Prospective Mathematics Teachers Research Articles

Developing Model Eliciting Activities for Teaching of Middle School Mathematics: Evaluations of Self, Peers, and Experts

This study aims to provide expert, peer and self-evaluations of MEAs designed by prospective mathematics teachers in terms of basic principles of modeling (reality, model construction, self-assessment, construct documentation, model generalization). Case-study was used in the study. The study group of this research consists of 15 mathematics teacher candidates studying at Kastamonu University. The activities that the teachers have created were used as data collection tools. The data obtained were analyzed descriptively. Research findings reveal that two activities were suitable for the modeling principle, all but one of the activities were evaluated as partially appropriate in terms of self-assessment and model generalization principles. When the proficiency evaluations are examined in detail, it is determined that the groups consider their activities generally sufficient and a higher scoring tendency compared to their peers. Similarly, it was determined that both peer and self-assessments differed from expert assessments. Keywords: mathematical modelling training, model eliciting activities, basic principles of mathematical modelling DOI: 10.7176/JEP/11-28-02 Publication date: October 31 st 2020

Commognitive analysis of the solving problem of logarithm on mathematics prospective teachers

This study aims to describe the commognitive analysis of the solving problem of logarithm on college students of Mathematics. This type of research is a qualitative description. The research subjects were three college students of Mathematics Education from Universitas Madura. The instruments used in this study were mathematical problem sheets and semi-structured interviews. The results of this study show that college students have many differences in working or mistake in mathematics problem-solving. In the word use or use precise words to inform the comprehension, the students have differences in writing base, degree of the numeral, or other symbols. In the visual mediators or use of precise object or media, the students have differences in the premise of working logarithm. In the narratives, students have differences in solving the problem systematically based on comprehension of logarithm form. In the routines, students have differences in understanding the basic concept of logarithmic characteristics.

On a math mission: The time and space compression of professional identity and values in prospective mathematics teachers’ stories

This article analyzes and discusses the professional values of prospective mathematics teachers. Theoretical approaches to the understanding of teachers’ professional values, such as critical mathematics education and relational perspectives, are well developed. Still, there are few empirical contributions to the field. Here, professional values are understood as interwoven with professional identity. The article raises the question of how prospective teachers construct their identity and values in time and space, and the analysis is based on data material from mathematics teacher students at two Norwegian teacher education institutions. The main finding is that the teacher students construct their professional identity and values in a compressed timespace. Their professional responsibility is located in and restricted to themselves and the relation to the individual student, not including concern for, for instance, social justice. The students do not express opposition to ideals of social justice, but it is beyond their constructed professional timespace identity, values and responsibility.

REFLECTIVE THINKING CHARACTERISTICS: A STUDY IN THE PROFICIENT MATHEMATICS PROSPECTIVE TEACHERS

Reflective thinking begins with repeated confusion and evaluation to solve a problem. There are four aspects to reflective thinking, namely techniques, monitoring, insight, and conceptualization. However, the problem-solvers’ reflective thinking characteristics in mathematical problems have not been discovered. The study describes the reflective thinking characteristics of proficient mathematics prospective teachers based on four aspects. The qualitative research was conducted at Universitas Muhammadiyah Surakarta with a total of 64 reflective thinkers. Data collected by test, observation sheets, and interview methods. The tests were administered twice. The instruments developed has been through the validation process and declared valid. Data analyzed through the stages of reduction, presentation, and verification. We successfully conclude that proficient mathematics prospective teachers have complete and consistent reflective thinking characteristics. Further research can be focused on the characteristics of reflective thinking based on another aspect.

Exploring Real Numbers as Rational Number Sequences With Prospective Mathematics Teachers

The understandings prospective mathematics teachers develop by focusing on quantities and quantitative relationships within real numbers have the potential for enhancing their future students’ understanding of real numbers. In this article, we propose an instructional sequence that addresses quantitative relationships for the construction of real numbers as rational number sequences. We found that the instructional sequence enhanced prospective teachers’ understanding of real numbers by considering them as quantities and explaining them by using rational number sequences. In particular, results showed that prospective teachers reasoned about fractions and decimal representations of rational numbers using long division, the division algorithm, and diagrams. This further prompted their reasoning with decimal representations of rational and irrational numbers as rational number sequences, which leads to authentic construction of real numbers. Enacting the instructional sequence provides lenses for mathematics teacher educators to notice and eliminate difficulties of their students while developing relationships among multiple representations of real numbers.

From Micro Teaching to Real Classrooms: Examination of Prospective Mathematics Teachers' Technology-Based Teaching

This study examines the changes and development of prospective secondary mathematics teachers‟ technology-based tasks through teaching practices. The Dynamic Geometry Task Analysis model consisting of the components of mathematical depth and technological action has been chosen as the conceptual framework of the study. In this study, a qualitative research paradigm has been adopted and action research methodology involving a cyclical process has been used. Participants of the study were four prospective secondary mathematics teachers, who were enrolled in a secondary mathematics education program at a state university in Turkey. This research was carried out within the scope of a 14-week Practicum course and focused on prospective mathematics teachers‟ implementations of their technology-based tasks through micro-teaching and classroom teaching. Data mainly consisted of each prospective teacher‟s one technology-based task, video recordings of their teaching practices (micro-teaching and classroom teaching) and interviews. Data was analyzed by using the video analysis method to examine how and why mathematical depth and technological action of the planned tasks changed or developed during micro-teaching and classroom practices. Findings of the study indicated that prospective mathematics teachers improved the levels of mathematical depth of their tasks by making use of their planned technological actions in a more effective way from micro-teaching to classroom teaching. In particular, it became apparent that micro-teaching supported the development of prospective mathematics teachers‟ technology-based tasks in terms of content and also the implementation processes of their tasks in classrooms.

Investigation Relationship Between Mathematics Teacher Candidates’ Mathematics Anxiety and Mathematics Teaching Anxiety

The aim of this study is to examine whether the mathematics anxiety of prospective elementary mathematics teachers predict their anxiety about mathematics teaching. In addition, it is aimed to examine the anxiety levels of prospective elementary mathematics teachers towards mathematics and mathematics teaching whether these concerns differ according to grade level. For this purpose, the research model is chosen as the general survey model. The research was carried out with a total of 307 prospective teachers studying in the department of mathematics education in the fall semester of the 2018-2019 academic year. In the research, “Mathematics Anxiety Scale for Teachers and Prospective Teachers” developed by Uldas (2005) and “Anxiety Scale for Teaching Mathematics” developed by Peker (2006) were used. At the end of the research, it is determined that both mathematics anxiety and mathematics teaching anxiety levels of prospective mathematics teachers are low. On the other hand, there is no significant difference as regards grade levels in mathematics anxiety and mathematics teaching anxiety levels of prospective mathematics teachers. It is concluded that there is a moderately positive significant relationship between mathematics anxiety and mathematics teaching anxiety of prospective mathematics teachers. Finally, it is determined that mathematics anxiety of prospective mathematics teachers predicts their mathematics teaching anxiety.

The Mediating Role of Prospective Mathematics Teachers’ Beliefs on the Relationship Between Perceptions and Attitudes

The Mediating Role of Prospective Mathematics Teachers’ Beliefs on the Relationship Between Perceptions and Attitudes

AN ANALYSIS OF A GEOMETRY LEARNING PROCESS: THE CASE OF PROVING AREA FORMULAS

Geometry is one of the courses in the curriculum for students of prospective mathematics teachers that can develop deductive thinking ability. The question is, how is the learning and teaching process of the geometry course implemented so as to develop this deductive thinking ability? This research, therefore, aims to investigate the learning and teaching process of a geometry course for prospective mathematics teachers. For reaching these aims, this qualitative study was conducted through observations on the learning process and the written test of a geometry course, for the case of area formulas, involving 56 students of mathematics education program. The results revealed that the learning process is implemented by emphasizing the use of the deductive approach, and from the written test we found various proof strategies in proving an area formula. We conclude that the learning and teaching process of the geometry course has influenced the development of student deductive thinking.

Dampak Perkuliahan Geometri Pada Penalaran Deduktif Mahasiswa: Kasus Pembelajaran Teorema Ceva

Geometry is one of branches of mathematics that can develop deductive thinking ability for anyone, including students of prospective mathematics teachers, who learning it. This deductive thinking ability is needed by prospective mathematics teachers for their future careers as mathematics educators. This research therefore aims to investigate the influence of the learning process of a geometry course toward deductive reasoning ability of students of prospective mathematics teachers. To do so, this qualitative research was carried out through an observation of the learning process and assessment of the geometry course, involving 56 students of prospective mathematics teachers, in one of mathematics education program, in one of state universities in Bandung. A geometry topic observed in the learning process was the Ceva’s theorem, and the assessment was in the form of an individual written test on the application of the Ceva’s theorem in a proving process. The results showed that the learning process emphasizes on proving of theorems and mathematical statements. In addition, the test revealed that ten students are able to use the Ceva’s theorem in a proving process and different strategies of proving are found, including the use of properties of similarity between triangles and of the concept of trigonometry. This indicates a creativity of student deductive thinking in proving process. In conclusion, the geometry course that emphasizes on proving of theorems and mathematical statements has influenced on filexibility of student deductive thinking in proving processes.

Why should you reverse the order when dividing a fraction? A study of pre-service mathematics teachers’ pedagogical content knowledge in fractional concept

This study was a part of larger study in examining pre-service mathematics teachers’ Pedagogical Content Knowledge. The aim of the present study was to elaborate the prospective teachers’ conceptual understanding in fraction and how they will teach it for the students. There were 50 participants in this study, all of them are the final year students of mathematics education study program of a state university in Bali who already took the teaching internship program in the school. The data were collected through written test and continued by interview with the participants. The data were analysed qualitatively using descriptive method. From the result, it is found that the prospective mathematics teachers have a difficulties in understanding the concept of fraction. It leads to the lack comprehension in teaching the concept to the students. Reflect to the result, it is recommended to the teacher training institution to emphasize the big ideas in school mathematics’ topics to ensure the prospective teachers have a sufficient knowledge to teach mathematics meaningfully.

The ability of prospective teachers to pose contextual word problem about fractions addition

The low understanding of students on fractional topic has hampered the development of mathematics learning in Indonesia. This study was conducted to investigate in depth the ability of prospective teachers in developing the problem. Thirty four mathematics prospective teachers were asked to ask about contextual word problem whose solution could be obtained from counting and . Data consists of a verbal protocol together with written notes made by the subjects. Qualitative analysis of the obtained data is focused on identifying the resulting problem structure and the type of context commonly used. The results showed that the most widely used contexts in the proposed story problem were the distribution of the cake, the weight of the object, the lots of the object, and the length of measurement. The structure of contextual problem produced by mathematicis prospective teacher has weaknesses in two components, namely: 1) in proposing appropriate contexts; and 2) in providing sufficient information so that the solution of the proposed problem can be obtained by applying the arithmetic concept of plus , These results suggest new findings about prospective teacher difficulties in conceptualizing fractions.

Flow-proof strategy in proof construction on geometry instruction

The purpose of this research is to assess the role of flowproof strategy implementation in improving students’ mathematical proof in similarity and congruence. Proofing similarity and congruence is a prerequisite in developing mathematical skills. The subjects include prospective mathematics teachers, and the study used a qualitative descriptive technique. The implementation of the flow-proof strategy was achieved through four activities, including re-writing existed information, stating what is needed to be proved, using existed rules such as postulate and definition, and writing the results in flowcharts. The findings shows that flow-proof strategy on Geometry construction was implemented appropriately, based on students’ performance in similarity and congruence proofs with percentage of 72% from all research subject.

Mentorship: Reflections from Middle School Mathematics Teachers

The aim of this phenomenology research is to define the perceptions of middle school mathematics teachers about internship trainers (mentor teachers and university supervisors). The perceptions of participant teachers about internship trainers are examined under three main themes: (i) the importance and contributions of internship trainers in their professional development, (ii) internship trainers' approach to internships and prospective mathematics teachers, (iii) characteristics that internship trainers must have. The results indicate that middle school mathematics teachers have very negative experiences and perceptions about internship trainers.

Examining Prospective Mathematics Teachers’ Conceptual Structure Regarding the Concept of Integral

The purpose of this research is to identify prospective mathematics teachers’ conceptual structure about the concept of “Integral”. In this research, phenomenology design, one of the qualitative research designs, was used. A total of 35 prospective mathematics teachers, studying at a state university, participated in the research. The Word Association Test was conducted to collect the data. The data were analyzed according to content analysis and categories were given according to frequency values. Conceptual networks that present prospective mathematics teachers’ cognitive structure about integral concept were drawn by using a “cut-off point” technique according to the frequency table. As a result, 14 categories related to integral concept were obtained.

Investigation of Prospective Mathematics Teachers' Awareness about the Development of Professional Knowledges': Teaching Practicum Sample

Bu çalışmada, ilköğretim matematik öğretmeni adaylarının mesleki bilgilerinin gelişimleri ile ilgili farkındalıklarının öğretmenlik uygulaması dersi kapsamında incelenmesi amaçlanmıştır. Bu kapsamda çalışmada nitel araştırma desenlerinden durum çalışması yöntemi kullanılmıştır. Çalışmanın katılımcılarını, Türkiye’de bir devlet üniversitesinin İlköğretim Matematik Öğretmenliği bölümünün dördüncü sınıfında öğrenim gören sekiz öğretmen adayı oluşturmaktadır. Çalışmanın verileri, öğretmenlik uygulaması dersi kapsamında gözlem ve öz-değerlendirme formu ile toplanmıştır. Gözlemler, öğretmen adaylarının öz-değerlendirme ile ilgili açıklamalarını teyit etmek amacıyla kullanılmıştır. Elde edilen veriler betimsel analiz tekniği ile analiz edilmiştir. Çalışmanın bulguları, öz-değerlendirme formundaki maddeler doğrultusunda kodlanmış ve öğretmen adaylarının yaptıkları açıklamalardan doğrudan alıntılara yer verilerek ayrıntılı bir şekilde tasvir edilmiştir. Çalışmadan elde edilen bulgular ışığında, öğretmen adaylarının, öğretmenlik uygulaması dersi kapsamında mesleki gelişimlerinin çoğunlukla farkında oldukları ancak bu gelişimlerinin yeterli düzeyde olmadığının farkında olmadıkları sonucuna ulaşılmıştır.

Prospective Mathematics Teachers’ Flow Experiences: From High School to University

Flow is a subjective experience that is a state of being totally involved, absorbed by activity and focused while enjoying doing the activity for its own sake. Researchers found out flow experience is effective in learning and teaching process. Therefore, the purpose of the research was to investigate the flow status of prospective mathematics teachers at major courses in university and whether their flow status is changed from high school to university, or not. It is also determined the factors affecting their flow experiences. The design of the longitudinal research conducted with 36 participants is a mixed study including descriptive study and multiple case study. Data collection tools are the form for the degree of difficulty of YGS 2017 questions in order to get information students’ flow experience in high school, Flow Short Scale developed by Rheinberg, Vollmeyer, and Engeser (2003) and semi-structured interviews are used. Results show a few numbers of student teachers experience flow; the majority feel at ease. Moreover, instructor factor, academic effort, goal orientation, and preparedness have impacts on student teachers’ flow status.

Understanding the Problem Solving Strategy Based on Cognitive Style as a Tool to Investigate Reflective Thinking Process of Prospective Teacher

The development of reflective thinking has been a highlight and important in the education of prospective mathematics teachers. It provides them with the opportunities to take a conscious and logical decision on the complex problems they faced. The quality of the problem solving and reflective thinking will differ between one student and another due to their characteristics. This study presents a description of reflective thinking skills of prospective teachers in solving mathematical problems based on the difference in cognitive style. The instruments used in this study consist of (1) GEFT cognitive-style test, (2) a mathematical problem solving task which is a non-routine and open-ended (3) the interview guidelines based on the reflective thinking component. By choosing analysis of qualitative approaches, the data of interviews that are in the form of interview's transcript based on mathematical problem solving results are gathered from two students of prospective mathematics teachers as research participants. One prospective teacher use cognitive field independent style (PTFI) and field dependent style (PTFD). Research findings show that PTFD tends to use the experience to be implemented in mathematical problem solving but PTFD cannot utilize the new information contained, so that PTFD has a reflective-dynamic characteristic. While PTFI tends to use the experience to utilize the new information contained in the problem in order to construct the problem solving strategy so that PTFI has reflective-generative characteristic. It is indicated that there are differences in the characteristics of reflective thinking process among prospective teachers based on difference of cognitive style.

History of Mathematics for Teaching Mathematics: The Case of Indonesian Prospective Teachers' Beliefs and Attitudes

The inclusion of History of Mathematics (HoM) in the official mathematics textbook published by Indonesian Ministry of Education and Culture became an essential aspect in supporting the national curriculum of mathematics education. This study aimed to examine Indonesian prospective mathematics teachers' pedagogical attitudes and beliefs in using HoM to teach mathematics. 305 prospective teachers from nine universities in Indonesia were involved as the respondents. Data were collected using Questionnaires of Attitude and Belief in using HoM to teach mathematics. The results showed that prospective teachers had positive attitudes and beliefs in using HoM to teach mathematics. However, those who had taken the mathematics history course tent to have a higher score compared to those who had not taken the course yet during their study times. Hence, this study recommends that involving the HoM course is vital in supporting the prospective teachers' learning process as a part of their future professional developments. However, both groups showed low scores in the questionnaire item of self-efficacy beliefs. This implies that teacher education programs should facilitate the improvement of prospective teachers' self-efficacy beliefs and skills, especially of using HoM in teaching mathematics.

Problem-based learning with role-playing: An experiment on prospective mathematics teachers

[English]: This study aimed to examine the effect of problem-based learning (PbL) with role-playing toward problem-solving skills of prospective mathematics teachers’ (PMTs) who take linear algebra courses. The study was a quasi-experimental with a non-equivalent control group post-test only design. Forty-two PMTs were involved and divided into experimental (taught using PbL combined with role-playing) and control groups (taught using PbL only). Data were collected using tests and video recordings. The test produces data on PMTs' problem-solving skills on linear algebra problems and video recordings resulted in the transcripts of PMTs’ discussion when they played a role. Data were analyzed through two stages. Firstly, the results of the test were analyzed quantitatively using F-test to measure the variance of the two groups, then measure the normality of the data using the interpretation of skewness and kurtosis, and finally, one-tail t-test to measure differences in test results between the two groups. Secondly, the sample of PMTs’ works in two groups and the transcripts of their conversation were qualitatively analyzed to strengthen the quantitative finding and reveal how PbL with role-playing support PMTs’ problem-solving in teacher education. This study shows that PbL with role-playing is more effective to improve students’ problem-solving skills than solely doing problem-based learning. Doing a role-playing provided students with the opportunity to be able to think and speak mathematics more formally in the context of problem-solving.
 Keywords: Problem-based learning, Role-playing, Prospective mathematics teachers, Problem-solving
 [Bahasa]: Penelitian ini bertujuan untuk menguji pengaruh pembelajaran berbasis masalah dengan bermain peran pada pemecahanmasalah calon guru matematika yang mengambil matakuliah aljabar linier pada semester ketiga. Penelitian ini adalah eksperimen semu dengan desain post-test kelompok kontrol yang tidak setara. Empat puluh dua calon guru matematika terlibat dalam penelitian ini dan mereka dibagi menjadi kelompok eksperimen (diajarkan menggunakan pembelajaran berbasis masalah dengan bermain peran) dan kelompok kontrol (diajarkan menggunakan pembelajaran berbasis masalah saja). Data dikumpulkan menggunakan tes dan rekaman video. Tes menghasilkan data tentang kemampuan calon guru untuk memecahkan masalah aljabar linier dan rekaman video yang menghasilkan transkrip diskusi calon guru ketika mereka memainkan suatu peran. Data dianalisis melalui dua tahap. Pertama, hasil tes dianalisis secara kuantitatif menggunakan uji-F untuk mengukur varian kedua kelompok, kemudian mengukur normalitas data menggunakan interpretasi skewness dan kurtosis, dan akhirnya dilakukan uji-t satu pihak untuk mengukur perbedaan hasil tes antara kedua kelompok. Kedua, sampel hasil tes calon guru matematikadari kedua kelompok dan transkrip diskusidianalisis secara kualitatif untuk memperkuat temuan kuantitatif dan mengungkapkan bagaimana pembelajaran berbasis masalah dengan bermain peran dapat mendukung pemecahan masalah pada calon guru matematika yang menempuhpendidikan guru. Penelitian ini menunjukkan bahwa pembelajaran berbasis masalah dengan bermain peran lebih efektif untuk meningkatkan keterampilan pemecahan masalah calon guru matematika daripada hanya melakukan pembelajaran berbasis masalah saja. Bermain peran memberikan kesempatan kepada mahasiswa untuk dapat berpikir dan mengomunikasikan matematika secara formal dalam konteks pemecahan masalah.
 Kata kunci: Pembelajaran berbasis masalah, Bermain peran, Calon guru matematika