Noticing students’ mathematical thinking: characterization, development and contexts

  1. Ceneida Fernández 1
  2. Gloria Sánchez-Matamoros 2
  3. Julia Valls 3
  4. M.Luz Callejo 3
  1. 1 Universidad de Alicante (España)
  2. 2 Universidad de Sevilla
    info

    Universidad de Sevilla

    Sevilla, España

    ROR https://ror.org/03yxnpp24

  3. 3 Universitat d'Alacant
    info

    Universitat d'Alacant

    Alicante, España

    ROR https://ror.org/05t8bcz72

Aldizkaria:
Avances de investigación en educación matemática: AIEM

ISSN: 2254-4313

Argitalpen urtea: 2018

Zenbakia: 13

Orrialdeak: 39-61

Mota: Artikulua

DOI: 10.35763/AIEM.V0I13.229 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

Beste argitalpen batzuk: Avances de investigación en educación matemática: AIEM

Garapen Iraunkorreko Helburuak

Laburpena

Este artigo apresenta uma síntese dos resultados da pesquisa do grupo de Didática da Matemática da Universidade de Alicante, realizada durante los últimos años em relação à competência de ensino para olhar profissionalmente. As investigações se concentraram em três enfoques: (i) caracterizar a relação entre as habilidades que compõem a competência de ensino para olhar profissionalmente; (ii) caracterizar graus de desenvolvimento e (iii) identificar características dos contextos que sustentam seu desenvolvimento. Os principais resultados são apresentados con os desafios para o futuro.

Finantzaketari buruzko informazioa

EDU2014-54526-R and EDU2017-87411-R, MINECO/FEDER;PROMETEO/2017/135, Generalitat Valenciana, Spain.

Finantzatzaile

Erreferentzia bibliografikoak

  • Barnhart, T., & van Es, E. A. (2015). Studying teacher noticing: examining the relationship among pre-service science teachers’ ability to attend, analyze and respond to student thinking. Teaching and Teacher Education, 45, 83-93
  • Bartell, T. G., Webel, C., Bowen, B., & Dyson, N. (2013). Prospective teacher learning: recognizing evidence of conceptual understanding. Journal of Mathematics Teacher Education, 16, 57-79.
  • Battista, M. T. (2012). Cognition-Based assessment and teaching of fractions: building on students’ reasoning. Portsmouth, USA: Heinemann.
  • Buforn, A., Llinares, S., & Fernández, C. (2018). Características del conocimiento de los estudiantes para maestro españoles en relación a la fracción, razón y proporción. Revista Mexicana de Investigación Educativa, 76(23), 229-251.
  • Callejo, M. L., & Zapatera, A. (2017). Prospective primary teachers’ noticing of students’ understanding of pattern generalization. Journal of Mathematics Teacher Education, 20, 309-333.
  • Chapman, O. (2008). Narratives in mathematics teacher education. In D. Tirosh & T. Wood (Eds.), International Handbook of Mathematics Teacher Education. Tools and processes in mathematics teacher education (Vol. 2, pp. 15-38). Rotterdam, Netherlands: Sense Publishers.
  • Choy, B. H. (2016). Snapshots of mathematics teacher noticing during task design. Mathematics Education Research Journal, 28, 421-440.
  • Clark, D., & Sampson, V. (2008). Assessing dialogic argumentation in online environments to relate structure, grounds and conceptual quality. Journal of Research in Science Teaching, 45(3), 293-321.
  • Coles, A., Fernández, C., & Brown, L. (2013). Teacher noticing and growth indicators for mathematics teachers’ development. En A. M. Lindmeier & A. Heinze, (Eds.), Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 209-216). Kiel, Germany: PME.
  • Cooper, S. (2009). Preservice teacher’s analysis of children’s work to make instructional decisions. School Science and Mathematics, 109(6), 355-362.
  • Design-Based Researcher Collective (2003). Design-Based Research: an emerging paradigm for educational inquiry. Educational Researcher, 32(1), 5-8.
  • Edgington, C., Wilson, P. H., Sztajn, P., & Webb, J. (2016). Translating learning trajectories into useable tools for teachers. Mathematics Teacher Educator, 5(1), 65-80.
  • Fernández, C., Llinares, S., & Valls, J. (2012). Learning to notice students’ mathematical thinking through on-line discussions. ZDM, 44, 747-759.
  • Fernández, C., Llinares, S., & Valls, J. (2013). Primary school teachers’ noticing of students’ mathematical thinking in problem solving. The Mathematics Enthusiast, 10(1-2), 441-468.
  • Fernández, C., Sánchez-Matamoros, G., Callejo, M. L., & Moreno, M. (2015). ¿Cómo estudiantes para profesor comprenden el aprendizaje de límite de una función? En C. Fernández, M. Molina & N. Planas (Eds.), Investigación en Educación Matemática XIX (pp. 249-257). Alicante: SEIEM.
  • Fernández, C., Sánchez-Matamoros, G., & Llinares, S. (2015). Learning about students’ mathematical thinking using “KDU”. En K. Beswick, T. Muir & J. Wells (Eds.), Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education (vol. 2, pp. 281-288). Hobart, Australia: PME.
  • Fernández, C., Sánchez-Matamoros, G., Moreno, M., & Callejo, M. L. (2018). La coordinación de las aproximaciones en la comprensión del concepto de límite cuando los estudiantes para profesor anticipan respuestas de estudiantes. Enseñanza de las Ciencias, 36(1), 143-162.
  • Goodwin, C. (1994). Professional vision. American Anthropologist, 96, 606-633.
  • Ivars, P., & Fernández, C. (2018). The role of writing narratives in developing pre service elementary teachers’ noticing. In G. Stylianides & K. Hino (Eds.), Research Advances in the Mathematical Education of Pre-service Elementary Teachers. ICME-13 Monographs. Hamburg, Germany: Springer.
  • Ivars, P., Fernández, C., & Llinares, S. (2016). Cómo estudiantes para maestro miran de manera estructurada la enseñanza de las matemáticas al escribir narrativas. La Matemática e La Sua Didattica, 24(1-2), 79-96.
  • Ivars, P., Fernández, C., & Llinares, S. (2017). Pre-service teachers’ uses of a learning trajectory to notice students’ fractional reasoning. In B. Kaur, W. H. Ho, T. L. Toh & B. H. Choy (Eds.), Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 25-32). Singapore: PME.
  • Jacobs, V. R., Lamb, L. C., & Philipp, R. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202.
  • Krupa, E., Huey, M., Lesseig, K., Casey, S., & Monson, D. (2017). Investigating secondary preservice teacher noticing of students' mathematical thinking. In E. O. Schack, M. H. Fisher & J. A. Wilhelm (Eds.), Teacher noticing: bridging and broadening perspectives, contexts, and frameworks (pp. 49-72). London, UK: Springer.
  • Llinares, S. (2012). Construcción de conocimiento y desarrollo de una mirada professional para la práctica de enseñar matemáticas en entornos en línea. Avances de Investigación en Educación Matemática, 2, 53-70.
  • Llinares, S. (2013). Professional noticing: a component of the mathematics teacher’s professional practice. SISYPHUS. Journal of Education, 1(3), 76-93.
  • Llinares, S. (2014). Experimentos de enseñanza e investigación. Una dualidad en la práctica del formador de profesores de matemáticas. Educación Matemática, March, 31-51.
  • Llinares, S., Fernández, C., & Sánchez-Matamoros, G. (2016). Changes in how prospective teachers anticipate secondary students’ answers. Eurasian Journal of Mathematics, Science & Technology Education, 12(8), 2155-2170.
  • Llinares, S., & Valls, J. (2010). Prospective primary mathematics teachers’ learning from on-line discussions in a virtual video-based environment. Journal of Mathematics Teacher Education, 13, 177-196.
  • Llinares, S., & Valls, J. (2009). The building of preservice primary teachers’ knowledge of mathematics teaching: interaction and online video case studies. Instructional Science, 37, 247-271.
  • Mason, J. (2002). Researching your own practice. The discipline of noticing. London, UK: Routledge-Falmer.
  • Nickerson, S., Lamb, L., & LaRochelle, R. (2017). Challenges in measuring secondary mathematics teachers’ professional noticing of students’ mathematical thinking. In E. O. Schack, M. H. Fisher, & J. A. Wilhelm (Eds.), Teacher noticing: bridging and broadening perspectives, contexts, and frameworks (pp. 381-398). London, UK: Springer.
  • Ponte, J. P., Segurado, I., & Oliveira, H. (2003). A collaborative project using narratives: What happens when pupils work of mathematical investigations? In A. Peter-Koop, V. Santos-Wagner, C. Breen & A. Begg (Eds.), Collaboration in teacher education: examples from the context of mathematics education (pp. 85-97). Dordrecht, Netherlands: Kluwer Academic Press.
  • Radford, L. (2014). The progressive development of early-embodied algebraic thinking. Mathematics Education Research Journal, 26, 257–277.
  • Schack, E., Fisher, M., Thomas, J., Eisenhardt, S., Tassell, J., & Yoder, M. (2013). Prospective elementary school teachers’ professional noticing of children’s early numeracy. Journal of Mathematics Teacher Education, 16, 379–397.
  • Sánchez-Matamoros, G., Fernández, C., & Llinares, S. (2015). Developing pre service teachers' noticing of students' understanding of the derivative concept. International Journal of Science and Mathematics Education, 13(6), 1305-1329.
  • Sánchez-Matamoros, G., Fernández, C., Valls, J., García, M., & Llinares, S. (2012). Cómo estudiantes para profesor interpretan el pensamiento matemático de los estudiantes de bachillerato. La derivada de una función en un punto. In A. Estepa et al. (Eds.), Investigación en Educación Matemática XVI (pp. 497 508). Jaén: SEIEM.
  • Sánchez-Matamoros, G., Moreno, M., Callejo, M. L., Pérez-Tyteca, P., & Valls, J. (2017). Desarrollo de la competencia “mirar profesionalmente”: un estudio de caso. In J. M. Muñoz-Escolano, A. Arnal-Bailera, P. Beltrán-Pellicer, M. L. Callejo & J. Carrillo (Eds.), Investigación en Educación Matemática XXI (pp. 457-466). Zaragoza: SEIEM.
  • Sánchez-Matamoros, G., García, M., & Llinares, S. (2008). La comprensión de la derivada como objeto de investigación en didáctica de la matemática. Revista Latinoamericana de Investigación en Matemática Educativa, 11(2), 267-296.
  • Santagata, R., & Yeh, C. (2016). The role of perception, interpretation, and decision making in the development of beginning teachers’ competence. ZDM, 48(1-2), 153-165.
  • Shute, V. J. (2008). Focus on formative feedback. Review of Educational Research, 78(1), 153-189.
  • Simon, M. (2006). Key Developmental Understanding in mathematics: a direction for investigating and establishing learning goals. Mathematical Thinking and Learning, 8(4), 359-371.
  • Son, J. (2013). How preservice teachers interpret and respond to student errors: ratio and proportion in similar rectangles. Educational Studies in Mathematics, 84, 49-70.
  • Stahnke, R., Schueler, S., & Roesken-Winter, B. (2016). Teachers’ perception, interpretation, and decision-making: a systematic review of empirical mathematics education research. ZDM, 48(1-2), 1-27.
  • Sztajn, P., Confrey, J., Wilson, P. H., & Edgington, C. (2012). Learning trajectory based instruction: toward a theory of teaching. Educational Researcher, 41(5), 147–156.
  • Van Es, E. A., & Sherin, M. G. (2002). Learning to notice: scaffolding new teachers’ interpretations of classroom interactions. Journal of Technology and Teacher Education, 10, 571-596.
  • Van Es, E. A., & Sherin, M. G. (2008). Mathematics teachers’ “learning to notice” in the context of a video club. Teaching and Teacher Education, 24(2), 244-276.
  • Verillon, P., & Rabardel, P. (1995). Cognition and artifacts: a contribution to the study of thought in relation to instrument activity. European Journal of Psychology of Education, 9(3), 77-101.
  • Walkoe, J. (2015). Exploring teacher noticing of student algebraic thinking in a video club. Journal of Mathematics Teacher Education, 18, 523-550.
  • Wells, G. (2002). Dialogic inquiry. Towards a sociocultural practice and theory of education. Cambridge, USA: Cambridge University Press.
  • Wenger, E. (1998). Communities of practice: learning, meaning, and identity. Cambridge, USA: Cambridge University Press.