Pre-service Mathematics Teachers Research Articles

Knowledge, Skills and Attitude of Pre-Service Mathematics Teachers Towards Higher-Order Thinking Skills

<p style="text-align:justify">This research was aimed to determine the level of knowledge, skills and attitude of pre-service Mathematics teachers in Universiti Pendidikan Sultan Idris (UPSI) towards higher-order thinking skills (HOTS) and whether the elements of HOTS were translated into the teaching courses. The research was also designed to analyze the relationship between the pre-service Mathematics teachers’ exposure to HOTS through the teaching courses and their level of knowledge, skills and attitude towards HOTS. The study utilized a quantitative approach by administration of a survey to a simple random sample of 110 pre-service Mathematics teachers from UPSI. A questionnaire with five different parts was used as the research instrument with a reliability value of .979. The collected data were then analyzed using descriptive and inferential statistics. The descriptive statistics were used to determine the mean scores of the level of knowledge, skills and attitude among the pre-service Mathematics teachers, whereas inferential statistics using Pearson-r correlation was implemented to describe the relationship between the studied variables. The findings demonstrated that the knowledge and skills of pre-service Mathematics teachers towards HOTS were at a moderate level as opposed to their attitude and exposure to HOTS which were found to be at a high level. The data analysis using Pearson correlation illustrated a significant positive relationship with <em>r</em> = .727, <em>r</em> = .757 and <em>r</em> = .667 between the exposure to HOTS through the teaching courses and the level of knowledge, skills and attitude regarding HOTS of pre-service Mathematics teachers at UPSI, respectively. In conclusion, the research here indicates that pre-service Mathematics teachers in general, are positive towards the implementation of HOTS but they are lacking in terms of knowledge and skills. This research is useful in the field of Mathematics education as it can serve as a guidance to further enhance the knowledge, skills and attitudes especially for future Mathematics teachers in implementing HOTS effectively and improving the quality of the teaching program offered by the university indirectly.</p>

지속가능발전교육(ESD)을 위한 예비수학교사의 사회 비판적 모델링 수업 설계와 성찰

Objectives This study is developing materials related to Education for Sustainable Development (ESD) and Lesson Plan connected to mathematics based on issues related to life to cultivate key concepts of mathematics and mathematical competencies. Methods This study is conducted as a part of development research in a mathematics teacher education course. Based on a comprehensive review of literature concerning Socio-critical modeling and ESD, this study identified the guiding principles and the methods on how to develop mathematics prospective teachers’ competencies of context levels to practice the SDGs. Results Prospective teachers were able to experience diverse social issues which they were unaware of in daily life. Pedagogical goals such as critical understanding of the surrounding world. A variety of controversial topics such as Climate Action. Practice-oriented teaching skills were improved. Conclusions Prospective teachers realized diverse social phenomena and mathematical connectedness through developing lesson plan in EDS-PBL. In addition, it is suggested that pre-service mathematics teachers should be given an opportunity to fully experience Socio-critical modeling which could lead to development of their creativity and creative teaching competency.

Changes in noticing multiple dimensions in classroom situations among pre-service mathematics teachers

This paper explores changes in pre-service mathematics teachers' (PSTs) noticing of critical events during a year-long preparation program. Twenty PSTs identified, described and interpreted critical events they witnessed during classroom observations and teaching. We used a previously developed model to examine changes in PSTs’ degree of attentional focus and interpretational focus. Findings revealed that for most participants, the attentional focus was broaden, and even for those whose not, the interpretational focus broadened. The paper then examines these changes in terms of the dimensions of learning and teaching—cognitive, affective, and social dimensions—and discusses the contributions and implications.

An Online Laboratory School research on pre-service mathematics teachers' experiences and mathematics teaching anxiety.

During the COVID-19 pandemic, we founded an Online Laboratory School (OLS) under the roof of a university in Turkey to support students from public schools that were not technologically prepared for an online education and to provide an opportunity for our pre-service teachers (PSTs) to continue their internship by teaching online. The purpose of this research, consisting of two studies, was to examine experiences of 43 PSTs (first-, third- and fourth-years) during the OLS period of 8 weeks and how the OLS affected their mathematics teaching anxiety during Fall 2020. In the first study, we administered a survey to inquire into PSTs' views on their experiences at the OLS, and in the second study we examined their mathematics teaching anxiety before and after the OLS experience using another survey. One main result was that the OLS experience served as an effective introduction to the profession for first-year PSTs and fourth- and third-year PSTs reported learning in-depth about online teaching in terms of the planning, teaching, and reflecting cycle. Another main result was that PSTs had mathematics teaching anxiety from "a little" to "a moderate amount" before the OLS and their teaching anxiety did not significantly change during the OLS period of 8 weeks. PSTs experienced highest mathematics teaching anxiety when they were observed and evaluated by supervisors during their teaching. The implications of these findings are discussed for teacher education programs.

Preservice mathematics teachers' perceptions of mathematical problem solving and its teaching: A case from China.

Preservice mathematics teachers' accurate understanding of mathematical problem solving and its teaching is key to the performance of their professional quality. This study aims to investigate preservice mathematics teachers' understanding of problem solving and its teaching and compares it with the understanding of in-service mathematics teachers. After surveying 326 in-service mathematics teachers, this study constructs a reliable and valid tool for the cognition of mathematical problem solving and its teaching and conducts a questionnaire survey on 26 preservice mathematics teachers. Survey results reveal that preservice mathematics teachers have a good understanding of mathematical problem solving and its teaching and are more confident in the transfer value of problem solving ability. By contrast, in-service teachers are more optimistic that problem solving requires exploration, continuous thinking, and the participation of metacognition. This article concludes that preservice mathematics teachers should focus more on the initiative and creativity of students and put students at the center of education. In addition, teacher educators should provide more teaching practice opportunities for preservice teachers. The findings also show that in-service teachers' understanding of problem solving and its teaching is inferior to that of preservice teachers on some indicators, implying the importance of post-service training for in-service teachers.

Preservice Mathematics Teachers’ Ability to Perform the Mathematizing Process: The Cylinder Packing Problem

The present study aims to examine the preservice middle school mathematics teachers’ ability to perform the process of mathematizing and to identify their competencies within this context. For this purpose, the study was conducted with 43 preservice teachers attending a state university. The research method used is descriptive research. As the data collection tool, a real-life problem called "cylinder packing problem" was presented to preservice teachers, with a view to finding the optimal and lowest-cost packing scheme for a hazelnut grower. The solutions presented by the preservice teachers were subjected to content analysis as well as descriptive analysis. The preservice teachers’ competencies were examined to see their level of effectiveness in the use of notations that are indicators of mathematizing, in achieving mathematical results in the process of problem-solving. The research findings indicate that the preservice teachers generally lacked sufficient comprehension of the problem in the real-life contexts and could not perform the requirements of important skills such as using notations, mathematical models and generalization method which are important in making abstract inferences in the mathematizing process. In light of these findings, further studies to contribute to preservice teachers’ mathematical sophistication levels are recommended in order to improve their competencies in mathematizing.

Üstbilişsel Sorgulamaya Dayalı Tasarlanan Öğrenme Ortamında Olasılık Öğrenme Süreci: Bir Öğretim Deneyi

Bu çalışma ilköğretim matematik öğretmeni adayları için tasarlanan üstbilişsel sorgulamaya dayalı öğrenme ortamını değerlendirmek amacıyla yapılmıştır. Bu amaç doğrultusunda olasılık kavramının öğretimi için üstbilişsel sorgulamaya dayalı bir öğrenme ortamı tasarlanmıştır. Bu öğrenme ortamında her uygulamanın ardından yapılan görüşmeler ve araştırmacının izlenimleri sonucunda öğrenme ortamında düzenlemelere gidilmiştir. Yapılan düzenlemeler kapsamında matematik öğretmeni adayları için üstbilişsel sorgulamaya dayalı alternatif bir öğrenme ortamı ortaya çıkmıştır. Nitel araştırma desenine göre yürütülen bu çalışmada öğretim deneyi modeli kullanılmıştır. Çalışmaya tamamı Türk 31 matematik öğretmeni adayı katılmıştır. Çalışmanın verileri görüşme formu, gözlem formu ve katılımcı günlükleri ile toplanmıştır. Çalışmada elde edilen sonuçlar üstbilişsel sorgulamaya dayalı tasarlanan öğrenme ortamında katılımcıları çözüme götürmek üzere hazırlanan ipucu kartlarının ilk uygulamalarda gerekli olduğunu ancak ilerleyen uygulamalarda katılımcıların bu ipucu kartlarına gerek duymadığını göstermiştir. Ayrıca küçük grup çalışması olarak başlayan etkinlikler öğretmen adaylarından alınan dönütler doğrultusunda bireysel etkinliklere dönüştürülmüştür. Bireysel uygulamalarda öğretmen adaylarının küçük grup çalışmasına göre daha fazla sorgulama yaptıkları belirlenmiştir.

Representation of Algebraic Reasoning in Sets through Argumentation

The purpose of the current study is to examine the ways in which preservice middle school mathematics teachers (PMSMT) apply and represent algebraic reasoning in their solution processes for the problems in the concept of sets. This model provides detailed information about the reasoning made through the process of the solution of set problems. The study group of this case study was composed of 20 preservice mathematics teachers. The data were collected through written documents and whole class discussions. Based on the findings of the study, three ways to represent algebraic reasoning in sets emerged; context-based representation of algebraic reasoning, generalization-based representation of algebraic reasoning and formulization-based representation of algebraic reasoning. These ways determined based on the argumentations that they formed. They produced different warrants since they reasoned differently.

Pre-Service Teachers’ Strategies in Solving Absolute Value Equations and Inequalities

Many secondary school students have encountered difficulties when dealing with absolute value equations and inequalities. This condition might be brought to higher education, including by pre-service mathematics teachers in teacher training colleges. The difficulties in dealing with absolute value equations and inequalities, which can be observed from solution strategies, indicate the lack of symbol sense. This study aims to investigate strategies that pre-service teachers used while solving absolute value equations and inequalities from the perspective of symbol sense. To investigate this, we conducted a qualitative case study through two written tests followed by interviews involving 36 pre-service mathematics teachers in one of the state universities in Bandung, Indonesia. The results revealed three different solution strategies for solving either absolute value equations or inequalities. Also, difficulties that occurred during the solution processes of equations and inequalities were addressed. We conclude that the symbol sense characteristics are fruitful for interpreting the selection of solution strategies used by pre-service teachers in solving absolute value equations and inequalities.

TPACK development model for pre-service mathematics teachers

TPACK development model for pre-service mathematics teachers

Pre-service Mathematics Teachers’ lesson plans as a source of Information about their readiness to teach online

This paper presents a study of lesson plans created by pre-service mathematics teachers (PMTs) from two universities (Faculty of Education, Charles University in Prague, and Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava) in the course Didactics of Mathematics. The collaboration of the two research teams brought new perspectives on several questions that were come across in one or the other group of PMTs. The focus of the study was on lesson plans since the lesson plan is one of the significant parts of mathematics teacher education. The studied issues were the PMTs’ willingness to implement digital technologies (DT) in their lesson plans and the changes in their lesson plans that could be linked to the COVID-19 pandemic. For data processing, a mixed research design was used. In the qualitative part of the research, the thematic analysis resulted in identification of several codes related to the hybrid mode of teaching. In the quantitative part, Statistical Implicative Analysis (C.H.I.C) was applied. Relations inside the groups of PMTs and among them are presented and discussed in the paper by interpreting the results from the implicative trees and graphs. We concluded that (i) PMTs from our sample are, to a limited extent, prepared for using DT in their teaching, (ii) PMTs used DT in their teaching mainly for testing and feedback collection, (iii) PMTs in our sample focused on the content and the choice of software (or application, applet, etc.) when preparing a lesson plan. Besides that, we found (by using C.H.I.C.) that not all codes identified in thematic analysis were connected to the others. The findings are of interest to teacher educators in general, researchers interested in teachers’ lesson planning, and in-service teachers in general. In this paper we focus on PMTs’ lesson plans. We plan to do a similar analysis of in-service teachers’ lesson plans in order to gain a deeper insight into the role of experience in the studied domain.

An Assessment of Pre-Service Mathematics Teachers’ Techno-Pedagogical Content Knowledge regarding Geometry

Despite the significance of incorporating technology into geometry instruction, many teachers still find it difficult to teach geometry using technology. This study employed a techno- pedagogical content knowledge (TPACK) survey of 70 pre-service mathematics teachers (29 males, 41 females) from a public university. The goal was to determine which domains, if any, were open for development so that a course could be designed to meet these needs. The data was analysed thematically according to the TPACK sub-domains. The results showed that the pre-service teachers were confident in the areas of pedagogy knowledge, content knowledge, and pedagogical content knowledge (90% confidence) and open to improvement in the areas of technology, technological content, and technological pedagogy knowledge (70% confidence). As a result, we suggest creating a 14-week course to increase pre-service mathematics teachers' TPACK of these components in the hopes of bridging the knowledge gap identified in this study.

The effect of a training program based on TIMSS to developing the levels of habits of mind and mathematical reasoning skills among pre-service mathematics teachers

This study aimed to investigate the effect of a training program based on the trends in international mathematics and science study (TIMSS) on developing the habits of mind and mathematical reasoning skills among pre-service math teachers in Oman. The study sample consisted of 24 female pre-service math teachers divided into two equal groups: experimental and control. The study data was collected by sued the mathematical reasoning test and questionnaire that measured the level of habits of mind after appropriate validity and reliability. The study results showed statistically significant differences between the two study groups in favor of the experimental group in the mathematical reasoning test and the habits of mind scale. The study recommended that the need for pre-service math teachers to use programs based on international studies such as TIMSS, PISA, PIRLS, and TAILS; this was done to prove their effectiveness in developing the levels of habits of mind and mathematical reasoning skills by subjecting them to training programs, courses, and workshops with the aim of training teachers to implement the training programs effectively.

Pre-service Mathematics Teachers’ Understanding of Rate of Change Throughout a Model Development Sequence

Pre-service Mathematics Teachers’ Understanding of Rate of Change Throughout a Model Development Sequence

Exploratory Case Study on Solving Word Problems Involving Triangles by Pre-Service Mathematics Teachers in a Regional University in Australia

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

Secondary pre-service teachers’ voices of becoming mathematics teachers

ABSTRACT This paper captures and reports on mathematics pre-service teacher (PST) voices. Mathematics PSTs, in a tertiary mathematics secondary curriculum teaching subject assessment, were asked to perform a small-scale literature review on an issue they identified as important in mathematics teaching. The assessment, written as an article, required literature-based recommendations, a reflection on how this would impact the PST’s future teaching and guidance for all mathematics teachers. The article was aimed for publication by the Mathematics Association of Victoria—a state-based mathematics professional association in Australia. PSTs were advised that articles would potentially be published, and their voice would reach practicing mathematics teachers. The published articles, which capture pre-career mathematics teacher voices were analysed for insight into what four PSTs said of their future teaching to a mathematics teacher audience. The professional teacher standards were recognised to influence comments given the strong emphasis of standards within initial teacher education courses. Findings speak to what mathematics PSTs expect of their future teaching role prior to being in-service. The paper contributes a snapshot of early established professional voices in a discipline where there is currently a shortage and highlights the messages that emerged.

Emerging Proof Productions of Freshmen in Euclidean Geometry Proof Tasks between Conjecturing and Proving

ABSTRACT This study was conducted to examine the effectiveness of proof tasks in the transition from conjecture to proof in Euclidean geometry on freshmen’s proof schemes. In line with this aim, the proof schemes of the freshmen who performed conjecture-proof and theorem-proof tasks were compared. The freshmen were composed of 109 pre-service middle school mathematics teachers who are enrolled in their first year of undergraduate education. The study was modeled as a multiple-case study. Fifty-three freshmen performed conjecture-proof tasks in Case-1, and fifty-six freshmen performed theorem-proof tasks in Case-2. The video recordings, including the written proof reports, reflection papers, and proof explanations of the freshmen, were used as data collection tools in the tasks. The proof schemes were used as construct maps to evaluate the proofs of freshmen and analyzed using Winsteps Rasch software. The proof schemes in freshmen’s proof tasks were evaluated by the Wright Map and supported with direct quotations from the proofs. In the study, it was observed that the proof schemes of freshmen who made proofs based on their own conjectures were mostly empirical and analytical proof schemes, while the proof schemes of freshmen who made proof of the presented theorem were generally external and empirical proof schemes.

Revealing Pre-service Teachers' Mind Maps on STEM Education through STEM Images

STEM education (based on the integration of the science, technology, engineering and mathematics disciplines) has recently been an integral part of education system and curriculum in many countries aiming to be more technologically competitive in this age of innovation. While the importance of STEM education has gradually increasing in education system with the complexities of today’s world, revealing pre-service teachers’ mind maps on STEM education and preparing them for STEM education is a crucial issue since the readiness of the teachers affects the quality of education. In this context, the aim of this study is to reveal pre-service science and mathematics teachers’ mind maps on STEM Education through STEM images. The research group consists of 6 pre-service teachers (3 of them are pre-service science teachers (PST) and 3 of them are pre-service mathematics teachers (PMT)) who are 4th grade level students from a public university in Istanbul, Turkey. In current research, case study design was used. The data of study were collected through drawings and focus group discussion. The data were analyzed with thematic analysis through Integrated Teaching (IT) Framework. As a result, 41 codes about pre-service teachers’ mind maps on STEM education were determined under 14 categories of 5 themes of IT Framework. The results of this study are crucial in terms of having potential to guide educational policy makers, curriculum developers, researchers and in-service and pre-service teachers about STEM education.

The relationship between technological pedagogical content knowledge of mathematics teacher candidates and teaching mathematics anxiety

The aim of this study is to examine the relationship between pre-service mathematics teachers' technological pedagogical content knowledge and their anxiety about teaching mathematics according to gender and class variables. The relational survey model, which is one of the general survey model types, was used in the research carried out by following the quantitative paradigm. Data were collected online from 196 pre-service teachers using the "Mathematics Teaching Anxiety Scale" and the "Technological Pedagogical Content Knowledge Scale". T-test, one way ANOVA and Pearson's Product Moments Correlation Analysis were used in the analysis of the data. The results showed that the pre-service teachers' genders and classes did not affect their mathematics teaching anxieties and technological pedagogical content knowledge. It also revealed a weak positive relationship between the pre-service teachers' technological pedagogical content knowledge and mathematics teaching anxieties.

Mathematical Proving Ability of Pre-service Teachers in Online and Blended Learning

Mathematical proving is an important ability to learn. However, mathematics pre-service teachers often find this skill difficult. This research aimed to describe the mathematical proving ability of mathematics pre-service teachers in an online classroom and in the blended classroom. A descriptive mixed methods approach was used. A mathematical proving test was used to collect the data. The results showed that the average score of mathematical proving ability from the blended classroom was 82.6 (categorized as high). Meanwhile, the average score of mathematics pre-service teachers in the online classroom was 65.4 (categorized as intermediate). Given these findings, there is a significant need to improve the mathematical proving ability of the mathematical preservice teachers in the online classroom by enhancing the conceptual understanding of group properties and ensuring the teachers are accustomed to practicing proving tasks.
 Keywords: mathematical proving, online learning, blended learning, mathematics pre-service teachers, group theory