What the Teacher Must Master to Direct the Learning Process

Neel Baez Urena; Ramon Blanco Sanchez

doi:doi:10.11648/j.sr.20221004.12

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What the Teacher Must Master to Direct the Learning Process

Neel Baez Urena, Ramon Blanco Sanchez

Published in Science Research (Volume 10, Issue 4)

Received: 24 May 2022 Accepted: 15 June 2022 Published: 16 September 2022

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Abstract

Determining what the Mathematics teacher must master is a fundamental aspect to specify what the correct preparation of said teacher should be, which is a widely debated topic, on which there are various proposals for action, in each of which can be find positive aspects, despite the different approaches found in the specialized literature, at least there is consensus that such preparation must be composed of mathematical knowledge and didactic knowledge, which is supported by research, experiences and proposals aimed at achieving a good preparation of these professionals; several authors have specified the notion of Pedagogical Content Knowledge for the teaching of Mathematics, understanding as such the mastery of the mathematical content to be explained together with the appropriate didactic procedures to explain said content, other authors refer to the Specific Knowledge of the Content, as the “mathematical knowledge to teach”. The objective of this work is to scientifically argue the domain of epistemological and ontological characteristics of Mathematics, which can allow the teacher to establish the appropriate link between mathematical knowledge and didactic knowledge.

Published in	Science Research (Volume 10, Issue 4)
DOI	10.11648/j.sr.20221004.12
Page(s)	99-107
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Ontology, Epistemology, Mathematics, Teacher

References

[1]	Ball, D., Thames, M. & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education [Revista de Formación de Profesores], 59 (5), pp. 389-407. https://www.researchgate.net/publication/255647628_Content_Knowledge_for_Teaching_What_Makes_It_Special
[2]	Biembengut, M. & Hein, N. (2004). Modelación Matemática y los desafíos para enseñar Matemática. Educación Matemática. Vol. 16, nº. 002, pp. 105 -125. https://dialnet.unirioja.es/servlet/articulo?codigo=1159552
[3]	Byas, R & Blanco, R (2017). Didáctica de la Matemática en la formación docente. Santo Domingo. Edit. SEDUCA. Sistema Editorial Universitario Centroamericano. República Dominicana.
[4]	D’Amore B. (2001). Una contribución al debate sobre conceptos y objeto smatemáticos. Revista: UNO. [Barcelona, España]. 27, 51-76. Microsoft Word - Concetti e oggetti in spagnolo.doc (unibo.it).
[5]	D’Amore B. (2003). The noetic in mathematics. Scientia Pedagogica Experimentalis. (Gent, Belgio). 39, 1, pp. 75-82. Microsoft Word - 462 D'Amore The noetic in mathematics.doc (unibo.it).
[6]	D’Amore, B. y Fandiño-Pinilla, M. (2017). Reflexiones teóricas sobre las bases del enfoque ontosemiótico de la Didáctica de la Matemática. En J. M. Contreras, P. Arteaga, G. R. Cañadas, M. M. Gea, B. Giacomone y M. M. López-Martín (Eds.), Actas del Segundo Congreso International Virtual sobre el Enfoque Ontosemiótico del Conocimiento y la Instrucción Matemáticos. Disponible en: enfoque ontosemiotico.ugr.es/civeos.html Microsoft Word - 274 DAmore Fandino Reflexiones teoricas EOS - Copia (unibo.it).
[7]	Davydov, V. V. (1990). Types of Generalization In Jeremy Kilpatrick (Ed.) Instruction: Logical and Psychological Problems in the Structuring of School Curricula. Virginia: National Council of Teachers of Mathematics. Types of generalization in instruction: logical and psychological problems in the structuring of school curricula (Libro, 1990).
[8]	De Olivera, L. & Cheng, D. (2011). Language and the multisemiotic nature of Mathematics. The Reading Matrix. Volume 11, Number 3, pp. 255-267. ERIC - EJ967315 - Language and the Multisemiotic Nature of Mathematics, Reading Matrix: An International Online Journal, 2011-Sep (ed.gov).
[9]	Duval R. (1998). Signe et objet (I). Trois grandes étapes dans la problématique des rapports entre répresentation set objet. Annales de Didactique et de Sciences Cognitives. 6, 139-163. 1998 Annales de didactique et de sciences cognitives. V. 6. p. 139-163. Signe et objet (1): Trois grandes étapes dans la problématique des rapports entre représentation et objet. (univ-irem.fr).
[10]	Duval, R. (2006). Un tema crucial en la educación matemática: La habilidad para cambiar el registro de representación. La Gaceta de la Real Sociedad Matemática Española, 9 (1), 143-168. C:\lagaceta\gaceta91\seccion\educacion\educacion91.DVI (rsme.es).
[11]	Elia, I. & Spyrou, P. (2006). How students conceive function: a triarchic conceptual-semiotic model of the understanding of a complex concept. The Montana Mathematics Enthusiast, The Montana Council of Teachers of Mathematics. ISSN 1551-3440, Vol. 3, no. 2, pp. 256-272.
[12]	Cunningham, R. & Roberts, A. (2010). Reducing the mismatch of geometry concept definitions and concept images Held by Pre-Service Teachers. The Journal. Vol. 1. Pp. 2-17. [www.k-12prep.math.ttu.edu]. Microsoft Word - Acr17C3.doc (ed.gov).
[13]	Even, R., & Ball, D. (2009). The professional education and development of teachers of mathematics: The 15th ICMI Study. New York: Springer. The Professional Education and Development of Teachers of Mathematics - The 15th ICMI Study \| Ruhama Even \| Springer.
[14]	Fandiño-Pinilla, M. (2011). Per una buona didattica ènecessario un buon Sapere. Bollettino dei Docenti di Matematica. 62, 51-58. Microsoft Word - 188 FANDINO Per una buona didattica uun buon Sapere (unibo.it).
[15]	Girnat, B. (2011). Ontological beliefs and their impact on teaching elementary geometry. PNA, 5 (2), 37-48. Ontological beliefs and their impact on teaching elementary geometry \| PNA. Revista de Investigación en Didáctica de la Matemática (ugr.es).
[16]	Godino, J. (2002). Un enfoque ontológico y semiótico de la cognición matemática. Recherches en Didactique des Mathématiques, Vol. 22, nº 2.3, pp. 237-284. Godino Vol. 22, n° 2.3, pp. 237-284 (ugr.es).
[17]	Godino, J. (2009). Categorías de análisis de los conocimientos del profesor de Matemáticas, Revista Unión, SSN: 1815-0640 (en línea), Número 20, pp. 13-31. Microsoft Word - 20-01-firma invitada.doc (ugr.es).
[18]	Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42 (2), 371–406. hillrowanball.pdf (umich.edu).
[19]	Hitt, F. (2003). Una reflexión sobre la construcción de conceptos matemáticos en ambientes con tecnología. Boletín de la Asociación Matemática Venezolana, Vol. X, No. 2. pp 213-223 fernandoHitt.tex (emis.de).
[20]	Medina. M. (2018). Estrategias metodológicas para el desarrollo del pensamiento lógico-matemático. Didasc@lia: Didáctica y Educación. Vol. IX.ISSN 2224-2643. pp 125-132. Estrategias metodológicas para el desarrollo del pensamiento lógico-matemático - Dialnet (unirioja.es).
[21]	Moreno-Armella, L. & Sriraman, B. (2010). Symbol sand mediation in Mathematics education. Advances in Mathematics Education, DOI 10.1007/978-3-642-00742-2_22,©Springer-Verlag. Berlin Heidelberg. Theories of Mathematics Education: Seeking New Frontiers - Google Books.
[22]	Ottmar, E. & Rimm-Kaufman. (2015). Mathematical knowledge for teaching, standards based mathematics teaching practices, and student achievement in the context. American Educational Research Journal. pp. 1-36. DOI: 10.3102/0002831215579484.
[23]	Pérez, O. (2020). La formación y desarrollo conceptual en el Cálculo Diferencial y el Álgebra Lineal en las carreras de ingeniería. Revista Paradigma: Vol XLI, pp. 571-599. https://doi.org/10.37618/PARADIGMA.1011-2251.
[24]	Radford, L. (2001). Factual, Contextual and symbolic generalizations in algebra. In M. van den Heuvel-Panhuizen (Ed.) Proc. 25th Conf. of the Int. Group for the Psychology of Mathematics Education, (Vol. 4, pp. 81-88). Utrecht, The Netherlands: PME. and Symbolic Generalizations in Algebra \| Luis Radford - Academia.edu.
[25]	Radford, L. (2010). Layers of generality and types of generalization in pattern activities. PNA, 4 (2), pp. 37-62. DOI 091217.
[26]	Radford, L. (2013). On semiotics and education. Éducation et Didactique, 7 (1), 185-204. On Semiotics and Education [*] \| Cairn.info.
[27]	Riccomini, P. Smith, G. Hughes, E & Fries, M. (2015). The Language of Mathematics: The importance of teaching and learning mathematical vocabulary, Reading & Writing Quarterly, 31: 3, 235-252, DOI: 10.1080/10573569.2015.1030995.
[28]	Vilanova, S. (2001). “La Educación Matemática. El papel de la resolución de problemas en el aprendizaje”. Revista Iberoamericana de Educación, OEI. Versión en línea: http://www.campus-oei.org/revista/did_mat10.htm.
[29]	Vygotsky, L. (1986). Thought and language, Kozulin, A. (ed. and trans.), Cambridge, MA, MIT Press. DjVu Document (s-f-walker.org.uk).
[30]	Winsløw, C. (2003). Semiotic and discursive variables in cas-based didactical engineering. Educational Studies in Mathematics. Kluwer Academic Publishers. 52: 271–288 Semiotic and discursive variables in cas-based didactical engineering \| Springer Link.

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Neel Baez Urena, Ramon Blanco Sanchez. (2022). What the Teacher Must Master to Direct the Learning Process. Science Research, 10(4), 99-107. https://doi.org/10.11648/j.sr.20221004.12

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Neel Baez Urena; Ramon Blanco Sanchez. What the Teacher Must Master to Direct the Learning Process. Sci. Res. 2022, 10(4), 99-107. doi: 10.11648/j.sr.20221004.12

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AMA Style

Neel Baez Urena, Ramon Blanco Sanchez. What the Teacher Must Master to Direct the Learning Process. Sci Res. 2022;10(4):99-107. doi: 10.11648/j.sr.20221004.12

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@article{10.11648/j.sr.20221004.12,
  author = {Neel Baez Urena and Ramon Blanco Sanchez},
  title = {What the Teacher Must Master to Direct the Learning Process},
  journal = {Science Research},
  volume = {10},
  number = {4},
  pages = {99-107},
  doi = {10.11648/j.sr.20221004.12},
  url = {https://doi.org/10.11648/j.sr.20221004.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sr.20221004.12},
  abstract = {Determining what the Mathematics teacher must master is a fundamental aspect to specify what the correct preparation of said teacher should be, which is a widely debated topic, on which there are various proposals for action, in each of which can be find positive aspects, despite the different approaches found in the specialized literature, at least there is consensus that such preparation must be composed of mathematical knowledge and didactic knowledge, which is supported by research, experiences and proposals aimed at achieving a good preparation of these professionals; several authors have specified the notion of Pedagogical Content Knowledge for the teaching of Mathematics, understanding as such the mastery of the mathematical content to be explained together with the appropriate didactic procedures to explain said content, other authors refer to the Specific Knowledge of the Content, as the “mathematical knowledge to teach”. The objective of this work is to scientifically argue the domain of epistemological and ontological characteristics of Mathematics, which can allow the teacher to establish the appropriate link between mathematical knowledge and didactic knowledge.},
 year = {2022}
}

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TY  - JOUR
T1  - What the Teacher Must Master to Direct the Learning Process
AU  - Neel Baez Urena
AU  - Ramon Blanco Sanchez
Y1  - 2022/09/16
PY  - 2022
N1  - https://doi.org/10.11648/j.sr.20221004.12
DO  - 10.11648/j.sr.20221004.12
T2  - Science Research
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AB  - Determining what the Mathematics teacher must master is a fundamental aspect to specify what the correct preparation of said teacher should be, which is a widely debated topic, on which there are various proposals for action, in each of which can be find positive aspects, despite the different approaches found in the specialized literature, at least there is consensus that such preparation must be composed of mathematical knowledge and didactic knowledge, which is supported by research, experiences and proposals aimed at achieving a good preparation of these professionals; several authors have specified the notion of Pedagogical Content Knowledge for the teaching of Mathematics, understanding as such the mastery of the mathematical content to be explained together with the appropriate didactic procedures to explain said content, other authors refer to the Specific Knowledge of the Content, as the “mathematical knowledge to teach”. The objective of this work is to scientifically argue the domain of epistemological and ontological characteristics of Mathematics, which can allow the teacher to establish the appropriate link between mathematical knowledge and didactic knowledge.
VL  - 10
IS  - 4
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Author Information

Neel Baez Urena

Department of Mathematics, Autonomous University of Santo Domingo, Santo Domingo, Dominican Republic
Ramon Blanco Sanchez

Department of Mathematics, University of Camagüey, Camagüey, Cuba

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APA Style

Neel Baez Urena, Ramon Blanco Sanchez. (2022). What the Teacher Must Master to Direct the Learning Process. Science Research, 10(4), 99-107. https://doi.org/10.11648/j.sr.20221004.12

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ACS Style

Neel Baez Urena; Ramon Blanco Sanchez. What the Teacher Must Master to Direct the Learning Process. Sci. Res. 2022, 10(4), 99-107. doi: 10.11648/j.sr.20221004.12

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AMA Style

Neel Baez Urena, Ramon Blanco Sanchez. What the Teacher Must Master to Direct the Learning Process. Sci Res. 2022;10(4):99-107. doi: 10.11648/j.sr.20221004.12

Copy | Download

@article{10.11648/j.sr.20221004.12,
  author = {Neel Baez Urena and Ramon Blanco Sanchez},
  title = {What the Teacher Must Master to Direct the Learning Process},
  journal = {Science Research},
  volume = {10},
  number = {4},
  pages = {99-107},
  doi = {10.11648/j.sr.20221004.12},
  url = {https://doi.org/10.11648/j.sr.20221004.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sr.20221004.12},
  abstract = {Determining what the Mathematics teacher must master is a fundamental aspect to specify what the correct preparation of said teacher should be, which is a widely debated topic, on which there are various proposals for action, in each of which can be find positive aspects, despite the different approaches found in the specialized literature, at least there is consensus that such preparation must be composed of mathematical knowledge and didactic knowledge, which is supported by research, experiences and proposals aimed at achieving a good preparation of these professionals; several authors have specified the notion of Pedagogical Content Knowledge for the teaching of Mathematics, understanding as such the mastery of the mathematical content to be explained together with the appropriate didactic procedures to explain said content, other authors refer to the Specific Knowledge of the Content, as the “mathematical knowledge to teach”. The objective of this work is to scientifically argue the domain of epistemological and ontological characteristics of Mathematics, which can allow the teacher to establish the appropriate link between mathematical knowledge and didactic knowledge.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - What the Teacher Must Master to Direct the Learning Process
AU  - Neel Baez Urena
AU  - Ramon Blanco Sanchez
Y1  - 2022/09/16
PY  - 2022
N1  - https://doi.org/10.11648/j.sr.20221004.12
DO  - 10.11648/j.sr.20221004.12
T2  - Science Research
JF  - Science Research
JO  - Science Research
SP  - 99
EP  - 107
PB  - Science Publishing Group
SN  - 2329-0927
UR  - https://doi.org/10.11648/j.sr.20221004.12
AB  - Determining what the Mathematics teacher must master is a fundamental aspect to specify what the correct preparation of said teacher should be, which is a widely debated topic, on which there are various proposals for action, in each of which can be find positive aspects, despite the different approaches found in the specialized literature, at least there is consensus that such preparation must be composed of mathematical knowledge and didactic knowledge, which is supported by research, experiences and proposals aimed at achieving a good preparation of these professionals; several authors have specified the notion of Pedagogical Content Knowledge for the teaching of Mathematics, understanding as such the mastery of the mathematical content to be explained together with the appropriate didactic procedures to explain said content, other authors refer to the Specific Knowledge of the Content, as the “mathematical knowledge to teach”. The objective of this work is to scientifically argue the domain of epistemological and ontological characteristics of Mathematics, which can allow the teacher to establish the appropriate link between mathematical knowledge and didactic knowledge.
VL  - 10
IS  - 4
ER  -

Copy | Download