Pre-service Middle School Teachers Research Articles

MATEMATİK ÖĞRETMEN ADAYLARININ OKUL DIŞI ÖĞRENME ORTAMLARINDA MATEMATİK ÖĞRETİMİNE YÖNELİK BAKIŞ AÇILARI

This study explored pre-service middle school mathematics teachers’ perspectives on teaching mathematics in out-of-school learning environments. The current study designed an online course on out-of-school mathematics education and investigated participants’ perspectives before and after the class. The phenomenology method, one of the qualitative methods, was employed. Participants of the study were 36 2nd and 3rd-year pre-service middle school teachers who enrolled in the course. The data sources of the study were participants’ open-ended responses to questionnaires. Open coding was used to analyze the data. The data analysis was carried out under four dimensions: (1) Identification of out-of-school mathematics education environments, (2) teaching contexts for teaching mathematics in out-of-school learning environments, (3) teaching purposes for teaching mathematics in out-of-school learning environments, and (4) frequency for using out-of-school education and their reasons. The findings of the study pointed to important changes in the participants' perspectives on teaching mathematics in out-of- school learning environments after taking the course. The findings of the study would shed light into studies on teacher education in the emerging field of out-of-school mathematics education.

Tutoring during the pandemic: mentoring tutors’ formative experiences using digital and digital multimodal texts

ABSTRACT This survey-design study examined how 228 middle school preservice teachers perceived the implementation of digital and digital multimodal texts during course-required, mentored, tutoring sessions delivered in face-to-face and online settings prior to, during and toward the end of the COVID-19 pandemic. Tutors were able to recognize that texts could be used to elicit affective responses from their students, and had the potential to differentiate their lessons in accordance with learners’ needs, but the technology challenges they faced seemed insurmountable to some. Given their lack of teaching experience, tutors struggled to determine the appropriateness of the resources and they held distinct perceptions of the accomplishments and challenges related to their tutoring sessions. Mentor responsiveness exhibited by honouring tutors’ adaptive expertise can be seen as an important aspect of fostering tutors’ confidence. Focusing on the role of the mentor in preservice teachers’ tutoring field placements is a suggested area for future research.

A learning trajectory for enumerating permutations: Applying and elaborating a theory of levels of abstraction

Permutations are fundamental to combinatorics and other areas of mathematics, and it is important that students develop efficient and conceptually supported ways of mentally constructing, listing, and enumerating them. To date, there is still much to learn about how students reason about enumerating permutations, and how instruction can support students’ conceptual development. We address this gap in the research literature by carefully tracing the evolution of two preservice middle school teachers’ permutation enumeration strategies and conceptualizations, which led to the formulation of levels of sophistication for combinatorial reasoning. These levels are explained by applying and extending a constructivist theory of levels of abstraction. Additionally, we outline an instructional approach that was instrumental in facilitating student learning. Together, the proposed levels and linked instructional approach constitute an initial learning trajectory for permutations that we believe could be useful for understanding and supporting post-secondary non-STEM students’ meaningful conceptualizations and enumerations of permutations.

A mixed-methods approach to analysing interdependencies and predictors of pre-service teachers’ beliefs about multilingualism

ABSTRACT This paper presents findings from a pre–post study on pre-service teachers’ beliefs about multilingualism and language use. A full cohort of pre-service middle school teachers in Germany (n = 259) was surveyed before and after completing a compulsory module on multilingualism using a validated instrument that captures participants’ beliefs about (a) multilingual language use in the home, (b) multilingual language use in the classroom, and (c) teacher responsibility for language support in teaching and learning. While mean average scores of the respondents’ beliefs are not as high as in comparable studies, the results show a significant increase between the pre- and post-test. Multivariate statistics are employed to explore different dimensions of beliefs improvement as well as predictors of positive beliefs. With a critical view about the Likert-scale type items, the quantitative dataset was expanded by structured interviews with five participants. The results of qualitative content analyses of these interviews make it possible to show different facets of the survey’s constructs of beliefs as well as individual backgrounds making them explainable, and thus help to gain a more nuanced picture of the respondents’ beliefs.

예비 중등교사 진로 관련 국내 연구 동향 및 향후 과제

Objectives This study aims to suggest future research directions by analyzing career-related research trends for pre-service middle school teachers and to provide implications for practical field applications. Methods To this end, from 2003 to 2021, 9 domestic dissertations and 42 academic journals with the theme of ‘career’ were selected for ‘College of Education, Preparatory Teachers, Completion of Teaching, and Teachers’ as the subject of analysis. By applying the analysis method, the frequency, medium frequency, and percentage were calculated and analyzed based on the publication status, research subject, research method, and research topic. Results As a result of the analysis on the status of research publications, 8 articles (15.7%) in 2018, 6 articles (11.8%) in 2017, 2012, 2016, and 5 articles (9.8%) in 2020 were found in that order. From 2015, when the 4th cycle of teacher training evaluation was conducted, it was confirmed that the research was steadily increasing. As a result of the analysis of the research subjects, it was found that there were 9 natural science education courses (42.9%), 8 arts and physical education courses (38.1%), 3 education departments (14.3%), and 1 language education course (4.8%). As a result of the study method analysis, quantitative research had the most with 32 studies (62.7%), followed by qualitative research with 15 studies (29.4%) and mixed studies with 3 studies (5.9%). As for the detailed analysis methods of quantitative research, 21 cases (35%) of difference analysis between groups and 15 cases (25.0%) of relationship analysis were the most common, and as detailed analysis methods of qualitative research, in-depth interview 8 cases (13.3%) and grounded theory 4 were used. Part 1 (6.7%) followed by narrative 2 part (3.3%). As a result of the analysis of research methods according to the research topic, the research topic with a large proportion of quantitative research was a problem area related to the career development stage, 35 (31.7%), and a research topic with a high proportion of qualitative research was a problem area related to the career development process, and 9 cases (8.7%) %) was analyzed. As a result of the analysis of the research topic, problems related to the stage of career development (33.0%), other career problems related to work (26.5%), career problems related to the career development process (16.7%), career problems related to education (15.2%), pleasure related to work It was confirmed that the study was conducted in the order of various emotions that did not (8.5%). Conclusions Based on these analysis results, directions for future research and implications for practical field applications were suggested.

Investigating Preservice Mathematics Teachers’ Definitions, Formulas, and Graphs of Directly and Inversely Proportional Relationships

This study investigates 48 preservice middle school teachers’ formal textbook definitions, formulas, and graphs of the directly and inversely proportional relationships. The connections among these three types of representations and how preservice teachers’ representations differ according to the two relationships are also examined. The data of the study included the preservice teachers’ responses to a paper-and-pencil test with two items. An explanatory research design model was followed when developing this study. The study findings indicated the preservice teachers’ over-attention to the simultaneous increases and/or decreases when representing the directly and inversely proportional relationships. Only four preservice teachers stated in their definitions that the ratio was constant in the directly proportional relationship. Whereas none of them stated constant product in their inversely proportional definition. Although the preservice teachers were slightly better at writing the direct proportion formula than the inverse proportion formula, this difference was much greater in terms of drawing the direct and inverse proportion graphs. Sixty percent of the preservice teachers drew their inverse proportion graphs as linear with negative slopes. Moreover, the analysis showed that the preservice teachers’ definitions were not well-linked with their graphs and formulas. On the other hand, the preservice teachers who were better at providing correct formulas were also better at drawing the correct graphs. Implications for teaching and future study suggestions are discussed.

Investigating preservice teachers' assessment skills: Relating aspects of teacher noticing and content knowledge for assessing student thinking in written work

AbstractThis mixed methods study explored the development of elementary and middle school preservice teachers' (PSTs) learning to assess student thinking through analysis of students' written work. Six sections of the first mathematics content course for teaching implemented two writing assignments focused on analysis of student work aligned to the mathematics topics covered in the PSTs' classes. Using quantitative methodology, we examined the PSTs' (n = 99) change in their noticing and assessment skills of attending to and interpreting students' thinking. We also documented their mathematical content knowledge (MKT) as measured by the Learning for Mathematics Teaching in the domains of specialized content knowledge and knowledge of content and students. Findings show that the PSTs increased in their assessment skills and in their MKT. Using a qualitative methodology on interview data of a subset of eight PSTs, we found they acknowledged that having a firm grasp of mathematical content is essential to understanding and explaining student thinking. Findings indicate that engaging PSTs in the real work of teaching such as noticing and assessing students' thinking through written work at the early stages of their teacher preparation may motivate PSTs to learn mathematics more deeply with an eye towards strengthening their assessment skills.

Pre-Service Teachers’ Knowledge Regarding the Area of Triangle

The aim of this study is to investigate the knowledge of pre-service middle school mathematics teachers on possible misconceptions and difficulties held by students regarding the area of triangle. In line with this aim, qualitative case study research design was used to obtain deep information. As the participants of the study, two pre-service middle school teachers were chosen purposively. Data were collected from lesson plans, semi-structured interviews and observations of pre-service teachers’ related lessons. The findings of the study showed that the pre-service teachers specified various misconceptions and difficulties regarding the area of triangle that might be observed among middle school students. When the determined misconceptions and difficulties were reviewed, it attracted attention that most of the misconceptions and difficulties were related to the concept of height. One of the findings of the study differed from other relevant studies in the respect that one of the pre-service teachers stated that students have the perception that a line segment cannot be extended. Difficulties and misconceptions and the reasons of them are discussed accordingly.

Pre-service Science Teachers’ Pedagogical Content Knowledge Integration of Students’ Understanding in Science and Instructional Strategies

In the current study, we address calls for research on the complex nature of integrations of pedagogical content knowledge (PCK) components. This is a multiple case study of six middle-school pre-service teachers (PSTs) as they taught science in their school practicum. We investigated the nature of PSTs’ integration between knowledge of students’ understanding (KSU) and instructional strategies (KIS), and their sources of these integrations. The primary data sources were two video stimulated recall interviews during which each PST viewed video recordings of their instruction, and shared reflections on their teaching. Results were represented as PCK maps. The PSTs frequently demonstrated integration of KSU and KIS, often developing topic-specific strategies. Instructional strategies served a variety of goals in response to students’ needs. PSTs referred to specialized science content courses, peer PSTs, learning experiences, and mentor teachers as sources that contributed to the integrations. Implications for research and teacher education are included.

Does Perceived Middle School Pre-Service Teachers’ Core Competencies Affect Learning Consultation Competencies?: The Mediating Effect of Grit

Does Perceived Middle School Pre-Service Teachers’ Core Competencies Affect Learning Consultation Competencies?: The Mediating Effect of Grit

중등 예비 영어교사들의 교생일지에 나타난 성찰적 교수과정 양상 및 지도교사 조언 분석

The current study examines pre-service English teachers’ reflective journals over the 4-week period of teaching practicum in one Korean middle school and one Korean high school. A total of twenty-one Korean college students majoring in English education completed their reflective journal on “class observation” and “impressions and plans for tomorrow” during the period. Their “mentor teachers’ comments and advice” were also included the journals. All the journal writings were constructed as text corpus and then analyzed through the Antconc programme by stages: introduction (1st week), development (2nd & 3rd weeks), and closing (4th week). As for class observation, the middle and the high school pre-service teachers initially considered lesson planning and classroom atmosphere most important, respectively. In the development stage, classroom observation were thought most importantly for the middle school pre-service teachers and lesson planning for the high school pre-service teachers. In the closing stage, both of the middle and the high school pre-service teachers considered classroom atmosphere as the most crucial factor. Concerning the impressions and plans for tomorrow, both of the middle and the high school pre-service teachers reported that figuring out students and their emotions would be important in the introduction and the closing stages. However, in the development stage, the high school pre-service teachers counted lesson planning as the most important factor. As for the mentor teachers’ comments and advice, both middle and high school mentor teachers regarded lesson planning as important in the introduction stage, and they tried to provide encouragement and help to the pre-service teachers at the closing stage. In the development stage, evaluation for teaching rehearsal and lesson planning were most frequently mentioned from the middle and the high school mentor teachers respectively.

“Is It Valid or Not?”: Pre-Service Teachers Judge the Validity of Mathematical Statements and Student Arguments

There is a wide recognition that reasoning abstractly, constructing arguments, or critiquing arguments should be an important educational goal in the mathematical experiences of all students in the standards for school mathematics. Seeing these standards as an essential element for developing deep mathematical understanding; however, call for a strong knowledge of proof for teachers. Thus, the purpose of this study is to investigate how pre-service middle school teachers (PSMTs) decide whether a presented mathematical statement is true or false and how they verify student arguments presented for these statements. 50 PSMTs participated in the study. Individual interviews were conducted with 7 PSMTs to further delve into the verification processes of the PSMTs. The results of the study demonstrated that meeting the expectations of the current standards is not an easy feat by documenting that most of the PSMTs struggled with evaluating mathematical tasks and constructing arguments.

The written and oral justifications of mathematical claims of middle school pre-service teachers

ABSTRACT Teaching meaningful and productive mathematical argument in school requires teachers who are comfortable with diverse forms of mathematical justification. This study examines the written and oral justifications of pre-service middle school teachers (PSTs) in a single classroom, focusing on the types of justifications they use during the patterns unit of a required mathematics class. Toulmin’s argument framework (1958), in conjunction with a coding scheme for classifying justification types, was used to investigate this question. The PSTs relied heavily on inductive justifications, including the use of counterexamples and applying inductive justifications at multiple levels when solving complex problems. When they used non-inductive justifications, the PSTs tended to support those justifications with inductive evidence. Taken together, these exploratory results suggest that PSTs have a deep understanding of inductive processes, raising questions about ways to leverage this knowledge to promote more diverse use of justifications in mathematics classrooms.

“Lies My Teacher [Educator] Still Tells”: Using Critical Race Counternarratives to Disrupt Whiteness in Teacher Education

The purpose of this study was to disrupt whiteness through the use of critical race counternarratives during a critical literacy workshop with middle-school preservice teachers. Over two years, 57 preservice teachers participated in and reflected on their experiences reading master narratives and viewing counternarrative texts in a critical literacy workshop. Students responded in a variety of ways that ranged from displacing responsibility for their ignorance about the counternarrative texts onto educational structures, to troubling their roles in reproducing oppressive school environments and considering action steps for future teaching. Our research has important implications for preservice teachers, teacher educators, and those interested in implementing preservice teacher educator curriculum using a critical race theory lens.

Collaborative Effort to Develop Middle School Preservice Teachers’ Mathematical Knowledge

This article describes reflections of two mathematicians and a mathematics teacher educator who collaborated on the development and implementation of courses (probability and statistics connections, number concept connections, and middle school mathematics methods) for middle school mathematics preservice teachers. The instructors of the courses, two in mathematics and one in mathematics education, worked together to more explicitly link course materials, assignments, and the pedagogical approaches. Collectively, the courses were designed to address the five components of preservice teachers’ mathematical knowledge for teaching (PT-MKT), and to model effective teaching practices. Using their collective experiences co-planning and implementing these course adjustments were made in the subsequent year. The instructors were pleased by their implementation and student outcomes in all three courses.We describe how each component of the PT-MKT framework was approached in these courses and discuss challenges experienced by the instructors, who were part of a larger effort to develop and implement a middle school teacher preparation program. The information shared is based on data collected as part of a program evaluation effort, and is bolstered by the instructors’ recollection of events. Overall, the instructors enhanced the curricula and their instructional practices and found that the attention placed on developing PT-MKT support the mathematical development of middle school mathematics preservice teachers.

Middle School Mathematics Pre-service Teacher’s Responses to a Mathematics Content and Specific Mathematics Pedagogy Intervention

Prospective middle school pre-service teachers’ knowledge and affect in Australia has had little empirical research. In this study, 108 graduate entry pre-service teachers were surveyed for their knowledge of middle years’ mathematics, confidence, and self-efficacy at the commencement of a mathematics curriculum course. It was found that their memory of middle years’ mathematics was very poor and this was accompanied by low levels of confidence and self-efficacy. An intervention was undertaken to address these issues. The findings are discussed in the context of the “genericism” of pre-service teacher preparation. In particular, the findings call into question the justification for pre-service entry to such a mathematics curriculum course on the basis of proxy measures of mathematics knowledge, without which the teaching of the discipline becomes challenging.

Common Visual Representations as a Source for Misconceptions of Preservice Teachers in a Geometry Connection Course

In this paper, we demonstrate how atypical visual representations of a triangle, square or a parallelogram may hinder students' understanding of a median and altitude. We analyze responses and reasoning given by 16 preservice middle school teachers in a Geometry Connection class. Particularly, the data were garnered from three specific questions posed on a cumulative final exam, which focused on computing and comparing areas of parallelograms, and triangles represented by atypical images. We use the notions of concept image and concept definition as our theoretical framework for an analysis of the students' responses. Our findings have implication on how typical images can impact students' cognitive process and their concept image. We provide a number of suggestions that can foster conceptualization of the notions of median and altitude in a triangle that can be realized in an enacted lesson.

Dancing on ice: mathematics of blade tracings

The art of ice dancing offers many possibilities for mathematical modelling. In this article, we present an artistic model-eliciting activity (MEA) based on skates’ blade trajectories formed by skaters’ bodily movements which uses mathematical content from algebra and geometry. We conducted the MEA in an undergraduate mathematics problem solving course for pre-service middle school teachers. The students’ models included two-dimensional choreographic drawings of envisioned skaters’ three-dimensional movements on the ice, and quantitative analyses of these drawings. Pre-service middle school teachers’ successes and challenges are discussed in relation to their working on a real-life, open-ended, artistic and mathematical problem.

Middle School Preservice Teachers’ Knowledge of Division with a Remainder

Middle School Preservice Teachers’ Knowledge of Division with a Remainder

On the Content of the Pre-service Teachers’ Teaching Reflection in the Practicum

Reflection plays an effective role in promoting teachers’ professional growth and improving teachers’ overall quality. As for Pre-service teachers, teaching practice is an indispensable period for their professional development. Therefore, reflective consciousness and ability should be trained in their practicum. This paper fully elaborates the importance of reflective consciousness for middle school pre-service teachers in the practicum from the contents of the pre-service teachers’ teaching reflection: classroom teaching, student study, teacher-student interaction, teachers’ development and education environment. From the research ,we find pre-service teacher often reflect on classroom teaching, student study and teacher-student interaction. The other two parts are usually neglected.