Preservice mathematics teachers' confidence in teaching algebra: A scale adaptation study

This study uses a narrative qualitative research design to explore the role of math applications in the learning experiences of preservice mathematics teachers. Data were collected through interviews with 15 preservice mathematics teachers enrolled in a teacher education program in La Union. The study focused on how preservice mathematics teachers made use of these applications, the difficulties they faced, and the possibilities for incorporating such tools into their future professional practices. Findings revealed that participants utilized Geogebra, Photomath, Gauthmath, Mathway, and Khan Academy applications. These tools enhanced their understanding of mathematical concepts through visual representations, interactive simulations, and step-by-step problem-solving. However, participants encountered difficulties such as poor internet connectivity, subscription limitations, and unfamiliar interfaces. Preservice mathematics teachers intended to incorporate these tools into their future teaching to promote student engagement, an interactive environment, and a deeper understanding of mathematics. These findings support integrating educational technology training among preservice mathematics teachers and highlight the role of digital tools in shaping 21st-century mathematics education. The study emphasizes equipping future educators with the necessary competencies to integrate technology into mathematics education effectively.

<p style="text-align: justify;">Preservice mathematics teachers' beliefs about actions related to the use of the technological tools in teaching mathematics may affect how they are going to use them in their classroom activities. However, there is a limited evidence of what beliefs they hold on their intended actions of using technological tools in teaching mathematics. This study presents two preservice high school mathematics teachers' actional beliefs related to their intended actions in teaching geometric transformations (GTs) using Geometer's Sketchpad (GSP). The study comprised of a series of five task-based qualitative interviews with each of two senior undergraduate preservice teachers at a medium-sized public university in the Rocky Mountain Region of the United States. This study used a radical constructivist grounded theory (RCGT) with five assumptions—symbiosis, voice, cognition, adaptation, and praxis as a theoretical framework to guide the study process. The thematic findings of the study included four in vivo categories of their beliefs associated with actions of teaching GTs with GSP – assessment of student learning, engaging students in a group activity in exploring GTs with GSP, engaging students in individual activity in exploring GTs with GSP, and exploring GTs with GSP as 'suck it up and do it.' Pedagogical implications of these categories have been discussed.</p>

Little emphasis has been given on the pre-service mathematics teachers’ learning needs on the required subject matter knowledge and skills for which they have been expected to possess at their final level of graduation, as a basis for teaching secondary school mathematics. This study employed qualitative research design, in which 30 pre-service mathematics have been interviewed on their mathematics learning needs. The finding of the study revealed that learning experiences of the training was adequate, but there is disconnection between the training curriculum and school mathematics subject matter for which the pre-service teachers have been train to teach. The pre-service mathematics teachers have viewed lecturer of the program as non-supportive which prevent them from active learning. This suggests that the program should include school mathematics curriculum in the training to enable the pre-service mathematics teachers to acquire the subject matter knowledge for which they have been train to teach. Lecturers of the program should change their attitude and behavior which might have adverse effect on pre-service mathematics teachers’ learning.

This study aimed to develop a specific Mathematical Content Knowledge (MCK) test focused on multiplication for pre-service mathematics teachers in Indonesia and Türkiye. No assessment tool exists to measure MCK related to multiplication among pre-service mathematics teachers. We used convenience sampling to obtain data from third- and fourth-year pre-service teachers in Indonesian and Turkish mathematics teacher education programs. The test items were administered to 423 Indonesian pre-service mathematics teachers and 413 Turkish pre-service mathematics teachers, and their responses were analyzed using factor analysis. The MCK test was found to be reliable, with 18 items that were grouped into four components: procedural knowledge of multiplication (C1), understanding of multiple representations (C2), conceptual knowledge of multiplication (C3), and anticipating students' thinking (C4). The study results suggest that a valid MCK test helps evaluate multiplication in these four components. Additionally, the study findings indicate that Indonesian pre-service teachers score higher in the C1 and C4 categories, while Turkish pre-service teachers score higher in the C2 and C3 categories.

This study aims to examine preservice science and mathematics teachers’ mathematics anxiety and beliefs about the nature of mathematics, as well as to reveal whether they differ according to the department. Moreover, this study investigates whether there is a relationship between beliefs about the nature of mathematics and mathematics anxiety. The participants of the study were 213 junior and senior preservice elementary science and mathematics teachers. Data collection tools were Philosophical Thoughts about the Nature of Mathematics Scale (PTNM) and Mathematics Anxiety Scale (MAS). Both descriptive and inferential statistics were used to analyze mathematics anxiety and beliefs scores of preservice elementary teachers. The study revealed that most of the preservice teachers’ scores on beliefs about the nature of mathematics high and their mathematics anxiety scores were low. The results indicated that there were significant differences in both belief scores and mathematics anxiety scores in favor of preservice mathematics teachers. In addition, there was a high negative correlation between pre-service teachers’ PTNM and MAS scores.

This exploratory mixed method study aimed to investigate the impact of occupational anxiety and academic hopelessness on pre-service mathematics teachers' academic achievement. The study also aimed to explore pre-service mathematics teachers' perspectives on this effect and to determine how these levels vary according to gender and grade level variables. In addition to a quantitative approach using the relational survey model, a qualitative approach with a case study design was also used in the study. The participants consisted of 184 prospective mathematics teachers who were selected using random sampling method. The qualitative dimension of the research was carried out with 12 pre-service teachers who were voluntarily selected among the participants. The measurement tools used in the study included the “Professional Anxiety Scale for Student Teachers”, the “Academic Hopelessness Scale”, the final semester “Weighted Grade Point Average” to assess academic achievement, and a semi-structured interview form developed by the researchers. The results show that pre-service mathematics teachers exhibit high levels of academic hopelessness and moderate levels of occupational anxiety. Gender was found to have a significant effect on occupational anxiety levels with a high effect size, and grade level was found to make a difference in favor of 4th graders in terms of academic hopelessness levels. Finally, there was a low level of positive correlation between pre-service teachers' academic hopelessness levels and their academic achievement.

This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling course, offered for the first time as an elective course in a secondary mathematics teacher training department in a public university in Turkey. The data were obtained from the modelling problems prepared by the pre-service mathematics teachers in the last 3 weeks of the Mathematical Modelling course, the video recordings of these problems’ presentations and the pre-service teachers’ responses to the questions they were asked about their presentations. When analyzing the participants’ approaches to construct and solve mathematical modelling problems, the main focus of attention included the appropriateness of the problems for modelling and of the solutions to the modelling process, as well as the approaches displayed in these stages. The study’s results demonstrated that the pre-service teachers considered various criteria when constructing modelling problems such as relevance to life, the possibility of being solved by mathematical knowledge and attracting attention and were found to be successful in understanding and simplifying the modelling process, however, they had difficulties in the interpreting and validating steps.

The aim of this study is to discuss the conceptual dimensions of pre-service mathematics teachers' approaches to the basic concepts and operations of mathematics. 25 pre-service mathematics teachers in the first semester of the 2022-2023 academic year, who were educated at a state university, participated in the research. Four open-ended questions about the basic concepts of mathematics were asked to pre-service mathematics teachers and their written opinions were received. Content and descriptive analysis were applied to the responses. As a result of the analyzes, pre-service teachers did not approach these questions in the context of conceptual knowledge, but generally gave the answers in the context of procedural knowledge. Pre-service mathematics teachers used reflective thinking, which they used to compare the procedural knowledge processes they gained in the formal education process with the previous solutions, in these question solutions as well.

This exploratory qualitative case study design aims to examine the mathematization process employed by pre-service mathematics teachers during instruction grounded in Realistic Mathematics Education (RME) within Plane Geometry. It was studied as this shall have a cascading effect on the teaching–learning of schools. Carried out at a teacher education college in the Oromia region of Ethiopia, the study used 27 pre-service mathematics teachers, who constituted one class as participants. The methods of data collection encompassed observation, informal discussions, and semi-structured interviews. The findings pinpoint significant progress, persistent challenges, and possible barriers to integrating realist mathematical artifacts and conceptions in class. Through the RME-centric mathematization instruction, these pre-service mathematics teachers crafted individual problem-solving strategies for comprehensive word problems relating to plane geometry and real-life contexts. Impressively, some participants even managed to leverage alternative equations and theorems not covered in the course materials. However, challenges emerged. The breadth of content, the nature of the curriculum, and specific limitations in the pre-service teachers' proficiencies were underscored as potential hurdles in the pre-service mathematics teacher's mathematization process to draw conjectures and mathematical concept formulations, including deriving relations among geometry concepts while solving geometry problems.

This research examines the correlation between pre-service mathematics teachers' perceptions of ethnomathematics-based instructional design and the quality of educational tools they produce during a university course. Employing a mixed-methods explanatory sequential design, quantitative data were gathered from 22 participants through a perception questionnaire utilizing a Likert scale. Descriptive statistics indicated generally positive perceptions, with a mean score of 42.36 and a standard deviation of 4.07, reflecting low variability among responses. Additionally, the final project assessments demonstrated moderately high performance, with a mean score of 37.77 and a standard deviation of 3.96. Qualitative analysis of lesson modules and student worksheets—evaluated via a rubric emphasizing cultural integration, mathematical coherence, and pedagogical quality—revealed diverse levels of success in incorporating local cultural elements into mathematics instruction. While many projects showcased innovative applications of ethnomathematical concepts, notable gaps persisted in aligning cultural contexts with explicit mathematical learning objectives and maintaining systematic lesson progression. The findings suggest that although pre-service teachers generally hold positive perceptions of ethnomathematics-based teaching design, these attitudes do not consistently translate into the development of high-quality, culturally embedded instructional materials. This discrepancy underscores the necessity for structured design training and reflective practice within teacher education programs. Such initiatives are essential to convert favorable perceptions into pedagogically sound and culturally responsive teaching tools. The study contributes to the ongoing discourse on integrating ethnomathematics into teacher education curricula. It highlights the importance of targeted curriculum development in culturally diverse educational settings and offers specific implications for enhancing instructional design through comprehensive training and reflective practices. Implementing these strategies can facilitate the effective translation of positive perceptions into practical, culturally relevant pedagogical approaches, ultimately enriching mathematics education in diverse cultural contexts.

Pre-service mathematics teachers’ metaphors about mathematics teacher concept

One of the key courses in the mathematics teacher education program in Israel is arithmetic, which engages in contents which these pre-service mathematics teachers (PMTs) will later teach at school. Teaching arithmetic involves knowledge about the essence of the concept of “number” and the development thereof, calculation methods and strategies. properties of operations on different sets of numbers, as well as the properties of the numbers themselves. Hence, the question arises: how to educate PMTs in order to supplement their mathematical knowledge with the required components? The present study explored the development of arithmetic thinking among pre-service teachers intending to teach mathematics at elementary school. This was done by matching the van Hiele theory of the development of geometric thinking to arithmetic. Analysis of findings obtained both in the present study and in many studies of geometry teaching indicates that this approach to considering the learners’ level of thinking development might lead to meaningful learning in arithmetic course for PMTs.

This study investigated the self-efficacy levels of pre-service science and mathematics teachers in a Philippine state university. A total of 172 pre-service science and mathematics teachers served as respondents of the study. Data collection was done through the use of the Science and Mathematics Teaching Efficacy Belief Instrument for Pre-service Teachers. The ANOVA indicated significant difference self-efficacy according to year level such that fourth year pre-service teachers indicated a statistically significant decrease. No significant difference was observed for gender and specialization. As regards to the type of courses as predictors of self-efficacy level, general education courses showed low positive predictive power (β = 0.180) whereas specialization courses and professional education courses showed a negative predictive power of β = -0.198 and β = -0.702 respectively. General education and professional education courses displayed significant predictive power at p < 0.05 whereas specialization courses did not (p=0.151). The overall explanatory power of the regression model was 61.1% (R2 = 0.611, F(3,171) = 90.419, p < 0.001). The 2 implications on the teacher education preparation as well as for future directions are likewise discussed.

Effective mathematics instruction requires teachers to diagnose students’ errors and provide scaffolding that is responsive to their learning needs. Yet, pre-service pre-service mathematics teachers (PMTs) frequently encounter challenges in identifying the nature of students’ mistakes and in designing appropriate instructional support. This study investigates the types of student errors diagnosed by pre-service pre-service mathematics teachers and the scaffolding patterns that emerge from their diagnostic practices. Adopting a qualitative descriptive approach, data were gathered through video analysis, microteaching, classroom practice, and in-depth interviews. The analysis indicates that pre-service pre-service teachers recognized four major categories of student errors: conceptual misunderstandings, procedural inaccuracies, representational mistakes, and strategic misapplications. In addressing these errors, they employed four corresponding scaffolding patterns. Conceptual scaffolding supported students in reconstructing mathematical meaning, procedural scaffolding provided step-by-step guidance, strategic scaffolding encouraged evaluation of alternative approaches, and metacognitive scaffolding fostered reflection on reasoning and symbolic interpretation. These findings underscore scaffolding as a dynamic and adaptive practice shaped by teachers’ professional vision. The study contributes to mathematics teacher education by demonstrating how practice-based programs can strengthen pre-service pre-service teachers’ capacity to notice, diagnose, and respond to students’ thinking, thereby promoting more inclusive and meaningful mathematics learning. This research provides new insights into how pre-service teachers’ scaffolding practices, shaped by error diagnosis, can inform teacher education globally.

The aim of this study was to examine the impact of developing WebQuests on the attention, confidence, relevance and satisfaction, or motivation, of pre-service secondary mathematics and chemistry teachers in the instructional technologies and material design course. There were a total of 67 pre-service teachers, 32 pre-service secondary mathematics teachers and 35 pre-service secondary chemistry teachers involved in this study, which took place over seven weeks. The pre-service teachers in both groups designed their WebQuests suitable for the level of high-school students. The researcher used a questionnaire in the collection of the data to find the motivational level of the participants. It was given to the participants by the researcher before and after the instruction during a single class period. The paired-samples t-test, independent samples t-test and ANCOVA were used in the analysis of the quantitative data. The study showed that designing WebQuests had more effect on the attention, confidence and relevance of the pre-service chemistry teachers than of the pre-service mathematics teachers. However, in general, although developing WebQuests had positive effects on the motivational levels of both pre-service secondary maths and chemistry teachers, there were no statistically significant differences found in relation to the motivational levels of both groups.    Keywords: WebQuests, pre-service teachers, attention, confidence, relevance, satisfaction