Prospective Mathematics Teachers Research Articles

The expertise of novices: A framework for prospective teacher’s noticing of children’s mathematical thinking

The purpose of this study was to articulate nuances within the process of learning to notice and to provide a framework for characterizing the capabilities of noticing in prospective mathematics teachers. We collected and analyzed data on teacher noticing based on classroom videos from prospective teachers in a mathematics content course. We analyzed data in accordance with existing research-based frameworks on noticing and in consideration with literature on expertise. We provide the Framework for the Expertise of Noticing, which describes noticing expertise along five dimensions: Evidence-based Noticing; Concrete vs. Abstract Characteristics in Noticing; Individual vs. Pattern Focus in Noticing; Task vs. Contextualized Perspective in Noticing; and Cognitive vs. Metacognitive Characteristics in Noticing. The framework is a tool for mathematics education researchers and teacher educators who study and support the development of noticing in prospective teachers.

Mathematical Connection of Prospective Mathematics Teachers in Constructing Graph-Based Real-life Problem

Mathematical connection ability is one of the important abilities that students should have. Connecting real-world problems to mathematical concepts can make learning mathematics more meaningful for students. In everyday life, there is a lot of information presented in graphs. Graphing competence consists of graph interpretation and graph construction. Even though graph construction is a crucial yet neglected skill. From the previous explanation, the purpose of this study is to describe the ability of students to construct a graph based on a real-life problem. This descriptive qualitative study is collected from 37 prospective mathematics teachers in a university. All students had to answer one question about constructing a graph based on a real-life situation given. The result of this study, students’ mathematical connection between everyday life and mathematics itself was still low. Using indicators in this study: 10.81% of the students could not represent the real-life situation in the graph that they constructed; 75.68% of the students made graphs but many features of the graphs did not represent the situation well; and 13.51% of the students made more representing graph but some features of the graph did not relevant. Therefore, in mathematics learning the teacher should give more experience to the students to explore everyday life situations using mathematics and encourage students to write their thoughts down so that mathematics becomes meaningful for students. Keywords: constructing graph-based real-life problem, mathematical connection, prospective mathematics teachers

Deductive Reasoning and Mathematical Resilience in Complex Analysis

The pre-research data of mathematics prospective teachers in one of the universities in Bandung showed that the deductive reasoning ability in complex analysis was still not at good level. Beside the cognitive aspect, the affective aspect could be considered too in doing learning process, such as mathematical resilience. This study aims to analyze and identify the correlation between deductive reasoning and mathematical resilience in complex analysis. The research was conducted in one of the mathematics education departments of a university in Bandung. Correlation was the method used in this study. Mathematics prospective teachers were the sample of this research. This study concluded that mathematical deductive reasoning of prospective teachers was on a moderate level, the mathematical resilience of prospective teachers was on the positive category, and there was a significant correlation between deductive reasoning and the mathematical resilience of prospective teachers on a moderate level. Keywords: deduktif reasoning, matchematical resilience, complex analysis

Prospective secondary teachers’ noticing of students’ thinking about the limit concept: pathways of development

AbstractResearch has shown that there is a need to examine prospective teachers’ development trajectories related to noticing expertise. An important content in the Spanish high school curriculum (16–18 years old) is the limit concept. Given the importance of this concept in the curriculum and the difficulties some prospective teachers have, developing their noticing of students’ mathematical thinking of this concept in teacher education programs is crucial to achieve high school student mathematics achievement. This study examines how prospective secondary school mathematics teachers (PTs) notice students’ mathematical thinking about the limit concept as they participated in a teaching module. PTs had to anticipate and interpret students’ mathematical understanding and make instructional decisions to support students’ conceptual progression using information about high school students’ understanding of the limit concept. We examined PTs changes related to how they anticipated, interpreted and made instructional decisions during the teaching module. We identified a change in how PTs conceived the understanding of the dynamic limit concept: from all-or-nothing dichotomy to progression; and a change in the instructional decisions they made: from decisions focused on changing the type of discontinuity to conceptual decisions. These changes allow us to characterise development noticing pathways. Our findings also help to identify the teaching module characteristics that support the development of PTs noticing.

What Are and What Are Not Extrema Points? Examining Definitions and Examples

AbstractThis paper reports on five secondary school mathematics prospective teachers’ conceptions of extreme point. The analysis of the data addressed students’ definitions, examples, and evaluation of given examples, with special attention to the related domain. Written assignments and individual interviews uncover salient, erroneous concept images regarding what is and what is not an extreme point. Participants viewed extrema points as points that necessarily satisfy f′ = 0 or as points that are always at a “change in monoticity” of the function. The topic “extreme points” is both an aim and a mean to address broader issues related to mathematical definitions, examples, and nonexamples. We conclude with possible next-step ideas.

Successfully preparing future mathematics teachers for digital technology integration: a literature review

Over the last several decades, digital technology (DT) integration in teaching and learning mathematics has received considerable attention, as such integration has not led to the expected results. Teacher education is a critical factor – even more important than access to tools and devices – in technology-enhanced teaching and learning. The purpose of this literature review is to examine and systematise core findings of studies that inform mathematics teacher education that supports the integration of digital technologies. We explore key considerations in mathematics teacher education for successfully preparing Prospective Secondary Mathematics Teachers (PSMT) for digital technology integration. This review includes 25 theoretical and empirical articles found using the keywords ‘Digital Technology’ and ‘Mathematics Education’. The review explores different topics that impact teachers’ technology integration classified into six categories according to their varying nature: (1) Mathematical digital competence, (2) Empirical and theoretical justifications, (3) Stages in DT integration, (4) Pedagogies for DT integration, (5) Mathematical skills, and (6) Systemic factors. It articulates and connects several findings reported in the extant literature previously seen as isolated and disconnected.

Didacticians introducing lesson study for the professional development of prospective mathematics teachers

Lesson study is recognised as a cultural activity and its implementation in a context different from Japan is a complex process. Researchers’ role in this process is assumed to be critical, although this has rarely been investigated. In this paper, we analyse a teaching experiment to introduce lesson study into a professional development course for prospective teachers at an Italian university, focusing our investigation on a group of researchers acting as teacher educators (didacticians). Using the anthropological theory of the didactic and meta-didactical transposition frameworks, we investigate their dual position as researchers and as teacher educators. We observe the evolution of the didacticians’ teacher-education praxeology (a model of practice and knowledge) during their interactions with prospective teachers. The results indicate that the didacticians’ teacher-education praxeology is distinguished, shaped, and actively influenced by their research praxeology. The results also imply that coordinating the two theoretical frameworks may guide the design and analysis of teachers’ professional development courses.

Factor analysis of low of the students' interest in Aceh Utara and Lhokseumawe Regencies to continue education in the Mathematics Tadris Department of IAIN Lhokseumawe

The growth in interest of SMA/MA graduates spread across Lhokseumawe City and Aceh Utara Regency has greatly decreased in interest in the IAIN Lhokseumawe Mathematics Tadris Department. This decline in interest can be seen in the decline in the number of students in this department from year to year over the last 5 years. The aim of this research is: To examine students' views, the factors causing low student interest and efforts to increase the interest of prospective new students in the Tadris Mathematics Department. The type of research used in this research is descriptive qualitative. The research objects were high school and MA class XII students in Lhokseumawe City and Aceh Utara Regency. The results obtained show that students' views on the Tadris Mathematics Department are 1) students do not know about the Tadris Mathematics Department, 2) students do not like mathematics subjects, 3) students do not understand that the Tadris Mathematics Department is a department that prepares prospective mathematics teachers. Furthermore, the factors that cause students' low interest in continuing their education at the Tadris Mathematics Department are 1) lack of information, 2) dislike of the teaching profession, 3) not being a favorite choice, 4) considering that mathematics is a difficult subject. The efforts to increase the interest of prospective new students to enter the Tadris Mathematics Department are 1) optimal introduction to the Department, 2) increasing accreditation, 3) demonstrating the uniqueness of the Department, 4) providing training in using applications appropriate to the department.

Analisis Kesulitan Calon Guru Matematika dalam Menyelesaikan Soal Olimpiade Bidang Aljabar

Mathematics Education Undergraduate Study Program students as prospective teachers need to be prepared with good competencies so that they are ready to carry out the Olympic preparation program when they are already in the profession as teachers. Therefore, research will be carried out that aims to analyze the difficulties of prospective mathematics teacher students in solving Olympiad questions, which are the basis for designing Olympiad learning in higher education. This research was carried out with students from the VII-semester Mathematics Education Study Program at a university in Magelang using a qualitative approach. Data obtained through written assessments and interviews were then analyzed to identify difficulties in understanding concepts, difficulties in applying principles, and difficulties in solving verbal problems experienced by the subjects. The results of the data analysis show that these three types of difficulties were found in the steps for solving olympiad questions in algebra.  Keywords: difficulty analysis, prospective mathematics teacher, mathematics olympiad

Prospective mathematics teachers’ reflections on their strategies for solving a simple combination problem

This article aims to analyze and highlight prospective mathematics teachers' reflections on the strategies used to solve a simple combination problem. We carried out a qualitative study in the context of theoretical classes in an undergraduate course on the theory of problem-solving. To this end, 11 students from Paraná solved a simple combination problem. The results showed that the participants believed the diagram and table strategies were the same. After the discussions, they understood that the strategies have their own representations but did not mention those linked to execution. We conclude that the reflections of the mathematics undergraduates provided an understanding of the representations of the strategies and that they began to value them when working in the classroom.

Comparative analysis of senior high school prospective mathematics teachers and students’ conceptual misunderstanding in algebra

The aim of this study is to compare the performance and conceptual misunderstanding of senior high school prospective mathematics teachers and students in algebra with an intent to statistically find out whether there is a significance difference in students and prospective teachers’ ability to identify and rectify algebraic conceptual misunderstanding. A test consisting of 21 tasks was used for data collection. A sample of 170 consisting of 60 prospective senior high school mathematics teachers from mathematics education department of University of Education Winneba and 110 senior high school students from four selected senior high schools in Ashanti Region of Ghana. The study employed convenience, purposive, and simple random sampling as sampling techniques. The result showed that the overall performance of prospective teachers and students’ performance on the algebra was generally poor. That is, their ability to identify and rectify algebraic conceptual misunderstanding was poor. However, the prospective teachers’ overall performance was comparatively better than the students. The independent <i>t-</i>test conducted between the prospective teachers and students on the test scores gave the results (mean [M]=20.67, standard deviation [SD]=11.98) for students and (M=33.91, SD=14.78) for prospective teachers with t(168)=-6.32, p=0.00 indicating that statistically there is difference between the mean scores of the two groups signifying that the prospective teacher’s ability to identify and rectify algebraic conceptual misunderstanding outperformed the students.

Specialized Knowledge of Prospective Mathematics Teachers on the Concept of Mathematical Proof

[Objetivo] En este artículo, se presentan los resultados de una investigación cualitativa de carácter descriptivo que tiene como objetivo caracterizar el conocimiento especializado de los profesores de matemáticas en formación inicial de la Universidad Nacional en Costa Rica (UNA), sobre el concepto de la demostración matemática, mediante el modelo Mathematics Teacher’s Specialized Knowledge (MTSK). [Metodología] La investigación se posiciona en el paradigma interpretativo y tiene un enfoque cualitativo. Se aplicó un cuestionario, durante el primer semestre del 2021, a 42 profesores de matemáticas en formación inicial de cuarto y quinto año de la carrera Bachillerato y Licenciatura en Enseñanza de la Matemática de la Universidad Nacional de Costa Rica. Para examinar la información, se empleó el análisis de contenido y se hicieron agrupaciones de las respuestas, con el propósito de generar ideas centrales sobre el concepto de demostración. [Resultados] De los resultados se desprenden cuatro ideas centrales sobre lo que es una demostración matemática para los sujetos de la investigación, cercanas a aspectos formales lógico-sintácticos y matemáticos (ALSM) o aspectos informales semánticos (AIS). Se encontraron evidencias de las cinco funciones de De Villiers (1993) para la demostración y surgieron nuevas funciones relacionadas con esta en las matemáticas y en las matemáticas escolares. [Conclusiones] Los resultados brindan insumos a formadores de profesores de matemáticas e investigadores, en la revisión y análisis de programas de formación docente, y contribuyen en la búsqueda de nuevas áreas de investigación relacionadas con el tema.

Sentiment analysis of prospective mathematics teacher on reasoning and proof questions using Naïve-Bayes classification

Reasoning and proof is the ability to arrange patterns, make conjectures, test conjectures, and carry out logical proof, which can be seen as negative or positive for students when solving proof problems requiring reasoning skills. Prospective mathematics teachers in the Mathematics Education Study Program of FKIP Universitas Sriwijaya became the subject of this study. As the research instrument, the questionnaire was designed to explore students' opinions and responses to problems with significant logical difficulty. Sentiment analysis was used to analyze the opinions of prospective mathematics teachers on reasoning and proof questions by grouping positive and negative opinions. The technique used in this study uses the Naïve Bayes algorithm. The classification results in this study were 58.2% positive and 41.86.7% negative, with a total of 70 data. The final result achieved an accuracy value of 53.33%, signifying the reliability of the Naïve Bayes algorithm in understanding and classifying the complex spectrum of sentiments expressed by students. The implications of these findings go beyond sentiment analysis, providing valuable insights for educators, curriculum developers, and policymakers in designing learning strategies and educational policies that can improve mathematics students' reasoning and proof abilities.

The Use of Case Technology for the Formation of Information Competence for the Future Teachers of Mathematics

The relevance of the selected research topic arises from the numerous challenges encountered in the education of prospective mathematics teachers. The purpose of this research is to substantiate the advisability of using the case technology in the formation of information competence for the future teachers of mathematics in the process of their preparation. This study employs a methodological approach that combines literature analysis, synthesis of pedagogical experiences, statistical observation and a pedagogical experiment to assess the impact of case technology on the development of information competence among students in the context of professional education for future mathematics teachers. The main results of this study include the creation of case groups and their integration into the curriculum for students specializing in ‘mathematics’ and ‘mathematics-informatics’, as well as a comparative analysis of the components of information competence among future graduates and their proficiency levels. The study’s findings hold significant relevance for educators at the Higher School of Natural Sciences at Zhetysu University named after I. Zhansugurov, with the overarching objective of preparing competent, highly skilled and competitive mathematics teachers for the job market.

ANALYZING STUDENTS' ABILITIES AS PROSPECTIVE TEACHERS OF MATHEMATICS IN CONSTRUCTING PROOFS: A STUDY OF GEOMETRY AND ALGEBRA

Mathematical proof demands accuracy and precision in formulating correct and logical arguments. Students need to develop their ability to produce accurate and precise proofs. This study aims to analyze the ability of prospective mathematics teachers in constructing geometry and algebraic proofs. The research subjects were 8 prospective mathematics teacher students, four male and four female. This descriptive qualitative research begins with giving tests to research subjects, then we conduct interviews. The results showed that male students were better at compiling geometry proofs than compiling algebraic proofs. While female students are better at compiling algebraic proofs than geometry. This is due to the spatial ability of men better than women.  When compiling geometry proofs apply procedural proofs, syntactic proofs, and semantic proofs. When compiling algebraic proofs only apply procedural proofs. Female students when compiling geometry proofs only apply procedural proofs. When compiling algebraic proofs, they apply procedural proofs and syntactic proofs.

ANALYSIS OF CRITICAL THINKING OF PROSPECTIVE MATHEMATICS TEACHERS IN SOLVING ASSESSMENT PROBLEMS

Simple qualitative descriptive research that describes the critical thinking skills of prospective mathematics teachers based on the percentage of achievement of critical thinking skills test results. we conducted research on 6th semester students of Mathematics Education Study Program consisting of 35 students. The research instrument used critical thinking skills test questions consisting of 5 questions prepared based on indicators of critical thinking skills consisting of identifying and interpreting, analyzing, evaluating, connecting, and solving problems. Data analysis used percentage. The results showed that the critical thinking skills of prospective mathematics teachers had a total average of 70% in the high category. This is supported by the percentage of critical thinking skills in each indicator as follows: interpreting and identifying indicators by 85%, analyzing indicators by 70%, connecting indicators by 82.14%, problem solving indicators by 20%, and evaluating indicators by 92.86%.

Self-concept, Self-efficacy, and Academic Achievement of Prospective Mathematics and Biology Teachers

This study investigates the intricate interplay between self-concept, self-confidence, and academic achievement among aspiring mathematics and biology teachers. Through a quantitative research approach and survey design, we explore the relationships among these psychological factors and their potential influence on the educational paths of future educators in these distinct disciplines. Seventy-six prospective biology education teachers and 115 prospective mathematics education teachers voluntarily participated as respondents in filling out the provided survey. Utilizing standardized self-concept and self-efficacy assessments in conjunction with academic performance records, we gather comprehensive data to analyze these dynamics by inferential statistics, independent t-tests, and Pearson's correlation. Our findings show that there is a significant difference in the self-concept of prospective biology education teachers and mathematics education teachers when studying mathematics or statistics material, highlighting significant correlations between self-concept, self-efficacy, and academic achievement. However, the nature of these relationships varies between mathematics and biology domains, suggesting the need for tailored strategies in each field. While a positive self-concept and self-efficacy foster academic success, their impact differs based on the subject matter. The findings from these analyses can shed light on how self-concept and self-efficacy in mathematical understanding and problem-solving contribute to the academic achievement of prospective teachers in mathematics and biology. This information has implications for teacher training programs and educational strategies aimed at enhancing both self-perception and teaching efficacy in mathematics-related subjects.

Examining How Prospective Mathematics Teachers’ Instructional Visions Align with Their Responding Practices Through Scripting Tasks

Examining How Prospective Mathematics Teachers’ Instructional Visions Align with Their Responding Practices Through Scripting Tasks

The effects of online learning self-efficacy and attitude toward online learning in predicting academic performance: The case of online prospective mathematics teachers

This study aims to discover if Online Learning Self-Efficacy (OLSE) and attitude toward online learning (AOL) significantly predict the academic performance (AP) among Turkish prospective mathematics teachers. Unlike the studies conducted in the literature, online learning self-efficacy and attitude towards online learning as predictor variables were included in the study and both quantitative and qualitative data were collected. The study included 1075 prospective mathematics teachers’ responses in the analysis. The Pearson correlation was employed to determine how strongly OLSE, AOL, and AP are related. Results indicated that OLSE and AOL influenced the level of AP. Also, the multiple regression aimed to predict AP based on OLSE and AOL, and this model explained 44.6% of the variance in AP. The beta weights demonstrated that OLSE and AOL (OLSE β = .36, t(1072) = 9.705, p < .001, and AOL β = .34, t(1072) = 9.176, p < .001) significantly contributed to the model. The results showed that the level of academic performance can be predicted by online learning self-efficacy and attitude toward online learning. In addition, this study revealed the factors that have favorable and adverse effects on the academic performance of prospective mathematics teachers to gain more extensive information. Under the theme of negative factors, there were 7 codes. The results obtained from the study can be a guide for practitioners, policy makers and teachers to take the necessary precautions for the effective execution of the distance education process.
 Received: 4 October 2021Accepted: 27 June 2023

Unveiling the TPACK profile: Exploring mathematics prospective teachers in the micro teaching course

The objective of this research is to ascertain the Technological Pedagogical Content Knowledge (TPACK) profile of prospective mathematics teachers in the microteaching course. The research methodology employed a survey research design. The target population for this investigation comprises prospective mathematics teacher students enrolled at a University in Banten, Indonesia. The sample for this study comprises students in their sixth semester of the Mathematics Education program who are currently enrolled in the microteaching course. The inclusion criteria for the sample require that these students have successfully completed coursework in foundational technology use, pedagogical principles, and both basic and advanced mathematics subjects. The research findings indicate that the majority of students exhibit a high level of Technological Content Knowledge (TCK) and Technological Pedagogical and Content Knowledge (TPACK), with percentages of 50% and 81.25% respectively. On the other hand, the majority of students demonstrate a moderate level of Pedagogical Knowledge (PK) and Technological Pedagogical Knowledge (TPK), with percentages of 56.25% and 31.25% respectively. Moreover, a significant portion of students show a low level of Technological Knowledge (TK) at 31.25%, Content Knowledge (CK) at 37.5%, and Pedagogical Content Knowledge (PCK) at 37.5%. It conluded, most prospective tezchers use the Technological Conten Knowledge (TCK) and Technological Pedagogical and Content Knowledge (TPACK) domains to conduct learning.