Mathematics Teacher Education Courses Research Articles

The Construction of Informatization System of Internet Technology Mathematics Teacher Education Course

Abstract This paper focuses on constructing a regional digital educational resource sharing platform. It applies optimized ant colony clustering technology to support the platform’s personalized service to achieve accurate distribution of educational resources. The research subjects were undergraduate and graduate students majoring in mathematics in teacher training, and by comparing their teaching abilities before and after using and not using the platform, it was found that the average scores of students using the platform were significantly higher than those of students who did not use the platform on each evaluation factor. Undergraduate students’ information literacy competence improved with the academic year, with first-year students’ scores between 20 and 50, while senior students’ scores between 70 and 100. At the graduate level, the difference between first-year graduate students and junior undergraduates was significant, but the difference with senior undergraduates was slight (p-values of 0.042 and 0.053, respectively). The digital education resource sharing platform effectively improved the teaching ability of teacher students. However, most of the students lacked experience in informatization practice activities.

자서전적 방법을 통한 예비수학교사 교육

As teacher identity affects teachers' decision making about teaching practice, there is an increasing concern about teacher identity. In this context, this study investigates the transformation of mathematics preservice teachers' identity by analyzing the autobiographies of the preservice teachers who had participated in a mathematics teacher education course at a college of education. The 12 preservice teachers wrote their autobiographies according to the four steps presented by Pinar: ‘regressive’, ‘progressive’, ‘analytical’, and ‘synthetical’. A total of 48 autobiographical articles were collected for analysis. We analyzed those articles qualitatively to identify 5 themes: ‘mathematics’, ‘mathematics teachers’, ‘peers’, ‘parents’, and ‘privilege’. The analysis focused on how these themes were represented in the preservice teachers' autobiographies to reveal the transformation of their identities.
 The results show that the autobiographical method helped the preservice teacher cultivate their identities to appreciate diversity and equity in mathematics class. Based on the results, we discuss implications for mathematics teacher education for educational equity.

Bringing Critical Mathematics Education and Actor–Network Theory to a Statistics Course in Mathematics Teacher Education: Actants for Articulating Complexity in Student Teachers’ Foregrounds

In this paper, we discuss how critical mathematics education (CME) and actor–network theory (ANT) come together in a mathematics teacher education course that focuses on the thematic context of climate change to study statistics. Acknowledging the complexity that student teachers encounter when asked to move from a mainly instrumental treatment of statistics toward a critical foreground of data in society, we turn to explore the actant networks, as theorized by ANT, utilized by student teachers when asked to imagine teaching from a CME perspective. For this, our study is based on a series of interviews with student teachers who participated in a statistics course where pollution data graphs were discussed, inquiring about their role as future critical mathematics teachers. The transcribed interviews, analyzed through ANT, inform us as to how student teachers’ foregrounds are being shaped by actants such as the curriculum, social justice, democracy, and source critique, among others. Based on the above, we recommend that teacher education should invite active discussion of the complexity created when a CME perspective is required. This move would allow for a critical approach to critical mathematics education itself that could prepare student teachers to navigate, instead of ignoring or opposing, such complexity.

The Construction of Definitions Through Padovan’s Combinatorial Model: An Investigation With Didactic Engineering in an Initial Education Course for Mathematics Teachers

Background: Given the oversight of specific topics in the history of mathematics books, this research was motivated by the extensive coverage of the Fibonacci sequence. In addition, the existence of the Padovan sequence, which is considered a Fibonacci cousin, stands out. Objectives: Investigating the Padovan sequence, building its definition through a combinatorial model using manipulative materials based on the theory of didactical situations in the initial mathematics teacher education course context. Design: The research methodological design follows didactic engineering, and a didactic teaching situation is created to investigate the Padovan sequence. Thus, manipulative material was developed to facilitate the teaching process and the construction of the sequence definition. Settings and participants: The interventions were done in the mathematics degree course of a higher education institution in Fortaleza. Five students enrolled in the component of History of Mathematics participated in the study. Data collection and analysis: Data were collected during classes, recorded through photos and audio recordings, based on didactic engineering and the theory of didactical situations. Results: The most relevant result of this study is constructing the definition of the Padovan sequence through the manipulative material. Conclusions: We concluded that the research allowed an investigation of the Padovan sequence, enabling the visualisation of its terms and their integration with other mathematical contents, contributing to teaching these numbers.

A critical ethnography on instructor-student interactions in a mathematics teacher education course

This study aimed to investigate the instructor-student interactions in a secondary level mathematics teacher education course through a critical ethnographic perspective. Participants in the study were 16 pre-service teachers at one of the large midwestern universities in the U.S. The data for the study consists of the transcribed audio recordings collected in four classroom meetings as well as exclusive field notes. It was revealed as a result of the current study that negotiation - re-negotiation mechanisms mediate the communications, which occur in accordance with the lifeworlds of students and instructor while system subordinates the lifeworld of these actors through its two main roots, contractual and normative systemic relationships. In addition, the reflection of these relationships on the instruction was also discussed. It is highly suggested for future researchers to investigate these interactions with extended sample sizes as well as in different learning environments.

Using video-recordings to enhance pre-service teachers’ abilities to identify mathematical activities in pre-school

Previous studies highlight the importance of investigate the construction in videorecorded learning situations. The aim of this study is to investigate how video-recordings can be used to enhance pre-service teachers’ abilities to identify children’s exploration of mathematics in preschools. Even if some previous studies have focused the use of video-recordings of learning situations to improve teaching, only a few of them focused how constructed videos enhance pre-service teachers’ abilities to identify when children explore mathematics through learning-situations in preschool. The participants were pre-service teachers in a higher education course. Data consisted of pre-service teachers’ written responses after viewing eleven edited video clips before, during, and after a compulsory mathematics teacher education course. The analysis is based on variation theory and show the impact of the construction of the video clips and how to design the clips to enhance the pre-service teachers’ abilities to define mathematical components during the children’s activities.

Aspects of the Social Construction of a Mathematics Teacher Education Course Curriculum

Resumo Este artigo aborda a construção social do currículo na Licenciatura em Matemática da Universidade do Vale do Rio Doce (Univale), na cidade de Governador Valadares (MG), em sua terceira e última fase (1997-2012). Com base em uma pesquisa que usou documentação escrita aliada à metodologia da História Oral, o trabalho se inspira em estudos desenvolvidos pelo pesquisador inglês Ivor Goodson comentados por pesquisadores brasileiros e busca analisar o currículo prescrito e o currículo narrativo do curso. Discutem-se conceitos importantes desses estudos e a pertinência da História Oral para colocar o foco nas ações dos sujeitos em relação ao currículo. As entrevistas de professores e estudantes iluminaram dimensões relevantes do currículo prescrito num momento em que o curso teve centralidade na formação de professores para a Educação Básica, repercutindo o desenvolvimento da área da Educação Matemática no Brasil e a legislação educacional a partir de 1996.

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.

Promoting Prospective Mathematics Teachers’ Professional Vision on a Whole-class Reflective Discussion: Contributions of Digital Resources

The present study aims to understand how the professional vision of prospective teachers (PTs) regarding whole-class reflective discussion develops as they explore a multimedia case (MC) in a mathematics teacher education course. The data come from the written productions of seven groups of PTs (N=15) related to whole-class discussion of one 6th grade lesson in two sections of the MC: first, they have focused on the teacher’s lesson plan and on her intentions for the whole-class discussion aiming at the students’ algebraic thinking; and in the second, they have analysed two video episodes of that lesson phase. The results show an integrated development of two processes of PTs’ professional vision – noticed events and the nature of the reasoning about them – with significant evolution from one section to another as they explore the MC. The study shows PTs’ alternative ways of accessing and making sense of the complexity of both ambitious and authentic teaching practices that can also be employed in at distance teacher education and mitigate the consequences of the impossibility to access the classrooms, such as that resulting from the recent COVID-19 pandemic.

Using Popular Films in History of Mathematics Courses: Reflections from Prospective Mathematics Teachers

This article examines the reflections of prospective mathematics teachers about the use of popular films in a history of mathematics course. Three films are used in the course are Agora, The Man Who Knew Infinity and A Beautiful Mind, which are describing mathematicians’ experiences and struggles in different historical moments. Following completion of the course, twelve middle school prospective mathematics teachers voluntarily participate in the face-to-face semi-structured interviews. According to the results, popular films are inspirational for prospective mathematics teachers to pursue further mathematical studies and the stories in the films are influential while making future decisions. For prospective mathematics teachers, popular films are also helpful to put mathematicians in context in which their life styles and experiences become more visible. Despite the benefits of watching mathematicians in the films, prospective mathematics teachers reflect on the fact that popular films are coming from a profit-driven sector and they reflect on how the commercial purposes can limit a full comprehension of mathematicians’ lives. In the light of the findings, popular films are recommended as productive instructional materials in mathematics teacher education courses while there is a need to reflect on the commercial purposes and disadvantages.

A Critical Ethnography on Instructor-Student Interactions in a Mathematics Teacher Education Course

A Critical Ethnography on Instructor-Student Interactions in a Mathematics Teacher Education Course

Providing access by integrating computer aided design in mathematics teacher education courses

This article condenses five years of professional development based on Technological Pedagogical and Content Knowledge (TPACK) integration principles, National Council of Teachers of Mathematics Principles to Actions (2014), and ISTE Student and Teacher standards to give a launch point for teachers and teacher educators to integrate 3D modeling and printing in their classroom instruction. Although the goal and aspects for integration may be different from a mathematics course to an introductory mathematics education course to a methods course, starting with the technology as learners and the types of activities have been the same. This article gives a taxonomy of types of activities; machine function, teacher-created model, and student-created model across elementary, middle, and high school grades.

수학교사의 다문화수학수업 설계역량 분석

This research aims to investigate the teachers’ pedagogical design capacity for multicultural mathematics education. For the purpose, we collected teaching plans developed by inservice teachers who registered in a multicultural mathematics teacher education course of graduate level. The analysis focused on how the teachers reorganized mathematical contents and adapted instructional strategies in order to achieve the instructional goals. The analysis shows that the teachers applied the ‘Principle of Equity’ most frequently compared to other principles of multicultural mathematics education. This means that it is necessary to provide teacher education programs to enhance teachers’ understanding of ethnomathematics and to develop PCK to reorganize curricula contents by integrating ethnomathematics. Second, it was observed that the teachers experienced difficulty in adapting the levels of multicultural mathematics education coherently.
 This suggests that when teachers tried to design lessons from a new perspective, they often turned back to teacher-centered teaching practices that they had been used to. Third, in the teaching plans adapting the ‘Principle of Transformation’, although Level 4 appeared most frequently, mathematical contents and social issues were placed separately without being integrated. Although the course helped the teachers recognize the relationship between mathematics and human practice, the teachers might keep their previous beliefs about mathematics as academic knowledge separated from human life. Thus, this limitation may persist without a change of the teachers’ beliefs regarding the cultural origin of mathematics. Based on the results, we draw implications for the future development of multicultural mathematics teacher education.

Transformar Exercícios em Cenários para Investigação

O texto descreve e analisa atividades sobre educação matemática crítica realizadas em uma disciplina de um curso de licenciatura em matemática. O referencial teórico adotado consistiu especialmente dos conceitos de paradigma do exercício e cenários para investigação, de Ole Skovsmose. A principal atividade consistiu em os licenciandos abrirem um exercício de um livro didático a fim de transformá-lo em uma atividade investigativa. O objetivo geral de ensino foi refletir sobre possibilidades de modificar as práticas docentes tradicionais de ensino de matemática. A pesquisa qualitativa teve como objetivo compreender os aspectos considerados pelos estudantes nesse processo de abrir um exercício e as características atribuídas por eles para uma atividade investigativa. Os primeiros resultados indicam que uma atividade investigativa precisa ter um apelo à realidade dos alunos da educação básica. A realização da atividade e sua discussão foram consideradas um primeiro passo dos licenciandos em direção à educação matemática crítica.

Exploring culturally sustaining practice for indigenous learners in initial teacher education in Aotearoa New Zealand

Culturally sustaining practices are advocated for enhancing learning experiences of Indigenous learners. Developing the use of culturally sustaining practice is challenging, in part as many educators do not have Indigenous heritage and have not themselves experienced such teaching. Here we discuss an investigation into how we develop student teacher understanding of practice culturally sustaining for Indigenous Māori learners in our initial mathematics teacher education courses. We show how a four-dimension framework (accommodation, reformation, transformation, and representation) can expose strengths and opportunities for improvement in course content and approaches towards developing culturally sustaining practices. Factors considered include education policy, resources, course development and content. Affordances (e.g., ease of use) and challenges (e.g., contextal factors) of using the framework are discussed. We demonstrate that the framework can be a useful tool for teacher educators working to strengthen their focus on developing culturally sustaining teacher practice to enhance educational opportunities of Indigenous learners.

Preparing Student Teachers to Teach Mathematics with GeoGebra

This paper shares the working process that has been carried out in a postgraduate mathematics teacher education course known as Technology in Mathematics Education. Many efforts around the world attempt to train student teachers on the use of technology without giving much attention to appropriate instructional model. Our work in this area gave special considerations in integrating technological pedagogical and content knowledge (TPACK) in taining student teachers to teach mathematics with Geogebra, a dynamic multi-purpose mathematics software. Specifically, this paper shares the (1) theoretical background that guides the structure of the course, (2) the course methodology, which includes teaching and learning activities to prepare 15 student teachers to teach mathematics with GeoGebra and (3) the learning outcomes of the 14 weeks course. The design for integrating teachers' knowledge of subject matter, and teaching with subject matter with the development of TPACK was discussed. Among the geogebra activities emphasized are (1) creating geometric constructions and exploring their mathematical properties (2) exploring ratio and proportions, (3) applying sliders to modify parameters, (4) visualizing algebraic input and functions, and (5) modelling and constructing transformations in geometric designs and animations. Elements of TPACK were traced as the student teachers carried out experimental teaching with geogebra in schools as part of the requirement of the course. The Malaysian mathematics curriculum in its latest development has incorporate geogebra activities in the textbooks. Hopefully with the course we described in this paper, not only more teachers are willing to adopt geogebra but to integrate geogebra effectively in their practices.

Mathematics Education of Pre-Service Teachers: As Reflected in Methods Course Syllabus

This study seeks to contribute a better understanding of what future pre-service teachers of mathematics learn in their mathematics methodology courses at the universities. Course syllabi from six countries were analyzed using the Mathematics Teacher Educator (MTEd) Instrument to examine the “ideal” curriculum trends in mathematics education courses of pre-service teachers. The MTEd identifies 11 research areas and these were our guiding theoretical and analytical frameworks. Each of the syllabi contained in the final syllabus data set (n = 31) were coded using the MTEd Instrument. Correlation analysis was conducted to examine the relationship between category levels and overall levels assigned to each syllabus in elementary-only and secondary-only syllabi. Mann-Whitney U test was conducted between the elementary and secondary data sets. Findings from the study indicated that research related to the mathematics education of pre-service teachers was moderately represented in the course syllabi analyzed. Technology and assessment were the only two categories that were correlated to overall score. Recommendations for mathematics teacher education courses are offered.

Characteristics of teacher knowledge produced by pre-service mathematics teachers: the case of open-ended problem-based learning

One major issue in mathematics teacher education regards the role of university-level mathematics in teacher knowledge. In the context of a design-based research project, an advanced mathematics teacher education course aimed at strengthening the connections between university-level mathematics and school mathematics was developed. In this paper, I present a case study, conducted within the education course, in which I analyse the characteristics of teacher knowledge produced by five small groups of pre-service teachers in an open-ended problem-based learning task. The results indicate the problem-based learning approach has the potential for enhancing specialised content knowledge such as knowledge of different representations of and applications of mathematical concepts. The results also highlight the challenges in using this approach for enhancing horizon content knowledge such as knowledge about the relationships between mathematical concepts. The findings in this case study suggest that problem-based learning can be used to develop mathematics teacher education, although further research is needed to design instructional practices that enhance pre-service teachers’ horizon content knowledge.

Training mathematics teachers for realistic math problems: a case of modeling-based teacher education courses

One important goal of teacher education has been to improve pre-service teachers’ understanding of the connection between real-life events and mathematics. Toward this goal, we designed two mathematics teacher education courses based on the Models-and-Modeling Perspective. This study presents a three-tier modeling investigation of (a) pre-service teachers’ views about characteristics of realistic mathematics problems, and (b) teacher-level skills required to write such problems. A team of researchers analyzed 15 pre-service mathematics teachers’ written artifacts and audio recordings of their discussion by employing the data analysis methods of constructivist grounded theory. In these two modeling-based courses, pre-service teachers completed several modeling cycles, during which they exhibited significant changes in their understandings about the characteristics of realistic problems and the skills that are needed to write–revise–refine such problems. The results thus indicated that modeling-based courses helped pre-service teachers think critically about stereotypical textbook problems, view realistic contexts as a medium through which mathematical ideas could be reasoned, understand the mathematical residuals of lessons involving realistic problems, and attain the skills needed to write and revise such problems. Hence, the modeling perspective provided an effective approach for pre-service mathematics teacher training, ensuring pre-service teachers’ development as they express–test–revise–refine their thinking, understandings, and skills.

Construção da reflexão na escrita acadêmica por professores em formação inicial

Resumo: Investigamos os usos de complexos oracionais em que as orações primárias são identificadas como orações mentais na escrita acadêmica reflexiva realizada em relatórios escritos por professores em formação inicial. Os textos foram produzidos como avaliação final de disciplinas obrigatórias de estágio supervisionado em três licenciaturas, Língua Portuguesa, Língua Inglesa e Matemática, sendo dada ênfase a essa última. As principais categorias analíticas são os componentes experiencial e lógico, integrantes da metafunção ideacional da linguagem, proposta na abordagem gramatical da Linguística Sistêmico-Funcional. Os resultados mostraram a construção recorrente de representações dos próprios autores como experienciadores dos fenômenos atrelados aos processos mentais perceptivos e cognitivos. Esses processos são responsáveis, respectivamente, pela elaboração de sequências textuais descritivas e narrativas e pela explicitação de posicionamentos mais críticos.