Understanding the Relationship of Pre-Service Teachers’ Beliefs in Math and Teaching Practices: An Exploratory Sequential Mixed-Methods Approach

Pre-service teachers’ beliefs about mathematics and their classroom practices are crucial for shaping effective mathematics education. This exploratory sequential mixed-methods study aims to bridge the gap between these two aspects by investigating the range of beliefs held by PST’s, how these beliefs translate into specific teaching practices, and individual variations in this translation process. The study employed a two-phase approach. Phase 1 involves qualitative data collection through semi-structured interviews with PSTs from Secondary Education program, with a focus on Math specialization. These interviews explored PST’s experiences with math education, perspectives on effective teaching strategies, and challenges faced. Additionally, classroom observations of PSTs during practice placements examined interactions with students,
pedagogical approaches, and instructional materials. Data from interviews and observations were administered using NVivo software for thematic analysis to identify recurring themes and patterns in beliefs and teaching practices. Phase 2 involves the administration of a survey online to a larger sampled group of PSTs. The researchers utilized validated scales such as the Beliefs about Mathematics Teaching and Learning (B-MTL) and a Teachers’ Practices survey. Quantitative data on beliefs and practices were analyzed using descriptive statistics. By examining this relationship, the study identified a range of beliefs held by PSTs about mathematics and its teaching, along with variations in how these beliefs translate into practices. The findings aim to inform the development of teacher education programs by suggesting the need for curriculum development that addresses potential limiting beliefs and fosters effective pedagogical approaches, as well as incorporating reflective practices that encourage PSTs to critically examine their beliefs and their impact on teaching practices. Ultimately, the study emphasizes the importance of understanding the complex interplay between beliefs and practices to improve mathematics education for all students.

Introduction

Pre-service teachers’ beliefs in math and teaching practices play a significant role in shaping their instructional strategies and mathematical understanding, which in turn affect the quality of their classroom teaching practices. The relationship between teachers’ mathematics education beliefs and their teaching practices is an important topic in teacher education all-round the world and many studies focused on this topic directly or indirectly (Li & Yu, 2010). Researchers and teacher educators study the connection between teachers’ beliefs about math and their teaching practices to better understand how teachers’ beliefs develop and influence their instruction (Lomaset al., 2012). Moreover, Chalkiadaki (2018) stated that teacher beliefs and classroom practices are closely connected. Numerous studies have shown that pre-service teachers’ beliefs about math influence how they teach. For instance, teachers who hold transmission-oriented beliefs often adopt teacher-centered approaches, while those with discovery or constructivist views favor student-centered methods (Kasaet al., 2024; Yanget al., 2020; Purnomoet al., 2016). However, research has shown that while beliefs can influence teaching practices, other factors, such as teachers’ knowledge and school context, also play a role (Purnomoet al., 2016).

While existing research acknowledges the influence of teachers’ beliefs, a gap exists in fully comprehending how pre-service teachers’ specific math beliefs translate into tangible teaching practices. A deeper understanding of this connection is crucial to effectively prepare future educators and student learning outcomes in mathematics. Examining the connection between pre-service teachers’ math beliefs and practices holds significant importance for Teacher Education programs, mathematics education research & pre-service teachers. Informing the development of curricula and interventions that effectively address and challenge potential limiting beliefs, fostering more effective and impactful instructional approaches. Expanding our understanding of the complex factors influencing classroom practices and student learning in mathematics. Providing self-awareness and critical reflection opportunities, empowering them to make conscious choices informed by their beliefs and aligned with effective pedagogy. Despite educational reforms advocating for active learner engagement and conceptual understanding in math, traditional, didactic practices often persist in classrooms. Teachers’ beliefs, external pressures, classroom management concerns and lack of effective professionals are the contributing factors to the disconnect between beliefs and practices. This may result in the learner’s disengagement, superficial understanding and equity concerns.

Studies on pre-service teachers’ mathematical reasoning skills can also provide clues about their beliefs about math teaching (Manila Central University, 2004). In the Philippines, the curriculum emphasizes a constructivist approach that encourages students to explore and discover mathematical concepts themselves (Baki, 2008). This makes it even more important to understand pre-service teachers’ beliefs about math. These beliefs can influence how effectively they implement these new methods in the classroom. While research directly exploring this specific topic in the Philippines is limited, studies on teacher beliefs in general can offer valuable insights (Romblon State University Research Journal, 2014). For example, understanding how teacher educators’ beliefs shape their teaching methods (Fadera & De Guzman, 2014) can inform how pre-service math teacher education programs are designed.

Moreover, existing research highlights the multifaceted nature of teachers’ beliefs, encompassing views on mathematics, teaching, learning and self-efficacy (Angel-Cuervoet al., 2024; Minarniet al., 2018). Studies suggest that these beliefs influence instructional decisions and student engagement (Hillet al., 2004). Other recent studies have explored the complex nature of pre-service teachers’ beliefs about mathematics teaching and learning. Research indicates that these beliefs can change during teacher preparation programs (Mohr & Santagata, 2018). However, the study of Purnomoet al. (2016), the relationship between beliefs and instructional practices is not always straightforward. Therefore, mixed-method approaches, such as combining Q methodology with traditional surveys, have been proposed to gain a more comprehensive understanding of teachers’ belief systems (Buchholtz & Vollstedt, 2024). Nevertheless, these findings highlight the importance of continued research on pre-service teachers’ beliefs and their impact on classroom practices. However, limited research utilizes mixed method approaches to provide a holistic understanding of how specific beliefs manifest in observable practices, particularly among pre-service teachers.

This study aims to identify the range of beliefs held by pre-service teachers about mathematics and its teaching. Examine the relationship between these beliefs and specific classroom practices employed by pre-service teachers. Also, investigate the individual variations in how pre-service teachers translate their beliefs into practices; and generate insights to inform the development of effective teacher education programs and support reflective practices among pre-service teachers.

By employing an exploratory sequential mixed-methods approach, this study seeks to bridge the gap in existing research and offer a richer understanding of the intricate link between pre-service teachers’ math beliefs and their teaching practices, ultimately contributing to improved mathematics education for all.

Research Questions

This research adopted post-positivist perspectives, acknowledging that perfect objectivity in understanding pre-service teachers’ beliefs in math and its teaching practices is difficult. The following research questions were guided by post-positivist perspectives:

1. What specific beliefs about mathematics do pre-service teachers hold, and how do these beliefs inform their personal experiences and perceptions of their teaching practices?

2. To what extent do specific pre-identified mathematics beliefs correlate with the frequency and type of student-centered and traditional teaching practices employed by pre-service teachers?

3. How do the personal experiences and challenges shared by pre-service teachers in interviews confirm, contradict, or add nuance to the trends identified in the quantitative questionnaire on their math beliefs and teaching practices?

Methodology

Research Design

In this study, an Exploratory Sequential Mixed-Methods Research (MMR) design was used in order to explore and understand pre-service teachers’ beliefs in math and teaching practices. This design prioritizes qualitative data collection followed by quantitative data to expand and refine initial findings. This aligns with the framework proposed by Creswell and Plano Clark (2011), Tashakkori and Teddlie (2008), and Onwuegbuzieet al. (2010), where qualitative data is first collected and analyzed, and themes are used to drive the development of a quantitative instrument to further explore the research problem. As a result of this design, three stages of analyses are conducted: after the primary qualitative phase, followed by secondary quantitative phase, and finally, an integration phase to connect and expand upon the findings from both phases (Creswell & Plano Clark, 2011).

The Exploratory Sequential Mixed-Method Approach was ideal for this research because it allows for a thorough exploration of pre-service teachers’ beliefs in math and their integration into teaching practices. By starting with qualitative methods such as interviews and observations, the study can gain rich insights that will inform the development of quantitative instruments. This sequential approach ensures a comprehensive analysis of the relationship between beliefs and teaching practices, aligning with the complexity of the research questions.

Research Setting

This study was conducted at St. Rita’s College of Balingasag a RVM institution located at Tres Martires St., Barangay 3, Balingasag, Misamis Oriental. It is established in 1901, and the school is accredited by PAASCU. It is run by the Religious of the Virgin Mary (RVM), offers transformative Ignacian Marian education. The map of St. Rita’s College of Balingasag was shown in Fig. 1.

Fig. 1. Map of St. Rita’s College of Balingasag (Photo retrieved from Google Map, 2024).

Research Instrument

In this study, two different instruments were used to gather data: semi-structured interview and structured survey.

1. The researchers utilized a semi-structured interview consisting of a guide with 5 open-ended questions to elicit in-depth responses from pre-service teachers about pre-service teachers’ personal experiences with math education, their perspectives on effective teaching strategies in math, and any challenges they encounter in integrating their beliefs into their teaching practices. This focus on open-ended questions allows participants to share their unique perspectives and experiences in their own words, providing rich, detailed data that reveals the complex interplay between pre-service teachers’ beliefs and their practices to teaching math.

2. B-MTL Survey Questionnaire. The researchers utilized this survey questionnaire, comprising 21 Likert-scale items (1 as Strongly Disagree, 5 as Strongly Agree), was used to measure pre-service teachers’ beliefs about mathematics teaching and learning. The scale assessed beliefs on three dimensions: a Transmissionist, Facts First, and Fixed Instructional Plan (Schoen & LaVenia, 2019).

3. Teachers’ Practices Survey Questionnaire. The researchers used this survey questionnaire consisted of 25 Likert-scale items to evaluate participants’ self-reported instructional practices. The items assessed the extent to which teachers employed student-centered or teacher-centered pedagogies, with a scale ranging from 1 represents “None of the time” to 5 represents “All of the time”.

Research Participants

The participants of this study were the pre-service teachers enrolled in Secondary Education program with a mathematics specialization at St. Rita’s College of Balingasag. Pre-service teachers were ideal participants because their beliefs about mathematics and teaching practices are still forming. Participation was entirely voluntary, and the researchers aimed to gather data from a sample size that allows for rich qualitative exploration and in-depth quantitative analysis, an exploratory sequential mixed-method approach.

Data Gathering Procedure

Phase 1 (Qualitative)

In this phase the researchers first secured an approval from the program head of the teacher education program and consent from the participants who were Pre-Service Teachers from Secondary Education major in Mathematics. The researchers explored the beliefs of secondary math education pre-service teachers about mathematics and teaching practices, the researchers conducted semi-structured interviews and observed the pre-service teachers during their practice teaching placements, focusing on their interactions with students, pedagogical approaches, and use of instructional materials. Combining these qualitative methods allows for integration of data, enabling a comprehensive understanding of the complex relationship between pre-service teachers’ beliefs and their teaching behaviors. Specifically, interviews provided in-depth insights into self-reported beliefs, while observation allowed for direct examination of how these beliefs manifest in real-world teaching context. The researchers’ audio-recorded with consent the semi-structured interview and transcribed the recordings. And transcripts analyzed using thematic analysis revealed recurring themes and patterns in beliefs and teaching practices. Transcripts were entered into NVivo, a qualitative data analysis software for coding.

The researchers used different strategies, including in-depth interviews and observations, integrated within a well-structured case study design.

Phase 2 (Quantitative)

The researchers used the data from the qualitative phase to develop a survey instrument for the second quantitative phase of this Mixed-Method Research study and ensured validity and reliability. To measure pre-service teachers’ beliefs about mathematics and their teaching practices, the researchers administered a quantitative survey incorporating validated scales. Descriptive statistical analysis was utilized to identify potential correlations between these beliefs and factors such as teaching effectiveness measured through classroom observations and student outcomes from standardized tests which are the B-MTL (Beliefs about Mathematics Teaching and Learning) and Teachers’ Practices survey questionnaire. The researchers then recruited a larger sample of pre-service teachers through convenience sampling or stratified sampling. Administered a survey online and collected quantitative data on beliefs and teaching practices. Survey data was analyzed using SPSS for descriptive data to quantitative data.

The researchers employed correlational study design for this part to investigate the relationship between pre-service teachers’ math beliefs and their teaching practices.

Results and Discussion

Pre-service Teachers’ Beliefs

Problem 1: What specific beliefs about mathematics do pre-service teachers hold, and how do these beliefs inform their personal experiences and perceptions of their teaching practices?

This part of the study presents findings based on the semi-structured interview conducted by the researchers. The researchers identified three themes in this part.

Theme 1: The Impact of Teachers on Math Learning

Participants highlighted the significant role of a teacher in shaping students’ attitudes and experiences with Math. They mentioned their experiences both positive and negative towards their teachers and learning math.

“So going back to my experiences especially during elementary school, I can conclude now that math is easy, it depends on the teacher because there are some teachers that didn’t like it and didn’t know how to explain well.” (Participant 1, personal communication, [March 26, 2024])

“…the biggest impact is the peers and also the teacher…” (Participant 2, personal communication, [March 26, 2024])

“…during my high school days I struggled in mathematics but it doesn’t mean that I got some grade of 7 so, it also belongs to 90 but mathematics is not my favorite subject anymore so, it’s a difficult subject for me. So, in high school, mathematics is not my favorite because I don’t understand it. Honestly, the impact of the teacher on me when I was in high school is that math became far from me because I don’t understand any of them.” (Participant 3, personal communication, [April 02, 2024])

This experience about the impact of teachers on math learning agrees with the article concluded by Agyekum (2019) that teacher-student relationship is one of the factors that promote students’ learning. Positive interaction creates a peaceful environment, but negative interaction leads to instability. A study on collaborative learning environments by Wang (2023) also supports the idea that peers also impact math learning.

Theme 2: The Importance of Flexibility and Teaching Strategies

Participants expressed that effective mathematics instruction requires teachers to utilize a variety of teaching strategies that cater to different learning styles and student needs. They emphasized the importance of flexibility and teaching strategies of teachers.

“…we need to be flexible enough as we teach our students since again we deal with diverse students, they have different learning styles…” (Participant 1, personal communication, [March 26, 2024])

“…you should be flexible at all times…” (Participant 2, personal communication, [March 26, 2024])

“So I am preparing to become a math teacher. I always told my students to practice so they can really practice, not just like to solve, they just look or analyze, they need to practice, so they know what is the process that will not be forgotten.” (Participant 3, personal communication, [April 02, 2024])

This experience about the importance of flexibility and teaching strategies agrees with the article concluded by Leikin and Dinur (2007) and Fredenberg (2015) both emphasizes teacher flexibility in adapting to students needs and promoting mathematical thinking. This teacher adaptability aligns with the concept of a “mathematical swiss army knife”, as explored by Newtonet al. (2020). A teacher with this flexibility can be prepared for any problem-solving challenge their students encounter.

Theme 3: Balancing Conceptual Understanding with Procedural Skills

Participants emphasized that effective mathematics instruction requires a balance between conceptual understanding such as understanding the “why” behind the procedures and developing procedural fluency such as knowing how to solve problems.

“…For me, the situation is similar to my current situation… they understand why the result is negative but when I asked them do you understand why negative times positive is negative, they will answer yes ma’am, we understand ma’am, then I will say solve it but they don’t know how to solve it so it’s really important that you can balance the two concepts because it’s difficult.” (Participant 2, personal communication, [March 26, 2024])

“There are always students that get confused about the lesson. The best thing about my principle is that it always makes them understand by asking them what they find hard or confusing about the lesson.” (Participant 4, personal communication, [April 02, 2024])

This experience about balancing conceptual understanding with procedural skills agrees with the article concluded by Wright (2017) which emphasizes that balance is crucial for effective instruction. This balance helps students grasp the “why” behind procedures and develop problem-solving abilities. However, as Engelbrechtet al. (2009) suggests, students may have a preference for procedural solutions, which can impact their learning.

Beliefs and Teaching Practices

Problem 2: To what extent do specific pre-identified mathematics beliefs correlate with the frequency and type of student-centered and traditional teaching practices employed by pre-service teachers?

The researchers conducted their survey among the pre-service teachers around the Municipality of Balingasag, Misamis Oriental. The descriptive statistical analysis of the results is presented in the Tables I–III.

Table I. Mean, Standard Deviation, and Interpretation of the B-MTL

Item No.	Questions	Mean	SD	Interpretation
1	Students learn through doing exercises.	4.30	1.15	Strongly agree
2	Students work on their own, consulting a neighbour from time to time.	3.43	1.04	Agree
3	Students only use the methods I teach them.	3.87	1.14	Agree
4	Students start with easy questions and work up to harder questions.	4.61	0.72	Strongly agree
5	Students choose which questions they tackle.	3.52	1.38	Agree
6	I encourage students to work more slowly.	3.87	1.01	Agree
7	Students compare different methods for doing questions.	3.87	1.14	Agree
8	I teach each topic from the beginning, assuming they don’t have any prior knowledge of the topic.	4.04	0.77	Agree
9	I teach the whole class at once.	3.39	1.23	Neutral
10	I try to cover everything in a topic.	3.39	1.23	Neutral
11	I draw links between topics and move back and forth between topics.	3.91	0.85	Agree
12	I am surprised by the ideas that come up in a lesson.	3.74	1.05	Agree
13	I avoid students making mistakes by explaining things carefully first.	3.74	1.05	Agree
14	I tend to follow the textbook or worksheets closely.	3.74	1.05	Agree
15	Students learn through discussing their ideas.	4.09	1.08	Agree
16	Students work collaboratively in pairs or small groups.	4.48	0.95	Strongly agree
17	Students invent their own methods.	3.35	1.11	Neutral
18	I tell students which questions to tackle.	3.74	1.05	Agree
19	I only go through one method for doing each question.	3.43	1.08	Agree
20	I find out which parts students already understand and don’t teach those parts.	3.78	1.17	Agree
21	I teach each student differently according to individual needs.	3.74	1.25	Agree
22	I tend to teach each topic separately.	3.87	1.36	Agree
23	I know exactly which topics each lesson will contain.	4.30	0.76	Strongly agree
24	I encourage students to make and discuss mistakes.	3.57	1.08	Agree
25	I jump between topics as the need arises.	3.57	1.08	Agree
	OVERALL MEAN	3.81	0.17	AGREE

Table II. Mean, Standard Deviation, and Interpretation of the Teaching Practices

Item No.	Questions	Mean	SD	Interpretation
1	Effective math teachers consistently create opportunities for students to solve problems in their own ways before the teacher has already shown them a good way to solve that type of problem.	4.22	1.09	Strongly agree
2	Before showing students how to solve math problems, teachers should encourage students to create their own ways to solve them.	3.96	1.19	Agree
3	It is very important for students to discover how to solve math problems in their own ways.	4.22	1.17	Strongly agree
4	Students can figure out ways to solve many math problems prior to formal instruction.	3.65	0.98	Agree
5	The teacher should demonstrate how to solve word problems before students are expected to solve word problems on their own.	4.39	0.94	Strongly agree
6	Most students cannot figure out how to solve math problems by themselves and must be explicitly taught.	4.22	1.00	Strongly agree
7	Asking students to solve problems in their own ways causes too much frustration.	3.96	0.93	Agree
8	Allowing students to develop their own strategies for solving math problems creates too much risk that students will learn to solve problem incorrectly.	3.22	1.17	Neutral
9	Students should be instructed to solve problems the way the teacher has taught them.	4.0	1.13	Agree
10	Teachers should not focus too much on expecting students to solve problems in their own way, because that leads to student frustration.	3.83	0.94	Agree
11	It is more effective to show students how to solve problems than to let them solve problems in their own way.	4.26	0.86	Strongly agree
12	Students should master some basic facts before they are expected to solve word problems.	4.57	0.95	Strongly agree
13	Students should master carrying out computational procedures before they are expected to understand why those procedures work.	4.30	0.97	Strongly agree
14	Students must know the basic facts before they can understand the meaning of the four operations (addition, subtraction, multiplication, and division).	4.70	0.88	Strongly agree
15	The ideal way to teach problem solving is to have a student repeatedly solve one kind of problem at a time until he or she has mastered that type of problem.	4.13	1.10	Agree
16	Even students who have not learned the basic facts can have efficient methods for solving word problems.	3.39	1.16	Neutral
17	If the teacher deviates from the the sequence in the textbook, students will not learn the mathematics they supposed to learn.	3.43	1.16	Agree
18	Following the textbook closely ensures that the teacher is focused on the right sequence of mathematical topics.	3.83	0.94	Agree
19	It is important to follow the textbook and/or pacing guide with fidelity, even if it seems that students do not yet understand a mathematical concept.	3.09	1.04	Neutral
20	If the scope and sequence in the math textbook is followed carefully, most students will eventually understand the mathematics they are supposed to learn.	4.09	0.90	Agree
21	Teachers should follow the sequence in the textbook rather than sequence instruction on their own.	3.61	1.16	Agree
	OVERALL MEAN	3.95	0.11	AGREE

Table III. Comparative Joint Discussion Table of Qualitative and Quantitative Results

Themes from lived experiences	Descriptive results on selected factors	Integration of two results
The impact of teachers on math learningOne of the participants stated that “… the biggest impact is the peers and also the teacher…” (Participant 1)	One of the items in the survey questionnaire states that effective math teachers consistently create opportunities for students to solve problems in their own ways before the teacher has already shown them a good way to solve that type of problem with the mean of 4.22 and a standard deviation of 1.09 which is interpreted as Strongly Agree.	Confirmed that Pre-Service Teachers must have an impact on math learning.
The Impact of Teachers on Math LearningOne of the participants stated that “…Honestly, the impact of the teacher on me when I was in high school is that math became far from me because I don’t understand any of them.” (Participant 3)	One of the items in the survey questionnaire states that teachers should not focus too much on expecting students to solve problems in their own way, because that leads to students’ frustration with the mean of 3.83 and a standard deviation of 0.94 which is interpreted as Agree.	Discordant Pre-Service Teachers must be impactful on math learning.
The importance of flexibility and teaching strategiesOne of the participants stated that “…we need to be flexible enough as we teach our students since again we deal with diverse students, they have different learning styles” (Participant 1)	One of the items in the survey questionnaire states that I teach each student differently according to individual needs with the mean of 3.74 and a standard deviation of 1.25 which is interpreted as Agree.	Confirmed that Pre-Service Teachers gives importance of flexibility and teaching strategies.
The importance of flexibility and teaching strategiesOne of the participants stated that “… you should be flexible at all times…” (Participant 1)	One of the items in the survey questionnaire states that I only go through one method for doing each question with the mean of 3.43 and a standard deviation of 1.08 which is interpreted as Agree.	Discordant Pre-Service Teachers must value the importance of flexibility and teaching strategies.
Balancing conceptual understanding with procedural skillsOne of the participants stated that “…For me, the situation is to my current situation…they understand why the result is negative but when I asked them do you understand why negative times positive is negative, they will answer a yes ma’am, we understand ma’am, then I will say solve it but they don’t know how to solve it so it’s really important that you can balance the two concepts because it’s difficult.” (Participant 2)	One of the items in the survey questionnaire states that students must know the basic facts before they can understand the meaning of the four operations (addition, subtraction, multiplication, and division) with the mean of 4.70 and a standard deviation of 0.88 which is interpreted as Strongly Agree.	Confirmed that Pre-Service Teachers know how to explain balancing conceptual understanding with procedural skills.
Balancing conceptual understanding with procedural skillsOne of the participants stated that “There are always students that get confused about the lesson. The best thing about my principle is that it always makes understand by asking them what they find hard or confusing about the lesson.”(Participant 4)	One of the items in the survey questionnaire states that students should master carrying out computational procedures before they are expected to understandwhy those procedures work with the mean of 4.30 and a standard deviation of 0.97 which is interpreted as Strongly Agree.	Discordant Pre-Service Teachers must teach students how to balance conceptual understanding with procedural skills.

Table I shows the mean, standard deviation, and interpretation of Pre-Service Teachers’ Beliefs in Mathematics. It gives the highest mean of 4.70 with a standard deviation of 0.88 which interpreted as Strongly Agree and lowest mean of 3.09 with a standard deviation of 1.04 which interpreted as Neutral.

Table II shows the mean, standard deviation, and interpretation of Pre-Service Teachers Teaching Practices with the highest mean of 4.61 with a standard deviation of 0.72 which interpreted as Strongly Agree and the lowest mean of 3.35 with a standard deviation of 1.11 which interpreted as Neutral.

Nuancing Trends through Interviews

Problem 3: How do the personal experiences and challenges shared by pre-service teachers in interviews confirm, contradict, or add nuance to the trends identified in the quantitative questionnaire on their math beliefs and teaching practices?

There are three identified themes in the study: (1) The Impact of Teachers on Math Learning, (2) The Importance of Flexibility and Teaching Strategies, and (3) Balancing Conceptual Understanding with Procedural Skills.

Based on the comparative joint discussion table of qualitative and quantitative results, there are three confirmed items and three discordant items supporting these themes. For instance, the theme The Impact of Teachers on Math Learning and the result about the question “Effective math teachers consistently create opportunities for students to solve problems in their own ways before the teacher has already shown them a good way to solve that type of problem” with the mean of 4.22 and a standard deviation of 1.09 is confirmed or the result are agree with each other, that Pre-Service Teachers must have an impact on math learning. Meanwhile, this theme and the question “Teachers should not focus too much on expecting students to solve problems in their own way because that leads to students’ frustration” with the mean of 3.83 and a standard deviation of 0.94 is discordant meaning they don’t go well with each other, Pre-Service Teachers must be impactful on math learning.

The theme The Importance of Flexibility and Teaching Strategies and the question “I teach each student differently according to individual needs” with the mean of 3.74 and a standard deviation of 1.25 is confirmed or the result agree with each other, Pre-Service Teachers gives importance of flexibility and teaching strategies. On the other hand, this theme and the question “I only go through one method for doing each question” with the mean of 3.43 and a standard deviation of 1.08 is discordant meaning they don’t go well with each other, Pre-Service Teachers must value the importance of flexibility and teaching strategies.

The theme Balancing Conceptual Understanding with Procedural Skills and the question “Students must know the basic facts before they can understand the meaning of the four operations (addition, subtraction, multiplication, and division)” with the mean of 4.70 and a standard deviation of 0.88 is confirmed or the result agree with each other, Pre-Service Teachers knows how to explain balancing conceptual understanding with procedural skills. Meanwhile, this theme and the question “Students should master carrying out computational procedures before they are expected to understand why those procedures work” with the mean of 4.30 and a standard deviation of 0.97 is discordant meaning they don’t go well with each other, Pre-Service Teachers must teach students how to balance conceptual understanding with procedural skills.

Conclusion and Recommendation

Conclusions

Based on the findings of the study, the researchers conclude that:

Pre-Service Teachers frequently hold various beliefs about mathematics such as its difficulty, its relevance to real life, and the importance of procedural vs. conceptual understanding. These beliefs are often shaped by their own experiences as learners and may influence how they perceive their teaching practices.

This research identified that mathematics beliefs align with the frequency and type of student-centered and traditional teaching practices that Pre-Service Teachers planned to employ. The correlation between specific mathematics beliefs and teaching practices, the strength and consistency of this correlation may vary among individual Pre-Service Teachers and across different teaching contexts.

Furthermore, by analyzing personal experiences and challenges shared by Pre-Service Teachers in interviews, the study was able to confirm, contradict or add nuance to the trends identified in the quantitative questionnaire on their mathematics beliefs and teaching practices. For instance, while the quantitative data suggested a strong correlation between beliefs in student-centered learning and the reported use of student-centered strategies, interviews revealed that some Pre-Service Teachers, despite expressing strong beliefs in student-centered approaches, faced challenges in implementing them due to concerns about classroom management, lack of confidence, and limited access to resources. Conversely, some Pre-Service Teachers who reported using teacher-centered strategies in the survey expressed a strong desire to incorporate more student-centered approaches but felt constrained by curriculum demands and external pressures. Additionally, the interview data provided valuable insights into the reasons behind certain beliefs and practices, such as the influence of past learning experiences and the impact of mentor teachers.

By recognizing and understanding these dynamics, teacher education programs can better support the development of reflective practitioners who are equipped to critically evaluate their beliefs, adapt their practices, and navigate the complexities of mathematics education in diverse classroom settings. Additionally, continued research in this area can contribute to the ongoing discourse on effective pedagogical strategies and professional development initiatives aimed at enhancing mathematics instruction and student learning outcomes.

Recommendations

This study recommends the pre-service teachers to reflect on their beliefs in math and math teaching. This self-awareness can help them identify and overcome any limiting beliefs that might hinder their teaching. They should also seek out professional development opportunities to learn new teaching strategies and challenges their own assumptions.

In addition, the researchers recommend the teacher education program to adopt curriculum development that addresses potential limiting beliefs and fosters effective pedagogical approaches, as well as incorporating reflective practices that encourage pre-service teachers to critically examine their beliefs and their impact on teaching practices.

The researchers also recommend the future researchers to delve deeper into the factors that influence the development and transformation of pre-service teachers’ beliefs about math teaching. Longitudinal studies can track changes in beliefs over time and identify key factors that contribute to belief change.