Three semiotic representations that give meaning to the learning of the concept of number: Proposal of a didactic strategy for preschoolers
Main Article Content
Keywords
Didactic strategy, Triads of significance, Number concept, Semiotic representations
Abstract
The number is a fascinating and endless concept that has been researched as a mathematical, psychological, and philosophical object. Numerous studies describe cognitively the ease and obstacles involved in acquiring cardinal numbers and ordinal numbers, but very few propose didactic strategies to achieve numerical learning. This research proposes a didactic strategy for learning with meaning the concept of number based on semiotic representations of graphic type, symbolic and semantic results obtained as a result of a longitudinal study for three consecutive years with the same preschool population from 3 to 5 years explained with multiple examples so that teachers can design and apply activities.
References
Benoit, L., Lehalle, H., & Jouen, F. (2004). Do young children acquire number words through subitizing or counting? Cognitive Development, 19(3), 291–307. https://doi. org/10.1016/j.cogdev.2004.03.005
Carey, S., Shusterman, A., Haward, P., & Distefano, R. (2017). Do analog number representations underlie the meanings of young children’s verbal numerals? Cognition, 168, 243–255. https://doi. org/10.1016/j.cognition.2017.06.022
Cicres, J., & Llach, S. (2019). ¿Para qué sirven los dictados? Representaciones de los futuros maestros de primaria. Didáctica. Lengua y Literatura, 31, 47–63. https://doi. org/10.5209/dida.65937
Colomé, À., & Noël, M. P. (2012). One first? Acquisition of the cardinal and ordinal uses of numbers in preschoolers. Journal of Experimental Child Psychology, 113(2), 233–247. https://doi.org/10.1016/j. jecp.2012.03.005
D’Amore, B. (2006). Objetos, Significados, Representaciones Semioticas y Sentido. 177–195.
D’Amore, B. (2008). Epistemología, didáctica de la matemática y prácticas de enseñanza. Enseñanza de La Matemática. Revista de La ASOVEMAT, 17(1), 87–106. www. dm.unibo.it/rsddm
D’amore, B., Fandiño, M., & Lori, M. (2013). La semiótica en la didactica de la matemática. p.181.
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1–2), 103–131. https:// doi.org/10.1007/s10649-006-0400-z
Duval, R. (2017a). Semiosis Y Pensamiento Humano (Segunda Ed). Editorial Universidad del Valle.
Duval, R. (2017a). Semiosis Y Pensamiento Humano (Segunda Ed). Editorial Universidad del Valle.
Elliot, J., & Manzano, P. (2005). El cambio educativo desde la investigación (p. 184). Ediciones Morata.
Fandiño, M. (2010). Multiples aspectos del aprendizaje de la matemática: evaluar e intervenir en forma mirada y especifica. Editorial Magisterio.
Fazio, L. K., Bailey, D. H., Thompson, C. A., & Siegler, R. S. (2014). Relations of different types of numerical magnitude representations to each other and to mathematics achievement. Journal of Experimental Child Psychology, 123(1), 53–72. https://doi.org/10.1016/j. jecp.2014.01.013
García-Baró, M. (1993). CATEGORIAS INTENCIONALIDAD Y NUMEROS (U. C. Departamento de filosofía (ed.); Primera Ed). Editorial Tecnos S.A.
Geary, D. C., & Hoard, M. K. (2001). Numerical and arithmetical deficits in learning-disabled children: Relation to dyscalculia and dyslexia. Aphasiology, 15(7), 635–647. https://doi. org/10.1080/02687040143000113
Gelman, R., & Butterworth, B. (2005). Number and language: How are they related? Trends in Cognitive Sciences, 9(1), 6–10. https://doi.org/10.1016/j.tics.2004.11.004
Godino, J. (2003). Teoría de las Funciones Semióticas. Facultad de Educación Universidad de Granada, p.318. https://doi. org/http://dx.doi.org/10.4330/wjc.v8.i7.383
Godino, J., & Batanero, C. (1994). Significado institucional y personal de los objetos matemáticos. Recherches En Didactique Des Mathématiques, 14(3), 325–335.
Goffin, C., & Ansari, D. (2016). Beyond magnitude: Judging ordinality of symbolic number is unrelated to magnitude comparison and independently relates to individual differences in arithmetic. Cognition, 150, 68–76. https://doi. org/10.1016/j.cognition.2016.01.018
González-Moreno, C. X., Solovieva, Y., & Quintanar-Rojas, L. (2012). Neuropsicología y psicología históricocultural: Aportes en el ámbito educativo. Rev. Fac. Med., 60(3), 221–231.
Guerrero-Ortiz, C., Mejía-Velasco, H. R., & Camacho-Machín, M. (2016). Representations of a mathematical model as a means of analysing growth phenomena. Journal of Mathematical Behavior, 42, 109–126. https://doi. org/10.1016/j.jmathb.2016.03.001
Hernandez, R., Fernandez, C., & Baptista, M. (2010). METODOLOGÍA DE LA INVESTIGACIÓN (Quinta Edi). McGraw Hill.
Hernández, R., Fernández, C., & Baptista, M. (2010). Metodología de la investigación (Quinta edi).
Husserl, E. (1972). On the concept of number: Psychological analysis. Philosophia Mathematica, s1-9(1), 52. https://doi. org/10.1093/philmat/s1-9.1.44
Kelly S, M. (2002). The construction of number concepts. Cognitive Development, 17(3– 4), 1345–1363.
Lyons, I. (2015). Numbers and Number Sense. In International Encyclopedia of the Social & Behavioral Sciences: Second Edition (Second Edi, Vol. 17). Elsevier. https://doi. org/10.1016/B978-0-08-097086-8.57031-7
Lyons, I. M., Vogel, S. E., & Ansari, D. (2016). On the ordinality of numbers: A review of neural and behavioral studies. In Progress in Brain Research (1st ed., Vol. 227). Elsevier B.V. https://doi.org/10.1016/ bs.pbr.2016.04.010
Lyons, Ian M., & Ansari, D. (2015). Foundations of Children’s Numerical and Mathematical Skills: The Roles of Symbolic and Nonsymbolic Representations of Numerical Magnitude. In Advances in Child Development and Behavior (1st ed., Vol. 48). Elsevier Inc. https://doi.org/10.1016/ bs.acdb.2014.11.003
Martins‐Mourão, A., & Cowan, R. (1998). The emergence of additive composition of number. Educational Psychology, 18(4), 377–389. https://doi. org/10.1080/0144341980180402
Meyer, C., Barbiers, S., & Weerman, F. (2018). Ordinals are not as easy as one, two, three: The acquisition of cardinals and ordinals in Dutch. Language Acquisition, 25(4), 392– 417. https://doi.org/10.1080/10489223.201 7.1391266
Mou, Y., Zhang, B., Piazza, M., & Hyde, D. C. (2021). Comparing set-to-number and number-to-set measures of cardinal number knowledge in preschool children using latent variable modeling. Early Childhood Research Quarterly, 54, 125–135. https:// doi.org/10.1016/j.ecresq.2020.05.016
Narens, L., & Luce, R. D. (1986). Measurement. The Theory of Numerical Assignments. Psychological Bulletin, 99(2), 166– 180. https://doi.org/10.1037/0033- 2909.99.2.166
Öçal, T., & Kızıltaş, E. (2019). The number zero: preschool teachers’ perceptions and teaching practices: a Turkish sample. Education 3-13, 47(6), 705–716. https:// doi.org/10.1080/03004279.2018.1521860
Peters, L., Bulthé, J., Daniels, N., Op de Beeck, H., & De Smedt, B. (2018). Dyscalculia and dyslexia: Different behavioral, yet similar brain activity profiles during arithmetic. NeuroImage: Clinical, 18(March), 663–674. https://doi.org/10.1016/j.nicl.2018.03.003
Radford, L. (2006). Introducción Semiótica y Educación Matemática. Relime, Vlumen esp(2), 7–21. http://funes.uniandes.edu. co/9699/1/Radford2006Semiotica.pdf
Rapin, I. (2016). Dyscalculia and the Calculating Brain. Pediatric Neurology, 61, 11–20. https://doi.org/10.1016/j. pediatrneurol.2016.02.007
Slusser, E. B., & Sarnecka, B. W. (2011). Find the picture of eight turtles: A link between children’s counting and their knowledge of number word semantics. Journal of Experimental Child Psychology, 110(1), 38–51. https://doi.org/10.1016/j. jecp.2011.03.006
Stock, P., Desoete, A., & Roeyers, H. (2009). Mastery of the counting principles in toddlers: A crucial step in the development of budding arithmetic abilities? Learning and Individual Differences, 19(4), 419–422. https://doi.org/10.1016/j.lindif.2009.03.002
Vukovic, R. K., & Lesaux, N. K. (2013). The relationship between linguistic skills and arithmetic knowledge. Learning and Individual Differences, 23(1), 87–91. https://doi.org/10.1016/j.lindif.2012.10.007
Wiese, H. (2003). Iconic and non-iconic stages in number development: The role of language. Trends in Cognitive Sciences, 7(9), 385–390. https://doi.org/10.1016/ S1364-6613(03)00192-X
Xu, C. (2019). Ordinal skills influence the transition in number line strategies for children in Grades 1 and 2. Journal of Experimental Child Psychology, 185, 109–127. https:// doi.org/10.1016/j.jecp.2019.04.020
Carey, S., Shusterman, A., Haward, P., & Distefano, R. (2017). Do analog number representations underlie the meanings of young children’s verbal numerals? Cognition, 168, 243–255. https://doi. org/10.1016/j.cognition.2017.06.022
Cicres, J., & Llach, S. (2019). ¿Para qué sirven los dictados? Representaciones de los futuros maestros de primaria. Didáctica. Lengua y Literatura, 31, 47–63. https://doi. org/10.5209/dida.65937
Colomé, À., & Noël, M. P. (2012). One first? Acquisition of the cardinal and ordinal uses of numbers in preschoolers. Journal of Experimental Child Psychology, 113(2), 233–247. https://doi.org/10.1016/j. jecp.2012.03.005
D’Amore, B. (2006). Objetos, Significados, Representaciones Semioticas y Sentido. 177–195.
D’Amore, B. (2008). Epistemología, didáctica de la matemática y prácticas de enseñanza. Enseñanza de La Matemática. Revista de La ASOVEMAT, 17(1), 87–106. www. dm.unibo.it/rsddm
D’amore, B., Fandiño, M., & Lori, M. (2013). La semiótica en la didactica de la matemática. p.181.
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1–2), 103–131. https:// doi.org/10.1007/s10649-006-0400-z
Duval, R. (2017a). Semiosis Y Pensamiento Humano (Segunda Ed). Editorial Universidad del Valle.
Duval, R. (2017a). Semiosis Y Pensamiento Humano (Segunda Ed). Editorial Universidad del Valle.
Elliot, J., & Manzano, P. (2005). El cambio educativo desde la investigación (p. 184). Ediciones Morata.
Fandiño, M. (2010). Multiples aspectos del aprendizaje de la matemática: evaluar e intervenir en forma mirada y especifica. Editorial Magisterio.
Fazio, L. K., Bailey, D. H., Thompson, C. A., & Siegler, R. S. (2014). Relations of different types of numerical magnitude representations to each other and to mathematics achievement. Journal of Experimental Child Psychology, 123(1), 53–72. https://doi.org/10.1016/j. jecp.2014.01.013
García-Baró, M. (1993). CATEGORIAS INTENCIONALIDAD Y NUMEROS (U. C. Departamento de filosofía (ed.); Primera Ed). Editorial Tecnos S.A.
Geary, D. C., & Hoard, M. K. (2001). Numerical and arithmetical deficits in learning-disabled children: Relation to dyscalculia and dyslexia. Aphasiology, 15(7), 635–647. https://doi. org/10.1080/02687040143000113
Gelman, R., & Butterworth, B. (2005). Number and language: How are they related? Trends in Cognitive Sciences, 9(1), 6–10. https://doi.org/10.1016/j.tics.2004.11.004
Godino, J. (2003). Teoría de las Funciones Semióticas. Facultad de Educación Universidad de Granada, p.318. https://doi. org/http://dx.doi.org/10.4330/wjc.v8.i7.383
Godino, J., & Batanero, C. (1994). Significado institucional y personal de los objetos matemáticos. Recherches En Didactique Des Mathématiques, 14(3), 325–335.
Goffin, C., & Ansari, D. (2016). Beyond magnitude: Judging ordinality of symbolic number is unrelated to magnitude comparison and independently relates to individual differences in arithmetic. Cognition, 150, 68–76. https://doi. org/10.1016/j.cognition.2016.01.018
González-Moreno, C. X., Solovieva, Y., & Quintanar-Rojas, L. (2012). Neuropsicología y psicología históricocultural: Aportes en el ámbito educativo. Rev. Fac. Med., 60(3), 221–231.
Guerrero-Ortiz, C., Mejía-Velasco, H. R., & Camacho-Machín, M. (2016). Representations of a mathematical model as a means of analysing growth phenomena. Journal of Mathematical Behavior, 42, 109–126. https://doi. org/10.1016/j.jmathb.2016.03.001
Hernandez, R., Fernandez, C., & Baptista, M. (2010). METODOLOGÍA DE LA INVESTIGACIÓN (Quinta Edi). McGraw Hill.
Hernández, R., Fernández, C., & Baptista, M. (2010). Metodología de la investigación (Quinta edi).
Husserl, E. (1972). On the concept of number: Psychological analysis. Philosophia Mathematica, s1-9(1), 52. https://doi. org/10.1093/philmat/s1-9.1.44
Kelly S, M. (2002). The construction of number concepts. Cognitive Development, 17(3– 4), 1345–1363.
Lyons, I. (2015). Numbers and Number Sense. In International Encyclopedia of the Social & Behavioral Sciences: Second Edition (Second Edi, Vol. 17). Elsevier. https://doi. org/10.1016/B978-0-08-097086-8.57031-7
Lyons, I. M., Vogel, S. E., & Ansari, D. (2016). On the ordinality of numbers: A review of neural and behavioral studies. In Progress in Brain Research (1st ed., Vol. 227). Elsevier B.V. https://doi.org/10.1016/ bs.pbr.2016.04.010
Lyons, Ian M., & Ansari, D. (2015). Foundations of Children’s Numerical and Mathematical Skills: The Roles of Symbolic and Nonsymbolic Representations of Numerical Magnitude. In Advances in Child Development and Behavior (1st ed., Vol. 48). Elsevier Inc. https://doi.org/10.1016/ bs.acdb.2014.11.003
Martins‐Mourão, A., & Cowan, R. (1998). The emergence of additive composition of number. Educational Psychology, 18(4), 377–389. https://doi. org/10.1080/0144341980180402
Meyer, C., Barbiers, S., & Weerman, F. (2018). Ordinals are not as easy as one, two, three: The acquisition of cardinals and ordinals in Dutch. Language Acquisition, 25(4), 392– 417. https://doi.org/10.1080/10489223.201 7.1391266
Mou, Y., Zhang, B., Piazza, M., & Hyde, D. C. (2021). Comparing set-to-number and number-to-set measures of cardinal number knowledge in preschool children using latent variable modeling. Early Childhood Research Quarterly, 54, 125–135. https:// doi.org/10.1016/j.ecresq.2020.05.016
Narens, L., & Luce, R. D. (1986). Measurement. The Theory of Numerical Assignments. Psychological Bulletin, 99(2), 166– 180. https://doi.org/10.1037/0033- 2909.99.2.166
Öçal, T., & Kızıltaş, E. (2019). The number zero: preschool teachers’ perceptions and teaching practices: a Turkish sample. Education 3-13, 47(6), 705–716. https:// doi.org/10.1080/03004279.2018.1521860
Peters, L., Bulthé, J., Daniels, N., Op de Beeck, H., & De Smedt, B. (2018). Dyscalculia and dyslexia: Different behavioral, yet similar brain activity profiles during arithmetic. NeuroImage: Clinical, 18(March), 663–674. https://doi.org/10.1016/j.nicl.2018.03.003
Radford, L. (2006). Introducción Semiótica y Educación Matemática. Relime, Vlumen esp(2), 7–21. http://funes.uniandes.edu. co/9699/1/Radford2006Semiotica.pdf
Rapin, I. (2016). Dyscalculia and the Calculating Brain. Pediatric Neurology, 61, 11–20. https://doi.org/10.1016/j. pediatrneurol.2016.02.007
Slusser, E. B., & Sarnecka, B. W. (2011). Find the picture of eight turtles: A link between children’s counting and their knowledge of number word semantics. Journal of Experimental Child Psychology, 110(1), 38–51. https://doi.org/10.1016/j. jecp.2011.03.006
Stock, P., Desoete, A., & Roeyers, H. (2009). Mastery of the counting principles in toddlers: A crucial step in the development of budding arithmetic abilities? Learning and Individual Differences, 19(4), 419–422. https://doi.org/10.1016/j.lindif.2009.03.002
Vukovic, R. K., & Lesaux, N. K. (2013). The relationship between linguistic skills and arithmetic knowledge. Learning and Individual Differences, 23(1), 87–91. https://doi.org/10.1016/j.lindif.2012.10.007
Wiese, H. (2003). Iconic and non-iconic stages in number development: The role of language. Trends in Cognitive Sciences, 7(9), 385–390. https://doi.org/10.1016/ S1364-6613(03)00192-X
Xu, C. (2019). Ordinal skills influence the transition in number line strategies for children in Grades 1 and 2. Journal of Experimental Child Psychology, 185, 109–127. https:// doi.org/10.1016/j.jecp.2019.04.020
Article Sidebar
Published
Mar 18, 2022
Article Details
How to Cite
1.
Three semiotic representations that give meaning to the learning of the concept of number: Proposal of a didactic strategy for preschoolers. bol.redipe [Internet]. 2022 Mar. 18 [cited 2024 Jul. 20];11(3):231-57. Available from: https://revista.redipe.org/index.php/1/article/view/1718
Section
Articles
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Authors will keep their copyright and guarantee the journal the right of first publication of their work, which will be simultaneously subject to the Creative Commons Recognition License that allows third parties to share the work whenever its author is indicated and his first publication this magazine.
Revista Boletín Redipe by Red Iberoamericana de Pedagogía is licensed under a Creative Commons Attribution 4.0 International License.
Author Biography
Fabio Durán Salas, University of San Buenaventura, Colombia
Doctoral candidate in educational sciences from the University of San Buenaventura (Colombia). Member of the ESINED research group (USB-Medellín).
How to Cite
1.
Three semiotic representations that give meaning to the learning of the concept of number: Proposal of a didactic strategy for preschoolers. bol.redipe [Internet]. 2022 Mar. 18 [cited 2024 Jul. 20];11(3):231-57. Available from: https://revista.redipe.org/index.php/1/article/view/1718