Pre-service Mathematics Teachers’ Conceptual Knowledge Related To Basic Concepts And Operations

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 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 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 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.

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 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 technological era has significantly impacted the quality of mathematics education. In reality, the frequency of technology usage in the classroom is minimal, and teachers continue to face challenges when utilizing learning management systems (LMS). Therefore, the purpose of this study is to identify the impact of LMS on the development of technological pedagogical content knowledge (TPACK) and digital skills of pre-service mathematics teachers. This mixed-methods study, employing an exploratory approach, involved 76 pre-service mathematics teachers (22 males, 54 females). Data was collected through questionnaires and interviews and subsequently compiled using Microsoft Excel and saved in CSV format. The data were then analyzed using Jamovi software version 2.4.8.0. Findings show that digital skills significantly influence TPACK development (β = 0.63, p < 0.001), more so than LMS usage (β = 0.49, p < 0.001), with a combined explanatory power of 65% (R² = 0.65). Higher digital skills improve pre-service teachers' ability to integrate technology into pedagogy and content. Additionally, final-year pre-service teachers show greater competencies. Male pre-service teachers generally exhibit higher digital skills than females (p < 0.001), influencing their capacity to effectively use digital tools in teaching. The strong correlation between digital skills and LMS usage (Spearman’s ρ = 0.86) underscores the need for structured digital competency development in teacher education. These findings emphasize the importance of fostering digital literacy and technology-integrated practicum experiences in mathematics instruction. Universities and school administrators should implement targeted training programs to enhance LMS utilization and help pre-service teachers develop strong TPACK competencies.

This study investigated Pre-Service Teachers’ mastery level, achievements differences, and correlation of their procedural knowledge and conceptual knowledge of rational numbers. The population of the study was four hundred and twenty-nine (429) level 100 Pre-Service Teachers of Evangelical Presbyterian College of Education, Bimbilla. Descriptive research design was used, where both convenient and purposive sampling techniques were employed to select a sample of 75. Out of the sample, 11 were females and 64 males representing 14.67% and 85.33% respectively. The instrument used was test items on conceptual and procedural knowledge on rational numbers designed by the researcher. The researcher used descriptive and inferential statistics to analyze the quantitative data, so as to answer the four research questions. The findings of the study indicated that the Pre-Service Teachers’ conceptual knowledge and procedural knowledge mastery levels were at average-low and high–average levels respectively. Also, there was a significant difference between conceptual and procedural knowledge in rational numbers in favor of procedural knowledge with very high effect size. There was a weak positive correlation and no significant relationship between the Pre-Service Teachers’ conceptual knowledge and procedural knowledge in rational numbers. The study recommended that College Tutors should be encouraged to adopt teaching methods and strategies that focus more on conceptual knowledge in rational numbers. Also, College Tutors evaluation exercises or assessment items should be balanced between conceptual knowledge and procedural knowledge because at the moment most assessment items are based on procedural knowledge to the neglect of conceptual knowledge assessment.

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.

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 study employs a descriptive-correlational design, using both qualitative and quantitative approaches, to investigate the self-efficacy levels of pre-service mathematics teachers in relation to their exposure to the 5Es instructional phases. Data was gathered from 106 pre-service mathematics teachers at Batangas State University Campuses during the academic year 2020-2021 using a researcher-made questionnaire and focus group discussions. Mean, Standard deviation, Pearson r, and Thematic Analysis were used to analyze the data. The results reveal a strong correlation between pre-service teachers' self-efficacy in mathematics and their exposure to the 5Es instructional phases. Additionally, it suggests the potential effectiveness of a researcher-made mathematics learning guide in enhancing students' self-efficacy in mathematics. This research underscores the importance of diverse learning strategies for mastering mathematical concepts, encourages instructors to innovate and adapt their instructional practices based on the 5Es model to enhance students' self-efficacy in mathematics, and calls for future research to explore additional factors that influence students' self-efficacy when exposed to 5Es instructional phases.

An examination of multiple intelligence domains and learning styles of pre-service mathematics teachers: Their reflections on mathematics education

Developing an activity design model for assessing teachers' mathematical understanding

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

Introduction: Although there is ambiguity about the elements of teacher knowledge, all researchers accept that being able to anticipate what errors can be made, the reasons for and the strategies to overcome these errors, in short, the knowledge of students is important for student achievement. In this study, knowledge of students refers to being aware of students’ possible errors and underlying reasons for these errors and knowing how to overcome these errors. Based on this consideration, the purpose of this study is to investigate pre-service elementary teachers’ knowledge of students on the subtraction topic. Methods: Considering the purpose, the data were collected from 118 pre-service elementary teachers who were enrolled in a four-year Elementary Teacher Education program via a task-based questionnaire related to the topic of subtraction and semi-structured interviews following the questionnaire. The task-based questionnaire included three completed incorrect subtraction tasks and was prepared considering the related literature and the elementary school mathematics curriculum of Turkey. Each task in the questionnaire contained a different type of error. The pre-service elementary teachers’ answers to the task-based questionnaire were categorized as correct, partially correct, wrong, or no answer by means of categorical analysis. The pre-service elementary teachers who gave correct and partially correct answers to the tasks were asked to participate in the second part of the study to learn their possible strategies to overcome the errors made in the tasks. Results: As a result of the quantitative and qualitative analysis of the pre-service elementary teachers’ responses, it was found that their knowledge of students for subtraction is limited. Specifically, although the pre-service elementary teachers were partially able to identify the errors in the first and second task, they were not able to identify the error in the third task. Furthermore, they were better able to determine a more commonly occurring subtraction error compared to the uncommon ones. The pre-service elementary teachers could not identify the underlying reasons that led the students to the errors. They could not explain what conceptual knowledge related to the topic of subtraction the student lacked that resulted in the errors. As the pre-service teachers did not attain these reasons, they were not able to provide strategies to overcome these errors different than restating the rules or procedures to overcome students’ errors. Discussion: Only being able to identify the errors is not enough to make the instruction effective. Teachers also need to know and provide a rationale for why the errors happen and how to overcome them (Even & Tirosh, 1995). Contrary to this statement, the pre-service elementary teachers in this study could not attempt to understand the students’ thinking or could not explain the reasons behind students’ errors with the notion of subtraction. Son (2013) emphasizes that pre-service teachers tend to explain the reasons for students’ errors as procedural. Similar to this emphasis, the pre-service teachers identified the errors as resulting from not applying procedures carefully or not enough knowing algorithms to find correct solutions. However, without addressing the reasons or focusing on procedures does not promote students’ understanding of the related topic (An, Kulm, & Wu, 2004). The pre-service teachers’ difficulties in identifying the possible conceptual reasons may result from deficits in knowledge of students (Fennema & Franke, 1992; Ball et al., 2008). Limitations: The findings were limited with the responses of the pre-service elementary teachers participating in this study. Moreover, the pre-service elementary teachers’ knowledge of students was investigated within the scope of subtraction. Conclusions: Although the pre-service elementary teachers could identify students’ errors on subtraction, they had difficulty in identifying the reasons and suggesting strategies to overcome the errors. Therefore, it can be concluded that the pre-service teachers’ knowledge of students for the topic of subtraction is limited. An implication of this is that teacher educators need to include error-analysis tasks to help pre-service teachers be aware of the importance of their knowledge of students.