Actions of a Trainee Teacher in Orchestrating Mathematical Discussions

Background/purpose. This article aims to identify and analyze the actions of a trainee teacher in orchestrating mathematical discussions in an Exploratory Teaching environment.

Materials/methods. This qualitative study of an interpretative nature and case study design focuses on analyzing the content of four Multimodal Narratives.

Results. The results show that the predominant actions focus on questioning to foster understanding. In the sessions where the students experienced the most difficulties, it proved necessary to interpret the interactions with the students and between the students by attributing meaning and sense to the different interactions. There was a need for the trainee teacher to understand the students' strategies better and to reflect on the questioning strategies. The characteristics of Exploratory Teaching facilitated actions related to the systematization of learning. The phase of systematizing mathematical learning led the trainee teacher to actions related to systematizing learning. Finally, the absence of some actions reinforces the importance of reflection for professional development.

Conclusion. These results indicate that during the orchestration of collective discussions, the teacher's main actions center on questioning and asking for clarification to interpret interactions with and between children. The study also shows that Exploratory Teaching helps to systematize learning, such as revisiting and summarizing the main topics of the discussion and recovering students' prior knowledge. The absence of some actions leads us to believe in the importance of analyzing and reflecting on practice for teachers' professional development.

Keywords: Whole-class discussions, practicum, mathematics teaching, exploratory teaching, multimodal narratives

References

Amado, J. (2017). Manual de Investigação Qualitativa em Educação (3ª ed.). Imprensa da Universidade de Coimbra. https://doi.org/10.14195/978-989-26-1390-1

Bardin, L. (2011). Análise de Conteúdo. Edições 70.

Borko, H., Jacobs, J., Seago, N., & Mangram, C. (2014). Facilitating Video-Based Professional Development: Planning and Orchestrating Productive Discussions. In: Li, Y., Silver, E., Li, S. (eds) Transforming Mathematics Instruction. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-04993-9_16

Brodie, K. (2010). Teaching mathematical reasoning in secondary school classrooms. Springer.

Canavarro, A., Oliveira, H., & Menezes, L. (2012). Práticas de ensino exploratório da matemática: o caso de Célia. In L. Santos, A. Canavarro, A. Boavida, H. Oliveira, L. Menezes, & S. Carreira (Eds.), Investigação em Educação Matemática (pp. 255–266). Sociedade Portuguesa de Investigação em Educação Matemática.

Carvalho, R., & da Ponte, J. P. (2013). Prática profissional para a promoção do cálculo mental na sala de aula: Uma experiência no 6. º ano. Quadrante, 22(2), 83-108. https://doi.org/10.48489/quadrante.22893

Cohen, l., Manion, L., & Marrison, K. (2018). Research Methods in Education (8ª ed.). Routledge.

Creswell, J. W. (2014). Educational Research: Planning, Conducting and Evaluating Quantitative and Qualitative Research (4ª ed.). Pearson.

Faria, F., Da Ponte, J. P., & Rodrigues, M. (2024). Teachers’ leading whole-class discussions in a mathematics lesson study: From initial understanding to orchestration in practice. European Journal of Science and Mathematics Education, 12(1), 156-174.

Ferreira, M. C. N., Ribeiro, A. J., & Ponte, J. P. D. (2023). Práticas e ações do formador de professores que ensinam Matemática na orquestração de discussões coletivas. Bolema, 37, 666-687. http://dx.doi.org/10.1590/1980-4415v37n76a14

Freitas, Y. (2024). A applet multiplicação da Plataforma Hypatiamat na compreensão dos sentidos da operação aritmética multiplicação [Relatório final de Mestrado, Escola Superior de Educação de Coimbra]. Repositório Comum.

Freitas, Y. A., Abbasi, M., Brito-Costa, S., Pinto, R., Rato, V., & Martins, F. (2024). Exploratory teaching: Integrating applet to teach arithmetic multiplication operation. Eurasia Journal of Mathematics, Science and Technology Education, 20(12). https://doi.org/10.29333/ejmste/15666

Freitas, Y. A., Pinto, R., Rato, V., Gomes, A., & ML Martins, F. (2023). Sentidos da multiplicação e a applet multiplicação da plataforma Hypatiamat. Revista APEduC, 4(1), 119-137. http://dx.doi.org/10.58152/APEduCJournal.401

Gomes, P., Ponte, J. P. e Quaresma, M. (2023). “O que descobriram?” Tarefas e discussões coletivas usando diferentes representações durante e após estudos de aula. PNA, 18(1), 77-103. https://doi.org/10.30827/pna.v17i4.27033

Gomes, P., Quaresma, M., & da Ponte, J. P. (2022). Leading whole-class discussions: from participating in a lesson study to teaching practice. International Journal for Lesson & Learning Studies, 12(2), 139-151. https://doi.org/10.1108/IJLLS-02-2022-0022

Guerreiro, A., Ferreira, R., Menezes, L., & Martinho, M. (2015). Comunicação na sala de aula: a perspetiva do ensino exploratório da matemática. Zetetiké, 23(44), 279–295.

Kuckartz, U. y Rädiker, S. (2019). Introduction: Analyzing Qualitative Data with Software. In U. Kuckartz & S Rädiker (Eds.), Analyzing Qualitative Data with MAXQDA: Text, Audio, and Video (pp. 1–11). Springer International Publishing. https://doi.org/10.1007/978-3-030-15671-8_1

Lopes, J., Viegas, M., & Pinto, A. (2018). Melhorar práticas de ensino de ciências e tecnologia – Registar e investigar com narrações multimodais. Edições Sílabo.

Martins, M., Ponte, J. P. e Mata-Pereira, J. (2024). O desenvolvimento do conhecimento didático de futuros professores: o estudo de aula como processo formativo integrado na formação inicial. PNA, 18(2), 105-130. https://doi.org/10.30827/pna.v18i2.27258

Oliveira, H., Menezes, L., & Canavarro, A. (2013). Conceptualizando o ensino exploratório da Matemática: Contributos da prática de uma professora do 3.º ciclo para a elaboração de um quadro de referência. Quadrante, 22(2), 1–25.

Ponte, J. (2012). Estudiando el conocimiento y el desarrollo profesional del profesorado de matemáticas. In N. Planas (Ed.), Teoría, crítica y práctica de la educación matemática (pp. 83–98). Graó.

Ponte, J. P. D., Mata-Pereira, J., & Quaresma, M. (2013). Ações do professor na condução de discussões matemáticas. Quadrante, 22(1), 55-81. https://doi.org/10.48489/quadrante.22894

Ponte, J. P., Branco, N., Quaresma, M., Velez, I., & Mata-Pereira, J. (2012). Perspetivas teóricas no estudo das práticas profissionais dos professores de matemática. In A. P. Canavarro, L. Santos, A. M. Boavida, H. Oliveira, L. Menezes & S. Carreira (Eds.), Práticas de ensino da Matemática: Atas do Encontro de Investigação em Educação Matemática (pp. 267-279).

Rodrigues, C., Da Ponte, J. P., & Menezes, L. (2020). Práticas discursivas de professores de Matemática na condução de discussões coletivas. Quadrante, 29(2), 24-46. https://doi.org/10.48489/quadrante.22575

Rodrigues, C., Menezes, L., & Ponte, J. P. D. (2018). Práticas de Discussão em Sala de Aula de Matemática: os casos de dois professores. Bolema: Boletim de Educação Matemática, 32, 398-418. http://dx.doi.org/10.1590/1980-4415v32n61a05

Rodrigues, R.N., Costa, C., Martins, F., & Ruiz Rey, F.J. (2022). Ações de uma estagiária na promoção e sustentação de práticas epistémicas. Revista Practicum, 7(2), 148-168. https://doi.org/10.24310/RevPracticumrep.v7i2.13518

Stavridis P., & Papadopoulou V. (2022). The Contribution of Teaching Practice to Preservice Teachers’ Training – Empirical Research of the Department of Primary Education of Western Macedonia University Students’ Evaluation. Educational Process: International Journal, 11(4): 92-111. https://dx.doi.org/10.22521/edupij.2022.114.5

Stein, M. K., & Smith, M. S. (2009). Tarefas matemáticas como quadro para a reflexão: da investigação à prática. Educação e Matemática, 105(5), 22-28.

Stein, M., Engle, R., Smith, M., & Hughes, E. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313–340. http://dx.doi.org/10.1080/10986060802229675

Vilelas, J. (2020). Investigação – O processo de construção de conhecimento (3ª ed.). Edições Sílabo.

Vygotsky, L. S. (1980). Mind in society: The development of higher psychological processes. Cambridge MA: Harvard University Press.

Announcement

EDUPIJ Citation Metrics

EDUPIJ News!

ANNOUNCEMENT

Message from the Editor-in-Chief,

We would like to inform our authors, reviewers, and stakeholders that EDUPIJ has entered Scopus’s re-evaluation process, as officially communicated (dated 2025-12-09). This assessment is a standard quality assurance practice applied to indexed journals and aims to ensure sustained editorial quality, ethical integrity, and alignment with Scopus’s evolving evaluation framework.

EDUPIJ welcomes this process and views it as an opportunity to further consolidate its editorial governance, strengthen publication ethics, and enhance peer-review rigor.

Strengthening Editorial and Ethical Standards

To ensure full compliance with international best practices and to proactively address Scopus evaluation criteria, the following measures have been formally implemented:

1. Selective Acceptance Policy for 2026 and Beyond

In response to increased submission volume in 2025 (see Journal Metrics: https://edupij.com/index/sayfa/18/journal-metrics), EDUPIJ will adopt a more selective acceptance policy starting in 2026 and continuing in the years ahead. In doing so, the geographic distribution of authors will also be taken into account to ensure that editorial decisions are informed by transparent, year-to-year submission and authorship patterns. Acceptance rates will be carefully aligned with editorial capacity to ensure a rigorous double-blind peer review process supported by active reviewer engagement and uncompromised editorial oversight. This policy reflects our commitment to quality-driven growth rather than volume-based expansion, and it directly addresses observations that the geographic spread of authors has changed significantly during the same period by ensuring that any such shifts are systematically monitored and considered within our quality assurance framework.

In line with this approach, we have adopted a Publication Volume Policy, enacted on 2025-12-07, which establishes clear upper limits on annual publication volume and defines a framework for maintaining EDUPIJ’s output at sustainable, long-term levels, comparable to pre-2025 volumes under normal conditions. This policy is also publicly available at https://edupij.com/index/sayfa/41/publication-volume-journal-metrics-policy.

From 2026 onwards, our objective is to maintain a moderate and stable annual volume, prioritising quality and selectivity rather than growth.

2. Enhanced Author and Manuscript Integrity Screening

All submissions now undergo mandatory integrity checks, including automated screening for retraction history and potential ethical risks prior to peer review. These procedures are designed to safeguard originality, research integrity, and transparency at every stage of the editorial process.

3. Establishment of a Publication Ethics Review Committee

A dedicated Publication Ethics Review Committee has been constituted to evaluate high-risk submissions, oversee ethical investigations when necessary, and ensure consistent adherence to COPE guidelines and internationally recognized publishing standards. All ethical decisions are documented and managed through a structured, transparent process.

Ongoing Commitment:

EDUPIJ remains firmly committed to rigorous double-blind peer review, transparent editorial policies, responsible scholarly communication, and the advancement of high-quality educational research at an international level.

Our journal continues to demonstrate steady progress in terms of international visibility, indexing coverage, and citation performance. We are confident that the Scopus re-evaluation process will further support the journal’s long-term sustainability and academic impact.

We sincerely thank our authors, reviewers, and the broader scholarly community for their continued trust and contribution to EDUPIJ.

Sincerely,
Prof. Turgut Karaköse, Editor-in-Chief

Posted: 2025-12-09