Vergnaud’s Additive Conceptual Field
an Overview of Brazilian Academic Dissertations from 2000 to 2021
DOI:
https://doi.org/10.58422/repesq.2023.e1426Keywords:
he State of art, Vergnaud, Conceptual field, Additive structuresAbstract
This research aimed to carry out a mapping of the Brazilian academic dissertations whose main focus was the Additive Conceptual Field proposed by Gérard Vergnaud. The methodology adopted was the State of the Art, using Google Scholar as a source, in the period from 2000 to 2021. On this basis, the keyword used was 'Vergnaud' and 'Additive Field', in which the results were located in the surroundings of Teaching and Education area of basic schooling. Twenty-two academic dissertations were found in this search. Academic dissertations in Education were predominant (54.53%) in fifteen Pos Graduate programs. The predominant school segment of the surveys were the early years of Elementary School (86.36%). As for the research subject, dissertations involving students were the most frequent (68.18%), followed by teachers (13.63%), textbooks (9.09%) and curriculum material (9.09%).
References
BITTAR, Marilena; MUNIZ, Cristiano Alberto. Mathematical learning from the perspective of conceptual field theory. Curitiba: Editora CRV, 2009.
BRASIL. Base Nacional Comum Curricular. Brasília: Secretaria de Educação Fundamental (MEC/SEF), 2017.
BRASIL Parâmetros Curriculares Nacionais: Matemática. Brasília: Secretaria de Educação Fundamental (MEC/SEF), 1997.
BRUN, J. Evolution of the relationships between the Psychology of Cognitive Development and the Didactics of Mathematics. Editora: Instituto Paiget. Lisboa, 1996.
DA ROSA, Marlusa Benedetti. Mathematics in the Early Years: Additive Field and Multiplicative Field as structuring concepts of Arithmetic and Algebra. Caderno de Aplicação, Porto Alegre. v. 32, n. 2, ago.-dez. 2019, p. 41-55.
MOREIRA, Marco Antonio. Vergnaud’s Conceptual Field theory, science teaching and research in this área. Investigações em Ensino de Ciências. v.7, n.1, 2002, p. 7-29. Avaiable in: <http://www.if.ufrgs.br/ienci/artigos/Artigo_ID80/v7_n1_a2002.pdf>. Acess in: 13 jul. 2021.
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SOARES, Magda. Alphabetization in Brazil: the State of Knowledge. Brasilia: INEP/MEC, 1989.
VERGNAUD, Gérard. The Theory of Conceptual Fields. In: BRUN, J. Evolution of the relationships between the Psychology of Cognitive Development and the Didactics of Mathematics. Editora: Instituto Paiget. Lisboa, 1996.
VERGNAUD, Gérard. The Theory of Conceptual Fields. Recherches en Didactique de Mathématiques, 1990, v. 10, n.2.3, p. 133-170. Pensée Sauvage: Grenoble, França.
VERGNAUD, Gérard. Multiplicative conceptual field: what and why? In: GUERSHON, H.; CONFREY, J. (Ed.). The development of multiplicative reasoning in the learning of mathematics. Albany, N.Y.: State University of New York Press, 1994. p. 41-59.
Appendix A – Academic Dissertations.
ALVES, Fabíola de Souza. There is an hour that we have learned to count by our head: a study on the construction of the number and the additive field in Early Childhood Education. 2016. 107f. Dissertation (Master in Education) – State University of Rio de Janeiro, Duque de Caxias, 2016.
ARAÚJO, Claudia Gomes. Additive Problems: A teaching proposal in the context of the game ‘Steals Mount’. 2015. 185f. Dissertação (Master in Education, Culture and Communication) - State University of Rio de Janeiro, Duque de Caxias, 2015.
AZEVEDO, Kelly de Lima. Board game with RPG elements “Adventure of a Magic Book”: contributions to mathematical education. 2017. 130f. Dissertation (Master Mathematical and Technological Education) - Federal University of Pernambuco, Ceará. 2017.
AZEVEDO, Simone Aparecida dos Anjos. The challenge of arguing in Mathematics classes: an investigation with first year students of Elementary School. 2019. 259f. Dissertation (Master in Mathematical Education) - Pontifical Catholic University of Sao Paulo, Sao Paulo. 2019.
BECK, Miguel Melendo. Additive field in the set of integers: a study from the theory of Conceptual Fields. 2019. 197f. Dissertation (Master in Education) - Federal University of Rio Grande do Sul, Rio Grande. 2019.
BECK, Vinicius Carvalho. Additive problems and algebraic thinking in the alphabetization cycle. 2015. 74f. Dissertation (Master in Education) - Federal University of Rio Grande do Sul, Rio Grande. 2015.
BRASIL, Isadora Gonçalves. Analyzing the mobilization of pedagogical knowledge of the 3rd year teacher (early years) in the field of Additive Structures. 2015. 99f. Dissertation (Master in Science Teaching) – Federal Rural University of Pernambuco, Pernambuco. 2015.
COSTA, Silvia Janine Rodrigues da. Mathematical learning of everyday life: action strategies in marble game. 2011. 137f. Dissertation (Master in Education). University of Vale do Itajai, Itajai, 2011.
DE SOUZA, César Augusto Pimentel. Alphabetization and Mathematical Literacy: perspectives and relationships between PNAIC and the textbook. 2017. Dissertation (Master in Mathematical Education) - Pontifical Catholic University of Sao Paulo, Sao Paulo. 2017.
DORNELES, Caroline Lacerda. Addition, subtraction and relational calculation: an intervention with students from PROEJA FIC/Elementary School. 2013. Dissertation (Master in Education) – Federal University of Rio Grande do Sul, Porto Alegre. 2013.
FAXINA, Josiane. Problem solving and the teaching of arithmetic concepts: perceptions of teachers from the early years of Elementary School. 2017. 167f. Dissertation (Master in Education) – São Paulo State University ‘Julio de Mesquita Filho’, Bauru. 2017.
FRANZOSI, Vito Rodrigues. Grouping and disagreements in the Multibase Application: A proposal to teach the concept of number and operations of the additive conceptual field. 2018. 141f. Dissertation (Master in Education for Science and Mathematics) - Federal Institute of Espirito Santo, Vitoria. 2018.
FURTUOSO, Patrícia. Analysis of the difficulties of oral respiratory students in problem solving of the additive concept. 2016. 109f. Dissertation (Master in Education) – State University of Maringá, Maringá, 2016.
GIOMBELLI, Cirlei. Implications of PNAIC formation on teachers’ understandings on the elaborations of mathematical concepts by children of the alphabetization cycle. 2016. 183f. Dissertation (Master in Education) - Federal University of Fronteira Sul, Chapeco. 2016.
KEHLER, Mirta Grisel García de. As numbers and operations are approached in textbooks of the mathematical alphabetization phase. 2012. 175f. Dissertation (Master in Education) - Federal University of Mato Grosso, Cuiabá. 2012.
LIMA, José Roberto de Campos. Algebraic thinking in the literacy cycle curriculum: comparative study of two proposals. 2018. 80f. Dissertation (Master in Mathematical Education) - Pontifical Catholic University of Sao Paulo, Sao Paulo. 2018.
OLIVEIRA, Ana Paula Andrade de. Technology in Mathematical Education: the use of different resources for understanding the decimal numbering system (SND). 2010. 115f. Dissertation (Master in Education) - Federal University of Pernambuco, Ceará. 2010.
PAVAN, Luciane Regina. The mobilization of the basic ideas of the concept of function by children in the 4th grade of Elementary School in problem situations of Additive and/or Multiplicative Structures. 2010. 194f. Dissertation (Master in Education for Science and Mathematics) – State University of Maringa, Maringa. 2010.
REIS, Keila Cristina de Araújo. Games, oral records and graphs: child development in the additive conceptual field. 2017. Dissertation (Master in Education) – University of Brasilia, Brasilia, 2017.
ROCHA, Eliano da. Additive field problem solving strategies: an approach from the perspective of Conceptual field theory. 2019. 144f. Dissertation (Mestrado em Ensino de Ciências e Matemática) - Federal University of Alagoas, Maceio, 2019.
SILVA, Gabriele Bonotto. Conceptual Field theory, skills and competencies: a teaching experience in Mathematics. 2014. 150f. Dissertation (Master in Education) - La Salle University, Canoas, 2014.
SILVA, Lílian Cristine Camargos. Resignifying the construction of the addition and subtraction algorithms. 2015. 166f. Dissertation (Master in Mathematical teaching) - Pontifical Catholic University of Minas Gerais, Belo Horizonte. 2015.
Appendix B – Gérard Vergnaud Works Used in Monographs
VERGNAUD, Gérard. A classification of cognitive tasks and operations of thought involved in addition and subtraction problems. In: CARPENTER, T.; MOSER, J.; ROMBERG, T. Addition and subtraction: A cognitive perspective. Hillsdale, N.J.: Lawrence Erlbaum, 1982. p. 39-59.
VERGNAUD, Gérard. The contribution of psychology in research on scientific, technological and professional education. In: FÁVERO, M. H.; CUNHA, Célio (Orgs.). The production of mathematical notations and their meaning Brasilia: Liber Livro, 2009a. p. 39-60.
VERGNAUD, Gérard. The child, mathematics and reality: problems of teaching mathematics in the Elementary School Curitiba: UFPR, 2009b.
VERGNAUD, Gérard. The genesis of Conceptual Fields. In: GROSSI, E. O. (org.) Why not there are not those who do not learn yet? The theory. Petrópolis, Rio de Janeiro: Vozes, 2003.
VERGNAUD, Gérard. The theory of Conceptual Fields. Recherches em didactique dês mathématiques, Grenoble, v. 10, n. 23, p. 133-170, 1991a. Available in: <https://www.researchgate.net/publication/238663171_Duality_Ambiguity_and_Flexibility_A_Proceptual_View_of_Simple_Arithmetic>. Acess: 14 mar. 2022.
VERGNAUD, Gérard. The theory of Conceptual Fields. IN: BRUN, Jean. Didatics of Mathematics. Lisboa: Instituto Piaget, 1996a. Cap. 3, p. 155-191.
VERGNAUD, Gérard. The theory of Conceptual Fields in the construction of knowledge. Revista GEEMA: Porto Alegre, 4. ed., p. 9-19, jul. 1996b.
VERGNAUD, Gérard. The plot of the conceptual fields. Revista do GEEMPA. Porto Alegre, (4), 1996c.
VERGNAUD, Gérard. Activity and operative knowledge. In: COOL, C. Genetic Psychology and School Learning: Collection of texts on the pedagogical applications of the Piaget’s theories. Madrid: SigloVeintiuno, 1983. p. 183-202.
VERGNAUD, Gérard.; RICCÓ, G. Didactics and acquisition of mathematical concepts. Revista Argentina de Educación, Buenos Aires, v. 4, n. 6, p. 67-92, 1986a.
VERGNAUD, Gérard. The child, mathematics and reality: problems of teaching mathematics in primary school México: Trilhas, 1991b.
VERGNAUD, Gérard. The theory of Conceptual Fields. Rechershes em Didactiques dês Mathématiques. v.10, n.23, 1990.
VERGNAUD, Gérard. A. The long and short term in the learning of mathematics. Educar em Revista, Curitiba, n. Especial 1/2011, p. 15-27, 2011.
VERGNAUD, Gérard. What is learning? In: BITTAR, M.; MUNIZ, C. A. (Orgs.). Mathematical learning from the perspective of Conceptual Fields. Curitiba: CRV, 2009c.
VERGNAUD, Gérard. Psicologia do desenvolvimento cognitivo e didática das matemáticas. Um exemplo: as estruturas aditivas. Revista Análise Psicológica, Lisboa, n.1, p. 75-90, 1986b.
VERGNAUD, Gérard. The theory of Conceptual Fields. In: Seminário Internacional de Educação Matemática do Rio de Janeiro, Rio de Janeiro, 1993. NASSER, L. (ed.). In: Anais ... 1º Seminário Internacional de Educação Matemática do Rio de Janeiro, Rio de Janeiro, 1993, p. 1-26.
VERGNAUD, Gérard. The Acquisition of Arithmetical Concepts. Educational Studies in Mathematics. v.10, n, 2, may, 1979.
VERGNAUD, Gérard. The nature of mathematical concepts. In NUNES, T. & BRYNT, P. (Eds.) Learning and teaching mathematics, an international perspective. Psychology Press Ltd, Hove (East Sussex), 1997.
VERGNAUD, Gérard. The Theory of Conceptual Fields. Human Development, v. 52, n. 2. Printed in Switzerland: Karger, p. 83-94, 2009d.
VERGNAUD, Gérard. Everyone loses when the research is not put into practice. 2008. Available in: <https://novaescola.org.br/conteudo/960/Gérard-vergnaud-todos-perdem-quando-a-pesquisa-nao-e-colocada-em-pratica >. Acess: 4 abr. 2022.
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