most students in this cluster are in their third year of study. A slightly higher percentage of students in this group lack prior teaching experience compared to Cluster 0. Moreover, their familiarity with interdisciplinary teaching is moderate.

Cluster 2 is positive toward interdisciplinary teaching, similar to Cluster 0, but with slightly less confidence. They agree that interdisciplinary approaches enhance learning and engage students more effectively. However, they feel they still need further training to be fully prepared for implementing such methods. Cluster 2 consists of younger students, averaging about 18.4 years old, with a somewhat more balanced gender distribution compared to Clusters 0 and 1. This group primarily consists of first- and second-year students, making them one of the least experienced groups in terms of teaching. They have the least familiarity with interdisciplinary teaching.

Cluster 3 consists of students who are somewhat neutral or mixed in their perspectives. They do not show extreme positivity or negativity toward interdisciplinary teaching but instead demonstrate a middle-ground stance. Their responses show that while they see some benefits, they also recognize challenges such as time constraints, curriculum limitations, or a lack of resources. Cluster 3 has a slightly older demographic, with an average age of around 21.1 years and a higher proportion of males. They are primarily second- and third-year students, with a greater percentage of them having prior teaching experience compared to other clusters. Their familiarity with interdisciplinary teaching is moderate, and they have mixed opinions on its implementation.

Cluster 4 is characterized by students who perceive significant barriers to interdisciplinary teaching. They are more likely to feel unprepared and believe that a lack of training and resources makes interdisciplinary teaching difficult. Their responses indicate lower confidence in integrating physics with other disciplines, and they might be more resistant to interdisciplinary approaches due to these perceived challenges. Cluster 4 is the youngest group, with an average age of about 18.3 years and the most balanced gender distribution. They are mostly in their first year of study and have the least prior teaching experience. Despite this, they report relatively high familiarity with interdisciplinary teaching and also perceive the most significant barriers to interdisciplinary teaching.

Figure 5 shows how different clusters responded to survey items using a Likert scale (1 to 5). Each line corresponds to a specific survey item, labeled with its ID (e.g., PB1, CB5), showing how responses vary across clusters.

From Figure 5, we can observe trends in how clusters perceive interdisciplinary teaching. Some items have relatively stable responses across clusters, while others show significant variation. Cluster 2 represents a group with highly contrasting views, Cluster 3 appears to be the least confident overall, and Clusters 0, 1, and 4 seem to have more balanced perspectives.

Figure 6 compares the average Likert-scale responses between gender groups (1 = Female, 2 = Male) across all survey items. Each line corresponds to a specific survey item, labeled with its ID (e.g., PB1, CB5), showing how responses change between males and females.

From Figure 6, we can observe whether male and female students respond differently to specific items. The lines in the plot are mostly parallel and closely clustered together, indicating that gender differences in responses are relatively small. There are no extreme changes, indicating that both male and female students generally agree on the benefits, confidence levels, and barriers related to interdisciplinary teaching. In most cases, male students have slightly higher scores compared to female students.

Stacked area plot for year groups (Figure 7) shows trends in student perceptions based on their year of study.

As seen in Figure 7, the second-year students report the lowest cumulative responses, as indicated by a visible dip, indicating that they rate interdisciplinary teaching lower compared to other year groups. Responses increase from the second year onward, with third-year responses beginning to rise and fourth- and fifth-year students showing the highest cumulative responses. Survey items remain relatively proportional across all year groups.

The stacked area chart (Figure 8) shows the percentage distribution of students in different clusters across five academic years, from the first year to the master’s level.

In Year 1, Cluster 0 (56.16%) and Cluster 1 (32.87%) are the most dominant. Cluster 4 accounts for only 9.59% of the students. In Year 2, Cluster 2 (53.44%) becomes the dominant group, and Cluster 4 increases to 22.41%. In Year 3, Cluster 0 (48%) regains dominance, and Cluster 4 also rises to 28%. In Year 4, Cluster 0 (90.91%) overwhelmingly dominates. In the master’s level (Year 5), Cluster 0 remains the largest (68.65%), but Cluster 4 (16.42%) is still present. Cluster 4 is not the most prominent in Year 1, but it grows significantly in Year 2 and peaks in Year 3 before declining.

A developmental trend was observed in students’ confidence regarding interdisciplinary teaching, particularly evident in the shifting cluster distributions across academic years. As shown in Figure 8, Cluster 0, characterized by high confidence and low perceived barriers, became increasingly dominant among Year 4 and master’s students. In contrast, Clusters 2 and 4, which reflect lower confidence levels, were more prevalent among students in their second and third years. This progression indicates that students gain confidence in applying interdisciplinary teaching methods as they advance through the program.

The bar chart in Figure 9 displays the percentage distribution of students in each cluster for two universities: OKPU and ENU. The data have been normalized to percentages within each university to account for differences in total student numbers.

Both universities have students distributed across all five clusters. The variation in cluster percentages across universities suggests differences in student characteristics or experiences. In OKPU, Clusters 0 and 3 have the highest percentage of students, with around 25–26%. In ENU, the distribution is more balanced, with percentages ranging from 18% to 22% across clusters. Cluster 0 and Cluster 3 are more dominant in OKPU than in ENU. Clusters 1 and 4 have a relatively lower representation in OKPU compared to ENU.

The exploratory factor analysis further validates the three-dimensional structure of the instrument, with clear factor loadings for items under confidence, perceived benefits, and challenges. Confidence and preparedness items (CP1–CP5) and barriers (CB1–CB6) showed strong, consistent loadings, while perceived benefits (PB3–PB6) loaded clearly onto their factor. Some cross-loading, particularly of PB1 and PB2, suggests conceptual overlap between benefits and confidence, which is theoretically coherent.

To provide a clear overview of how each figure contributes to addressing the research questions,

Table 2. Figures, descriptions and RQ relationship.

Figure	Description (Assumed from Earlier Text)	Likely Justification
Figure 1	Elbow method plot	Justifies number of clusters (RQ-related)
Figure 2	Silhouette score plot	Validates clustering (supports RQ structure)
Figure 3	Stacked area for survey dimensions across clusters	Core result, supports RQs 1–3
Figure 4	PCA-based cluster visualization (2D)	Useful to show cluster separation
Figure 5	Likert item responses by cluster	Insightful for interpreting cluster profiles
Figure 6	Gender comparison plot	Supports discussion for demographic analysis
Figure 7	Perceptions by academic year	Related to RQ1 and RQ2
Figure 8	Cluster distribution across academic years	Related to RQ1–RQ3
Figure 9	Cluster distribution across institutions	Directly related to RQ4

summarizes the figures presented in the manuscript, along with brief descriptions of their content and the specific research questions (RQs) they support. This table is intended to help readers understand the logical flow of the data presentation and how each visualization aligns with the study’s analytical framework. By explicitly linking each figure to the relevant RQs, the table also clarifies the role of visual data in supporting the study’s findings and interpretations.

5. Discussions

RQ1. 

How do students’ perceptions of the benefits of interdisciplinary teaching change as they progress through academic years?

The results of this study show that students’ perceptions of interdisciplinary teaching evolve over time, particularly in terms of perceived barriers and confidence, rather than a linear increase in perceived benefits. This aligns with the findings of Nadelson et al. (2013), who reported that pre-service teachers often begin with relatively high enthusiasm for interdisciplinary approaches, but their confidence in applying such methods tends to grow only with experience and structured exposure. Similarly, Becker and Park (2011) noted that while teachers generally support the idea of integrated STEM teaching, their practical confidence and readiness improve gradually through programmatic support. The present study confirms that students may enter teacher education programs with a favorable view of interdisciplinary teaching, but it is the progressive reduction in perceived barriers, rather than a change in perceived value, that marks their development over time. This finding differs from studies like Spelt et al. (2009), which suggested that interdisciplinary competence builds steadily across all dimensions, including perceived benefit.

RQ2. 

How does students’ confidence and preparedness for interdisciplinary teaching change across academic years?

Contrary to the common assumption that students’ support for interdisciplinary teaching grows steadily with academic progression, our cluster analysis and factor structure suggest that students tend to recognize the benefits of interdisciplinary approaches early in their training. This observation is consistent with findings by Laius and Presmann (2024) and Becker and Park (2011), who reported that even novice pre-service teachers often express positive attitudes toward interdisciplinary methods, especially when they see relevance to real-world applications. In our study, the perceived benefits factor showed high and stable loadings (PB3–PB6), and Figure 3 illustrated consistent endorsement of these benefits across all clusters. This stability indicates that perceived value is not necessarily dependent on academic advancement. Instead, the primary developmental trend lies in the reduction of perceived barriers and increased confidence, particularly as students transition from Year 2 to Year 4. This trajectory supports Spelt et al. (2009), who emphasized that while interdisciplinary competence is multidimensional, some components, like attitudinal appreciation, may precede actual instructional readiness.

RQ3. 

What are the key challenges and barriers that prevent students from adopting interdisciplinary teaching, and how do these barriers change over time?

The transitional dip observed in Years 2 and 3, where Cluster 2 and Cluster 4 become more prominent, may be due to increasing academic demands and shifting expectations. These students report lower confidence and higher perceived barriers, indicating a temporary disruption before confidence stabilizes in the final academic stages. This pattern is consistent with previous research showing that students face increased cognitive and instructional demands mid-program, which may temporarily lower their sense of preparedness (Ivanitskaya et al., 2002; Ellermeijer & Heck, 2002). These findings also support Piaget’s theory of cognitive development, in which learners experience temporary dissonance before achieving new levels of understanding, and Vygotsky’s sociocultural theory, which shows the importance of scaffolded support during academic transitions (Vygotsky, 1978).

RQ4. 

How do interdisciplinary teaching perceptions vary between universities, and what institutional factors contribute to these differences?

Institutional factors also appear to influence students’ readiness and confidence. Figure 9 illustrates that students from OKPU are more frequently found in Clusters 0 and 3, characterized by higher confidence and moderate barrier perception, while ENU students are more evenly distributed and show greater representation in Clusters 1 and 4. This variation could be attributed to differences in the extent and structure of interdisciplinary training at each institution. Research shows that institutional support and structured interdisciplinary coursework improve students’ confidence and reduce perceived barriers (Becker & Park, 2011; Descamps et al., 2020).

RQ5. 

To what extent does prior training impact students’ confidence and reduce barriers in interdisciplinary teaching?

The data suggest that students with more interdisciplinary exposure, such as those at OKPU, exhibit higher confidence and perceive fewer barriers. This supports existing research that structured interdisciplinary training enhances teacher preparedness. However, even among master’s students, some barriers remain, highlighting the need for continuous professional development and curriculum refinement.

Gender-based analysis in Figure 6 shows minimal differences in students’ responses. Both male and female students display closely aligned perceptions across all items. While male students report slightly higher confidence levels, this aligns with existing findings that gender differences in STEM fields tend to manifest more in confidence than in performance (Bøe et al., 2024; Nadelson et al., 2013).

Theoretical Interpretation of Findings

The results of this study can be better understood through the lens of the theoretical frameworks that guided its design. Constructivist theory (Piaget, 1972) posits that learners actively build new knowledge by connecting it to existing cognitive structures. This is reflected in the findings that pre-service physics teachers showed early recognition of the benefits of interdisciplinary teaching, indicating that students are conceptually capable of integrating new pedagogical ideas when those ideas align with their prior experiences or perceived relevance. The gradual increase in confidence and the reduction in perceived barriers over time support Vygotsky’s (1978) sociocultural theory, which emphasizes the importance of scaffolding and social interaction in advancing learners through their zone of proximal development. As students progress academically, they are likely exposed to more peer discussion, practical examples, and teaching practice, all of which contribute to reducing their sense of unpreparedness and strengthening their instructional self-efficacy. Furthermore, the temporary dip in confidence observed during the second and third years is consistent with Inquiry-Based Learning models (Dewey, 1938), where moments of cognitive dissonance and struggle are critical for promoting deeper learning. The shift from theoretical appreciation in the early stages to applied confidence in the later stages illustrates how interdisciplinary teaching competencies develop in phases, each requiring appropriate support, consistent with Spelt et al.’s (2009) model of interdisciplinary competence as a multidimensional construct.

Along with addressing the individual dimensions of interdisciplinary teaching perceptions, our study employs clustering analysis to capture the complex, interconnected nature of these dimensions within student profiles (Darcan & Badur, 2012). This clustering approach allows for the identification of latent combinations of confidence, perceived benefits, and perceived barriers. Unlike traditional variable-centered methods that analyze each dimension independently, clustering enables us to detect patterns of co-occurrence among these factors (Saenz et al., 2011), revealing meaningful subgroups of students with shared perception profiles.

Furthermore, the use of clustering provides theoretical perspectives about how interdisciplinary teaching competencies develop in a non-linear manner. Students may simultaneously recognize benefits while feeling unprepared, or they may feel confident despite perceiving external barriers. By conceptualizing these dimensions as interrelated clusters, we gain a deeper understanding of the paths through which interdisciplinary teaching skills emerge during teacher preparation programs.

6. Conclusions

This study examined students’ perceptions of interdisciplinary teaching, focusing on how confidence, preparedness, and perceived barriers evolve across academic years and how institutional and demographic factors shape these perceptions. Our findings show that students recognize the benefits of interdisciplinary teaching from the early years, while their confidence in applying it increases over time as perceived barriers decrease. However, barriers such as lack of training and feeling unprepared persist for some students, even at the master’s level, indicating the ongoing need for structured interdisciplinary education.

Key findings indicate that institutional differences play a significant role in shaping student perceptions, with OKPU students exhibiting higher confidence levels compared to ENU students, likely due to differences in curriculum structure and training opportunities. Cluster distribution varied across academic years, with students experiencing a temporary decline in confidence and increased perceived barriers in the second and third years, indicating that academic transitions and curriculum complexity may momentarily hinder interdisciplinary engagement before confidence is restored in later years.

These findings have several important implications for teacher education programs. First, given that students recognize the benefits of interdisciplinary teaching early in their academic journey, programs should capitalize on this positive disposition by introducing structured interdisciplinary modules in the early years of study. Such modules could include co-taught courses involving multiple subject experts or project-based assignments that require cross-disciplinary thinking. Second, the temporary decline in confidence observed during the second and third years suggests a need for targeted support, such as mentorship, peer collaboration, or scaffolded practice, in these transition periods. Universities might consider embedding interdisciplinary teaching practicums or case-based learning into these mid-program phases to maintain student engagement and self-efficacy. At the institutional level, reducing disparities in interdisciplinary confidence across universities calls for more consistent curricular frameworks and faculty development initiatives (Hofstein et al., 1982). Faculty training workshops focused on designing and delivering interdisciplinary instruction could help ensure more equitable student experiences.

Despite its contributions, this study has some limitations. The findings are based on self-reported survey data, which may be subject to response bias. Additionally, while the study identifies key trends in interdisciplinary teaching perceptions, it does not explore the specific curricular elements or faculty interventions that contribute to these differences. Future research should investigate the impact of specific pedagogical strategies on confidence and preparedness in interdisciplinary teaching.

It is important to note that the clustering analysis used in this study is descriptive and exploratory in nature. While it provides rich findings about student profiles and their developmental trajectories, it does not establish causal relationships between the measured dimensions. Future research should consider employing longitudinal study designs to track changes in student clusters over time and apply hypothesis-driven modeling approaches, such as latent transition analysis or structural equation modeling, to test specific causal mechanisms underlying shifts in interdisciplinary teaching perceptions. Additionally, future studies could systematically derive and test hypotheses related to the movement of students between clusters as they progress through their academic programs.