Pre-service Mathematics Teachers Research Articles

The impact of instruction on Web 2.0 tools on pre-service mathematics teachers' self-efficacy beliefs and their activity development experiences

The purpose of this study is to determine the impact the training has had on pre-service mathematics teachers' beliefs and opinions regarding Web 2.0 tools, and to determine their views about the use of Web 2.0 tools. The study employs the explanatory sequential design of mixed methods research with 37 sophomore pre-service mathematics teachers as participants. The data collected through the use of Web 2.0 Practical Content Development Self-Efficacy Belief Scale and semi-structured interviews were analyzed using content analysis. The quantitave findings of the study showed that the implementation in the experimental process had an impact on pre-service mathematics teachers’ self-efficacy beliefs for Web 2.0 content development and its subdimensions which are preparation, presentation and evaluation. The qualitative findings also revealed the views of pre-service mathematics teachers towards the benefits of use of Web 2.0 tools for students, teachers and in terms of functionality. Benefits for students include benefits for learning, and affective and aptitudinal contribution, while benefits for teacher consist of contribution for instruction and professional development. On the other hand, the study also revealed the negative features of Web 2.0 tools in addition to their positive contributions and advantages. The main findings of negative aspects include requiring internet, lack of language support, and having paid services for some extra features. Furthermore, Kahoot and Puzzle Maker were the most preferred tools by pre-service mathematics teachers.

Contradictions in the learning of Euclidean constructions with GeoGebra by pre-service mathematics teachers

Contradictions in the learning of Euclidean constructions with GeoGebra by pre-service mathematics teachers

Model Oluşturma Etkinliklerinde Matematiksel İlişkilendirmelerin Belirlenmesi: Tasarımcı Olarak Matematik Öğretmen Adaylarıyla Bir Durum Çalışması

This paper aimed to explore mathematical connections that pre-service elementary mathematics teachers identified in model-eliciting activities that they designed. The study used a qualitative, in-depth exploratory case study approach conducted with a total of 42 undergraduate students selected using a purposive sampling method. Data were collected from mathematical modeling problems prepared by pre-service mathematics teachers and from written assignments in which pre-service teachers evaluated their problems in terms of mathematical connections. Data analysis utilized open coding to identify and label common patterns thematically. Results showed that most of the problems designed were consistent with the principles of the model-eliciting activities. A cross-case analysis of model-eliciting activities revealed that four types of mathematical connections were identified: (i) connections to real-world situations, (ii) connections between mathematical concepts, (iii) connections between different modes of representation, and (iv) connections to other disciplines. The mathematical connections identified in the modeling activities did not seem to be mutually exclusive, but rather supportive and sometimes overlapping. Pre-service mathematics teachers’ identification of mathematical connections in modeling problems reflects both their awareness of mathematical connections and their perception that the skills required for the mathematical modeling process are directly related to mathematical connection skills. Therefore, it is important that pre-service mathematics teachers have a comprehensive understanding of mathematical connections and believe that this is an essential element of the modeling process so that the various dimensions of mathematical connections, along with relevant mathematical, pedagogical, and curricular knowledge, can be effectively integrated into model-eliciting activities.

Half a mathematician? How preservice teachers are connected to their studied discipline

ABSTRACT Preservice teachers study an academic discipline (e.g. mathematics) and – just like students majoring in that discipline – have a certain level of connectedness to it. While studying, students may compare themselves to peers studying the same discipline within alternative degree programs, characterized by different study contexts. Notably, preservice mathematics teachers may engage in such comparisons with major mathematics students, potentially fostering preservice teachers’ feelings of being less connected with the mathematics discipline. Thus, using the constructs of task value and sense of belonging, we investigate how preservice teachers’ and major students’ perceived connectedness to mathematics differs and how it differs from the connectedness they anticipate is experienced by students in the respective other degree program. Data from 174 preservice mathematics teachers and 96 major mathematics students in Germany suggest that preservice teachers perceive themselves as less connected to the discipline of mathematics than major students perceive themselves to be. These findings are supported by contrasting participants’ own perspectives with their anticipated perspectives of what students in the respective alternative degree program would indicate. This comparison yields even more pronounced effect sizes. Differences between levels of comparison as well as implications for higher education and teacher education are discussed.

Focus on the Assessment Concerns of In-service and Pre-service Mathematics Teachers

Evaluation in mathematics is an inherent part of the discipline. In the current study, issues in the assessment of mathematics that concern MTs and S-MTs are studied. The basic assumption for this study is that improving teachers’ ability to deal with the challenges of assessment necessitates examining whether those issues are essential or technical. We first identified assessment issues that concern teachers and student teachers and then defined them as essential or technical difficulties. Sample questions included: What concerns do elementary and middle school MTs and S-MTs have with respect to student assessment, particularly with respect to alternative assessment methods? To what degree do these concerns represent essential or technical difficulties? At what frequency do elementary and middle school MTs and S-MTs encounter these difficulties? We found three main concerns – validity and reliability of exams; heterogeneity of the evaluated students; knowledge and achievements as reflected in the evaluation. The found that teachers seek solutions to practical assessment concerns and aspire to professional and credible evaluations that contribute to the students’ math development.

A framework to support teacher noticing of students' mathematical thinking in technology‐mediated environments

AbstractThe practice of teacher noticing students' mathematical thinking often includes three interrelated components: attending to students' strategies, interpreting students' understandings, and deciding how to respond on the basis of students' understanding. This practice gains complexity in technology‐mediated environments (i.e., using technology‐enhanced math tasks) because it requires attending to and interpreting students' engagement with technology. Current frameworks implicitly assume the practice includes noticing the ways students use tools (including technology tools) in their work, but do not explicitly highlight the role of the tool. While research has shown that using these frameworks supports preservice secondary mathematics teachers (PSTs) developing noticing practices, it has also shown that PSTs largely overlook students' technology engagement when they are working on technology‐enhanced tasks (Journal for Research in Mathematics Education, 2010; 41(2):169–202). In this article, we describe our adaptation of Jacobs et al.'s framework for teacher noticing student mathematical thinking to include a focus on making students' technology‐tool engagement explicit when noticing in technology‐mediated environments, the Noticing in Technology‐Mediated Environments (NITE) framework. We describe the theoretical foundations of the framework, provide a video case example, and then illustrate how the framework can be used by mathematics teacher educators to support PSTs' noticing when students are working in technology‐mediated environments.

The Points to be Considered while Developing the Activities for the Mathematics Course

The need for constructivist classroom environments in mathematics teaching cannot be ignored in order for sustainable development to continue. One of the most important applications of constructivist classroom environments in mathematics education all over the world is mathematical activities. The proficiency of pre-service mathematics teachers in developing activities will support constructivist classroom environments. In this study, it was aimed to reveal pre-service mathematics teachers' thoughts about what points they consider while they develop activities for mathematics courses. With this aim, an open-ended question was addressed to 23 pre-service teachers taking education at Elementary Mathematics Teaching program of a state university and having received the elective course of Activity Development in Mathematics Teaching. The obtained data was analyzed via the content analysis method. As a result of the study, it was determined that the participant elementary pre-service mathematics teachers expressed the points which they considered while developing activities with a total of 161 sentences or words. The statements obtained as a result of the analysis of the answers which the pre-service teachers gave to the research problem were gathered and examined under five sub-themes, namely general, purpose, scope, planning and the role of the teacher in practice. In respect of the points which elementary pre-service mathematics teachers considered while developing activities for mathematics courses, participants considered while developing activities for mathematics courses, they were observed to use statements which were mostly related to the sub-theme of the role of the teacher in practice. When it was evaluated in general, it has been observed that the participant elementary pre-service mathematics teachers are generally aware of the points to be emphasized. However, due to the low number of pre-service teachers who emphasized some points, it was concluded that they did not have enough knowledge about developing activities.

How do Mentor Teachers Implement Mathematical Tasks?: The Perspective of Preservice Mathematics Teachers

This study aims to investigate mentor teachers’ task implementation and instructional dispositions from the perspective of preservice mathematics teachers. Twelve preservice mathematics teachers examined four mentor teachers' task selection and implementation in terms of cognitive demand and instructional dispositions that affect their cognitive demand. The data were gathered from detailed observation notes and focus group interviews of preservice teachers. The results indicated that only one teacher selected most of the tasks at a high level and maintained them without declining their cognitive demand. His instructional dispositions showed us that he displayed an approach that allowed students to explore the tasks, reason, and discuss ideas. Launching fewer problems per lesson, he enabled students to examine the tasks in depth. He discussed student-invented strategies and sometimes focused on multiple solutions and misconceptions. Instead of algorithmic solutions, he emphasized underlying concepts, multiple representations, and daily life situations. On the other hand, other teachers mostly implemented tasks at low-level, however, they had different instructional dispositions towards student explorations, classroom discussions, and utilizing multiple representations. Based on these results, this study highlights the importance of mentor teachers for the professional development of preservice teachers.

Cognitive and Metacognitive Strategies in Problem-Posing Tasks in the Context of Science

This study aims to determine the cognitive and metacognitive strategies used by pre-service mathematics teachers for activating mental processes in a semi-structured problem-posing task. A holistic multiple-case design was used to in this study. For the case study, five voluntary pre-service mathematics teachers participated in this study. This task involves problem-posing in the context of science appropriate for different mathematical expressions. A think-aloud protocol, a semi-structured interview, observation and the pieces of papers for each question were used in this study. Open coding was performed using the continuous comparative analysis technique. The main results are that (a) they used various cognitive and metacognitive strategies to activate mental processes in problem-posing, (b) these strategies differed both in diversity and the usage of frequency of them and some strategies are either domain-specific or general-specific and (c) the use of metacognitive strategies is more common than cognitive strategies.

Mathematics Preservice Teachers’ Perceptions Regarding ICT Use in Teaching and Learning Practices

Mathematics Preservice Teachers’ Perceptions Regarding ICT Use in Teaching and Learning Practices

“My noticing lens disrupts this narrative”: Preservice mathematics teachers' awareness of the self as noticer

AbstractTeacher noticing has been identified as central to enacting responsive and equitable mathematics instruction. Mathematics teachers' noticing is shaped by institutional and sociopolitical narratives and ideologies that persistently marginalize culturally, socially, linguistically, and neuro‐diverse learners. Gaining insight into how one's noticing is related to these narratives can enable a teacher to identify and reflect on how they frame, attend to, and interpret classroom activity, and how that in turn can perpetuate or disrupt inequitable mathematics instruction. We conjectured that learning to systematically analyze and reflect on their own noticing can enable preservice mathematics teachers to develop their awareness of themselves as noticers to support more responsive and equitable instructional practice. Using data from summative assignments in a course focused on learning from teaching, we investigate whether and how preservice teachers (PSTs) take up frameworks for responsive and equitable teaching to narrate their noticing, and examine what their narrations reveal about how they frame mathematics instruction. Analysis reveals PSTs problematized instruction to adopt aspirational frames for equitable practice, while also re‐narrating classroom interactions from dominant perspectives. These findings have implications for PSTs' learning to notice for equity and for designing teacher education experiences for this purpose.

Investigation of Pedagogical Content Knowledge of In-service and Pre-Service Pre-school Teachers in Pre-school Mathematics

Investigation of Pedagogical Content Knowledge of In-service and Pre-Service Pre-school Teachers in Pre-school Mathematics

Research on the Cognitive Degree of Pre-service Mathematics Teachers for Mathematical Reasoning Ability in Junior High School in China

Currently, the education of junior high school mathematical reasoning ability has been widely concerned by all walks of life. Many relevant problems about it have been studied except the cognitive degree of pre-service mathematics teachers for the mathematical reasoning ability in junior high school. To address this problem, this study investigates 25 pre-service mathematics teachers’ cognitive degree of junior high school mathematical reasoning ability through open-ended interviews, obtains the current situation of pre-service teachers’ cognitive degree of mathematical reasoning ability in junior high school, and gives targeted suggestions for training pre-service mathematics teachers, so as to promote the implementation of the training goal of mathematical reasoning ability in junior high school. After analyzing, it can be found that: (1) The cognitive scope of the current pre-service mathematics teachers’ mathematical reasoning ability is not wide, more than half of the people do not recognize half of the content; (2) The cognition of many pre-service teachers is not deep, and their understanding of ability performances is simple; (3) The cognition of many pre-service teachers for many aspects of mathematical reasoning ability is not clear. Therefore, it is suggested that: (1) Experts and teachers who are responsible for educating teachers should pay more attention to mathematical reasoning ability in junior high school and add relevant courses; (2) Pre-service mathematics teachers should understand the content of junior high school mathematical reasoning ability comprehensively and deeply, and clarify relevant statements.

How To Improve Pre-Service Mathematics Teachers' Problem-Solving Competencies (Case Study)

Lower and upper secondary school mathematics offers a few tools for solving mathematical problems (e. g., equational strategy or other algorithmic ones). At the beginning of the university study our students (pre-service mathematics teachers) know how to use them, but they have no experience with solving strategies such as systematic experimentation or drawing a picture. This paper presents our lesson plan to improve their solving competencies and its results. The special attention is given to the process of mathematics problem-solving and its fourth phase ‘looking back’ that we understand in a broader sense, not only as a test of correctness. The results of this case study aim to show and understand how students learn and use various solving strategies in problem-solving and how they pose other word problems with the same solution as the solution of the given word problems. The analysis finds that even though students understand the importance of non-standard strategies (e.g., trial and error or estimation-verification-correction), they still understand the school equational strategy as the most advantageous. For problem-posing to contribute to the improvement of problem-solving competences, it must be more often involved in the problem-solving process.

How Prepared are China's Preservice Mathematics Teachers? An Insight into their Cognition of Space Concept Literacy

At present, the research on space concept literacy in junior high school is a hot topic in the field of education in China. Many scholars have conducted research from different directions, but there is still a gap in the current research on preservice mathematics teachers' cognitive degree of space concept literacy. Therefore, this study used a semi-structured interview method to investigate 10 undergraduates and 10 graduates in a normal university in China to obtain their understanding of the contents related to space concept literacy. The results show that: 1. The cognitive breadth of space concept literacy is high, and most preservice mathematics teachers can cognize all the contents. 2. The cognitive clarity is relatively high. Most preservice teachers have a clear understanding of the cognitive contents, but the cognition of the value is relatively vague. 3. The cognitive accuracy is not high, and only a few preservice teachers can accurately master all the contents, among which the connotation is better, while the cultivation goals and value are worse. 4. The common implementation focus is the following three aspects: preparation of space concept literacy, cultivation of space concept literacy, and intensification of space concept literacy. 5. The cognition of the implementation focus is rational. However, preservice teachers have little understanding of content structuring and overall unit instructional design as suggested by the Standards, and lack the ability to capture emerging technologies such as AR technology.

Examining the differentiation in pre-service mathematics teachers’ learning and studying approaches according to self-reinforcing, and persistence

The aim of this study is to reveal the profiles of pre-service mathematics teachers in terms of learning and studying approaches by cluster-analyzing them on the basis of self-reinforcing and persistence. Learning and studying approaches inventory scale, self-reinforcing and persistence subscales were used to collect the data in the study, which was carried out with a descriptive research design. The participants of the study comprised of 487 pre-service mathematics teachers. According to the results, it was determined that the surface learning approach of the pre-service teachers did not differ according to gender while the strategic learning approach and the deep learning approach differed in favor of males. There was no significant difference in the learning approaches of the participants according to the grade level. According to the cluster analysis, it was revealed that pre-service teachers can be clustered as low motivation, high motivation, high self-reinforcing and high persistence.

Pre-service mathematics teachers’ geometric reasoning skills with technology-integrated guided inquiry approach

This study was intended to examine the progress of the geometric reasoning skills of pre-service mathematics teachers (PSMTs) in the College of Teacher Education, Oromiya, Ethiopia. In the study, there were three different classes: EG1 (n=48), EG2 (n=38), and CG (n=30), where PSMTs in EG1 were treated with technology into guided inquiry-based learning (TGIBL), EG2 with guided inquiry-based learning (GIBL), and CG with a conventional learning approach. A geometric reasoning test was used to collect data. The data were analyzed using a one-way ANOVA and a paired sample t-test. The findings showed that the effect of using the GIBL model assisted by technology was higher when compared to the other two models. On the other hand, a paired t-test showed significant mean gains in reasoning skills in the TGIBL and GIBL approaches. Hence, technology must be integrated into teaching and learning geometry at CTEs to promote PSMTs’ geometric reasoning skills.

Mathematically Giftedness from the Perspectives of Preservice Mathematics Teachers

This research aimed to examine the views of preservice mathematics teachers (PMTs) on mathematically giftedness. Case study, one of the qualitative research design, was used and the study involved 25 sophomore mathematics teaching undergraduate students from Turkey. Data were collected with a semi-structured interview form with open-ended questions and analyzed with content analysis method. As a result of the analysis of the data three themes comprising of definitions of giftedness, characteristics of gifted students including sub-themes of cognitive, affective and social traits, and mathematically gifted students including sub-themes of cognitive and affective traits were emerged. As a result of the study it was determined that the majority of the participants thought that the gifted students have exceptional performance in intelligence or creativity in a spesific area. The cognitive traits of gifted students were favorably listed as being curious or asking questions, strong verbal skills, high performance compared to the peers, fast thinking and learning, creativity and abstract thinking. The affective traits mainly included sensitivity, sense of justice, impatience, sense of humour, intense interest/concentration, diligence and patience, responsibiltiy, curiosity, perfectionism and motivation. The social characteristics of gifted were emerged as preference to communicate with adults, enhanced social relationship (resulting in leadership), rarity in society and valued by society. On the other hand, characteristics of mathematically gifted students have been classified as cognitive and affective traits according to the views of PMTs. Cognitive traits of mathematically gifted students mostly composed of quick, unusual and multiple solutions to problems, analytical thinking, proficiency in mathematics, interest in numbers at an early age, and questioning. Affective characteristics of mathematically gifted students have been found to be introversion, peer disapproval, self-confidence, responding maturely, good sense of self-expression, sense of wonderment, and willingness to learn. As a result, most of the views of PMTs were found to be similar to the literature. Considering that the participants took elective course "Teaching Mathematics to Gifted Students", it can be stated that it is important to give lectures on giftedness to prospective teachers in their undergraduate education.

The Preservice Teachers’ Approaches Toward Incorrect Probability Problems

Identifying the mistakes in student responses and being able to manage the solution process are among the fundamental skills that should be acquired by the pre-service teachers. This skill is important in probability, about which students have a great number of misconceptions. The aim of this study was to determine the misconceptions in the student answers given by the researcher about probability and to examine the solution explanations of the preservice teachers. In this context, the student answers containing five wrong solutions were examined. Case study, one of the qualitative research methods, was used. Forty-two third grade preservice mathematics teachers participated in the study. A task-based interview was used in the study. The findings revealed that the participants were able to recognize simple and discrete probability problems more easily and provided correct solutions; however, they had difficulty in determining the universal space independent events and failed to detect the mistakes in the student answers successfully. As a result of the research, it was concluded that the importance attached to procedural knowledge should also be given to conceptual knowledge, what a concept means as well as what it does not mean should be explained, open-ended questions that will increase the power of reasoning should be used instead of typical problems, and more effective learning should be carried out by using different teaching methods and techniques.

Matematik Öğretmen Adaylarının Dijital Teknolojiye Yönelik Tutumlarının Bazı Değişkenler Açısından İncelenmesi

The role of technology continually increasing and its use is becoming no longer an option but inevitable in all fields of education. From teachers to students, technology literacy and the knowledge and skills to use it are now expected. Along with studies on the adequacy, skills, and approaches of students and educators from all levels regarding the use of technology, the attitudes of all these groups towards technology also fall under the scope of educational researchers. This study investigates whether the attitudes of pre-service mathematics teachers towards digital technology differ according to gender, university type, department, grade level and final grades in information technology courses, using statistical methods. The data set consists of the survey results of 440 mathematics pre-service teachers from two universities. According to the statistical results of the research, significant differences have been found in the attitudes of mathematics pre-service teachers towards digital technology in the sub-dimensions of technology use, conscious use of technology, and game-oriented use of technology, by gender; in the sub-dimensions of interest and willingness, technology use, and social media, by university type; and in the sub-dimensions of technology use and negative factors, based on the final grades of the information technology course. According to the data mining algorithms of the research, the branches generated by the Random Tree algorithm yielded the best results. According to the Random Tree algorithm, it was concluded that gender is the most dominant factor affecting the attitudes of mathematics pre-service teachers towards digital technology.