Teacher leadership competencies in supporting argumentation in the mathematics classroom

Authors

DOI:

https://doi.org/10.11606/issn.2236-4242.v36i3p369-386

Keywords:

Mathematics, Development of argumentation, Teacher professional, Noticing, Improvement of Teacher Experiences

Abstract

In order to strengthen teacher professional development, collaborative training proposals are required, which include teacher leadership competencies to supervise, provide feedback on, and model teaching practices. This article presents a training experience in which 27 teacher leaders from 11 educational establishments participated, in which the training model "Improving the Teaching Experience" (MED) is used to accompany teachers in the development of argumentation in the math classroom. The analysis of this experience shows how the characteristics and stages of the MED, such as questioning the teacher's practice, generating cognitive conflict in the teacher, eliciting teachers' ideas and encouraging teachers to analyze evidence in the classroom, are related to the three competencies of an intermediate leader in supervising, providing feedback on, and modeling teaching practices.

Downloads

Download data is not yet available.

Author Biographies

  • Horacio Solar, Pontificia Universidad Católica de Chile

    Doctor en Didáctica de la Matemática por la Universidad Autónoma de Barcelona (2009).
    Profesor Asociado de la Facultad de Educación de la Pontificia Universidad Católica de Chile (Chile).

  • Pilar Peña-Rincón, Pontificia Universidad Católica de Chile

    Doctora en Matemática educativa y la Maestría en Ciencias en Matemática Educativa en el Centro de Investigación en Ciencia Aplicada y Tecnología Avanzada del Instituto Politécnico Nacional de México (México). 
    Profesora Planta Especial en la Pontificia Universidad Católica de Chile (Chile).

  • Andrés Ortiz, Universidad Católica de la Santísima Concepción

    Magíster en Enseñanza de las Ciencias: mención matemática (2003).
    Profesor Asociado de la Universidad Católica de la Santísima Concepción (Chile).

References

AMADOR, J. Teacher Leaders Mathematical Noticing: Eliciting and Analyzing. International Journal of Science and Mathematics Education, v. 18, p. 295–313. 2020. DOI: http://doi.org/10.1007/s10763-019-09956-5.

AN, S.; PETER-KOOP. A. In-Service Education, Professional Development of Mathematics Teachers. In: CHO. S. (ed). The Proceedings of the 12th International Congress on Mathematical Education. Intellectual and Attitudinal Challenges Heidelberg. New York Dordrecht London: Springer Open, 2015. p. 513-516.

AVALOS-BEVAN, B; BASCOPÉ, M. Teacher Informal Collaboration for Professional Improvement: Beliefs, Contexts, and Experience. Education Research International, v. 2017, p. 1357180, 2017. DOI: https://doi.org/10.1155/2017/1357180.

AYALON, M.; HERSHKOWITZ, R. Mathematics teachers’ attention to potential classroom situations of argumentation. Journal of Mathematical Behavior, v. 49, p. 163-173, 2018. Disponible en: https://www.sciencedirect.com/science/article/abs/pii/S0732312317301141?via%3Dihub. Acceso en: 25 jun. 2023.

BENNETT, N. Assessing the impact on practice of professional development activities. Sage Publications, 2003

BERKOWITZ, D.; FERNÁNDEZ, M.; ZORO, B. Una revisión al Desarrollo Profesional Directivo y de Nivel Intermedio en el contexto del desafío de creación del Sistema de Educación Pública. Informe técnico. Informe Técnico Nº 3. LÍDERES EDUCATIVOS, Centro de Liderazgo para la Mejora Escolar. 2019.

BORKO, H.; CARLSON, J.; DEUTSCHER, R. ET AL. Learning to Lead: an Approach to Mathematics Teacher Leader Development. International Journal of Science and Mathematics Education. v. 9, p. 121-143, 2021. DOI: https://doi.org/10.1007/s10763-021-10157-2.

CERVANTES-BARRAZA, J.; CABAÑAS-SÁNCHEZ, G.; ORDOÑEZ-CUASTUMAL, S. El poder persuasivo de la refutación en argumentaciones colectivas. Bolema - Mathematics Education Bulletin, v. 31. n. 59, p. 861-879, 2017. Disponible en: https://www.scielo.br/j/bolema/a/k77PKndWNSkSWGkxDpKRWGB/abstract/?lang=es. Acceso en: 25 jun. 2023.

CONNER, A. M.; SINGLETARY, L. M.; SMITH, R. C.; WAGNER, P. A.; FRANCISCO, R. T. Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities. Educational Studies in Mathematics, v. 86, n. 3, p. 401-429, 2014. Disponible en: https://link.springer.com/article/10.1007/s10649-014-9532-8. Acceso en: 25 jun. 2023.

DINHAM, S. The secondary Head of Department and the achievement of exceptional student outcomes. Journal of Educational Administration, v. 45. n. 1, p. 62–79. 2007. DOI: https://doi.org/10.1108/09578230710722458.

EDUCA, F. B. Proyecto Educativo Institucional. Santiago, Chile. 2017

ESPAÑA. Real Decreto 157, de 1 de marzo de 2022. Por el que se establecen la ordenación y las enseñanzas mínimas de la educación primaria. Boletín oficial del estado, Madrid, n. 52, p. 24386-24504, de 3 de marzo de 2022. Disponible en: https://www.boe.es/buscar/act.php?id=BOE-A-2022-3296. Acceso en: 19 abr. 2023.

GIBBONS, L.; KAZEMI, K.; LEWIS, R. Developing collective capacity to improve mathematics instruction: Coaching as a lever for school-wide improvement. The Journal of Mathematical Behavior, v. 46, p. 231-250, 2017. DOI: https://doi.org/10.1016/j.jmathb.2016.12.002.

GOODCHILD, S. Mathematics teaching development: Learning from developmental research in Norway. ZDM - International Journal on Mathematics Education, v. 46, p. 305–316. 2014. DOI: https://doi.org/10.1007/s11858-013-0567-6.

GOIZUETA, M.; PLANAS, N. Temas emergentes del análisis de interpretaciones del profesorado sobre la argumentación en clase de matemáticas. Enseñanza de las Ciencias, v. 31, n. 1, p. 61-78. 2013.

GOIZUETA, M.; SOLAR, H. Relaciones entre la argumentación en el aula de matemáticas y la mirada profesional del profesor. In: OLFOS, R; RAMOS, E.; ZAKARYAN, D. (ed.). Formación docente: Aportes a la práctica docente desde la didáctica de la matemática, Barcelona, Graó, 2019, p. 241-280.

INGLIS, M.; MEJIA-RAMOS, J. P.; SIMPSON, A. Modelling mathematical argumentation: The importance of qualification. Educational Studies in Mathematics, v. 66, p. 3-21. 2007. DOI: https://doi.org/10.1007/s10649-006-9059-8.

HIGHFIELD, C. The impact of middle leadership practices on student academic outcomes in New Zealand secondary schools. [Tesis Doctoral, Universidad de Auckland, Auckland], 2012. Disponible en https://researchspace.auckland.ac.nz/handle/2292/19796.

KRUMMHEUER, G. The ethnography of argumentation. In: COBB, P.; BAUERSFELD. H. (ed.). The emergence of mathematical meaning: Interaction in classroom cultures. Hillsdale: Lawrence Erlbaum, 1995. p. 229-269.

LESSEIG, K.; ELLIOTT, R.; KAZEMI, E.; KELLEY-PETERSEN, M.; CAMPBELL, M., MUMME, J.; CARROLL, C. Leader noticing of facilitation in videocases of mathematics professional development. Journal of Mathematics Teacher Education, v. 20, n. 6, p. 591–619. 2017. DOI: https://doi.org/10.1007/s10857-016-9346-y.

LINEK, W.; PADAK, N.; RASINSKI, T.; STURTEVANT, E. Mentoring Literacy Researchers. Journal of Literacy Research, v. 35, n. 4, p. xi–xiv. 2003.

MINISTERIO DE EDUCACIÓN DE CHILE- MINEDUC. Bases curriculares chilenas 7o básico a 2o medio. Santiago: Mineduc, 2013.

MINISTERIO DE EDUCACIÓN DE CHILE -MINEDUC. Fundamentos Modelo de Desarrollo de Capacidades para el Apoyo Técnico-Pedagógico. Santiago: Dirección de Educación Pública. División de desarrollo Educativo. 2022.

NISS, M; HØJGAARD, T. Mathematical competencies revisited. Educational Studies in Mathematics, v. 102, p. 9-28, jun. 2019. DOI: https://doi.org/10.1007/s10649-019-09903-9.

ORGANIZATION FOR ECONOMIC COOPERATION AND DEVELOPMENT - OECD. PISA 2018 Assessment and Analytical Framework (PISA). Paris: OECD, 2019. Disponible en: https://www.oecd-ilibrary.org/education/pisa-2018-assessment-and-analytical-framework_b25efab8-en. Acceso en: 19 abr. 2023.

REID, D.; KNIPPING, C.; CROSBY, M. Refutations and the logic of practice. PNA, v. 6, n. 1, p. 1-10, jul 2011.

RHODES, C.; BRUNDRETT, M. Growing the leadership talent pool: perceptions of heads, middle leaders and classroom teachers about professional development and leadership succession planning within their own schools. Professional Development in Education, v. 35, n. 3, p. 381–398. 2009. DOI: https://doi.org/10.1080/19415250902987122.

RITCHIE, S. M.; MACKAY, G.; RIGANO, D. L. Individual and collective leadership in school science departments. Research in Science Education, v. 36, n. 3, p. 141–161. 2006. DOI: https://doi.org/10.1007/s11165-005-9001-6.

ROBINSON, V.; HOHEPA, M.; LLOYD, C. School Leadership and Student Outcomes: Identifying what works and why. Winmalee: Australian Council for Educational Leaders. 2007.

ROESKEN, B. Hidden Dimensions in the Professional Development of Mathematics Teachers. In-service Education for and with teachers. Rotterdam: Sense Publishers, 2011.

ROGERS, M. P.; ABELL, S.; LANNIN, J.; WANG, C. Y.; MUSIKUL, K.; BARKER, D.; DINGMAN, S. Effective professional development in science and mathematics education: Teachers' and facilitators' views. International journal of science and mathematics education, v. 5, n. 3, p. 507-532. 2007. DOI: https://doi.org/10.1007/s10763-006-9053-8.

SÁNCHEZ-MATAMOROS, G.; FERNÁNDEZ, C.; LLINARES, S. Developing pre-service teachers’ noticing of students’ understanding of the derivative concept. International Journal of Science and Mathematics Education, v. 13, n. 6, p. 1305–1329. 2015. DOI: https://doi.org/10.1007/s10763-014-9544-y.

SCHOENFELD, A. H. Toward professional development for teachers grounded in a theory of decision making. ZDM Mathematics Education, v. 43, p. 457–469. 2011. DOI: https://doi.org/10.1007/s11858-011-0307-8.

SEPÚLVEDA, R.; VOLANTE, P.; MONTENEGRO, M. Validación de un cuestionario de liderazgo intermedio para profesores responsables de un departamento didáctico. Revista complutense de educación, v. 33, n. 3, p. 435-445. 2022. DOI: https://doi.org/10.5209/rced.74479.

SHAPIRA-LISHCHINSKY, O.; LEVY-GAZENFRANTZ, T. Authentic leadership strategies in support of mentoring processes. School Leadership & Management, v. 35, n. 2, p. 183–201. 2015. DOI: https://doi.org/10.1080/13632434.2014.992777.

SHERIN, M. G.; JACOBS, V. R.; PHILLIP, R. A. Situating the study of teacher noticing. In SHERIN, M. G.; JACOBS, V. R.; PHILIPP R. A. (ed.), Mathematics teacher noticing: Seeing through teachers’ eyes. New York: Routledge. 2011. p. 3–13. DOI: https://doi.org/10.1080/13632434.2014.992777.

SHERIN, M. G.; VAN ES, E. A. Effects of video club participation on teachers’ professional vision. Journal of Teacher Education, v. 60, n. 1, p. 20–37. 2009. DOI: https://doi.org/10.1177/0022487108328155.

SHULMAN, L. Those who understand: knowledge growth in teaching. Educational Researcher, v 15, n. 2, p. 4–14. 1986. DOI: https://doi.org/10.2307/117586.

SOLAR, H.; DEULOFEU, J. Condiciones para promover el desarrollo de la competencia de argumentación en el aula de matemáticas. Bolema - Mathematics Education Bulletin, v. 30, n. 56, 1092–1112. 2016. Disponible en https://www.scielo.br/j/bolema/a/LRQCNDLqMwwbtcHfhyf5LDs/?lang=es. Acceso en: 25 jun. 2023.

SOLAR, H.; ORTIZ, A.; DEULOFEU, J.; ULLOA, J. Teacher support for argumentation and the incorporation of contingencies in mathematics classrooms. International Journal of Mathematical Education in Science and Technology, v. 52, n. 7, p. 977-1005. 2021. Disponible en https://www.tandfonline.com/doi/full/10.1080/0020739X.2020.1733686. Acceso en: 25 jun. 2023.

SOLAR, H.; ORTIZ, A.; ULLOA, R. MED: Modelo de formación continua para profesores de matemática, basada en la experiencia. Estudios Pedagógicos, v. 42, n. 4, p. 281-298. 2016. Disponible en https://www.scielo.cl/scielo.php?pid=S0718-07052016000500016&script=sci_arttext. Acceso en: 25 jun. 2023.

STAHNKE, R., SCHUELER, S.; ROESKEN-WINTER, B. Teachers’ perception, interpretation, and decision-making: a systematic review of empirical mathematics education research. ZDM Mathematics Education, v, 48, p. 1-27. 2016. DOI: http://doi.org/10.1007/s11858-016-0775-y.

TOULMIN, S. The uses of argument. Reino Unido, Cambridge, MA: Cambridge University Press. 2003.

VAN EEMEREN, F. H.; GROOTENDORST, R.; JOHNSON, R. H.; PLANTIN, C.; WILLARD, C. A. Fundamentals of argumentation theory: A handbook of historical backgrounds and contemporary developments. Routledge, 2013.

VERGARA, C; COFRÉ, H. Conocimiento pedagógico del contenido: ¿el paradigma perdido en la formación inicial y continua de profesores en chile? Revista Estudios Pedagógicos, v. 15 (Número Especial 1), p. 323-338. 2014. DOI: http://doi.org/10.4067/S0718-07052014000200019.

YACKEL, E. What we can learn from analyzing the teacher’s role in collective argumentation. Journal of Mathematical Behavior, v. 4, n. 21, p. 423-440, 2002. DOI: http://doi.org/10.1016/S0732-3123(02)00143-8.

Published

2023-12-28

How to Cite

SOLAR, Horacio; PEÑA-RINCÓN, Pilar; ORTIZ, Andrés. Teacher leadership competencies in supporting argumentation in the mathematics classroom. Linha D’Água, São Paulo, v. 36, n. 3, p. 369–386, 2023. DOI: 10.11606/issn.2236-4242.v36i3p369-386. Disponível em: https://periodicos.usp.br/linhadagua/article/view/211390.. Acesso em: 19 may. 2024.

Funding data