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Different Approaches in Mathematics Teacher Education

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A special issue of Education Sciences (ISSN 2227-7102).

Deadline for manuscript submissions: closed (30 August 2025) | Viewed by 16271

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Special Issue Editors

Prof. Dr. Salvador Llinares

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Guest Editor

Department of Innovation and Didactic Training, University of Alicante, 03690 San Vicente del Raspeig, Spain
Interests: preservice mathematics teacher and teacher’s learning; mathematics teaching; specific professional practices; mathematics teacher education context; teaching competence

Dr. Alessandro Jacques Ribeiro

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Guest Editor

Center for Mathematics, Computing and Cognition, Universidade Federal do ABC (UFABC), Santo André, SP, Brasil
Interests: preservice and in-service mathematics teacher education; teacher and teacher educator’s learning; mathematics teaching

Special Issue Information

Dear Colleagues,

This Special Issue focuses on different approaches to mathematics teacher education. Specifically, it focuses on participants and key actors (preservice and in-service teachers and mathematics teacher educators), different institutional contexts and learning and development processes.

Mathematical knowledge for teaching, specific professional practices in mathematics teaching and mathematics teacher educators’ knowledge and learning are issues of prominence in research and relevant to our understanding of mathematics teacher education in different contexts. Furthermore, issues about the assessment of learning and teaching competence development in relation to different institutional contexts throughout the world are of great importance. Additionally, we must address issues related to mathematics teacher educators’ learning and development. We also consider the attitudinal dimensions of key actors in these processes. Other issues are the development of different theoretical approaches with specific tasks in mathematics teacher education programs, and different methodological approaches.

To these ends, this Special Issue welcomes articles examining topics such as the following:

Preservice mathematics teachers’ learning;
Preservice mathematics teachers’ knowledge and practice;
Preservice and in-service mathematics teachers’ specific professional practice development;
Mathematics teacher professional development;
Representations of practice to support mathematics teachers’ learning;
Mathematics teacher educators’ knowledge, learning, practices and development;
Digital technology integration in mathematics teacher education;
Technology and mathematics teacher education;
Collaboration among mathematics teacher educators, mathematics teachers and researchers;
Methodological approaches in mathematics teacher education;
Tools for supporting preservice mathematics teacher-specific professional practices;
Relationships between the discipline of mathematics and the mathematical knowledge of teachers;
Mathematics teacher education and inclusive mathematics education;
Equity, inclusion and diversity in mathematics teacher education;
Field-based mathematics teacher preparation programs;
Lesson study.

Prof. Dr. Salvador Llinares
Dr. Alessandro Jacques Ribeiro
Guest Editors

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Keywords

mathematics teacher education
mathematics teacher learning
specific professional practices
mathematics teacher knowledge
mathematics teacher educator
representations of practice
practice-based teacher education
teacher noticing
field-based teacher preparation program

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Published Papers (11 papers)

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Editorial

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5 pages, 159 KB

Open AccessEditorial

Different Approaches in Mathematics Teacher Education: Participants, Tools, Contexts and Professional Learning

by Salvador Llinares and Alessandro Ribeiro

Educ. Sci. 2026, 16(2), 328; https://doi.org/10.3390/educsci16020328 - 18 Feb 2026

Viewed by 471

Abstract

This Special Issue focuses on different approaches to teacher education in mathematics [...] Full article

(This article belongs to the Special Issue Different Approaches in Mathematics Teacher Education)

Research

Jump to: Editorial, Review

17 pages, 2070 KB

Open AccessArticle

Pre-Service Teachers’ Interpretations and Decisions About a 3D Geometry Activity Sequence

by Ceneida Fernández, Zaira Ortiz-Laso, Antonio Saorín and Melania Bernabeu

Educ. Sci. 2026, 16(1), 54; https://doi.org/10.3390/educsci16010054 - 31 Dec 2025

Viewed by 421

Abstract

The most widespread lesson preparation resource used by mathematics teachers is the textbook. Initial teacher training programmes should therefore develop the skill of curricular noticing, i.e., the ability to critically analyse and make decisions concerning an activity sequence from a textbook. This mix-method study focused on the interpretations and decisions adopted by 85 Spanish pre-service primary school teachers (PTs) in relation to a three-dimensional (3D) geometry activity sequence from a textbook. The PTs were assigned two tasks: the first was identifying the limitations of the activity sequence for supporting students’ geometrical understanding regarding three aspects—attributes, geometrical processes, and modes of representation—and the second was completing the sequence. Most PTs interpreted a number of activity sequence limitations. In terms of their decision-making, the PTs prioritised certain characteristics over others, such as introducing further attributes rather than changing representation modes, or adding geometrical processes to their activity sequence designs. Moreover, the analysis allowed determining how PTs completed the activity sequence to address limitations, thereby revealing relationships between their interpretations and decisions. The study findings help teacher educators to design courses aimed at supporting the PTs’ ability to make more informed and effective teaching choices that enhance student learning. Full article

(This article belongs to the Special Issue Different Approaches in Mathematics Teacher Education)

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18 pages, 381 KB

Open AccessArticle

Examining Coherence in Preservice Mathematics Teachers’ Noticing of Students’ Thinking About Classification in Geometry

by Hélia Oliveira, Fernanda Caroline Cybulski and Márcia Cristina de Costa Trindade Cyrino

Educ. Sci. 2025, 15(11), 1543; https://doi.org/10.3390/educsci15111543 - 16 Nov 2025

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Abstract

This study aims to examine the thematic coherence among preservice mathematics teachers’ noticing components when analysing students’ thinking about classification in geometry, as well as the actions they propose to respond to those students. The research was conducted within an instructional module on the teaching of geometry, embedded in a mathematics methods course of a master’s programme. The module was designed to foster preservice secondary mathematics teachers’ pedagogical content knowledge alongside their noticing skills. Considering the mathematics education literature about the process of classification in geometry and the components of noticing, an analytical framework was developed to identify the thematic coherence of preservice mathematics teachers’ noticing of students’ thinking from two fictitious classroom episodes. Data came from individual written responses of 12 preservice mathematics teachers to an instructional task. The results overall patterns reveal strong thematic coherence in attending and interpreting, with responding also showing substantial, though comparatively lower, coherence. The findings also indicate that preservice teachers frequently proposed coherent responses that were both specific and may foster students’ conceptual understanding. This study highlights that promoting coherence in professional noticing, particularly within the responding component, is vital for cultivating teaching practices that are both responsive and conceptually grounded. Full article

(This article belongs to the Special Issue Different Approaches in Mathematics Teacher Education)

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24 pages, 3475 KB

Open AccessArticle

Development of Epistemic Meta Didactic–Mathematical Knowledge in Mathematics Teachers When Teaching Functions: A Scoping Review

by Neus Inglada, Adriana Breda, Gemma Sala-Sebastià and Yuly Vanegas

Educ. Sci. 2025, 15(11), 1526; https://doi.org/10.3390/educsci15111526 - 12 Nov 2025

Viewed by 675

Abstract

In this study, a PRISMA-guided scoping review of research papers on teachers’ epistemic meta didactic–mathematical knowledge with regard to functions is carried out. The objective is to identify the factors that characterize the epistemic meta didactic–mathematical knowledge of teachers who lead epistemically suitable instructional processes for functions. The Web of Science and Scopus databases were used to select 15 papers published between 2019 and 2024 that examine mathematics teachers’ epistemic meta didactic–mathematical knowledge when teaching functions. Two qualitative analyses of the chosen texts were performed. With the support of the R interface for multidimensional analysis of texts and questionnaires, five categories were obtained from the first analysis. Those categories guided the second analysis, which consists of a manual study of the documents. The result is the following characterization of the meta didactic–mathematical knowledge a teacher should have when teaching functions: (1) complexity of functions in the history of mathematics and in the curriculum, (2) personal practice of multiple processes using functions in different contexts, and (3) analysis of the tasks designed in instructional processes and reflection on teaching practice. The main conclusion of this research is that the presence of these contents in teacher preparation programs can contribute to improving the teaching of functions. Full article

(This article belongs to the Special Issue Different Approaches in Mathematics Teacher Education)

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17 pages, 1325 KB

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Views on Mathematics Education: A Comparative Study of Future Primary and Future Mathematics Teachers

by Vana Colić, Zorana Lužanin, Bojan Lazić, Sanja Maričić and Jasmina Klemenović

Educ. Sci. 2025, 15(10), 1370; https://doi.org/10.3390/educsci15101370 - 14 Oct 2025

Cited by 1 | Viewed by 1355

Abstract

Teacher identity emerges from the intertwined relationship of past, present, and future experiences, shaped through active reflection within individual, social, and cultural contexts. This study investigates how initial teacher education programs for future primary school teachers and future mathematics teachers influence their perceptions of mathematics education. Questionnaires with predominantly open-ended questions were distributed to 369 students: 195 enrolled in mathematics teacher education programs and 174 in primary school teacher education programs. The survey examined their preferences for school subjects in prior education, motivations for choosing teaching as a profession, important teacher qualities, and attitudes toward mathematics. The results reveal significant differences between the two groups: future primary school teachers emphasize the focus on children and relational aspects of teaching, while future mathematics teachers highlight mathematics as a scientific discipline. Both groups’ responses reflect their respective educational programs and experiences. The findings suggest that adopting a holistic approach in teacher education, integrating content knowledge with pedagogical practice, and supporting reflective processes can foster deeper self-understanding and the development of a professional teacher identity. Full article

(This article belongs to the Special Issue Different Approaches in Mathematics Teacher Education)

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24 pages, 11350 KB

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Criteria Used by Teachers of Non-Mathematical Subjects to Assess an Interdisciplinary Task That Includes Mathematics

by Pere Joan Falcó-Solsona, Gemma Sala-Sebastià, Adriana Breda and Vicenç Font

Educ. Sci. 2025, 15(10), 1284; https://doi.org/10.3390/educsci15101284 - 25 Sep 2025

Viewed by 783

Abstract

This study analyses the criteria teachers from different non-mathematical subjects use to assess an interdisciplinary learning situation that includes mathematical content. Their relationship with the didactic suitability criteria of the onto-semiotic approach is explored. An interdisciplinary learning situation was designed and implemented to promote the use of inquiry and mathematical modelling within a realistic historical-archaeological context, integrating content from the subjects of social sciences, natural sciences, and technology. After its implementation, a reflection session was held with the participating teachers of subjects other than mathematics to observe what criteria guided their assessment of the implementation. The results show that most of the criteria used by the teachers can be reinterpreted as several components of the didactic suitability criteria. Elements characteristic of interdisciplinary learning situations that are not currently included in those criteria were also identified. These findings open up the possibility of enriching and adapting the didactic suitability framework so as to fully address the challenges and potential of interdisciplinary proposals that include mathematics from an integrated perspective. Full article

(This article belongs to the Special Issue Different Approaches in Mathematics Teacher Education)

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28 pages, 2069 KB

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Stepping Stones: Adopting a Fading Programme Design to Promote Teachers’ Use of Metacognitive Strategies for Mathematical Problem Solving

by Kirstin Mulholland, William Gray, Christopher Counihan and David Nichol

Educ. Sci. 2025, 15(7), 892; https://doi.org/10.3390/educsci15070892 - 12 Jul 2025

Cited by 2 | Viewed by 2562

Abstract

Metacognition and self-regulated learning are widely understood to offer significant benefits for pupils’ mathematical problem solving; however, the existing literature highlights that the under-representation of these concepts in curriculum, policy, and teacher professional development means that their potential for impact remains unfulfilled. This article, therefore, examines the potential value of an innovative fading professional development programme—“Stepping Stones”—in enhancing teachers’ understanding and use of metacognitive strategies for mathematical problem solving. Adopting a convergent mixed methods design, this pilot evaluation involved Year 2 teachers across five primary schools. The results from both qualitative and quantitative data demonstrate that, as the scaffolding provided by programme materials faded and teachers assumed greater responsibility for session planning, they incorporated metacognitive strategies into their planning and delivery with increased independence. The results also indicate the acceptability of this professional development model, suggesting that, when combined with peer collaboration, the fading design was associated with improvements in knowledge and confidence regarding both metacognition and mathematical problem solving, alongside increased ownership and buy in. The conclusions advocate further examination and implementation of fading models of professional development to promote the understanding and use of metacognition for mathematical problem solving and recommend exploration into different professional development contexts. Full article

(This article belongs to the Special Issue Different Approaches in Mathematics Teacher Education)

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20 pages, 1139 KB

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Levels of Complexity in Mathematics Teachers’ Knowledge Connections: An Approach Based on MTSK and Piaget’s Schemas

by Estela Juárez-Ruiz, Eric Flores-Medrano, Keylla Otero-Valega and Lina Tascón-Cardona

Educ. Sci. 2025, 15(6), 641; https://doi.org/10.3390/educsci15060641 - 22 May 2025

Cited by 3 | Viewed by 1846

Abstract

This paper presents a study whose aim was to formulate a conceptual framework that allows us to understand the degree of complexity of the connections between the knowledge that a mathematics teacher can possess, based on the model of the mathematics teacher’s specialized knowledge model and the Piaget’s schemas. To this end, a literature review was carried out to analyze how these connections are made in the minds of mathematics teachers and how complex they are, identifying a deficit. Therefore, the schema structure proposed by Piaget, with its three stages of intra-, inter-, and trans-development, was considered. Based on an instrumental case study with two prospective teachers, an analysis was performed on semi-structured interviews conducted while the teachers separately discussed a lesson plan based on the understanding of multiplication and division of natural numbers, aimed at third-grade students. The results show that three types of knowledge schemas emerged among the participating teachers, with the respective types of connections between the knowledge. This shows that the connections between the knowledge of the model in teachers’ minds can vary in complexity. Full article

(This article belongs to the Special Issue Different Approaches in Mathematics Teacher Education)

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20 pages, 998 KB

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Influence of Professional Materials on the Decision-Making of Preservice Secondary Teachers When Noticing Students’ Mathematical Thinking

by Mar Moreno, Gloria Sánchez-Matamoros and Julia Valls

Educ. Sci. 2025, 15(4), 418; https://doi.org/10.3390/educsci15040418 - 26 Mar 2025

Cited by 2 | Viewed by 1279

Abstract

This research aims to investigate the impact of professional materials’ interpretation on the decision-making of preservice secondary teachers when analyzing the mathematical thinking of a 15–16-year-old high school student engaged in arithmetic problem-solving. Our conceptual framework considers the model of curricular noticing and the specific model of noticing students’ mathematical thinking, establishing connections between both. The participants were 20 preservice teachers taking part in a training program in two Spanish universities. They were grouped randomly into five groups. The data were preservice secondary teachers’ written responses to a professional task of noticing students’ mathematical thinking by solving two arithmetic problems. A qualitative analysis was carried out considering the skills that make up the theoretical models considered. Findings show that the various interpretations made by the preservice secondary teachers of the professional materials gave rise to different interpretations of the secondary school student’s error and this led them to propose different instructional responses. There were two groups focused on a relational interpretation and three focused on a procedural interpretation (and response). We conclude that the way in which secondary school student teachers begin to make sense of professional materials is influenced by their experiences, background, and beliefs about mathematics teaching. Full article

(This article belongs to the Special Issue Different Approaches in Mathematics Teacher Education)

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18 pages, 1447 KB

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Introducing Exploratory Teaching in Preservice Teacher Education Through Lesson Study

by Nicole Duarte, João Pedro da Ponte and Filipa Faria

Educ. Sci. 2025, 15(3), 315; https://doi.org/10.3390/educsci15030315 - 4 Mar 2025

Cited by 5 | Viewed by 3046

Abstract

In exploratory teaching, the pupils learn from their work on tasks that aim to introduce new concepts, procedures, representations and mathematical ideas. Lesson study, with its focus on teachers’ collaborative and reflective work around issues of pupil learning, is a powerful formative process that may be used in preservice teacher education, sustaining an exploratory teaching approach. In this article, we present a lesson study experience in preservice teacher education, addressing the case of a preservice teacher who is preparing to teach in grades 1–6. Our aim is to identify what key aspects of knowledge of teaching practice does the preservice teacher use when preparing and leading an exploratory lesson during her participation in a lesson study. Our methodology is qualitative, with data collected from the lesson study sessions and the collection of documents produced during the lesson study work, and the data are analysed using a model that presents the key aspects of knowledge of teaching practice. The results show that the structure and the activities carried out in the lesson study, such as designing the lesson, selecting the task and anticipating questions to be posed to pupils, promoted the use of the preservice teacher’s didactic knowledge regarding the phases of an exploratory lesson. Full article

(This article belongs to the Special Issue Different Approaches in Mathematics Teacher Education)

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Review

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23 pages, 518 KB

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Mathematical Knowledge for Teaching the Area of Plane Surfaces: A Literature Review on Professional Noticing

by Ana Cristina Ferreira and Alfonso Jiménez Espinosa

Educ. Sci. 2025, 15(10), 1272; https://doi.org/10.3390/educsci15101272 - 23 Sep 2025

Viewed by 1091

Abstract

Mathematics teaching is a social practice, shaped by distinct ways of recognizing, interpreting, and responding to situations that emerge in the classroom. This professional noticing, however, requires a kind of mathematical knowledge that is specific to teaching. This study aims to identify discussions have taken place in Brazil regarding the mathematical knowledge necessary for teaching the concept of area of plane surfaces in Basic Education, based on a literature review conducted through the CAPES Theses and Dissertations Catalog. The theoretical framework is grounded in Moreira’s distinctions between school mathematics and academic mathematics, as well as in the body of literature concerning the concept of professional noticing. The analysis of the 17 selected studies revealed, among other aspects, that by understanding area as a magnitude through the lens of the Game with Frames—originally developed by Douady and Perrin-Glorian in the 1980s and later expanded by Brazilian researchers—it is possible to infer mathematical knowledge relevant to teaching the area of plane surfaces in Basic Education. This perspective supports the development of professional noticing of students’ errors, difficulties, and misconceptions observed both in classrooms and in teacher education contexts. Some elements of this knowledge are discussed in the present article. Full article

(This article belongs to the Special Issue Different Approaches in Mathematics Teacher Education)

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