Pre-service Mathematics Research Articles

Ways to develop soft skills in pre-service mathematics and physics teachers when studying certain topics of olympiad mathematics

The development of soft skills in pre-service teachers helps to improve the quality of teaching, create a positive classroom environment and ensure an individualized approach to learning. The integration of soft skills, in particular flexibility and adaptability to change, helps teachers to respond effectively to new teaching methods, technological innovations and the requirements of the modern educational environment. The authors of this article aimed to investigate the possibilities of developing soft skills within the educational components of the training programme for pre-service mathematics and physics teachers. The methodological basis of the study was the analysis of scientific literature, synthesis, formalization of scientific sources, description, comparison, and theoretical generalization of own pedagogical experience of teaching the course “Olympiad Mathematics”. The results of the study reveal some ways of developing soft skills of future masters of secondary education of Sumy State Pedagogical University named after A.S. Makarenko in the process of studying the course “Olympiad Mathematics”. At the same time, among the various topics of the course, the topic “Proof of Inequalities” was singled out. The peculiarities of applying the following methods and techniques to the proof of inequalities in the context of development of soft skills are revealed: the method of strengthening (weakening) of inequality, the method of mathematical induction, the Malikov's method, the method of transforming the common term in sums and its evaluation, the method of evaluating the terms of the product and introducing an additional factor, the method of applying the properties of functions to the proof of inequalities, the method of using the properties of the definite integral of a certain function on a segment. It has been found that the most common methods of proving inequalities have wide possibilities in the context of development of soft skills. Each of the methods of proving inequalities discussed in the article is illustrated by relevant examples with detailed explanations. It is proved that this topic opens up wide opportunities for the acquisition and development of a number of soft skills. The research allows identifying specific ways to improve soft skills in pre-service mathematics and physics teachers, which are practically significant for further development of these professions when studying specific topics of the “Olympiad Mathematics” course: using group work formats during seminars, problem-based learning in mathematics, applying digital technologies in the study of Olympiad Mathematics, self-analysis and reflection, using mentoring support technology, public speaking during seminars with presentations of own solutions

Pre-Service Mathematics and Primary School Teachers’ Design and Application of Mathematics Materials in Woodworking Workshops

Pre-Service Mathematics and Primary School Teachers’ Design and Application of Mathematics Materials in Woodworking Workshops

Fixed mindset as a challenge in teaching practice: A pre-service teacher’s experiences of received feedback

Teaching practice is a critical component in teacher education, and better understanding of how pre-service teachers experience and interpret the feedback received in this setting is needed to understand teacher development in initial teacher education. Arguably, the mindset theory can help explain pre-service teachers’ responses to and reception of feedback. This narrative study examines one pre-service mathematics and science teacher’s experiences of received feedback from her supervisors during teaching practice and discusses the impact of her mindset on her reception of feedback. Esteri displayed a so-called fixed mindset regarding her qualities as a teacher and towards the feedback received, which greatly hindered her reception of the feedback. Interestingly, we observed characteristics of fixed mindset also in the feedback given by her supervisors. We discuss the challenges that fixed mindset poses for feedback practices, and what narrated experiences of feedback can teach us about supporting teacher development of future teachers in teaching practice.

Matematik ve Fizik Öğretmen Adaylarının Akran Değerlendirmesini Uygulama Deneyimleri

The aim of the presented research is to investigate how pre-service mathematics and physics teachers have experienced peer-assessment. The study took place within the context of one classroom assessment course designed for pre-service teacher education. Ninety-four (94) students in four cohorts participated. They were giving written feedback to peer’s coursework, writing reflective journals and participating in semi-structured interviews. The participants reported that grading is more difficult than giving feedback because grades are important as they “count” for students’ success. Secondly, during the course, their thinking “shifted” to the idea that giving comments is more crucial than grading, because feedback helped them understand the assessment criteria and subsequently, improve coursework. Based on the findings, the main argument of the paper is about the role of pre-service teacher education for the development of classroom assessment skills and assessment knowledge in teachers.

Teacher educators’ nature of understanding of adult learning theories application in pre-service teachers’ classes

Research publications show that they are many different theories which explain how adults learn, but none of them individually fully explains what happens when adults learn, hence cannot be applied universally. Each theory has its own merits and demerits, therefore to maximise learning, a combination of theories should be used. Adult teacher educators’ familiarity with this knowledge base of adult learning improves effectiveness in meeting adult learner needs, since implementation of the most effective ways for adult learning is made possible. The current study sought to find out the nature of experiences of secondary school teachers recruited to be teacher educators at a secondary teachers’ college, had during the transition from teaching children (pedagogy) to teaching adults (pre-service mathematics and science teachers). Interviews were done, with the view to enable teacher educators to compare their experiences during training (as adult learners) in various teacher education institutions, teaching children at secondary school level, and teaching adults at the teachers’ college in the current study. Interview responses were coded to come up with themes which were analysed. Findings show that learning and application of adult learning theories is a missing link in teacher preparation institutions in Zimbabwe. In order to align teacher preparation with the current Zimbabwean curriculum, training institutions must prepare prospective teachers for both pedagogy and adult learning theories, so that they adapt as the situation requires. This resonates with metagogy, a hybrid of pedagogy and adult learning theories. Preparing teachers this way is in line with best practices, which engender competitiveness to deal with diverse teaching and learning situations, in the 21st century.

Preservice Elementary Teachers’ Mathematical Knowledge on Fractions as Operator in Word Problems

The preservice primary school mathematics teacher needs training that focuses on school mathematics and its didactics. Research has shown the importance of developing mathematical content knowledge as well as adequate didactic knowledge. Teacher education programs must address both to provide an effective teaching-learning process. The present research aims to assess the mathematical content knowledge of 194 prospective teachers about fraction word problems faced by students at the Primary Education stage, based on the Mathematics Teachers′ Specialized Knowledge (MTSK) model. By means of the preservice teachers’ written answers, we explored their knowledge and identified the associated error to fraction word problems (one-step and multistep) in which the fraction has a meaning as an operator. Preservice teachers showed some difficulties when working with this content, difficulties that were intensified when they solved multistep problems. The most common error founded in both types of problems is related to the meaning of fraction as operator. The results show a weak prior mathematical content knowledge and as a consequence, it is necessary to establish preventive actions in the training degrees since an insufficient mathematical content knowledge prevents them having a proper didactic knowledge.

The process of problem posing: development of a descriptive phase model of problem posing

The aim of this study is to develop a descriptive phase model for problem-posing activities based on structured situations. For this purpose, 36 task-based interviews with pre-service primary and secondary mathematics teachers working in pairs who were given two structured problem-posing situations were conducted. Through an inductive-deductive category development, five types of activities (situation analysis, variation, generation, problem-solving, evaluation) were identified. These activities were coded in so-called episodes, allowing time-covering analyses of the observed processes. Recurring transitions between these episodes were observed, through which a descriptive phase model was derived. In addition, coding of the developed episode types was validated for its interrater agreement.

Preservice Science and Mathematics Teachers Mathematics Anxiety and Beliefs about the Nature of Mathematics

Preservice Science and Mathematics Teachers Mathematics Anxiety and Beliefs about the Nature of Mathematics

Effects of Teaching in a Summer STEM Camp on the Mathematics Teaching Self-efficacy of Highly Qualified Preservice Secondary Mathematics Teachers

Educational opportunity gaps experienced by students of color living in poverty, with accompanying lower levels of mathematics achievement, remain a roadblock to their access to college-level training in STEM fields. To address this problem, secondary teachers must be confident in their ability to share mathematics content effectively with students from cultures different than their own. Bridging the opportunity gap is more likely with two elements in place: intellectually stimulating pre-college experiences and community partnerships that establish connections between underserved neighborhoods and resource-filled environments such as university campuses.
 This study explored the effects of teaching in a four-week STEM summer camp for ethnically diverse, high-needs middle school girls on the teaching self-efficacy of highly-qualified preservice secondary mathematics teachers, a group that has been less studied than preservice elementary teachers. Participants were scholarship students in a federally-funded teacher preparation scholarship program at an urban, metropolitan university. Teaching self-efficacy was measured by the Mathematics Teaching Efficacy Belief Instrument (MTEBI) and by follow-up qualitative analysis of questionnaire responses and focus groups. Participants’ gains on the MTEBI were significant for Personal Mathematics Teaching Efficacy, but not for Mathematics Teaching Outcome Expectancy. Qualitative analyses suggested that both instructional coaching and everyday interactions in a summer camp setting contributed strongly to the preservice teachers’ increased confidence about teaching mathematics to culturally diverse, high-needs learners.

Developing Pre-service Teachers Conceptualization of STEM and STEM Pedagogical Practices

Science, Technology, Engineering, and Mathematics (STEM) integrated curricular approach has become the leading type of education reform worldwide. This paper presents a STEM integrated collaborative activity to enhance STEM knowledge among pre-service mathematics and chemistry teachers. Well-structured and planned on-site workshops on STEM activities were delivered to pre-service teachers while growing mathematics and science content knowledge and pedagogical practices. The qualitative content analysis research methodology was used to identify relevant topics related to post reflective questions regarding pre-service teacher perspectives on the experience gained through the collaborative practices at the STEM workshop. The results show that the workshop had a positive effect on pre-service teachers’ conceptualization of STEM—through collaborative, participatory practices, an effective learning environment while bringing attention to teacher professional development and education policymakers. Key elements of this study approach included: (1) collaboration between university professors to teach and incorporate STEM in higher education; (2) unique partnership among mathematical and chemistry pre-service teachers; and (3) professional development, which is devoted and adopted into a study course.

Towards conceptualising failure in mathematics as an autobiographical experience

ABSTRACT Studies have shown that failure experiences play a role in pre-service teachers’ development. Given that autobiographical experiences are a foundation of learning and that failure is a wide-spread experience, particularly in mathematics, we need further insight into what kind of experience failure actually is. This paper draws on 59 pre-service teachers’ written experiences of failure in order to map them out and provide insight into what counts as failure from the perspective of the future teachers of mathematics, that is, pre-service mathematics and pre-service elementary school teachers. The findings, alongside the earlier research on negative experiences, form a basis for conceptualising failure in mathematics as an autobiographical experience and distinguishing it from a negative experience. A theoretical insight into the nature of failure is gained; the failure experiences seem to be less relational than anticipated. The paper also discusses the relevance of failure experiences for teacher education.

Pre-service Mathematics and Physical Education Teachers' Perceptions of using Play-based Teaching Strategy across the Foundation Phase

This qualitative case study explores early childhood pre-service educators' perceptions of using play-based teaching strategy across the Foundation Phase. A play-based approach promotes a special mode of thinking, sense of possibility, ownership, control, and competence in maths and PE learners. That is why scholars believe that hybrid pedagogical content knowledge that integrates play-based learning sustains learner attention throughout the lesson and promotes problem-solving skills. Therefore, the main objective of this study is to propose alternative pathways that promote the implementation of a hybrid pedagogical teaching strategy in the Foundation Phase. This study draws from a qualitative case study conducted at one of the universities in KwaZulu-Natal to explore the perception of pre-service teachers about using a play-based teaching strategy in pre-Grade R and Grade R classes. Five preservice teachers who teach both mathematics and PE were purposively and conveniently sampled to generate data using narratives and semi-structured interviews to describe their perceptions and experiences. Zoom group meetings and WhatsApp one-on-one semi-structured interviews were used during the data generation process. The findings reveal that pre-service mathematics and PE teachers perceive play-based pedagogies as necessary to provide a wide range of opportunities for learners to learn to count, visualising groups, and problem-solving skills. They underscore the importance of drawing from a hybrid approach that draws strength from play-based learning to complement formal learning.

KNOWLEDGE AND IMAGES OF PRE-SERVICE ELEMENTARY MATHEMATICS TEACHERS ABOUT ENTREPRENEURSHIP AND ENTREPRENEURSHIP SKILLS

Entrepreneurship is related to awareness, ideas, imagination, and effort. Entrepreneurship training is now being carried out in order to increase the extent of entrepreneurial activities. In this regard, when entrepreneurship education practices are examined in many countries, it is seen that students are introduced to entrepreneurship and entrepreneurship education before they reach high school. In Turkey, entrepreneurship skills are among the basic skills in all curriculum programs since 2005. By establishing relations through images, people build stronger and understandable connections when they encounter a new concept or new knowledge. In this respect, the aim of this study is to reveal pre-service elementary mathematics teachers’ perceptions of entrepreneurship and the skills of the concept from freshmen to seniors in terms of what they know from their previous and current educational experiences and their perceptions about the importance of the concept of entrepreneurship. Twelve pre-service elementary mathematics teachers (6 women and 6 men) from each grade level for a total of 48 pre-service teachers (24 women and 24 men) studying at Bolu Abant Izzet Baysal University participated in the study. During the selection process of the participants, only voluntary participants were considered. As a data collection tool, the interview protocol, which included 6 questions and was based on the literature, was prepared by the researcher. Data were collected through interviews, and interviews took approximately 40 minutes for each participant. The content analysis technique was used in the analysis of the collected data. The data were analyzed under headings of the prior knowledge and perceptions of entrepreneurship and entrepreneurship skills, the importance of entrepreneurship and entrepreneurship skills, the place of entrepreneurship in daily life, and findings about images of entrepreneurship skills. According to the findings of the research, it is concluded that the concepts of entrepreneurship and entrepreneurship skills are not sufficiently heard of or recognized among pre-service elementary mathematics teachers. As the image categories of entrepreneurship and entrepreneurship skills, 4 image categories and related subcategories were determined for entrepreneurship. For “entrepreneurship skills,” 3 image categories and related subcategories were determined. Entrepreneurship training can be given in entrepreneurship courses or teaching courses in faculties of education. In these courses, not only theoretical knowledge about entrepreneurship skills, which are among the skills that should be acquired by individuals within the scope of lifelong learning, but also studies involving applications can be applied for pre-service teachers. There is no previous study in the literature that reveals the knowledge and images of pre-service elementary mathematics teachers regarding the concepts of entrepreneurship and entrepreneurship skills. Therefore, other studies that support the results of this study should be pursued. Article visualizations:

Errors In Using Convergence Tests In Infinite Series

Abstract: The present study aimed to identify the errors made by pre-service elementary mathematics teachers while investigating the convergence of infinite series. A qualitative exploratory case study design was used with a total of 43 undergraduate students. Data were obtained from a test administered in a paper-and-pencil form consisting of seven open-ended questions. The data analysis was done using descriptive and content analysis techniques. Findings were presented as follows: inappropriate test selections; failure to check convergence criteria; incorrect use of a comparison test; limit comparison test error; re-test convergence test results; considering ∑ as a multiplicative function; misunderstanding of special series; considering that series has no character when the convergence test is inconclusive; confusing sequences with series; misunderstanding of the nth-term test; misinterpretation of convergence test results. Findings showed that students with insufficient procedural knowledge had difficulty in solving the given problem even if they understood it, whereas those with insufficient conceptual knowledge could not literally understand what they did even if they solved the problem. Therefore, the establishment of a moderate balance between procedural and conceptual knowledge in the learning of the convergence of series is essential in reducing the errors or learning difficulties for developing deep mathematical understanding

Mathematics anxiety and mathematics teaching anxiety of in-service and pre-service primary school teachers

ABSTRACT This study explores effects of teaching experience and specialized mathematics education on mathematics anxiety and mathematics teaching anxiety. Fifty-nine female pre-service and in-service mathematics primary school teachers with varied specialized mathematics education and teaching experience responded to a questionnaire measuring mathematics anxiety and mathematics teaching anxiety. The results illustrate that specialized mathematics education affects in-service primary school teachers’ mathematics anxiety, and that teaching experience is associated with mathematics teaching anxiety. Moreover, mathematics anxiety of some in-service primary teachers without specialization does not fade with time. The discussion highlights the importance of identifying mathematics anxiety in primary school teachers with no specialized mathematics education, aiming to lower it. The small sample and participants’ background limit the power of the findings. This study recommends conducting further studies according to the suggested mathematics anxiety cognitive-behavioral model; addressing cultural differences, teachers with and without specialized mathematics education, and comparing middle and secondary teachers.

Design Principles for Examining Student Practices in a Technology-Mediated Environment

In this article, we present a set of design principles to guide the development of instructional materials aimed to support preservice secondary mathematics teachers (PSMTs) examining student practices in technology-mediated environments. To develop design principles, we drew on the literature related to technological pedagogical content knowledge (TPACK; Niess, 2005), video cases as learning objects (Sherin & van Es, 2005), and professional noticing (Jacobs, et al., 2010). After presenting the design principles, we share a task created using these design principles. Finally, we share PSMTs’ reflections about changes in their own understanding after examining students’ practices. Their responses provide insights into the usefulness of the design principles for deepening PSMTs’ mathematical knowledge and knowledge of students’ understanding, thinking, and learning with technology.

Growth of pedagogical content knowledge and ‘understanding mathematics in depth’: conceptions of pre-service teachers

ABSTRACTIt is generally agreed that good subject knowledge is an important prerequisite for successful teaching. However, what constitutes good subject knowledge is debated, with multiple perspectives taken by policymakers, researchers and schools. This article reports on research into interpretations of ‘understanding mathematics in depth’ (UMID) of pre-service secondary mathematics teachers at an English university, some of whom had completed a Subject Knowledge Enhancement course prior to their teacher training programme. Qualitative data were drawn from semi-structured interviews with the teachers, and an in-depth case study of one of the sample. Analysis of data revealed that knowledge growth was located mostly within pedagogical content knowledge. UMID was articulated as ‘knowing why’ and ‘being able to communicate’. Additionally, non-elicited themes emerged, relating to the way in which teachers’ knowledge develops. Findings highlight relevant messages for policy and practice regarding the integration of subject matter knowledge and pedagogical content knowledge.

Reflective Journal Writing and Classroom Performance: Improvement and Correlation among Pre-Service Mathematics and Science Teachers

This study investigated improvements in reflective journal writing and classroom performance among pre-service mathematics and science teachers as well as the correlation between reflective journal writing and classroom performance. The study was conducted during a clinical experience where pre-service mathematics and science teachers were placed in 10-week field-based learning experiences during their final semester of the Bachelor of Education degree in Primary Education. Study participants included 30 pre-service mathematics and science primary school teachers, and the study was conducted during the two academic semesters of spring 2017 and fall 2017. A quantitative research approach was followed, and descriptive statistics were determined using Statistical Packages for Social Sciences (SPSS). Data were gathered using two research instruments: the Clinical Experience Evaluation (CEE) survey and a weekly reflective journal. The results of the study revealed that within the 10-week study period, participants improved, with statistically significant differences (p E‚ 0.05), in most dimensions of reflective writing (reflectivity, thoroughness, variety, growth), with the exception of the professionalism dimension. Participants also improved, with statistically significant differences (p E‚ 0.05), in all domains related to classroom performance, except for the assessment domain. Furthermore, throughout the clinical experience, participants showed improvement in the reflective journal dimensions. Finally, we observed that the variety dimension of reflective journal writing contributed statistically to the development of classroom performance. https://doi.org/10.26803/ijlter.18.11.21

Turkish Pre-service Middle Level Mathematics Teachers’ Knowledge for Teaching Fractions

Fractions are a crucial mathematical topic, which is known as being challenging for both students, pre- and in-service teachers. The current study attempted to explore the extent of pre-service middle level mathematics teachers’ knowledge for teaching fractions. Fifty-one senior pre-service teachers took part in the study. The Knowledge for Teaching Fractions Test, which includes almost all characteristics of fractions, was employed to measure participants’ knowledge for teaching fractions. The Pre-service Teachers’ Mathematics Knowledge for Teaching Framework was used to conceptualize participants’ responses to the tasks in the Knowledge for Teaching Fractions Test. The findings showed that participants’ mathematical knowledge for teaching fractions was not satisfactory. Meanwhile, while they had sound common content knowledge for teaching fractions, their specialized content knowledge for teaching this topic was very poor. The implications for teaching fractions are discussed in the context of pre-service middle level teacher preparation.

Pre-service secondary mathematics teachers’ anticipation and identification of students’ thinking in the context of modelling problems

This study investigated pre-service secondary mathematics teachers’ (PSMTs’) anticipation and identification of students’ thinking as they engaged in examining and analyzing student work on four modelling problems. The study comprised four two-week-long cycles. The data were collected through individual reflection papers and written group reports on students’ ways of thinking from 25 PSMTs enrolled in a semester-long (15-week) elective course. Data analysis focused on the PSMTs’ anticipation and identification of students’ ways of thinking in the context of modelling problems over the cycles. Results indicated that the PSMTs were able to anticipate and identify some of the students’ possible solution approaches, errors, and difficulties for each modelling problem used in the study. However, some of their anticipations remained vague throughout the study. On the other hand, identifying students’ different responses helped most of the PSMTs to increase their awareness of students’ various ways of thinking throughout the study. The implications of the findings for PSMTs’ anticipations, identification, and learning about students’ thinking are discussed.