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International Electronic Journal of Mathematics Education

Semiotic Conflicts in the Learning of Proportionality: Analysis of a Teaching Experience in Primary Education
María Burgos 1 * , Juan D. Godino 1
1 Universidad de Granada, SPAIN
* Corresponding Author
AMA 10th edition
In-text citation: (1), (2), (3), etc.
Reference: Burgos M, Godino JD. Semiotic Conflicts in the Learning of Proportionality: Analysis of a Teaching Experience in Primary Education. INT ELECT J MATH ED. 2020;15(3), em0588. https://doi.org/10.29333/iejme/7943
APA 6th edition
In-text citation: (Burgos & Godino, 2020)
Reference: Burgos, M., & Godino, J. D. (2020). Semiotic Conflicts in the Learning of Proportionality: Analysis of a Teaching Experience in Primary Education. International Electronic Journal of Mathematics Education, 15(3), em0588. https://doi.org/10.29333/iejme/7943
Chicago
In-text citation: (Burgos and Godino, 2020)
Reference: Burgos, María, and Juan D. Godino. "Semiotic Conflicts in the Learning of Proportionality: Analysis of a Teaching Experience in Primary Education". International Electronic Journal of Mathematics Education 2020 15 no. 3 (2020): em0588. https://doi.org/10.29333/iejme/7943
Harvard
In-text citation: (Burgos and Godino, 2020)
Reference: Burgos, M., and Godino, J. D. (2020). Semiotic Conflicts in the Learning of Proportionality: Analysis of a Teaching Experience in Primary Education. International Electronic Journal of Mathematics Education, 15(3), em0588. https://doi.org/10.29333/iejme/7943
MLA
In-text citation: (Burgos and Godino, 2020)
Reference: Burgos, María et al. "Semiotic Conflicts in the Learning of Proportionality: Analysis of a Teaching Experience in Primary Education". International Electronic Journal of Mathematics Education, vol. 15, no. 3, 2020, em0588. https://doi.org/10.29333/iejme/7943
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Burgos M, Godino JD. Semiotic Conflicts in the Learning of Proportionality: Analysis of a Teaching Experience in Primary Education. INT ELECT J MATH ED. 2020;15(3):em0588. https://doi.org/10.29333/iejme/7943

Abstract

In this paper, we analyse the results of an experience designed and implemented to evaluate the epistemic and cognitive conflicts identified in the study of proportionality, carried out by a group of 21 students in their last year of primary education. Initially the students exhibit difficulties to recognize situations where proportionality can be applied, to distinguish magnitudes, quantities and proportionality tables, and to identify procedures to solve proportionality problems other than the rule of three. Nevertheless, in the group discussion session, oriented to develop the dialogue and collective justification of the assessment tasks solutions, they are able to justify the methods employed, linking the rule of three with the equivalence of fractions and the proportionality relation.

Keywords

learning proportionality primary education didactic models epistemic and cognitive conflicts

References

  • Artigue, M. (2011). L’ingénierie didactique: un essai de synthèse. In C. Margolinas, M. Abboud-Blanchard, L. Bueno-Ravel, N. Douek, A. Fluckiger, P. Gibel, F. Vandebrouck, & F. Wozniak (Eds.), En amont et en aval des ingénieries didactiques (pp. 225-237). Grenoble: La pensée Sauvage.
  • Burgos, M., & Godino, J. D. (2018). Trabajando juntos situaciones introductorias de razonamiento proporcional en primaria. Análisis de una experiencia de enseñanza centrada en el profesor, en el estudiante y en el contenido. Bolema, 33(63), 389-410. https://doi.org/10.1590/1980-4415v33n63a19
  • Burgos, M., & Godino, J.D. (2019) Emergencia de razonamiento proto-algebraico en tareas de proporcionalidad en estudiantes de primaria. Educación Matemática, 31(3), 117-150 https://doi.org/10.24844/EM3103.05
  • Burgos, M., Castillo, M. J., Beltrán-Pellicer, P., Giacomone, B., & Godino, J. D. (2020). Análisis didáctico de una lección sobre proporcionalidad en un libro de texto de primaria con herramientas del enfoque ontosemiótico. Bolema, 34(66) (to appear).
  • Cramer, K., & Post, T. (1993). Connecting research to teaching proportional reasoning. Mathematics Teacher, 86(5), 404-407.
  • Dole, S., & Shield, M. (2008). The capacity of two Australian eighth-grade textbooks for promoting proportional reasoning. Research in Mathematics Education, 10(1), 19-35. https://doi.org/10.1080/14794800801915863
  • Fernández, C., & Llinares, S. (2011). De la estructura aditiva a la multiplicativa: Efecto de dos variables en el desarrollo del razonamiento proporcional. Infancia y Aprendizaje, 34(1), 67-80. https://doi.org/10.1174/021037011794390111
  • Fernández, C., & Llinares, S. (2012) Características del desarrollo del razonamiento proporcional en la Educación Primaria y Secundaria. Enseñanza de las Ciencias, 30(1), 129-142. https://doi.org/10.5565/rev/ec/v30n1.596
  • Fernandez, P., Caballero, P., & Fernandez, J. A. (2013). ¿Yerra el niño o yerra el libro de matemáticas? Números. Revista de Didáctica de las Matemáticas, 83, 131-148.
  • Ferrero, L., Martín, P., Alonso, G., & Bernal, E. (2015) Matemáticas 6. Aprender es crecer. Madrid: Grupo Anaya, S. A.
  • Fielding-Wells, J., Dole, S., & Makar, K. (2014). Inquiry pedagogy to promote emerging proportional reasoning in primary students. Mathematics Education Research Journal, 26, 47-77. https://doi.org/10.1007/s13394-013-0111-6
  • Gairín, J. M., & Escolano, R. (2009). Proporcionalidad aritmética: buscando alternativas a la enseñanza tradicional. Suma: Revista sobre Enseñanza y Aprendizaje de las Matemáticas, 62, 35-48.
  • Godino, J. D. Batanero, C., & Font, V. (2019). The onto-semiotic approach: implications for the prescriptive character of didactic. For the Learning of Mathematics, 39(1), 37-42.
  • Godino, J. D. Beltrán-Pellicer, P., Burgos, M., & Giacomone, B. (2017) Significados pragmáticos y configuraciones ontosemióticas en el estudio de la proporcionalidad. In J. M. Contreras, P. Arteaga, G. R. Cañadas, M. M. Gea, B. Giacomone & M. M. López-Martín (Eds.), Actas del segundo Congreso International Virtual sobre el Enfoque Ontosemiótico del conocimiento y la instrucción matemáticos. Available in www.enfoqueontosemiotico.ugr.es/civeos.html
  • Godino, J. D., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM, 39(1-2), 127-135. https://doi.org/10.1007/s11858-006-0004-1
  • Godino, J. D., Rivas, H., Arteaga, P., Lasa, A., & Wilhelmi, M. R. (2014) Ingeniería didáctica basada en el enfoque ontológico-semiótico del conocimiento y la instrucción matemáticos. Recherches en Didactique des Mathématiques, 34(2/3), 167-200.
  • Guacaneme, E. (2001). Estudio didáctico de la proporción y la proporcionalidad: Una aproximación a los aspectos matemáticos formales y a los textos escolares de matemáticas (Unpublished Master Dissertation). Universidad del Valle, Cali, Colombia.
  • Hilton, A., Hilton, G., Dole, S., & Goos, M. (2016) Promoting middle school students’ proportional reasoning skills through an ongoing professional development programme for teachers. Educational Studies in Mathematics, 92(2), 193-219. https://doi.org/10.1007/s10649-016-9694-7
  • Karplus, R., Pulos, S., & Stage, E. (1993). Early adolescents proportional reasoning on “rate” problems. Educational Studies in Mathematics, 14(3), 219-233. https://doi.org/10.1007/BF00410539
  • Kelly, A., Lesh, R., & Baek, J. (Eds.) (2008). Handbook of design research in methods in education. Innovations in science, technology, engineering, and mathematics learning and teaching. New York, NY: Routledge.
  • Lamon, S. (2007). Rational number and proportional reasoning. Toward a theoretical framework for research. In F. K. Lester (Ed.). Second handbook of research on mathematics teaching and learning. (pp. 629-667). Charlotte, NC: NCTM and IAP.
  • Lesh, R., Post, T., & Behr, M. (1988). Proportional reasoning. In J. Hiebert & M. Behr (Eds.), Number concepts and operations for the middle grades (pp. 93-118). Reston, VA: NCTM.
  • Lin, P. J. (2018). The development of students’ mathematical argumentation in a primary classroom. Educação & Realidade, 43(3), 1171-1192. https://doi.org/10.1590/2175-623676887
  • Lin, P. J., & Tai, W-H. (2016). Enhancing students’ mathematical conjecturing and justification in third-grade classrooms: the sum of even/odd numbers. Journal of Mathematics Education, 9(1), 1-15.
  • Modestou, M., & Gagatsis, A. (2010). Cognitive and metacognitive aspects of proportional reasoning. Mathematical Teaching and Learning, 12(1), 36-53. https://doi.org/10.1080/10986060903465822
  • Oller, A. M. (2012). Proporcionalidad aritmética: Una propuesta didáctica para alumnos de secundaria. Tesis doctoral. Universidad de Valladolid, Spain.
  • Rezat, S. (2010). The utilization of mathematics textbooks as instruments of learning. In V. Durand-Guerrier, S. Soury-Lavergne & F. Arzarello (Eds.), Proceedings of CERME 6, Working Group 7 (pp. 1260-1269). Lyon: Institute National de Recherche Pédagogique.
  • Riley, K. (2010). Teachers’ understanding of proportional reasoning. In P. Brosnan, D. B. Erchick, & L. Flevares (Eds.), Proceedings of the 32nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1055-1061). Columbus, OH: The Ohio State University.
  • Sánchez, E. A. (2013). Razones, proporciones y proporcionalidad en una situación de reparto: Una mirada desde la teoría antropológica de lo didáctico. Revista Latinoamericana de Investigación en Matemática Educativa, 16(1), 65-97.
  • Singh, P. (2000) Understanding the concepts of proportion and ratio constructed by two grade six students, Educational Studies in Mathematics, 43(3), 271-292. https://doi.org/10.1023/A:1011976904850
  • Streefland, L. (1985) Search for roots of ratio: some thoughts on the long term learning process (towards… a theory) part II: the outline of the long term learning process. Educational Studies in Mathematics, 16(1), 75-94. https://doi.org/10.1007/BF00354884
  • Stylianides, A., Beda, K., & Morselli, F. (2016) Proof and Argumentation in Mathematics Education Research. In A. Gutiérrez, G. Leder & Boero, P. (Eds.). Second Handbook of Research on the Psychology of Mathematics Education: the journey continues (pp. 315-351). Rotterdam: Sense Publishing. https://doi.org/10.1007/978-94-6300-561-6_9

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