Exploring pre-service mathematics teachers’ thinking for solving linear programming word problems

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.

Most mathematics word problems contain real-life context, but not all are relevant to real-life reality. Despite the mathematical solvability of these problems, their contexts may be contrary to the facts in the real world. This study explored the responses of pre-service mathematics teachers while facing the mathematics word problem containing contradictory information within a real-life context. A total of 48 pre-service mathematics teachers from various cohorts participated in this study. The participants were asked to solve a mathematics word problem that was designed to be solvable mathematically but presented a situation that contradicted to real-life context. The findings reveal that while the participants are adept at mathematical procedures, many did not realize and some were confused by the anomalies within the problem context. Only a few of them recognized the contradictory information and stated that the problem was illogical or impossible. This study specifically explores the gap between mathematical solvability and the relevance of real-world contexts in word problems. Most previous research has primarily focused on pre-service teachers’ ability to solve mathematical problems without examining whether they notice the anomalies in the problem’s context. This study emphasizes raising pre-service mathematics teachers’ awareness of the real-life context in mathematics word problems.

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.

Studies have shown that solving real-world problems involving triangles is one of the most difficult topics for the pre-service secondary mathematics teachers engaging study and training in metropolitan institutions. We have known little about performances of the pre-service mathematics teachers from regional, rural and remote (RRR) areas engaging study and training in regional universities. This case study intends to explore whether solving word problems involving triangles would also be challenging for the RRR pre-service mathematics teachers, and what unique factors may negatively affect the RRR student teachers’ performances in solving word problems involving triangles. This study compared the works of two groups of the first-year pre-service mathematics teachers who enrolled in an undergraduate education program in a regional university in Australia. The two chosen word questions for comparison were parts of the assignments involving solving triangles to the students. Through statistical analysis, this study indicates that the considerable proportion of no attempts among the enrolled RRR students is the distinctive difference between the metropolitan and RRR pre-service mathematics teachers. Although still challenging, the RRR student teachers who attempted the word problems seemed performed better than the metropolitan students in solving word problems involving triangles.

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 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.

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 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 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.

<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>

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

This article addresses a special class of non-linear programming problems, viz., linear fractional programming problems having multiple objectives. In solving the real-life linear fractional optimization problems, the ambiguity and hesitation in the decision are inherent and ever-present, therefore, it is perfectly viable to formulate and solve these optimization models using the intuitionistic fuzzy environment. The purpose of this study is to propose a simple and computationally efficient approach to obtain the solution of multiple objective linear fractional programming problems having all the decision variables and parameters expressed in terms of triangular intuitionistic fuzzy numbers. The proposed solution algorithm is primarily based on the goal programming approach, fuzzy-based linearization technique, and a membership function strategy. The original linear fractional programming problem is first converted to its equivalent deterministic/crisp multi-objective linear fractional optimization problem using the weighted goal programming methodology along with the linear membership technique to resolve the intuitionistic fuzzy constraints into the crisp one. Finally, the variable transformation technique for the under- and over-deviational variables of the goal programming model is employed to linearize all the fractions involved in the problem so as to convert the original problem to an equivalent linear optimization problem. Further, this linear programming problem can be solved using any available commercial packages. Moreover, a numerical illustration is provided to demonstrate the steps of the proposed technique followed by the analysis and solution of an E-education set-up problem. The discussion and comparisons of the practical case establish the relevancy and usefulness of the proposed model.

Education institutions worldwide implemented remote teaching and learning to ensure the sustainability of their academic programmes and continuity of study. However, evidence from the literature revealed that remote teaching and learning posed challenges to teaching and learning. This study seeks to explore whether there is a relationship between remote teaching and learning and the challenges faced by preservice mathematics teachers when learning mathematics education during COVID-19. It focuses on remote teaching at four universities: two in South Africa, one in Ghana, and one in New Zealand. The study design followed a quantitative research approach, with 95 preservice mathematics teachers from the four universities randomly assigned to complete an online survey after signing informed consent forms. This study revealed two challenging factors facing preservice mathematics teachers during remote teaching and learning: data, and technological devices for learning. The findings revealed no significant difference (p < 0.000) between remote teaching and learning and the challenges faced by preservice mathematics teachers when learning during the COVID era. Therefore, the null hypothesis is rejected, since p < 0.05. This study concludes that a significant relationship exists between accessibility to technological devices for learning as a challenge to preservice teachers and remote teaching and learning during COVID-19. It is recommended that appropriate technological devices are provided to assist preservice teachers to study mathematics education, thus ensuring continuing access to quality education.