Pre-service Mathematics Teachers Research Articles

Delving into the Critical Thinking Skills of Pre-Service Mathematics Teachers with Their Metacognitive Awareness

Metacognitive awareness (MA) and critical thinking (CT) are crucial higher-order thinking skills in mathematics education. MA and CT skills of pre-service teachers are considered important predictors of their future teaching practices in the teaching and learning of mathematics. In this context, the study examines the potential effects of socio-demographic (e.g., gender) and academic variables (e.g., academic year and academic achievement) on MA and CT skills of pre-service mathematics teachers (PSTs). Additionally, the aim of this study is to explore the relationship between the MA and CT skills of PSTs. Employing a quantitative research methodology, the study was structured around a correlational model. It involved 218 PSTs, using the “MA Inventory” and “CT Standards Scale” for data collection. The data were analyzed through independent sample t-test, one-way analysis of variance, correlation analysis, and simple linear regression analysis. The findings indicate that PSTs possess a high level of MA and CT skills. Significant differences in MAs of PSTs were observed with respect to academic year and academic achievement, while the CT skills of PSTs showed significant differences concerning gender and academic achievement. A strong, positive, and significant correlation was found between MA and CT skills of PSTs. Furthermore, the MAs of PSTs were identified as a significant predictor of their CT skills, explaining 38% of the variance in CT skills.

Mathematical connections made by preservice mathematics teachers when solving tasks about systems of linear equations

The study reported had the aimed to identify the mathematical connections made by a group of Mexican preservice mathematics teachers (PMTs) when solving tasks on systems of linear equations. We consider a mathematical connection as a true relationship that a person makes between two or more ideas, concepts, definitions, theorems, procedures, representations, and meanings with each other, with other disciplines or with real life. Four PMTs participated voluntarily in task-based interviews, providing the primary data for analysis. Thematic analysis was employed to analyze the data. The findings revealed that the preservice teachers made mathematical connections of procedural, implication, feature, meaning, and different representations. However, the findings also revealed that some preservice teachers faced challenges when attempting to solve the tasks, leading to difficulties in establishing certain mathematical connections.

Algebraic thinking profile of pre-service teachers in solving mathematical problems in relation to their self-efficacy

Algebraic thinking is a person’s ability to understand, analyze, and solve problems using algebraic concepts to simplify statements and find solutions. Currently, many prospective teachers still lack proficiency in applying algebraic thinking skills. Self-efficacy is one of the factors that influences algebraic thinking ability. This study aims to reveal the relationship between self-efficacy and algebraic thinking skills in pre-service mathematics teachers. In the context of solving math problems, especially algebraic ones, algebraic thinking skills are crucial. Using a qualitative method with a descriptive approach, the study employed interview guidelines, questionnaires, and tests as instruments. The results show a clear correlation between the level of self-efficacy and algebraic thinking ability. Pre-service teachers with high self-efficacy can effectively evaluate information, use symbols to represent variables, and solve algebraic equations well. They are also able to determine the values of unknown variables. On the other hand, participants with moderate self-efficacy can interpret and communicate information but are less systematic in selecting problem-solving steps that involve abstraction. Participants with low self-efficacy struggle to interpret information and cannot explain the relationship between the information in the problem and the question asked, leading to incorrect solutions. The conclusion of this study is that the higher the level of self-efficacy, the better one’s algebraic thinking ability. This indicates the importance of enhancing students’ self-efficacy to support more effective algebra learning.

Critical thinking disposition and learning approach as predictors of mathematics performance

In the Philippines, improving pre-service math teachers’ critical thinking is receiving increasing attention, emphasizing the importance of tailoring instructional methods to students’ learning approaches for a more equitable environment and enhanced mathematics performance. Thus, this study aimed to determine if the critical thinking disposition subscales (reflective, attentiveness, open-mindedness, organization, perseverance, and intrinsic motivation) and learning approach (deep approach and surface approach) predict the mathematics performance of pre-service math teachers. This study employed a descriptive-correlational research design to randomly selected 125 pre-service math teachers from Central Luzon, Philippines. The survey instruments are administered through the student-educator negotiated CTDs scale, the revised two-factor study process questionnaire, and the 40- item validated test. Using descriptive analysis, findings revealed that preservice mathematics teachers have moderate levels of CTD, most of which use a deep approach and have average mathematics performance. Regression analysis showed that CTD and the deep approach were predictors. Therefore, pre-service mathematics teachers with a higher CTD and a deep approach are likelier to perform better in mathematics. These findings provide valuable insights into enhancing mathematics teacher education.

Investigation of the Concept Images of Mathematics Educators and Preservice Mathematics Teachers Regarding Slope, Rate of Change, and Derivative

The aim of this study is to examine the concept images of mathematics educators and pre-service elementary mathematics teachers regarding the relationships between the concepts of slope, rate of change and derivative. Four mathematics educators working in different state universities and responsible for Analysis courses, three pre-service elementary mathematics teachers who successfully completed the Calculus 1 course at a state university, and four pre-service elementary mathematics teachers who successfully completed the Calculus 1 and Calculus 2 courses participated in the study. In order to determine the concept images of the participants about the concepts of slope, rate of change and derivative, the participants were asked semi-structured interview questions prepared by the researcher and application questions including the second stage questions. The audio recordings obtained from the interviews were transcribed and then the second stage questions were applied to the participants. The second stage questions were received in writing from the participants and analysed by the researcher through descriptive content analysis. As a result of this study, mathematics educators were able to use the concept images they had in the first stage questions in the second stage questions. On the other hand, pre-service elementary mathematics teachers were able to use the concept images they had in the first stage questions in the second stage questions.

Creating Digital Storytelling as Digital Materials in Mathematics Education

The digitalization of stories through technology-supported software has created the concept of digital stories. In recent years, researchers have been making efforts to investigate the effects of digital stories that have started to be used as digital materials in education. This study aims to evaluate the digital stories created by preservice mathematics teachers for mathematics courses, their experiences in the process of creating digital stories, and their views on the use of digital storytelling as digital materials in mathematics courses. This qualitatively designed study was conducted with the participation of 49 preservice elementary mathematics teachers and lasted 7 weeks. It was found that the digital stories created by the participating preservice teachers were moderately acceptable. Participants characterized digital storytelling as materials that are interesting, support teaching, and provide visual richness. They also stated that they intended to use digital storytelling when they begin working as teachers. However, due to the time-consuming nature of the process, most participants stated that they would use ready-made digital stories instead of creating them themselves. Additionally, the results of this study provide information about the experiences of preservice teachers regarding the process of creating digital storytelling.

The Effectiveness of Feedback Provided by Middle School Mathematics Teachers and Preservice teachers on Student Solutions: An Evaluative Study

The aim of this study is to reveal the suggestions of middle school mathematics teachers and preservice mathematics teachers that can both correct errors in students’ incorrect solutions and contribute to the advancement of students who have provided correct solutions. The study is based on the case study method. Initially, six problems related to proportional reasoning were posed to middle school students in a public school, and the solutions obtained from the students were classified according to their proportional reasoning strategies. These solutions were then examined by the students' mathematics teachers and by preservice mathematics teachers. Two questions were asked to mathematics teachers and preservice mathematics teachers during these examinations. After the examination, interviews were conducted to discuss the suggestions made to (1) correct the errors in incorrect solutions and (2) advance the proportional reasoning skills of students who obtained correct solutions. The findings indicate that both mathematics teachers and preservice mathematics teachers were adequate in providing suggestions to correct errors in students’ incorrect solutions. However, it was also found that both groups had difficulties in making suggestions to further the advancement of students who provided correct solutions.

Sustaining Teacher Education During COVID-19: Challenges with Remote Teaching and Learning Faced by Preservice Mathematics Teachers

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.

Using large language models to support pre-service teachers mathematical reasoning-an exploratory study on ChatGPT as an instrument for creating mathematical proofs in geometry.

In this exploratory study, the potential of large language models (LLMs), specifically ChatGPT to support pre-service primary education mathematics teachers in constructing mathematical proofs in geometry is investigated. Utilizing the theoretical framework of instrumental genesis, the prior experiences of students with LLMs, their beliefs about the operating principle and their interactions with the chatbot are analyzed. Using qualitative content analysis, inductive categories for these aspects are formed. Results indicate that students had limited prior experiences with LLMs and used them predominantly for applications that are not mathematics specific. Regarding their beliefs, most show only superficial knowledge about the technology and misconceptions are common. The analysis of interactions showed multiple types of in parts mathematics-specific prompts and patterns on three different levels from single prompts to whole chat interactions.

A Study on Pre-service Mathematics Teachers’ Perceptions of Class Demonstration and Teaching Practicum

A Study on Pre-service Mathematics Teachers’ Perceptions of Class Demonstration and Teaching Practicum

Computational Thinking Processes in Solving the Corona Epidemic Model: Pre-service Maths Teachers

In the 21st century, pre-service mathematics teachers are expected to have problem-solving skills that are effective, efficient, and solutive and are in line with the mindset of computer experts. In learning mathematics, the concept of computational thinking (CT) is also needed and at this time, many still have difficulty solving mathematical problems in general, especially in solving problems in epidemic mathematical models. The subjects of this study were twenty-seven pre-service mathematics teacher students who took mathematical modeling courses. The researcher used the purposive sampling technique to select two research samples. The research method used was a descriptive qualitative research method in exploring the thinking process of pre-service mathematics teacher students in solving the problem of modeling the epidemic spread of disease. The results showed that the thinking process of the first subject began with identifying the problem and existing information by writing down the data in the form of a graph so as to get a certain pattern, which was then used as the basis for the process of transforming the problem into mathematical language. By adding assumptions related to the existence of environmental limitations in the next epidemic model, the concept of differential equations, in which there are integral properties and natural logarithms, can be used to find the solution to the epidemic model. The second subject was unable to solve the integral at hand. The researcher discovered that pre-service mathematics teacher students who correctly solved the problem in the mathematical model used CT components, namely decomposition, abstraction, pattern recognition, algorithm and mathematical literacy.

The Development of Non-Formal Learning Organization Skills in Preservice Math Teachers

Although the effects of out-of-school learning on students' learning have attracted significant attention among education researchers in science and social sciences, little is known about the development of pre-service elementary mathematics teachers' skills in utilizing out-of-school learning in mathematics lessons. The aim of this research is to investigate the impact of activities conducted within the scope of the out-of-school learning environments in mathematics education on pre-service elementary mathematics teachers' skills in organizing non-formal learning. The study utilized a sequential explanatory design, which is a mixed-method approach. The quantitative part of the research employed a "single-group pretest-posttest design without a control group" from experimental designs. This study involved 35 third-year teacher candidates enrolled in the Primary Education in Math Program (PREDMAP) at a state university located near Ankara, the capital city of Turkey. The data collection instrument used in the study was the Out-of-School Learning Regulation Scale (OOSLRS). Additionally, teacher candidates were asked to write reflective essays about their thoughts on the program at the end of the study. The analyses revealed that prior to the program, pre-service math teachers had the highest scores in the knowledge dimension and the lowest scores in the implementation dimension of organizing out-of-school learning. Significant differences were found in the pretest scores of preservice math teachers only in the knowledge dimension based on their previous experiences in organized out-of-school learning environments during their educational lives. Significant improvements favoring the post-test application were observed across all dimensions between pretest and posttest scores. Data from reflective essays written by the preservice math teachers indicated their emphasis on active participation and included suggestions particularly in the implementation dimension.

Self-Regulation Profiles of Pre-Service Mathematics Teachers for Primary Education in Mathematical Problem-Solving Contexts

Self-regulation in mathematical problem solving is of particular importance in the initial training of Primary Education teachers as it can contribute to improving their own competence in mathematics and at the same time enable them to teach effectively and in a personalized way. With this idea in mind, this study identifies self-regulation profiles present in university students in mathematical problem-solving contexts based on data from the application of a validated scale on a sample of 402 pre-service teachers of primary education at University of the Basque Country. The cluster analysis carried out made it possible to identify and characterize three profiles, labelled according to the level of self-regulation represented by each of them (low, medium, high). In view of the results obtained, we perceive a need to design didactic proposals that allow these profiles to evolve from the lowest to the highest levels.

Investigating preservice secondary mathematics teachers' skills in posing realistic mathematics tasks

Mathematics tasks situated in realistic situations play a central role in developing and applying mathematical knowledge. However, mathematics educators face difficulties in designing realistic mathematics tasks. This study was conducted to gain deeper insights into the characteristics of mathematical problems that underprepared preservice secondary mathematics teachers pose. This study examined 32 preservice secondary mathematics teachers' problem-posing skills based on three problem-posing situations: structured problem-posing, semi-structured problem-posing, and free problem-posing. As the context of the participants, they did not have learning experiences in designing realistic mathematics tasks. In evaluating the preservice teachers' works, the researchers used several evaluation criteria, namely the compatibility of the problem with the mathematical principles, plausibility and sufficiency of information, the problem text, level of context authenticity, cognitive demand, and the correctness of the solution. The results revealed that most preservice teachers posed problems with the first-order level of context use and low cognitive demand. Additionally, many of them encountered difficulties when attempting to solve the problem. The findings of this study were expected to serve as a basis for developing a curriculum for pedagogic and mathematics courses in teacher education.

Enhancing Geometry Achievement in Pre-Service Mathematics Teachers: The Impact of a Scaffolded Flipped Classroom Using a Learning Management System

This study investigates the effectiveness of a flipped classroom approach integrated with scaffolding through a Learning Management System (LMS) in enhancing the geometry achievement of pre-service mathematics teachers. The study utilized an experimental post-test-only control group design involving 63 randomly selected pre-service mathematics teachers. The experimental group received instruction through a flipped classroom model supplemented with scaffolding and LMS support, while the control group experienced traditional teaching methods enhanced by scaffolding and LMS. Quantitative data were collected via a geometry essay test and analyzed using descriptive and inferential statistics, including t-tests. The results revealed that the experimental group significantly outperformed the control group in geometry achievement. Additionally, qualitative data from thematic analysis of semi-structured interviews indicated that the flipped classroom approach fostered improved comprehension, peer interaction, and active discussion, despite challenges such as varying levels of motivation and scheduling conflicts. The scaffolding provided was found to be an effective strategy in clarifying complex topics and enhancing student success. This study underscores the potential of integrating a flipped classroom with scaffolding and LMS to improve geometry achievement and overall instructional quality.

PRE-SERVICE MATHEMATICS TEACHER’S ABILITY IN DESIGNING MATHEMATICAL TASK: AN ANALYSIS OF LESSON PLANS

Mathematical tasks have an essential role in the mathematics learning process. Well-designed mathematical tasks will provide a learning opportunity for students to develop their mathematical ideas. The ability of pre-service mathematics teachers to design mathematical tasks during their academic studies significantly influences how they teach in actual learning. One of the ways to investigate pre-service mathematics teachers' ability to design tasks is by analyzing the tasks in the lesson plans they proposed. This study aims to scrutinize the level of cognitive demand for mathematics tasks designed by pre-service mathematics teachers in their lesson plans to get a thorough understanding of their ability to design tasks. This descriptive qualitative research analyzed mathematical tasks in 25 lesson plans proposed by pre-service mathematics teachers using the framework developed by Stein and Smith (1998). The results of this study show that most pre-service teachers designed tasks with a lower cognitive demand classification with types of memorization and procedures without connections. The mathematical tasks designed by pre-service mathematics teachers also have yet to lead to argumentation and the development of mathematical ideas through exploration or doing mathematics. Thus, based on the findings in this study, designing mathematics tasks with the potential to promote students' mathematical understanding remains a challenge for pre-service mathematics teachers. This article discusses and presents the implications of research results and recommendations for designing mathematical tasks.

Metacognitive awareness and mathematics teaching anxiety on knowledge of content and teaching of pre-service mathematics teachers

The problem and the aim of the study. Anxiety while teaching mathematics is one key component that may influence both teaching and learning. By investigating the relationship between anxiety levels and metacognitive awareness, the result of such investigation is expected to be able to assist pre-service teachers in overcoming obstacles and developing confidence in their abilities to teach mathematics. Based on that, this study attempts to find out how metacognitive awareness and anxiety in teaching mathematics influence the knowledge of content and teaching of pre-service mathematics teachers. Research methods. The metacognitive awareness and mathematics teaching anxiety questionnaires were used to assess pre-service mathematics teachers’ knowledge of content and teaching as well as their teaching abilities. The research employed a mixed-method approach, which combines quantitative and qualitative research. The quantitative research sample consisted of 135 pre-service mathematics teachers, with 75 being females and 60 being males. In the next step, two research participants were randomly selected to investigate the impact of metacognitive awareness and mathematics teaching anxiety on topic knowledge and instruction in the qualitative research. The two selected subjects were selected based on their knowledge of content and teaching. One had high levels of metacognitive awareness and the other one had low levels of metacognitive awareness, as well as teaching anxiety in mathematics. Results. This study found that the impact of metacognitive awareness and mathematics teaching anxiety on knowledge of content and teaching was confirmed by a multiple linear regression analysis. The results of the multiple linear regression analysis using SPSS 25 showed the influence of metacognitive awareness (X1) and anxiety (X2) on knowledge of teaching and teaching (Y). The regression model Y = – 27,077 – 0.621 X1 + 1,205 X2. According to the results of the multiple regression test, pre-service mathematics teachers with high metacognitive awareness were able to maximize their existing knowledge of content and teaching, whereas those with low metacognitive awareness were unable to do so. Additionally, pre-service mathematics teachers with low mathematics teaching anxiety were able to employ effective ways to maximize knowledge of content and teaching, but pre-service mathematics teachers with high mathematics teaching anxiety struggled to convey knowledge of content and teaching. In conclusion, the study showed that pre-service mathematics teacher students with a high level of metacognitive awareness were more able to explore their understanding of material and teaching to prepare for teaching and learning activities effectively. On the other hand, pre-service mathematics teachers with low metacognitive awareness might find it difficult, as they might struggle with content understanding and instruction. Mathematics teaching anxiety was found to have a considerable negative impact on knowledge of content and teaching. High mathematics teaching anxiety can have an impact on both material understanding and teaching.

Pre-Service Mathematics Teachers' Performance on Reflection on Mathematics Teaching and Learning Using GeoGebra Programme

The advancement of applied mathematics founded upon information technology represents a pivotal aspect of contemporary mathematical development, with the integration of (IT) information technology into the mathematics curriculum becoming an indispensable necessity. The study of relevant IT-based courses by pre-service mathematics teachers will contribute to their professional development, as will their reflection on their teaching. This study combines the two, using 40 Master of Education students from a university as respondents and employing open-ended interviews to investigate the reflective performance of pre-service mathematics teachers in teaching mathematics after completing the GeoGebra course. Subsequently, the data were analysed from three perspectives: dimensions of reflection, level of reflection and degree of collaboration. The results were concluded as follows: 1. The dimensions of pre-service teachers' reflection was extensive but skewed, and reflection on the students' aspect was not yet evident; 2. The level of reflection was "describes only" (Level 1) and single-angle analytical (Level 2); 3. The degree of collaboration in teaching reflection was predominantly limited to "integration" and "self only"; 4. In conclusion, the GeoGebra programme can be considered an effective tool for assisting pre-service teachers in teaching mathematics. Therefore, it is suggested that: 1. It is recommended that higher education institutions reinforce the training of prospective mathematics teachers by incorporating pertinent GeoGebra courses into their curriculum. 2. Pre-service mathematics teachers should take the initiative to conduct learning, research, and reflection, and to improve their own awareness and ability to reflect, so that they can: (1) Strengthen their own mathematical knowledge and technical knowledge, and improve their own quality and professionalism; (2) Conduct multiple analyses by considering both teachers, students, and mathematics. knowledge reserves, improve their own quality and professionalism; (3) Pay attention to both group work and be able to think independently to identify problems.

Effect of Technology-Integrated Guided-Inquiry Approach on Geometry Learning of Preservice Mathematics Teachers

Effect of Technology-Integrated Guided-Inquiry Approach on Geometry Learning of Preservice Mathematics Teachers

Socio-Cognitive Factors Affecting the Behavioral Intention of Preservice Teachers to Use Educational Technology

In today’s fast-changing educational settings, technology integration offers the opportunity to enhance mathematics instruction. This study determines the significant socio-cognitive factors among preservice mathematics teachers (PMTs) affecting their behavioral intention toward the use of technology. A descriptive-correlational research design was employed with 130 participants. Revised UTAUT construct items and behavioral intention scales were utilized through survey forms. Findings revealed that the participants were more inclined to use technology in their pedagogical approach. The only socio-cognitive factors significantly affecting the participants’ positive inclination to utilize educational technology were performance expectancy, effort expectancy, and social influence. However, when controlling for the effects of the participants’ willingness to use technology, social influence became insignificant. Developing favorable impressions of technology’s effectiveness and ease of use may encourage greater technology integration in mathematics education.