Mathematics Teacher Education Research Articles

Professionalisation for inclusive mathematics—teacher education programs and changes in pre-service teachers’ beliefs and self-efficacy

AbstractTraditionally, in many countries there exist different teacher education programs for special education and for regular or inclusive education, not at all with similar underlying paradigms for teaching and learning or similar definitions and understanding of the term inclusion. In this context, one central question is how to define inclusive mathematics education, how to address the manifold aspects, and how to reduce discrimination and marginalization. On the one hand, teacher education programs might focus on diverse groups and specific students, like students with special needs and integrate important questions of special education. On the other hand, teacher education programs might take explicitly a broader perspective, considering the mathematical learning of all students and not taking a specific focus. In this contribution we present research results of the project ProViel (‘professionalisation for diversity’) to discuss how a teacher education program can be designed to address both with the underlying paradigm of making mathematics accessible for all students, and what role pre-service teachers’ beliefs as well as their self-efficacy might play. The project aimed at subject-specific concept development and research concerning teacher education for inclusive mathematics on the primary level, considering different points in time within the whole education program. Quantitative data of pre-service teachers’ beliefs and self-efficacy have been analysed, while they participated in different university courses and a practical phase at school. Key findings of this study are, that pre-service teachers’ beliefs about student achievement and their self-efficacy for inclusive mathematics teaching changed during the teacher education program.

The expertise of novices: A framework for prospective teacher’s noticing of children’s mathematical thinking

The purpose of this study was to articulate nuances within the process of learning to notice and to provide a framework for characterizing the capabilities of noticing in prospective mathematics teachers. We collected and analyzed data on teacher noticing based on classroom videos from prospective teachers in a mathematics content course. We analyzed data in accordance with existing research-based frameworks on noticing and in consideration with literature on expertise. We provide the Framework for the Expertise of Noticing, which describes noticing expertise along five dimensions: Evidence-based Noticing; Concrete vs. Abstract Characteristics in Noticing; Individual vs. Pattern Focus in Noticing; Task vs. Contextualized Perspective in Noticing; and Cognitive vs. Metacognitive Characteristics in Noticing. The framework is a tool for mathematics education researchers and teacher educators who study and support the development of noticing in prospective teachers.

Professional development and teacher agency in Mathematics Teacher Education for Sustainability

Professional development and teacher agency in Mathematics Teacher Education for Sustainability

Combining enactivism and systemic functional linguistics: a methodology for examining (mathematics teacher educator) language

AbstractAs mathematics teacher educators (MTEs), we are motivated by the lack of research concerning the language that MTEs use in initial teacher education settings. In this paper, we turn our attention towards developing a methodological approach to studying the language-in-use during teacher education situations, with a specific focus on the language of the MTE in the form of a monologue. The methodological approach that we present draws upon two theoretical perspectives, specifically, the situated cognition theory of enactivism and the social semiotic perspective of systemic functional linguistics (SFL). To develop this methodology, we explore both of these theoretical perspectives, focussing on their respective conceptualisations of language, from which we derive a set of methodological principles and practices. A significant feature of the methodology presented in this paper, is that it takes into account the researchers’ relationships with the subject of research. Thus we propose this methodology as being of particular significance to practitioner–researchers studying the language of other practitioners within the same field (e.g. MTEs studying the language of other MTEs), as well as to the study of one’s own use of language in mathematics education settings. From our methodological perspective we explore the meaning of quality research, proposing relevant criteria. We exemplify the methodological principles and practices by analysing a transcript of a mathematics teacher education lecture for prospective primary teachers in Sweden.

Experiencing Tensions When Integrating Language Diversity into Mathematics Teacher Education

ABSTRACT Mathematics teacher educators experience tensions when developing their practices in order to integrate social justice issues, such as language diversity. Research on what in fact causes the experiencing of these tensions and how to navigate them to improve professional practice is yet limited. As part of an action research project, I investigate my reflections on planning to integrate language diversity issues into mathematics teacher education. I discuss three main tensions to do with: focusing on my teaching or the pre-service teachers’ teaching; wanting to change my practices but struggling to let go of control; identifying alternative activities but struggling to choose from them. The analysis revealed that each of these tensions was connected to different moments of my planning and to the uncertainties of wanting to achieve multiple aims simultaneously. Understanding the characteristics and implications of the tensions I experienced provides insights into the complexities of planning, such as the blind spots of aiming to be responsive to pre-service teachers’ needs, whilst at the same time contradicting my assumptions about good practice. Knowledge about these complexities can support future research about what aspects of practice might influence the improvement of integrating language diversity issues into mathematics teacher education.

Integrating computational thinking in elementary STEM using the engineering design process

AbstractModel‐eliciting activities (MEAs) challenge students to interpret a problem and collaboratively create solutions using the engineering design process. This Innovation to Practice article describes how science, technology, engineering, and mathematics (STEM) teacher educators can use MEAs to build elementary teachers' understanding of computational thinking (CT). Our Countdown Timer MEA is aligned with Grade 2 mathematics and computer science standards. We discuss how this MEA created opportunities for teachers in an online graduate STEM education course to engage as learners in unplugged and plugged CT activities. Teachers used algorithmic design and debugging to model a digital display and to create block‐based code for a recess countdown timer. Teachers' reflections on how their learning experiences were different than those offered in step‐by‐step CT lessons allowed teachers to envision how MEAs can promote important CT dispositions of persistence in open‐ended problem solving and tolerance for ambiguity. By aligning MEA design and facilitation with the phases of the engineering design process, teacher educators can use modeling to engage elementary teachers in facets of CT that are transferable to the elementary STEM classroom.

Centering Mathematics Pre-Service Teachers’ Whole Selves: A Collaborative Approach to Course Syllabus Design

In this participatory research, two pre-service teachers (PSTs) and a mathematics teacher educator (MTE) collaboratively analyzed multiple voices that influence syllabi from elementary mathematics teaching methods courses. Findings suggest syllabi fall along a continuum from harmonious to dissonant orchestration of the voices of past and present children, PSTs, MTEs, universities, and state policies. Formatting, stance makers, and content and wording influenced the kind of multivocality that addressivity, ventriloquation, and hybridization constituted. These findings informed our use of collage method to create a sample syllabus that centers the voices of PSTs and their future students. We discuss implications that intentional syllabus design decisions may have in humanizing these documents and fostering a relationship of mutuality and support between PSTs and MTEs.

Examining interpersonal aspects of a mathematics teacher education lecture

In this paper we present findings from an initial phase of a more extensive study focussed on ways in which prospective mathematics teachers negotiate meaning from mathematics teacher education situations. The focus of this paper is on the language of one mathematics teacher educator and specifically the interpersonal aspects from one mathematics teacher education lecture in Sweden for prospective upper-primary school teachers. We draw on the enactivist view of cognition as a theoretical basis for a methodology we develop that utilises Systemic Functional Linguistics as an analytical tool for studying language-in-use. We exemplify our interpretations through a series of extracts from the mathematics education lecture. This initial phase of our study has exposed several important questions about how participating in an initial teacher education situation may contribute to the development of teacher identities, questions we raise throughout our analyses to provoke further investigation as part of our future research.

Gödel's Theorem in the Continuing Education of Mathematics Teachers

Gödel's Theorem in the Continuing Education of Mathematics Teachers

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.

The Use of Case Technology for the Formation of Information Competence for the Future Teachers of Mathematics

The relevance of the selected research topic arises from the numerous challenges encountered in the education of prospective mathematics teachers. The purpose of this research is to substantiate the advisability of using the case technology in the formation of information competence for the future teachers of mathematics in the process of their preparation. This study employs a methodological approach that combines literature analysis, synthesis of pedagogical experiences, statistical observation and a pedagogical experiment to assess the impact of case technology on the development of information competence among students in the context of professional education for future mathematics teachers. The main results of this study include the creation of case groups and their integration into the curriculum for students specializing in ‘mathematics’ and ‘mathematics-informatics’, as well as a comparative analysis of the components of information competence among future graduates and their proficiency levels. The study’s findings hold significant relevance for educators at the Higher School of Natural Sciences at Zhetysu University named after I. Zhansugurov, with the overarching objective of preparing competent, highly skilled and competitive mathematics teachers for the job market.

Teacher Characteristics and Attitudes in Learning Mathematics as Perceived by Mathematics Teacher Education Students: A Mixed Method Study

This study employed a mixed methods design, utilizing a parallel convergent approach to explore the quantitative status and lived experiences of Mathematics major students regarding their perceived teacher’s characteristics and attitudes. The participants were Mathematics education students, with 80 respondents for the quantitative phase and 14 for the qualitative phase, selected through total enumeration and purposive sampling, respectively. The quantitative results indicated a very high status of perceived teacher characteristics and students’ attitudes. A positive low correlation (r = .27, p = .0064) was found between the two variables. In the qualitative phase, students revealed positive experiences with instructors, emphasizing their good qualities and influence on learning, while also highlighting teacher-related difficulties. Student insights emphasized the crucial role of fair treatment and interaction in learning, predictors of learning attitudes, and the significance of positive attitudes. Notably, the quantitative data largely aligned with the qualitative findings. Keywords: attitude in learning mathematics, mathematics, mixed methods, teacher’s characteristics, Philippines

Conceptions of teaching and justice as pivotal to mathematics teacher educators’ thinking about mathematical knowledge for teaching

Conceptions of teaching and justice as pivotal to mathematics teacher educators’ thinking about mathematical knowledge for teaching

Special Issue Introduction: Critical Perspectives on Mathematics Teacher Education

Nowadays, the field of mathematics education research is more diverse than ever [...]

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.

Teacher educator learning to implement equitable mathematics teaching using technology through lesson study

PurposeThis paper examines how mathematics teacher educators (MTEs) learn to enact equitable mathematics instruction using technology through lesson study (LS).Design/methodology/approachA LS team with three MTEs conducted three iterations of LS on teaching the Pythagorean Theorem in an in-person, technology-mediated environment. Many forms of data were collected: Desmos activities, videos of research lessons (RLs), videos of MTE RL debriefings, artifacts of student learning in the Desmos Dashboard, and MTEs' written self-reflection. The authors investigate the teacher educators' learning through LS by analyzing the MTE debriefings of the RLs using Bannister’s (2015) framework for teacher learning in communities of practice.FindingsThe MTEs learned to enact equitable mathematics instruction using technology through addressing emerging issues related to intellectual authority and use of student thinking. Throughout the LS, the MTEs sought ways of promoting students' mathematical authority and using student thinking through features of the Desmos platform.Research limitations/implicationsThis study focuses on MTEs' learning without examining participating preservice teachers' learning. It demonstrates the benefits of LS for MTEs' professional learning.Practical implicationsThis study showcases how a research-based Desmos activity is used and refined to promote MTE learning how to implement equitable mathematics instruction.Originality/valueThe study contributes to better understanding of how LS could be used to develop MTEs' professional learning. Moreover, the dual process of participation and reification was concretized through diagnostic and prognostic frames in the LS context, which enriches the concept of community of practice.

Mathematics and science teacher educators experiences of using the WhatsApp platform as a tool for supporting teaching during the Covid-19 pandemic

This article problematises the media used for delivery of curriculum at the onset of lockdowns due to the outbreak of the Covid-19 pandemic, which resulted in a sudden cessation of all face-to-face teaching and learning at a South African university. The article reports on how the otherwise neutral WhatsApp social media platform was appropriated to become a serious teaching tool for mathematics and science pre-service teacher educators. The study draws predominantly on connectivism learning theory to understand how WhatsApp was used to continue the teaching of mathematics and science during the Covid-19 lockdowns. The sample consisted of 10 mathematics and science teacher educators from whom data were collected through authentic conversations and questionnaires. The article reports on the affordances and constraints the WhatsApp platform presented, as well as how it reshaped the teaching of mathematics and science. Findings indicate that teacher educators transformed the use of WhatsApp from a social media tool to a tool for supporting teaching. However, being a social tool, WhatsApp does have affordances and constraints when used for teaching. The affordances include ease of access and ease of use, while constraints include the risk of students not possessing smartphones and intrusion into the personal lives of teacher educators.

Secondary prospective mathematics teachers learning to notice: The need for a dual perspective of teaching

AbstractThe Association of Mathematics Teacher Educators recommends that well‐prepared beginning mathematics teachers apply their understanding of mathematics, curriculum, pedagogy, student learners, and social constructions to facilitate mathematics learning for all students. Using the context of a secondary methods course, where prospective mathematics teachers (PMTs) participate in six teaching cycles of peer taught lessons, we analyzed lesson debriefings of PMTs' questions and comments to determine what PMTs notice over the course of the semester and how their noticing changed based on their role as a teaching or peer PMT. Analysis of these data reveals that participating in both roles as student and teacher provided PMTs with different opportunities to connect the teaching elements (i.e., curriculum, mathematics, and pedagogy). Using these data, we present an observed learning trajectory for secondary PMTs that mathematics teacher educators can use as they design learning activities within their methods class to promote PMTs to begin to notice the dual (student/teacher) perspective.

Maintaining Tensions: Braiding as an Analogy for Mathematics Teacher Educators’ Political Work

Although the field of mathematics education has made gains in centering the need for justice-oriented approaches and antiracist teaching practices in teacher education, much of this work remains in its infancy. Moreover, research focused on this area highlights teacher candidates’ knowledge and dispositions and often ignores the role of the mathematics teacher educators facilitating the process. We contend that mathematics teacher educators must pay more attention to how intersectional identities, contexts, Mirror Tests, and principles of Rehumanizing Mathematics manifest in teacher education to better understand how teacher candidates develop political knowledge in teaching mathematics. To this end, we introduce a framework of considerations, which we call a compass, that identifies four dimensions (or strands) and offers guiding questions for mathematics teacher educators to consider. We offer examples from a multi-site research study to illuminate each dimension and build the case for the necessity of braiding the four strands together as we engage in this line of work. Implications for practice and future research are discussed.