Skip to main navigation menu Skip to main content Skip to site footer
Logo Revista Latinoamericana de Investigación en Matemática Educativa

Artículos

Vol. 21 No. 2 (2018): July

LEARNING PATHWAY OF LENGTH AND ITS MEASUREMENT AS A CONCEPTUAL INSTRUMENT USED BY FUTURE TEACHERS

DOI
https://doi.org/10.12802/relime.18.2124
Submitted
November 4, 2022
Published
2018-06-25

Abstract

The objective of this work is to characterize the use of a learning trajectory of length and its measurement as a conceptual instrument to favor the acquisition of the teaching competence "to look professionally" at children's mathematical thinking. Participated 64 students of the early childhood education teacher career who followed a teaching module. This module was articulated around a learning trajectory about length and its measurement, so that future teachers would use it as a conceptual instrument to describe and interpret the responses of children in early childhood education to teaching-learning situations (first scheme instrumental action) and propose tasks based on the inferred understanding (second instrumental action scheme). The results show that there are students who are preparing to be teachers who do not develop any instrumental action scheme, and others develop the first scheme and some, both; this provides evidence of the acquisition of the aforementioned competence.

References

  1. Barnhart, T., & van Es, E. (2015). Studying teacher noticing: examining the relationship among preservice science teachers’ ability to attend, analyze and respond to student thinking. Teaching and Teacher Education, 45, 83–93. DOI: https://dx.doi.org/10.1016/j.tate.2014.09.005
  2. Choy, B.H. (2016). Snapshots of mathematics teacher noticing during task design. Mathematics Education Research Journal, 28, 421-440. DOI: https://dx.doi.org/10.1007/s13394-016-0173-3
  3. Clements, D. H. (2010). Teaching length measurement: Research challenges. School Science and Mathematics, 99 (1), 5–11. DOI: https://dx.doi.org/10.1111/j.1949-8594.1999.tb17440.x
  4. Clements, D., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6 (2), 81-89. DOI: https://dx.doi.org/10.1207/s15327833mtl0602_1
  5. Confrey, J., Maloney, A. P., Wilson, P. H., & Nguyen, K. H. (2010). Understanding over time: The cognitive underpinnings of learning trajectories. In annual meeting of the American Education Research Association, Denver, CO, USA.
  6. Drijvers, P., Kieran, C., & Mariotti, M.A. (2010). Integrating technology into mathematics education: Theoretical perspectives. In C. Hoyles y J.B. Lagrange (Eds.), Mathematics education and technology: Rethinking the terrain (pp. 89-132). New York, USA: Springer.
  7. Drijvers, P., & Trouche, L. (2008). From artifacts to instruments: A theoretical framework behind the orchestra metaphor. In G. W. Blume & M. K. Heid (Eds.), Research on technology and the teaching and learning of mathematics: Vol. 2. Cases and perspectives (pp. 363-392). Charlotte, NC, USA: Information Age.
  8. Ellis, S., Siegler, R. S., & Van Voorhis, F. E. (2003). Developmental changes in children’s understanding of measurement procedures and principles. Paper presented at the Society for Research in Child Development, Tampa, FL, USA.
  9. Gupta, D., Soto, M., Dick, L., Broderick, S.D., & Appelgate, M. (2018). Noticing and deciding the next steps for teaching: A cross-university study with elementary pre-service teachers. In G.J. Stylianides & K. Hino (eds.). Research advances in the mathematical education of pre-service elementary teachers, ICME-13 Monographs (pp. 261-275), Cham, Germany: Springer.
  10. 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.
  11. Krupa, E. E., Huey, M., Lesseig, K., Casey, S., & Monson, D. (2017). Investigating secondary preservice teacher noticing of studets’ mathematical thinking. In E.O. Schack et al. (Eds.). Teacher Noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks (pp. 49-71). Cham, Germany: Springer.
  12. Llinares, S. (2004). La generación y uso de instrumentos para la práctica de enseñar matemáticas en educación primaria. UNO. Revista de Didáctica de la Matemática, 36, 93-115.
  13. Mason, J. (2002). Researching your own practice: The discipline of noticing. London, U.K.: Routledge Falmer.
  14. NCTM (2000). Principles and Standards for School Mathematics. Reston, VA, USA: NCTM.
  15. Nunes, T., & Bryant, P. E. (1996). Children doing mathematics. Cambridge, MA, USA: Blackwell.
  16. Parks, A.M., & Wager, A.A. (2015). What knowledge is shaping teacher preparation in early childhood mathematics? Journal of Early Childhood Teacher Education 36 (2), 124-141. DOI: https://dx.doi.org/10.1080/10901027.2015.1030520
  17. Piaget, J. (1972). Judgment and reasoning in the child. MD, USA: Littlefield, Adams.
  18. Rabardel, P. (1995). Les hommes et les technologies: approche cognitive des instruments contemporains. Paris, France: Armand Colin.
  19. 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), 305-1329. DOI: https://dx.doi.org/10.1007/s10763-014-9544-y
  20. 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. DOI: https://dx.doi.org/10.1007/s11858-015-0737-9
  21. Sarama, J., & Clements, D. (2009). Early Childhood Mathematics Education Research. Learning Trajectories for Young Children. London and New York, UK and USA: Routledge. Schack, E.O., Fisher,
  22. M.H., Thomas, J.N., Eisenhardt, S., Tassell, J., & Yoder, M. (2013). Prospective elementary school teachers’ professional noticing of children’s early numeracy. Journal of Mathematics Teacher Education 16 (5), 379-397. DOI: https://dx.doi.org/10.1007/s10857-013-9240-9
  23. Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (Eds.) (2011). Mathematics teacher noticing: Seeing through teachers’ eyes. New York, USA: Routledge.
  24. Skoumpourdi, C. (2015). Kindergartners measuring length. In K. Krainer & N. Vondrová (Eds.), Proceedings of the Ninth Conference of the European Society for Research in Mathematics Education (CERME 9), (pp. 89-1995). Prague, Czech Republic: Charles University.
  25. Son, J. (2013). How preservice teachers interpret and respond to student errors: ratio and proportion in similar rectangles. Educational Studies in Mathematics, 84 (1), 49-70. DOI: https://dx.doi.org/10.1007/s10649-013-9475-5
  26. Stahnke, R., Schueler, S., & Roeskem-Winter, B. (2016). Teachers’ perception, interpretation, and decision-making: a systematic review of empirical mathematics education research. ZDM Mathematics Education 48, 1-17. DOI: https://dx.doi.org/10.1007/s11858-016-0775-y
  27. Stephan, M., Bowers, J., Cobb, P., & Gravemeijer, K. P. E. (2003). Supporting students’ development of measuring conceptions: Analyzing students’ learning in social context (Vol. 12). Reston, VA, USA: National Council of Teachers of Mathematics.
  28. Strauss, A., & Corbin, J. (1994). Grounded theory methodology. Handbook of Qualitative Research, 17, 273-85.
  29. Szilagyi, J., Clements, D.H., & Sarama, J. (2013). Young children’s understanding of length measurement: Evaluating a learning trajectory. Journal for Research in Mathematics Education, 44 (3), 581-620. DOI: https://dx.doi.org/10.5951/jresematheduc.44.3.0581
  30. 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. DOI: https://dx.doi.org/10.3102/0013189X12442801
  31. Thomas, J., & Tabor, P.D. (2012). Developing quantitative mental imagery. Teaching Children Mathematics, 19 (3), 174-183.
  32. Trouche, L. (2004). Managing the complexity of human/machine interactions environments: Guiding student's command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9 (3), 281-307. DOI: https://dx.doi.org/10.1007/s10758-004-3468-5-vanden
  33. Heuvel-Panhuizen, M., & Elia, I. (2011). Kindergartners’ performance in length measurement and the effect of picture book reading. ZDM Mathematics Education, 43, 621–635. DOI: https://dx.doi.org/10.1007/s11858-011-0331-8
  34. 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, 10 (1), 77-101. DOI: https://dx.doi.org/10.1007/BF03172796
  35. Wilson, P.H., Mojica, G., & Confrey, J. (2013). Learning trajectories in teacher education: Supporting teachers’ understanding of students’ mathematical thinking. Journal of Mathematical Behavior, 32 (2), 103-121. doi: 10.1016/j.jmathb.2012.12.003
  36. Wilson, P. H., Sztajn, P., Edgington, C., & Confrey, J. (2014). Teachers’ use of their mathematical knowledge for teaching in learning a mathematics learning trajectory. Journal of Mathematics Teacher Education, 17 (2), 149-175. doi: 10.1007/s10857-013-9256-1
  37. Wilson, P.H., Sztajn, P., Edgington, C., & Myers, M. (2015). Teachers’ use of a learning trajectory in student-centered instructional practices. Journal of Teacher Education, 66 (3), 227-244. DOI: https://dx.doi.org/10.1177/0022487115574104

Downloads

Download data is not yet available.

Similar Articles

1 2 3 4 5 6 7 8 9 10 > >> 

You may also start an advanced similarity search for this article.