Pre-service Mathematics Teachers Research Articles

Preservice Mathematics Teachers’ Promotion of Self-Regulation (PSRL) in Time: A Mixed Methods Study

Preservice Mathematics Teachers’ Promotion of Self-Regulation (PSRL) in Time: A Mixed Methods Study

Students' Errors in Constructing Mathematical Proofs by Direct Method

In mathematics, there are several methods for proving mathematical statements, two of them are direct method and indirect method. Both the methods were included in the mathematics curriculum at senior high school level as a learning topic. It implied that the teachers or pre-service teachers must master these methods. In addition, learning advanced mathematics courses also needed the ability of mathematical proving. The direct method was often used in proving mathematical statements. This descriptive qualitative study was conducted to examine what errors were written by the students in constructing mathematical proofs by direct method. Two basic problems (mathematical statements) were administered to 13 college students. They were pre-service mathematics teachers in one of the public universities in Aceh, Indonesia, and were asked to prove the statements by direct method. The data were analyzed by using Miles and Huberman step. The results showed that there were three main errors, (1) errors in using definition correctly, (2) errors in algebraic process, and (3) proving by examples. It concluded that the students must be accustomed to mathematical proving activities to avoid errors in constructing mathematical proofs. Keywords: constructing mathematical proofs, direct method, students’ errors

Radian π: Concept images evoked by quantitative representations of radian angle measure

ABSTRACT This article investigates evoked concept images (CIs) of seven secondary preservice mathematics teachers (PMTs) as they interact with different types of representations of radian angle measure. A thematic analysis indicates that representations emphasizing quantitative aspects of angle measure evoke conceptions that are attuned to quantitative elements of radian angle measure. Specifically, quantitative representations evoked CIs relating the length of the arc subtending the angle to the radius. Non-quantitative representations evoked CIs of radian in terms of π or in relation to degrees, even when the representation did not contain angles in these measurements. To foster a quantitative understanding of radian angle measure, teachers and curriculum developers are encouraged to consider how visual representations might support students in conceptualizing radian angle measure quantitatively.

Mathematical Thinking Among Pre-Service Teachers: A Critical Component of Teacher Preparation

This research examined pre-service mathematics teachers' mathematical thinking abilities, focusing on problem-solving, mathematical representation, reasoning, mathematical communication, and mathematical connection. Additionally, the study aimed to determine whether there were significant differences in mathematical thinking between pre-service students majoring and minoring in mathematics. The research employed a quantitative approach and involved 277 pre-service mathematics teachers enrolled in the Mathematics Teaching course at the Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris in Malaysia. The research design utilized a survey method, and data were collected through a mathematical thinking questionnaire. The collected data were analyzed using statistic descriptive including mean and standard deviation, while inferential statistics use t-test analyses. The study results revealed that the overall mean is 4.506, followed by standard deviation is 0.541, indicating that the pre-service teachers show a higher positive mathematical thinking. The result also shows a significant relationship between problem-solving, mathematical representation, reasoning, mathematical communication and mathematical connection. The findings also indicated significant differences in mathematical thinking between pre-service mathematics teachers based on gender. Lastly, the result shows that the study recommended the inclusion of mathematical thinking development in teacher education programs to enhance the mathematical thinking abilities of pre-service mathematics teachers. In conclusion, mathematical thinking is an essential aspect of teacher preparation, as it contributes to ensuring the quality of the next generation.

PERCEIVED PROFESSIONAL DEVELOPMENT NEEDS AND EMOTIONAL INTELLIGENCE AS PREDICTORS OF MATHEMATICS TEACHING ANXIETY AMONG MATHEMATICS PRE-SERVICE TEACHERS

The primary purpose of this study was to determine whether perceived professional development needs and emotional intelligence predicts mathematics teaching anxiety among mathematics pre-service teacher. This study employed descriptive and correlational designs. Using the stratified random sampling, 103 mathematics pre-service teachers were selected as participants from Davao del Nortes seven higher education institutions during the school year 2021–2022. Moreover, this study utilized three adapted and validated survey questionnaires to gather data, which were treated using mean, Pearson-r, and regression analysis. The findings suggested that pre-service teachers perceived professional development needs are highly addressed, and emotional intelligence is manifested most of the time. Furthermore, the mathematics teaching anxiety of mathematics pre-service teachers is less evident. Findings also revealed that both perceived professional development needs and emotional intelligence exhibit a significant negative correlation with mathematics teaching anxiety. In addition, only perceived professional development needs to predict mathematics teaching anxiety among mathematics pre-service teachers. Future researchers may consider the studys findings which may help them uncover other factors that might improve the conduct of perceived professional development needs and emotional intelligence in relation to mathematics teaching anxiety among mathematics pre-service teachers. With these, teachers and school administrators are encouraged to address professional development needs and assess and boost emotional intelligence to help eliminate mathematics teaching anxiety among mathematics pre-service teachers. KEYWORDS: mathematics education, perceived professional development needs, emotional intelligence, mathematics teaching anxiety, pre-service teachers, descriptive and correlational designs, regression analysis, Philippines

Bridging Gaps: Pre-Service Mathematics Teachers’ Handling the Difficulties in Posing Real-World Mathematical Problems

Real-world mathematical problem (RWMP) solving and posing are important aspects of teaching and learning mathematical modelling, as well as developing a mathematization disposition for both teachers and students. Several researchers have explored blockages or difficulties in such modelling processes and in problem posing. However, prior research has identified difficulties that the pre-service mathematics teachers (PSMTs) encountered when they tried to pose a modelling problem by choosing the general topic themselves, as there is little known about possible obstacles that PSMTs can encounter when trying to pose a real-world problem relevant to a given mathematical topic. The current study explored the difficulties encountered by PSMTs in a RWMP-posing activity. The target group was 23 PSMTs with prior experience in mathematical modelling and mathematical problem posing. The findings showed that the PSMTs struggled with: (a) task organization, which involved selecting and understanding mathematical knowledge; (b) specialized content knowledge, which included a lack of real-world knowledge and difficulty in connecting mathematical concepts to real-world contexts; and (c) individual considerations of aptness, which encompassed authenticity, interest, complexity, language, and relevance to task organization. The PSMTs applied various strategies to complete the posing task, such as using problem-posing and solving heuristics, adapting existing problems, sharing and discussing with friends, and considering the perspective of a typical student. The implications of these findings should help in developing preparatory instructional practices for mathematics teachers.

Pre-service mathematics teachers' performance prediction using a modified Mann-Tseng forward-backward splitting algorithm

Pre-service mathematics teachers' performance prediction using a modified Mann-Tseng forward-backward splitting algorithm

Analysis of STEM Knowledge of Pre-Service Science and Mathematics Teacher

This research is motivated by the importance of STEM knowledge for pre-service science and mathematics teachers in the 21st century. This research aims to analyze the STEM knowledge of pre-service science and mathematics teachers. The research method was carried out by distributing questionnaires with STEM knowledge indicators to the sample. The sample in this research was 86. They were 59 pre-service science teachers and 27 pre-service mathematics teachers, with different years of education, namely the 1st, 2nd, 3rd, and 4th year of Universitas Negeri Semarang. The results of this research show that the average understanding of pre-service science and mathematics teachers regarding to the STEM-based learning in the definition aspect is 4.11, objectives are 3.94, benefits are 3.94, aspects are 3.69, components are 3.71, characteristics is 3.75, and implementation is 3.86. This proves that pre-service science and mathematics teachers' understanding of the definition of STEM-based learning is very good, while pre-service science and mathematics teachers' understanding of the objectives, benefits, aspects, components, characteristics, and implementation of STEM-based learning is good.

Mathematical Thinking and Problem Solving Performance: The Mediating Role of Hope

The purpose of the present study is to provide a mediation model by exploring the relationships among mathematical thinking, hope and problem solving performance in mathematics. The participants of the present study were composed of 311 preservice mathematics teachers. In this mixed method research, these preservice mathematics teachers were conducted to the scales of Dispositional Hope and Mathematical Thinking, and Problem Solving Test. Based on the quantitative data analysis, it was observed that statistically significant relationships among the variables of hope, mathematical thinking and problem solving performance. The quantitative data collected through these instruments were also analyzed by mediation analysis techniques. The qualitative data gathered through semi-structured interviews were analyzed by content analysis technique. These data encouraged the findings acquired from quantitative data analysis. The qualitative findings confirmed the findings of the mediator role of hope. The qualitative findings encouraged the relationships among the variables and the role of mediator.

Using different digital tools in designing and solving mathematical modelling problems

AbstractWhile existing studies acknowledge the importance of using technology in the mathematical modelling process, questions about how to integrate digital tools into mathematical modelling are not still answered. This study aims to examine pre-service mathematics teachers’ designing and solving mathematical modelling problems by using different digital tools through the collaboration of two different courses in their education program. The GeoGebra-supported modelling cycle was adopted as the conceptual framework of the study. The case study was used to design the research. The participants of the study were three volunteer pre-service secondary mathematics teachers, who were able to use and integrate digital tools in mathematics education. The pre-service teachers were asked to design a mathematical modelling problem by integrating different digital tools as the final assignment in both courses. The designed mathematical modelling problem, the video records of pre-service teachers’ explanations including the designing and solving process, and the video records of the focus group interview were the data of the study. The results showed that the pre-service teachers were able to design and solve an effective and comprehensive  mathematical modelling problem using technology by combining their skills that they had learnt through different courses. In particular, they were able to use different digital tools in both designing and solving a mathematical modelling problem. Their solution also led to the extension of the adopted framework by adding new technological actions into the modelling stages.

Preservice Mathematics Teachers’ Experiences in Designing STEM Lessons

This study aims to investigate the views of pre-service mathematics teachers pertaining to STEM education and the challenges encountered during the process of lesson planning. The primary objective of the study is to provide guidance to enhance the efficiency of STEM education practices within mathematics courses. In this study, qualitative research method was utilized for in-depth analysis with three pre-service mathematics teachers. Three semi-structured interviews were conducted, and the participants were asked to prepare a STEM lesson plan. Following the initial interview, STEM education practices were conducted by the researcher. Then, the STEM lesson plans prepared by the participants were analyzed. The analysis of the findings revealed a remarkable progress in the pre-service teachers’ comprehension of STEM education following the intervention. Furthermore, it was observed that the participants were able to integrate mathematics and science into their lesson plans and did not have as much difficulty in this integration as other disciplines. Conversely, it was found that challenges were more pronounced when it came to the integration of engineering principles. The participants who stated that the integration of mathematics and technology was not challenging were weak in this integration. Finally, the participants stated that STEM education is an essential educational approach within the field of mathematics education, expressing their intentions to incorporate STEM activities into their future lesson plans.

Understanding pre-service mathematics teachers’ intentions to use GeoGebra: The role of technological pedagogical content knowledge

AbstractThe research investigated the “Technological Pedagogical Content Knowledge” (TPACK) of pre-service mathematics teachers and its impact on their sustained intention to utilize GeoGebra in teaching mathematics. This study introduced a novel research model by extending the “Unified Theory of Acceptance and Use of Technology” (UTAUT) with TPACK. Through “Structural Equation Modeling” (SEM) applied to data collected from 205 pre-service teachers, the research model was evaluated. The results revealed that factors like effort expectancy, social influence, performance expectancy, and TPACK significantly predicted the continuous use intention of GeoGebra. However, no substantial relationship was found concerning facilitating conditions. The findings have managerial and practical implications for academics, teachers, principals, and decision-makers promoting the use of GeoGebra in educational settings.

Where experience makes a difference: teachers' judgment accuracy and diagnostic reasoning regarding student learning characteristics.

The concept of teacher professional vision suggests that experienced teachers, compared to novice teachers, might be better at making accurate judgments of students' learning characteristics, which can be explained by their advanced reasoning in diagnostic situations. This study examines experienced and novice teachers' diagnoses of different student characteristic profiles: three inconsistent profiles (overestimating, uninterested, and underestimating) and two consistent profiles (strong and struggling). We examined both experienced (n = 19 in-service mathematics teachers) and novice teachers (n = 24 pre-service mathematics teachers) to determine the extent of differences in their judgment accuracy and their diagnostic reasoning about observable cues when diagnosing student profiles while watching a lesson video. ANOVA results indicate that experienced teachers generally achieved a higher judgment accuracy in diagnosing student profiles compared to novice teachers. Moreover, epistemic network analysis of observable cues in experienced and novice teachers' diagnostic reasoning showed that, compared to novice teachers, experienced teachers make more relations between a broader spectrum of both surface cues (e.g., a student's hand-raising behavior) and deep cues (e.g., a student being interested in the subject). Experienced teachers thereby construct more comprehensive and robust reasoning compared to novice teachers. The findings highlight how professional experience shapes teachers' professional skills, such as diagnosing, and suggest strategies for enhancing teacher training.

An Analysis of Instructional Factors for Development of AI Course for Pre-service Mathematics Teachers

An Analysis of Instructional Factors for Development of AI Course for Pre-service Mathematics Teachers

The Effect of Supervisors Feedback in Extended Teaching on Pre-Service Mathematics Teachers Practice

This study examined the influence of supervisor feedback on the teaching practices of pre-service mathematics teachers during Extended Teaching (off-campus teaching practice). The research design adopted for the study was action research. The target population was level 400 students of a College of Education and the population size was three hundred and ninety-two (392) whilst the sample size was sixty-three (63), comprising of pre-service mathematics teachers, which was selected based on purposive sampling. The instruments used for the study were Intern Teaching Assessment Form (ITAF) and Teaching Evaluation Comment Form (TECF). In the pre-intervention stage, a first supervision was conducted to identify the strength and weaknesses of the students before the feedback from the observation was discussed and reflections were held with the pre-service teachers to serve as the intervention. A second supervision was conducted to evaluate the intervention strategies. The results of the study showed a significant improvement in students’ second supervision scores (M=71.0000) compared to the first supervision scores (M=64.8033). A third supervision was conducted 7 weeks after the second supervision using ITAF and TECF to check students’ retention of teaching skills and knowledge, which the result showed no significant improvement in pre-service mathematics teachers’ second supervision scores (M=71.0000) compared to the third supervision scores (M=71.1475), indicating pre-service mathematics teachers’ retention of the teaching skills and knowledge had been exceptionally good. Supervisors' post-observation feedback enhances pre-service mathematics teachers' interpersonal communication, classroom management, student support strategies, leadership, and practical knowledge of standard-based curriculum implementation, thereby improving their instructional style. The study recommends the extension of the Extended Teaching duration to encompass an entire academic year in order to enhance the practical component of the preservice teacher training program and potentially impact the quality teaching and learning policy agenda.

Preservice teachers' mathematical knowledge for teaching: Focus on lesson planning and reflection

AbstractMathematics teacher educators have suggested preservice mathematics teachers' (PMTs') practices provide evidence of their mathematical knowledge for teaching (MKT). PMTs engage in approximations of practice to rehearse teaching. To explore connections between MKT and PMTs’ practices, we operationalized six MKT subdomains in terms of approximations of practice. We used that operationalization to investigate, which subdomains were evidenced in PMTs’ lesson plans and their lesson plan reflections. Eleven secondary PMTs participated in our study. Using a qualitative content analysis method, we found Knowledge of Content and Teaching most evidenced, suggesting that the PMTs demonstrated MKT when they described mathematical tasks and associated instructional activities. Also, the PMTs demonstrated Knowledge of Content and Students when they described how their students would engage with proposed mathematical tasks. However, the PMTs struggled to plan for activities by building on students’ potential mathematical thinking and reasoning. Only limited instances of Horizon Content Knowledge suggest that the PMTs had limited opportunities to demonstrate how their advanced mathematical knowledge connected with their mathematics teaching in the approximations of practice provided. We propose alternative forms of approximations of practice to optimize PMTs’ opportunities to demonstrate and develop MKT.

Problem Posing and Quantitative Reasoning Opportunities Provided by Mathematics Textbooks for Pre-service Elementary Teachers: A Qualitative Document Analysis

ABSTRACT This qualitative document analysis study reports on opportunities to learn provided by textbooks for mathematics content courses for pre-service elementary teachers. Specifically, the study examined opportunities to engage in problem posing and quantitative reasoning, in the context of fractions, provided by six textbooks commonly used in the teaching of content knowledge courses for pre-service elementary mathematics teachers in the United States. Among other things, this examination revealed two key findings. First, all the textbooks provide numerous opportunities that could potentially trigger students’ quantitative reasoning. This is commendable, and a positive response to growing calls to increase such opportunities in mathematics education. Second, there is a paucity of opportunities to engage in problem posing in all the textbooks. Given the numerous benefits of using problem posing in the teaching and learning of mathematics, we recommend that authors of textbooks for mathematics content courses for pre-service elementary teachers provide more opportunities to engage in problem posing in their textbooks. We argue that the act of problem posing requires significant quantitative reasoning, and thus problem posing provides the opportunity for students to develop such reasoning. Implications for instruction and directions for future research are discussed.

Investigating Problems Posed by Pre-Service Mathematics Teachers for the Four Operations in Fractions

Investigating Problems Posed by Pre-Service Mathematics Teachers for the Four Operations in Fractions

Centering Mathematics Pre-Service Teachers’ Whole Selves: A Collaborative Approach to Course Syllabus Design

In this participatory research, two pre-service teachers (PSTs) and a mathematics teacher educator (MTE) collaboratively analyzed multiple voices that influence syllabi from elementary mathematics teaching methods courses. Findings suggest syllabi fall along a continuum from harmonious to dissonant orchestration of the voices of past and present children, PSTs, MTEs, universities, and state policies. Formatting, stance makers, and content and wording influenced the kind of multivocality that addressivity, ventriloquation, and hybridization constituted. These findings informed our use of collage method to create a sample syllabus that centers the voices of PSTs and their future students. We discuss implications that intentional syllabus design decisions may have in humanizing these documents and fostering a relationship of mutuality and support between PSTs and MTEs.

Investigation of Pre-service Middle School Mathematics Teachers Habits of Mind in Pattern Generalization Problems

In this study, it was aimed to determine pre-service middle school mathematics teachers’ habits of mind. The method of the study was determined as a case study. Participants are 23 junior pre-service middle school mathematics teachers. Data were collected with four open-ended linear and quadratic pattern problems. The clinical interviews were conducted with six of the pre-service teachers. In the analysis of the data, content analysis was carried out using habits of mind framework for pattern generalization. The results of the study show that similar habits of mind revealed by pre-service teachers in problem situations. The pre-service teachers had more difficulty in balancing exploration and reflection compared to the other. It was found that the pattern types of the problems affected the habits of mind. It is suggested that more studies need to be done to reveal and foster the quality of algebra and algebraic thinking.