Views on Mathematics Education: A Comparative Study of Future Primary and Future Mathematics Teachers

Abstract

Teacher identity emerges from the intertwined relationship of past, present, and future experiences, shaped through active reflection within individual, social, and cultural contexts. This study investigates how initial teacher education programs for future primary school teachers and future mathematics teachers influence their perceptions of mathematics education. Questionnaires with predominantly open-ended questions were distributed to 369 students: 195 enrolled in mathematics teacher education programs and 174 in primary school teacher education programs. The survey examined their preferences for school subjects in prior education, motivations for choosing teaching as a profession, important teacher qualities, and attitudes toward mathematics. The results reveal significant differences between the two groups: future primary school teachers emphasize the focus on children and relational aspects of teaching, while future mathematics teachers highlight mathematics as a scientific discipline. Both groups’ responses reflect their respective educational programs and experiences. The findings suggest that adopting a holistic approach in teacher education, integrating content knowledge with pedagogical practice, and supporting reflective processes can foster deeper self-understanding and the development of a professional teacher identity.

1. Introduction

Mathematical literacy and critical thinking represent key competencies in the modern world. A strong understanding of mathematics forms the foundation for successful careers in fields such as engineering, finance, research, and others, as well as for solving numerous problems in everyday situations. Therefore, mathematical education, which encompasses the entire pre-university schooling, is of the utmost importance for every individual and is one of the pillars of educational systems (The European Commission, 2019; Yorkovsky & Levenberg, 2021). The impact of mathematics teachers on students’ achievements and attitudes is immense (Lavrijsen et al., 2021; Romero Ariza et al., 2021; Roorda et al., 2019; Sansone, 2017; Virtanen et al., 2022).

This study focuses on two models of initial teacher education (ITE) and identifies key similarities and differences that may indicate the shortcomings of each of the observed models. On the one hand, this study examines predominantly pedagogical programs attended by future primary school teachers (PTs) who teach all subjects in primary school (ages 6.5–10.5), including mathematics. These teachers introduce students to the world of mathematics and significantly influence their attitudes and relationships toward the subject. On the other hand, this study considers predominantly mathematics-oriented program attended by future mathematics teachers (MTs) for lower and upper secondary schools (ages 10.5–18.5). These teachers take over students at the age of 10.5 from PTs and build upon the previously established mathematical foundations.

2. Literature Review

Teacher identity is a complex construct that involves connecting past, present, and future experiences, which are continuously linked and reshaped by external conditions, initial education, school practice, and perspectives on schools in general (Arvaja et al., 2020). The choice of teaching as a profession may not always result from an individual’s genuine inclination toward teaching. This choice may stem from familiarity with the profession due to previous schooling and insufficient exploration of other careers (Crowe & McGarr, 2022). Subject preference in school is important for the career decision-making process (Davies & Ercolani, 2018; Franz-Odendaal et al., 2016; Madden et al., 2018), and is linked to students’ perceptions of subject teachers’ engagement, their approach to teaching and learning, and the opportunities for students to connect learning material to their own lives, even regardless of their preferences (Akyıldız et al., 2021; Lavrijsen et al., 2021; Perkins et al., 2007; Sansone, 2017).

In the motivation for the teaching profession, intrinsic, extrinsic, and altruistic motivations are highlighted as the most important groups of reasons for choosing a teaching career (McLean et al., 2019; Watt et al., 2012). Altruistic motives emphasize the essential value of the career and the value of social utility in career choice. Intrinsic motives focus on personal abilities, compatibility with other interests and activities, and compatibility with family life. Extrinsic motives may include perceiving the chosen profession as a backup career and highlighting the value of personal gain and social impact (McLean et al., 2019). Motivation for the teaching profession is subject to change, fluctuations, and vicissitudes throughout the educational process, influenced by professional practices and the socio-cultural environment (Yuan & Zhang, 2017). In addition to motivation, the development of professional identity plays a key role in the early stages of a teaching career, with identity motives such as authenticity, efficacy, and belonging significantly influencing retention (Abramson & Schachter, 2024).

Teachers’ competence in teaching mathematics is multidimensional and encompasses content knowledge, pedagogical content knowledge, and contextual knowledge (Copur-Gencturk & Tolar, 2022). These forms of knowledge are in a complex interrelationship; so, various ways of integrating mathematics instruction and developing specific pedagogy for teaching mathematical content are proposed when structuring ITE programs (Charalambous, 2016; Norton, 2019). Since school subjects are not direct translations of academic disciplines, it is necessary for teachers, in addition to knowledge of the academic discipline, to be familiar with the content of the school subject, with a focus on what is truly happening in the classroom (Deng, 2012). It is essential to clearly define and conceptualize ITE so that future MTs can develop knowledge that is useful and applicable in teaching (Charalambous et al., 2009). During ITE, it is crucial to enable future teachers to build their identity, comprehend what it means to know and engage with mathematics, and understand how children learn mathematics (Swars et al., 2009).

3. Research Context

Compulsory education in the Republic of Serbia includes primary and lower secondary education. Primary school lasts from approximately the age of 6.5 to 10.5, while lower secondary education lasts from the age of 10.5 to 14.5. When students transition from primary to lower secondary school at the age of 10, they remain in the same school and class, following the national curriculum. During primary education, one teacher (the PT) teaches all the subjects, while in lower secondary education, subject teachers teach individual subjects. Mathematics, along with the mother tongue, is a key subject and is mandatory in all grades of compulsory education. In primary school, students have five math classes per week taught by their PT, while in lower secondary school, they have four classes per week taught by an MT.

It is stipulated in law that the required qualification level for teachers in pre-university education in the Republic of Serbia is 300 European Credit Transfer and Accumulation System (ECTS) credits, specifically 240 ECTS from undergraduate studies and 60 ECTS from master’s studies. In addition, study programs must provide at least 30 ECTS credits in psychological, pedagogical, and methodological disciplines, and 6 ECTS credits for school practice. In Figure 1, the left column illustrates two pathways for obtaining ITE through two distinct study programs conducted within different faculties. The blue path represents a student who is studying to become an MT, while the red one is for a PT. Candidates with a completed four-year high school education are eligible to apply for both study programs, subject to passing an entrance exam. The entrance exam for PT studies tests knowledge of the mother tongue and literature, while the entrance exam for MT studies assesses mathematical knowledge. The number of students who can enrol depends on the material and staffing capacities of the faculty.

Figure 1. Graphic representation of the students’ path and the research instrument.

In the initial education of future PTs, subjects in pedagogy, psychology, and methodology account for 52% of the total 300 ECTS credits. Mandatory pedagogical practice constitutes 7–9%, while mandatory mathematics subjects represent 3–5%. For future MTs, theoretical mathematics subjects constitute 65% of the 300 ECTS credits, subjects in pedagogy, psychology, and methodology account for 10%, and mandatory pedagogical practice for 5%. Graduates who are PTs can teach all subjects in primary school. Graduates who are MTs can teach mathematics in lower and upper secondary schools. They also have employment opportunities in various fields as mathematicians. PTs cannot teach in lower secondary education, while MTs cannot teach in primary education.

4. Methods

This study was designed to investigate similarities and differences between MT and PT education programs, with a focus on how prior experiences, motives for choosing the profession, perceptions of teaching qualities, and conceptions of mathematics shape future teachers’ professional identity and preparation. Specifically, this research was guided by the following questions:

• What reasons do future teachers give for identifying mathematics as either the most interesting or the most difficult subject in high school?
• What are the main differences between MT and PT students in their stated motives for choosing the teaching profession?
• How do MT and PT students differ in ranking the importance of teaching qualities such as subject knowledge, pedagogical skills, and teacher image-related characteristics?
• How do future teachers explain the concept of mathematics to a ten-year-old child, and what differences emerge between MT and PT students in these explanations?

4.1. Sample Description

The sample was convenient and consisted of 369 students divided into two cohorts: 195 (52.85%) were enrolled in an MT education program at the University of Novi Sad (hereafter referred to as subject), while 174 (47.15%) were enrolled in PT education programs at the University of Novi Sad and the University of Kragujevac (hereafter referred to as class). The main criterion for selecting students for the research sample was that, for the subject cohort, they had passed the Pedagogy course, while for the class cohort, they had passed the Mathematics 1 course. All MT participants in the sample were in their fourth year of study, while PT participants ranged from the second year (n = 19) and third year (n = 47) to the fourth year (n = 108). Of the 369 students, 87.53% were female, and 12.47% were male. In the MT education program there were 21 males, while in the PT education programs there were 25. The gender ratio in the sample aligns with the gender ratio in the general population of teachers in the Republic of Serbia. Participation in this research was voluntary and anonymous.

4.2. Instrument

Participants completed paper questionnaires during regular classes throughout the 2021/2022 school year. The questionnaire predominantly features open-ended questions that allow participants to describe their experiences and feelings in a way that suits them best, which can result in more thoughtful and informative responses. The questionnaire was designed to gather information about participants’ experiences at different stages of their education and professional journey. Teacher identity emerges from the intertwined relationship of the past, present, and future, in active reflection and interpretation between the individual and the social and cultural context (Arvaja et al., 2020).

The research instrument used was a questionnaire that, in addition to questions about gender and the study program they are attending, consists of four parts, as shown in Figure 1, right column. The first part—past experiences from high school: the respondent answers open-ended questions about which subject was the most interesting and which was the most difficult during high school, along with the reasons for their choices. The second part—present experiences: explores the reasons for choosing the teaching profession through an open question in which the respondent expresses their motives for entering the profession. The third part—current experiences: the respondent ranks teaching qualities such as conducting interesting classes, maintaining order in the classroom, knowing their students, being well-prepared, knowing their subject, looking good, and being able to entertain. The qualities are listed, and the respondent ranks them by importance, from 1 (most important) to 7 (least important). The provided answers include qualities related to mathematical and pedagogical education, and some characteristics of teachers that appear as part of the teachers’ public image (Chang-Kredl & Colannino, 2017; Copur-Gencturk & Tolar, 2022). The fourth part—future experiences: consists of an open-ended question in which the respondent is asked to explain to a ten-year-old pupil what mathematics is.

4.3. Data Analysis

The responses were qualitatively analyzed to identify and categorize recurring themes, followed by statistical analysis of these categories to explore differences between the cohorts. A qualitative analysis of the responses was conducted using an inductive coding approach. First, all open-ended responses were read independently by three coders to obtain a general understanding of the data. In the second step, each coder generated initial codes directly from the participants’ wording, without using a predefined coding frame. These codes were then compared and discussed jointly, and overlapping or conceptually similar codes were merged into broader categories. In the third step, categories were further refined into themes that captured recurring patterns across data sets.

To establish inter-coder reliability, each researcher re-coded 20% of another coder’s dataset. The degree of agreement was then calculated by dividing the number of identical code assignments by the total number of compared code assignments. Disagreements were discussed until consensus was reached, and the coding scheme was adjusted accordingly. The final level of agreement exceeded the commonly accepted threshold of 80%.

Responses that could not be meaningfully assigned to a category (<3% of total) were excluded. In cases where a response contained multiple aspects, it was assigned to all relevant categories. This step-by-step coding process ensured both the validity of category development and the reliability of the analysis. The ranked qualities (from 1 = most important to 7 = least important) were analyzed quantitatively, with ranks transformed into ordinal data. After coding was completed, a two-proportion Z-test and a chi-square test of independence were used to test hypotheses about differences between the two cohorts, with p-values < 0.05 considered statistically significant.

5. Results and Discussion

The results are presented in four sections that follow the questionnaire structure shown in Figure 1. Each section presents the developed codes for the corresponding data set, alongside the results, which are discussed.

5.1. Preferences for School Subjects

Mathematics is the most frequently mentioned subject by the subject cohort as the most interesting subject (48.72%), while the class cohort mentions mother tongue (17.24%). For the most difficult subject, the subject cohort most commonly mentions physics (13.85%), whereas the class cohort most frequently mentions mathematics (29.89%). The unexpected result that the subject identifies physics as the most challenging subject may be associated with students’ experiences viewing physics as a collection of unrelated information and problems that have less connection to the real world, which diminishes interest in studying the subject (Perkins et al., 2007). Regarding the choice of favourite and least favourite subjects, it is considered significant to question whether teachers and students share common values regarding the subject, and the teaching approach in the process of teaching and learning (Akyıldız et al., 2021).

Responses to questions about the most interesting and most difficult subjects in high school were divided into science, technology, engineering, and mathematics (STEM) and noSTEM subjects. The most interesting subjects for the subject cohort are predominantly from the STEM group (68.21%), while for the class cohort, they are noSTEM subjects (61.49%). The most difficult subjects for the subject cohort are mainly noSTEM subjects (56.41%), whereas, for the class cohort, they are STEM subjects (66.09%). These results align with the claims of Davies and Ercolani (2018) that subject preference in schools is crucial for future employment, and with Madden et al. (2018), who state that preferences for subjects in school influence the choice of study programs in further education. Early experiences and exposure to mathematics and science within the formal school system are crucial for the career decision-making process (Franz-Odendaal et al., 2016).

The codes developed based on the responses to the question about the reasons for choosing the most interesting and difficult subjects, along with examples and response results, are presented in Table 1. A statistically significant difference between the two cohorts was found regarding the reasons related to student engagement and the teacher’s role in the most interesting and the most difficult subjects. The subject cohort mentioned these reasons at a higher percentage.

Table 1. Codes and answer results to the reasons for choosing subjects as the most interesting and the most difficult.

Codes	Description and Example	Subject	Class	p-Value
Most interesting
Individual dispositions	The answers reflect individual preferences and skills. “I love the Serbian language, especially literature. Reading and writing are my hobbies; I enjoy them.” (female PT004)	32.82%	40.80%	0.114
Subject content	They predominantly state that the content of the subject is interesting, highlighting the applicability of knowledge. “Because the subject is focused on practical knowledge and necessary information for further work.” (female PT001)	25.13%	27.59%	0.594
Student engagement	The quality of teaching is measured by pupil activities (problem-solving, thinking, developing understanding, practical examples, experiments, discussions). “The subject was such that we did something new every class; we had the opportunity to develop creative and critical thinking through writing essays and analysing novels.” (female MT146)	40.00%	22.99%	<0.001
Teacher’s role	They primarily mention that the teacher was interesting and taught and explained well. “Because the professor taught and explained the content of this subject in an engaging way.” (female PT085)	40.51%	24.14%	<0.001
Most difficult
Individual dispositions	The answers reflect a lack of individual preferences and skills. “I struggled with foreign languages, especially English, even though I put in more effort than in other subjects.” (male MT147)	42.05%	41.95%	0.985
Subject content	They primarily emphasize that there is too much theory, unnecessary material, and boring, uninteresting content. “Because of the extensive and dull material.” (female MT109)	25.13%	29.31%	0.370
Student engagement	They highlight that they were expected to study by heart, with excessive learning and memorization. “Because to get a high grade, a large amount of material had to be studied, it was all about memorization.” (female MT057)	15.90%	6.90%	0.006
Teacher’s role	They emphasize that the teacher had high expectations, taught poorly, and did not effectively convey knowledge. “Because the professor was very demanding and didn’t explain the subject matter well.” (female PT074)	44.62%	27.01%	<0.001

An individual’s memory of their teachers influences the public perception of the teachers (Chang-Kredl & Colannino, 2017). The most common reasons subject chooses the most interesting and the most difficult subject are student activities and the role of the teacher, as seen in the response: “There was a lot to study, and it had to be memorized exactly as the teacher dictated (the same words and the same order of words). And the teacher was terrifying.” That aligns with Sansone’s (Sansone, 2017) assertion that what is primarily important for students’ interest in a subject is the teacher’s ability to make the subject engaging and to create a positive learning environment, which means preparing their lessons well and supporting their students. Enjoyment of the subject is linked to students’ perceptions of the subject teacher’s engagement, who are passionate about their subject and succeed in connecting the learning material to students’ lives, even regardless of students’ preferences (Lavrijsen et al., 2021), as expressed in the response: “Because the professor knew how to convey knowledge to us, he loved what he did, and we felt that too; the class was interesting, and we could learn a lot from that professor, including things not just related to mathematics.”

Class as the most important reason for subject preference mentions personal preferences and abilities, as illustrated by the response: “Because I love logical tasks. I always have to be focused, and that subject always kept my attention.” For learning mathematics and natural sciences, creating a positive learning environment is crucial for students’ interest and self-confidence, which is fostered by teachers who value and listen to students’ ideas and make their subject engaging (Sansone, 2017). Additionally, students’ affective aspects can influence positively or negatively their learning of science and academic performance, which can have long-term significance for their future career paths (Larkin & Jorgensen, 2016; Rachmatullah et al., 2017).

5.2. Motivation for the Teaching Profession

Descriptions of the extracted codes and examples of responses to why they chose the teaching profession, along with the results, are presented in Table 2. The codes are grouped into three categories: altruistic, intrinsic, and extrinsic motives. A statistically significant difference between the cohorts emerged in the category of intrinsic motives, which were mentioned more frequently by the subject than by the class.

Table 2. Codes and answer results to why they chose to teach.

Motive and Code	Description and Example	Subject	Class	p-Value
Altruistic motives		76.92%	77.01%	0.984
working with children	They predominantly emphasize that they love working with children. “I love to teach children new things.” (female MT169)	50.77%	63.79%	0.012
approach to mathematics	They predominantly state that they want to change the approach to mathematics. “I want to show children and young people that mathematics is not as scary as most perceive it, and I want them to realize how wonderful and useful it is.” (female MT012)	37.95%	0.00%	<0.001
supporting children	Predominantly express a desire to influence children positively. “I would like to provide support to children, awaken humanity in them, foster love for others, and inspire a desire for learning and progress.” (female PT005)	0.00%	24.14%	<0.001
Intrinsic motives		49.23%	28.18%	<0.001
I am good	There is a dominant belief that they will be good at their chosen profession. “I believe that being a teacher is something I would excel at.” (female MT186)	11.28%	11.49%	0.949
I love mathematics	They emphasize that they love mathematics. “Because I love mathematics.” (male MT151)	42.56%	0.00%	<0.001
since childhood	They highlight that they have wanted to pursue this profession since they were young. “This has been my desire since childhood.” (male PT006)	0.00%	18.97%	<0.001
Extrinsic motives		9.74%	9.77%	0.852
adult influence	They primarily mention being inspired by their parents, teachers, or educators when choosing their profession. “I come from a family with many teachers.” (female MT186)/“My mathematics teachers certainly influenced my choice by their example.” (female MT034)	6.15%	8.62%	0.363
working hours	They mention that they like the working hours “Shorter working hours, free weekends, and holidays.” (female MT186)	4.10%	1.15%	0.081

Within the category of altruistic motives, a statistically significant difference between the cohorts appeared in the reasons for working with children and supporting children, which were mentioned more often by the class, while the subject cited approach to mathematics more frequently. In the category of intrinsic motives, a statistically significant difference between the cohorts showed that the subject stated I love mathematics more often, while the class mentioned since childhood more frequently.

In both cohorts of respondents, the highest number of answers to the question about the reasons for choosing the teaching profession fell into the category of altruistic motives, while the least was attributed to extrinsic motivations. That can be considered a very favourable result, as there is a strong positive correlation between teacher education, subsequent professional development, career satisfaction with the choice of the teaching profession, and retention in the profession, all associated with altruistic and intrinsic motivation, while extrinsic motives are not decisive (Falch et al., 2009; Rice et al., 2023; Watt et al., 2012; Watt & Richardson, 2007; Willén, 2021). Similar conclusions were drawn by Gomila-Grau et al. (2025), who found that future educators often frame their motivation through ethical commitment, personal reflection, and a desire for social transformation. The research by Watt et al. (2012), conducted in four different social contexts, yielded similar results, indicating that the highest-rated reasons for choosing a teaching career were intrinsic motivations, perceived teaching ability, and altruistic motivations, such as the desire to contribute to society and work with children and adolescents. Similarly, McLean et al. (2019) found that future teachers as essential factors in their career choice cited personal abilities and the intrinsic value of a career, both intrinsic motivations. However, contrary to the results of this study, the findings by McLean et al. (2019) did not demonstrate the significance of altruistic motivation in contributing to society as an imperative reason for choosing a teaching career.

The subject stated relatively often that they love mathematics, as in the response: “Because I love mathematics, it’s interesting. I have always preferred practicing various tasks over studying theoretical subjects.” They also expressed a desire to change the approach to mathematics, as noted in the response: “Because I want to try to present mathematics, which is one of the worst (most difficult) subjects for everyone, something that most people tend to ‘getaway’ from in further schooling, in an easier way and perhaps even make them love it.” Authors Yorkovsky and Levenberg (2021) found similar results regarding the unexpectedly small significance of family influence on the choice of a teaching career, which they interpreted as a reduction in the impact of the nuclear family on young people along with an increase in social influences, such as the significance of discipline in society, social status, and the image of MTs.

In contrast to the subject, the class mentioned relatively frequently that they want to have a positive influence on children, as exemplified by the response: “I chose to be a teacher to educate and nurture the youngest age group (children) in the spirit of love, kindness, and solidarity.” They also indicated that they have wanted to pursue this vocation since childhood, as noted in the response: “Since I was little, I played teacher; I can’t imagine myself in any other profession.” There is a possibility that these respondents may choose teaching as a profession not because their personality is suited for teaching, but rather because it is all they believe they know and something familiar from their previous schooling, without exploring other career options, which would suggest that their education limits their career choices (Crowe & McGarr, 2022).

These findings suggest that the subject is more focused on mathematics as a science, while the class shows a greater emphasis on the children they will work with, which can be associated with the differences in the programs they are enrolled in (Swars et al., 2009; Yuan & Zhang, 2017). It is essential to consider what perspectives future teachers adopt about teaching, and to support student teachers so they can better navigate the complex process of becoming a teacher (Mtika & Gates, 2011). That becomes even more important when we know that pupils transitioning from primary to lower secondary school need better motivational support during this transitional period, with long-term stable support from teachers playing an even more critical role than support from parents and peers in overcoming the difficulties students face in learning (Raufelder et al., 2022; Roorda et al., 2019; Tommasi et al., 2022; Virtanen et al., 2022).

5.3. Important Teacher Qualities

Table 3 shows the percentage by cohort, of the ranks assigned to the offered teachers’ qualities. A statistically significant difference between the cohorts emerged in the qualities of subject knowledge and conducting interesting classes, which were ranked higher in importance by the subject compared to the class. Conversely, the quality of knowing the students was ranked as more important by the class than by the subject.

Table 3. Percentage display of codes assigned to teacher qualities by cohort.

Teacher Qualities	Assigned Ranks	1st	2nd	3rd	4th	5th	6th	7th
		%	%	%	%	%	%	%
knowledge	subject	62.89	17.53	10.31	5.67	3.09	0	0.52
	class	38.37	22.67	15.12	10.47	8.14	4.65	0.58
preparation	subject	9.79	38.66	24.74	12.37	7.22	6.19	1.03
	class	16.86	31.4	13.95	15.12	11.63	9.88	1.16
students	subject	3.61	10.31	12.37	18.56	35.05	18.04	2.06
	class	16.28	18.02	22.09	16.86	18.6	7.56	0.58
interestingness	subject	17.01	14.43	25.26	25.26	16.49	1.03	0.52
	class	13.95	12.79	14.53	18.02	27.91	12.79	0
discipline	subject	8.25	18.04	24.74	27.32	14.95	6.19	0.52
	class	12.21	8.72	29.07	23.84	15.7	8.72	1.74
entertainment	subject	0	1.03	2.58	10.31	19.07	59.28	7.73
	class	1.74	4.65	5.23	15.12	17.44	51.74	4.07
appearance	subject	0	0	0	0	3.09	9.28	87.63
	class	0.58	1.74	0	0.58	0.58	4.65	91.86

Respondents from both cohorts identified the most valuable quality of a teacher as knowing the subject they teach, although the subject rated this significantly higher than the class. This is one of the three theoretically important manifestations of teacher expertise related to the content of mathematics instruction (Copur-Gencturk & Tolar, 2022; Deng, 2012). This finding differs from the study by Haser et al. (2024), in which future MTs most often describe an MT as a didactic expert, which appeared as the second most important quality in this study. The cause of the observed difference may lie in the different programs they are enrolled in.

The second-ranked quality was being well prepared, which covers the second theoretically significant manifestation of expertise, namely pedagogical content knowledge (Brunner et al., 2024; Copur-Gencturk & Tolar, 2022; Deng, 2012). That may be regarded as a favourable result, as both cohorts ranked qualities related to two dimensions of expertise important for teaching mathematics: content knowledge and pedagogical content knowledge. Authors Yorkovsky and Levenberg (2021) found that the most important characteristic required of teachers is knowledge, which aligns with the results of this study, followed by personal attributes and interpersonal skills, which were ranked lower in this research. Grunder (2016) posits that pedagogical education and teaching methods are crucial for success and productivity, a finding that also proved relevant for future teachers in this study through lesson preparation, conducting engaging classes, and maintaining discipline. This finding is not in line with contemporary didactics. Unlike traditional didactics, where the teacher is content-oriented, modern approaches to the concept of curriculum focus more on the processes of teaching and learning in the classroom rather than on the curriculum content (Werler & Tahirsylaj, 2020).

In the further distribution of responses, it is observed that the subject prioritizes conducting interesting classes over maintaining order in the classroom. In contrast, the class ranks maintaining order higher. This finding aligns with the expressed motives for choosing the profession, where the subject identified a desire to change the approach to mathematics as one of their main motivations. In the responses from the class, the quality of knowing their students is ranked significantly higher, most often in third place, while in the subject, it is most frequently in fifth place. This again corresponds to the expressed motivation of the class for choosing the profession, wanting to have a positive impact on children, and the highlighted differences in the programs they are enrolled in. These findings indicate that during ITE, future teachers should be allowed to reflect on their motivations for choosing the teaching profession, nurturing and promoting motivation toward teaching as a lifelong career (Yuan & Zhang, 2017).

The qualities of being able to entertain and looking good were ranked the lowest in both cohorts, which is a positive result as it shows that both the class and subject prioritize professional and pedagogical qualities of teachers.

5.4. Mathematics as a Science and Mathematics as a School Subject

The extracted codes and results for responses to the question of how they would explain what mathematics is to a ten-year-old pupil are presented in Table 4. A statistically significant difference exists in thinking and scientific benefit, which the subject mentions more frequently, while the class cites numbers more often.

Table 4. Codes and answer results to how to explain what mathematics is to a ten-year-old pupil.

Codes	Description and Example	Subject	Class	p-Value
thinking	They emphasize that mathematics develops logical thinking and problem-solving skills. “Mathematics is a science that teaches easier and faster reasoning and problem-solving.” (female MT051)	35.38%	6.90%	<0.001
everyday life	They highlight that mathematics is useful in everyday life and the world around us. “Mathematics is a science that helps us understand the world around us. It is present in almost every area of life.” (female MT020)	35.38%	38.51%	0.534
scientific benefit	They stress the usefulness of mathematics in other subjects and sciences. “Mathematics is the foundation for all other sciences; we just need to pay attention and understand that everything is based on it because mathematics is not just numbers.” (female MT046)	12.82%	4.02%	0.003
creativity	They connect mathematics with play, imagination, and creativity. „Mathematics is the most interesting game in the world.” (female MT036)	9.74%	4.60%	0.058
numbers	They define mathematics as a science that deals with numbers and geometry. “Mathematics is a science that deals with numbers and geometric figures.” (female PT264)	22.05%	47.13%	<0.001

When considering both cohorts, the largest number of responses to how they would explain to a ten-year-old what mathematics is highlights the usefulness of mathematics in everyday life and the world around us. For example, one response stated: “Mathematics is a subject that is very useful in life, because wherever we go, without basic mathematical knowledge we can’t manage, neither in the store nor at school, etc.” That can be considered a favourable result, as students better understand mathematics when its usefulness is emphasized in teaching (Akyıldız et al., 2021). This result aligns with findings by Seckel et al. (Seckel et al., 2020), where most future PTs had a positive attitude toward the usefulness of mathematics during their ITE. The significance of how students perceive the usefulness of science for their positive attitude toward studying natural sciences and its connection to their career aspirations in science has also been confirmed (Sheldrake et al., 2017).

The second most common response indicated that mathematics is a science concerned with numbers and geometry, as exemplified by: “Mathematics is the science of understanding arithmetic operations, geometric shapes and bodies.” The class provided significantly more of these responses than the subject did. We can assume that ITE influenced this result (Marušić et al., 2020; Phelps-Gregory et al., 2019; Swars et al., 2009). This finding is particularly significant for the class, as their understanding of mathematics may diminish students’ interest in the subject, leading to students receiving an incomplete message about the importance of mathematics from the very beginning of their education. The literature provides examples of how such beliefs among teachers have changed due to altering the nature of the mathematical experiences offered in mathematics education programs (Leavy & Hourigan, 2018). Studying practically applicable knowledge is a valuable learning experience, as it leads to students being more active, feeling better during the learning process, and consequently achieving better learning results (Hargreaves et al., 2017).

The third most common response was that mathematics develops logical thinking and problem-solving skills, as illustrated by: “Mathematics is a science that enables the development of thinking and logic, which helps develop perseverance, effort, and work.” The subject used such formulations in their definitions of mathematics more frequently. This finding, in a way, aligns with the previous one and confirms that the subject has a broader and deeper understanding of what mathematics is compared to the class. Given that critical thinking is considered a 21st-century skill, it is very important for both the class and subject to recognize mathematics education as an opportunity for developing critical thinking, and in this regard, it is necessary to improve their ITE (Romero Ariza et al., 2021).

Explanations of mathematics that emphasize its usefulness in other subjects and sciences, such as the response: “A set of mechanisms for solving problems in other sciences,” appeared less frequently in both cohorts, although such responses were more common among the subject group than the class group. This result is unexpected, considering that the class group is preparing to teach all subjects across various fields of science, and it could be anticipated that they would more readily recognize the connections between mathematics and other subjects. The experience from Nigeria, where students are explicitly taught the educational values of mathematics during their ITE, may be beneficial (Awofala & Ojaleye, 2018). The significant responses from the subject further confirm their deep and broad understanding of the science they will teach in school.

The smallest number of responses from both cohorts associated mathematics with play, imagination, and creativity, as exemplified by the following: “Mathematics is a game with numbers, imagination, shapes, pencils, and erasers. These are toys in a room we will call mathematics. Enjoy the game!” However, the subject provided slightly more such responses than the class. That is one of the least favourable results of this research. Similar findings were reported by authors Phelps-Gregory et al. (2019), whose results indicated that beliefs about mathematics and learning mathematics require logical thinking, which lacks creativity. Previous research by De-la-Peña et al. (2021) showed that future MT who are more creative and flexible in formulating mathematics instruction have a more positive attitude toward mathematics, which will help their future students better understand mathematics and be more effective in learning. Working to create positive attitudes toward mathematics during ITE is fundamental for nurturing teachers’ mathematical competence (De-la-Peña et al., 2021).

6. Conclusions and Recommendations

Future PTs and MTs predominantly choose the teaching profession for altruistic and intrinsic reasons. A noticeable difference is that future MTs are more focused on mathematics as a science, while future PTs are more oriented toward the children they will work with, which is linked to the differences in the educational programs they attend (Swars et al., 2009). Changes in ITE are needed to create a better balance between content knowledge and pedagogical content knowledge. In addition to theoretical knowledge about mathematics, ITE should provide exposure to new theories and approaches in teaching and, as much as possible, include practical experience, a thorough understanding of their context, and reflection on how to adapt these theories to their students in their teaching (Bremner et al., 2023; Gildehaus et al., 2024; Greefrath et al., 2022).

Active teaching methods enhance student engagement and learning, but their effectiveness depends on context, student age, and level; therefore, teacher training and a mix of strategies tailored to students’ needs are essential (Aguilar-Moya et al., 2025). To address this issue, it is recommended to initiate discussions about the value of the child’s place in the reasoning of future PTs and MTs, which would be conducted based on focused viewing of recorded lessons, paying attention to specific aspects significant for the teaching and learning process. There is a belief that when future teachers see a child struggling to understand a concept covered in class, they will begin to recognize the difficulty of the topic for the child and integrate mathematical content with children’s mathematical thinking (Philipp et al., 2002). Individual interviews and teaching sessions, combined with video recordings, can further engage future teachers in analyzing children’s mathematical thinking, fostering reflection on how to support learning and integrate content with students’ reasoning (Philipp et al., 2002).

The research data generally indicate that previous positive personal experiences with mathematics have influenced the development of altruistic motives for choosing the teaching profession. A significant finding is that reasons related to the teacher are given as a preference for the subject, confirming the thesis about the importance of the teaching profession and the impact teachers have on their students and their development and learning. Previous negative experiences with mathematics have shaped perceptions of mathematics as a science of numbers and geometry, while prior positive experiences have led to mathematics being explained as a science that is useful in everyday life, developing logical thinking and problem-solving skills. This means that, in addition to its connection to motivation for choosing the teaching profession, the previous experiences of future teachers with the subject of mathematics are significant for their understanding of the mathematics they will teach in school.

In teacher education, it is important to recognize and incorporate multiple motives for choosing the profession, as well as their prior school experiences, which shape a teacher’s pedagogical identity (Bergmark et al., 2018). The emphasis in identity work should be on professional self-understanding that reflects personal experiences, values, and beliefs related to the contextual aspects of a teacher’s work (Abramson & Schachter, 2024; Gomila-Grau et al., 2025; Schellings et al., 2021). Strategies that foster a positive attitude toward teaching and a sense of belonging should be prioritized in teacher education programs, as they enhance knowledge sharing, professional development, and prepare future teachers for successful careers and meaningful contributions to education (Al-Mahdy & Elwakil, 2025).

There are significant differences in the approaches of future PT and MT toward mathematical education, even though both attribute equal importance to the two dimensions of expertise essential for teaching mathematics: content knowledge and pedagogical content knowledge. The most noticeable differences are in the focus on children, which is more prominent in the responses of future PTs, and the emphasis on mathematics as a science, which is dominant in the answers of future MTs. This finding indicates the need for establishing a stronger connection between theory and practice in ITE. Real change in educational practice can only be achieved through a solid link between theory and practice in teacher education (Bremner et al., 2023; Charalambous et al., 2009; Puustinen et al., 2018). Furthermore, ITE should be based on research into practice, implying the need for improved partnerships between schools and universities (Christiansen & Erixon, 2021; Van Katwijk et al., 2021). A holistic approach should be adopted in teacher education to support deeper self-understanding through planned reflections (Arvaja et al., 2020).

This study provides insights into future teachers’ perceptions by combining qualitative analysis with statistical testing. However, several limitations should be acknowledged. The sample was convenient and consisted of students from only two teacher education programs in Serbia, which restricts the representativeness of the findings. Nonetheless, it is important to note that all teacher education programs in Serbia are developed in accordance with the same national standards and are accredited by the National Accreditation Body, which enhances comparability across institutions. Moreover, the data were collected through self-reports, which may be influenced by personal perceptions or social desirability bias. These factors limit the generalizability of the results beyond the studied cohorts and institutions.

Future research could address these limitations by including participants from multiple institutions and cultural contexts. Comparative international studies would be particularly valuable to examine whether the identified patterns are consistent across different educational systems, thereby strengthening the external validity of the findings.