Skip to main content

Cognitive and Linguistic Processes in Brazilian Mathematics Education: Theoretical Considerations and Educational Implications

  • Chapter
  • First Online:
Mathematics Education in Brazil

Abstract

The aim of this chapter is to contribute to the debate about the trends, objects of study, and theoretical and methodological assumptions that have marked and constituted the current identity of working group Cognitive and Linguistic Processes in Mathematics Education of the Brazilian Society of Mathematics Education. The considerations presented bring together a range of investigations that explore the cognitive and linguistic aspects involved in the teaching and learning of mathematics in different learning contexts and different levels of schooling. The work developed by the group has been characterised by investigations conducted on language and communication in the classroom and their sociocultural aspects, alongside studies into the cognitive processes involved in mathematical reasoning. The discussion about the theoretical-methodological questions underlying the reflections on the cognitive and linguistic processes in the Brazilian scenario has been divided into two parts. In the first, we present a historical review of the main trends considered during the first 10 years of working group’s history. In the second, explore the more recent objects of study. We describe how this development indicates a convergence of Brazilian researchers with different theoretical and methodological affiliations, as they search for theoretical models that can explain the role of language, cognition and cultural aspects in the teaching and learning of mathematics. The advances made in terms of knowledge of cognitive and linguistic processes in mathematics education within Brazil are also presented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The educational system in Brazil is divided into basic education and higher education. Basic education corresponds to: nursery or early-years education (0–5 years old), (2) elementary school (elementary and middle school, from 6 to 14 years), and high school (15–17 years). Higher education corresponds to university education, undergraduate and postgraduate courses (Masters and PhD). This educational system also includes youth and adult education (EJA) , distance learning and educational technologies, technological education and vocational training, special education and indigenous education.

  2. 2.

    The solving of problems continues to be a relevant topic in the field of mathematics education. It has been the topic of numerous international conferences, such as the 13th International Congress on Mathematical Education (ICME) in 2016, the 40th Conference of the International Group for the Psychology of Mathematics Education (PME) also in 2016, and of many of the National Council of Teachers of Mathematics (NCTM) documents.

References

  • Bakhtin, M., & Voloshinov, V. (1992). Marxismo e Filosofia da Linguagem (6th ed., M. Lahud & Y. L. Vieira, Trans.). São Paulo: Ed. Hucitec. (Original work published 1929).

    Google Scholar 

  • Borges, F. A., & Nogueira, C. M. I. (2012). Aulas de matemática para alunos surdos inclusos no ensino fundamental. In Anais do V Seminário Internacional de Pesquisa em Educação Matemática (pp. 1–20), Petrópolis, Rio de Janeiro.

    Google Scholar 

  • Burton, L., & Morgan, C. (2000). Mathematicians writing. Journal for Research in Mathematics Education, 31(4), 429–453.

    Article  Google Scholar 

  • Carrião, A. (2012). A nominalização como marca do discurso na aula de matemática. In Anais do V Seminário Internacional de Pesquisa em Educação Matemática (pp. 1–18), Petrópolis, Rio de Janeiro.

    Google Scholar 

  • Charnay, R. (2001). Aprendendo (com) a resolução de problemas. In C. Parra & I. Saiz (Orgs.), Didática da matemática: reflexões pedagógicas (pp. 36–47). Porto Alegre: Artmed.

    Google Scholar 

  • Chica, C. (2001). Por que formular problemas? In K. Smole & M. Diniz (Orgs.), Ler, escrever e resolver problemas: habilidades básicas para aprender matemática (pp. 151–173). Porto Alegre: Artmed.

    Google Scholar 

  • Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52, 243–270.

    Article  Google Scholar 

  • Cunha, M. J. G. (2015). Elaboração de problemas combinatórios por professores de matemática do ensino médio. Dissertação de Mestrado, Programa de Pós-graduação em Educação Matemática e Tecnológica da Universidade Federal de Pernambuco, Brazil.

    Google Scholar 

  • David, M. M., & Tomaz, V. S. (2012a). Perspectiva de análise micro da estrutura da atividade matemática em sala de aula. In Anais do V Seminário Internacional de Pesquisa em Educação Matemática (pp. 1–20), Petrópolis, Rio de Janeiro.

    Google Scholar 

  • David, M. M., & Tomaz, V. S. (2012b). The role of visual representations for structuring classroom mathematical activity. Educational Studies in Mathematics, 80, 413–431.

    Article  Google Scholar 

  • David, M. M. M. S., & Watson, A. (2008). Participating in what? Using situated cognition theory to illuminate differences in classroom practices. In A. Watson & P. Winbourne (Orgs.), New directions for situated cognition in mathematics education (pp. 31–57). New York: Springer.

    Google Scholar 

  • Duval, R. (1993). Registres de représentation sémiotique et fonctionnement cognitif de la pensée. In Annales de Didactique et de Sciences cognitives, IREM de Starsbourg (Vol. 5, pp. 37–65).

    Google Scholar 

  • Duval, R. (1995). Sémiósis et pensée humaine:registres sémiotiques et apprentissages intellectuels. Suisse: Peter Lang.

    Google Scholar 

  • Engeström, Y. (1987). Learning by expanding: An activity-theoretical approach to developmental research. Helsinki: Orienta-Konsultit.

    Google Scholar 

  • English, L. (1997). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics, 34, 183–217.

    Article  Google Scholar 

  • English, L., & Sriraman, B. (2005). Theories of mathematics education. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International. Group for the Psychology of Mathematics Education (Vol. 1, pp. 170–202). Melbourne: PME.

    Google Scholar 

  • Fernandes, S. H. A. A., & Healy, L. (2010). Embodied Mathematics: Relationships between doing and imagining in the activities of a blind learner. In Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 345–352), Belo Horizonte, Brazil.

    Google Scholar 

  • Fernandes, S. H. A. A., Healy, H., & Serino, A. P. (2012). Das relações entre figuras para relações em um espaço matematizável: as percepções de alunos cegos sobre transformações geométricas. In Anais do V Seminário Internacional de Pesquisa em Educação Matemática (pp. 1–19), Petrópolis, Rio de Janeiro.

    Google Scholar 

  • Fonseca, M. C. F. R. (2010). Adult education and ethnomathematics: Appropriating results, methods, and principles. ZDM Mathematics Education, 42(3), 361–369.

    Google Scholar 

  • Frade, C., & Borges, O. (2006). The tacit-explicit dimension of the learning of mathematics: An investigation report. International Journal of Science and Mathematics Education, 4, 293–317.

    Article  Google Scholar 

  • Frade, C., & Falcão, J. (2007). Exploring connections between tacit knowing and situated learning perspectives in the context of mathematics education. In A. Watson & P. Winbourne (Orgs.), New directions for situated cognition in mathematics education (Vol. 1, pp. 203–231). Norwell: Springer.

    Google Scholar 

  • Frade, C., & Tatsis, K. (2009). Learning, participation and local school mathematics practice. The Montana Mathematics Enthusiast, 6, 96–112.

    Google Scholar 

  • Frade, C., Winbourne, P., & Braga, S. A. M. (2009). A mathematics-science community of practice: Crossing boundaries. For the Learning of Mathematics, 29, 14–22.

    Google Scholar 

  • Frant, J. B. (2009). As time goes by: Technology, embodiment and Cartesian graphics. In Proceedings of the 33th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, p. 343), Tessaloniki, Greece.

    Google Scholar 

  • Frant, J. B. (2012). Linguagem, compressão e algumas implicações para a matemática escolar. Perspectiva de análise micro da estrutura da atividade matemática em sala de aula. In Anais do V Seminário Internacional de Pesquisa em Educação Matemática (pp. 1–10), Petrópolis, Rio de Janeiro.

    Google Scholar 

  • Freire, P. C., & Lima, R. N. (2012). O subconstruto parte-todo: uma análise com os três mundos da matemática. In Anais do V Seminário Internacional de Pesquisa em Educação Matemática (pp. 1–20), Petrópolis, Rio de Janeiro.

    Google Scholar 

  • Garnica, A. V. M., Soares, M. T. C., & Buriasco, R. L. C. (2006). Anais do III Seminário Internacional de Pesquisa em Educação Matemática. Águas de Lindoia: Sociedade Brasileira de Educação Matemática, São Paulo.

    Google Scholar 

  • Gonzales, N. A. (1994). Problem posing: A neglected component in mathematics courses for prospective elementary and middle school teachers’. School Science and Mathematics, 94(2), 78–84.

    Article  Google Scholar 

  • Hazin, I., Da Rocha Falcão, J. T., & Leitão, S. (2006). Mathematical impairment among epileptic children. In Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 249–256), Prague, Czech Republic.

    Google Scholar 

  • Healy, L., & Fernandes, S. H. A. A. (2008). The role of gestures in the mathematical practices of blind learners. In Proceedings of the Joint Meeting of PME 32 and PME-NA XXX (Vol. 3, pp. 137–144). Morelia, México: Cinvestav-UMSNH.

    Google Scholar 

  • Healy, L., & Fernandes, S. H. A. A. (2011). The role of gestures in the mathematical practices of those who do not see with their eyes. Educational Studies in Mathematics, 77(2), 157–174.

    Article  Google Scholar 

  • Hoffmann, M. H. G. (2006). What is a “semiotic perspective”, and what could it be? Some comments on the contributions to this special issue. Educational Studies in Mathematics, 61, 279–291.

    Article  Google Scholar 

  • Itacarambi, R. R. (2010). Resolução de problemas nos anos iniciais do ensino fundamental. São Paulo: Editora Livraria da Física.

    Google Scholar 

  • Kistemann, M. A., Jr. (2012). A produção de significados e a tomada de decisão de indivíduos-consumidores. In Anais do V Seminário Internacional de Pesquisa em Educação Matemática (pp. 1–13), Petrópolis, Rio de Janeiro.

    Google Scholar 

  • Lakoff, G., & Johnson, M. (1999). Philosophy in the flesh: The embodied mind and its challenge to western thought. New York: Basic Books.

    Google Scholar 

  • Lautert, S. L., & Spinillo, A. G. (2012). Os princípios invariantes da divisão como foco de um estudo de intervenção com crianças. In Anais do V Seminário Internacional de Pesquisa em Educação Matemática (pp. 1–13), Petrópolis, Rio de Janeiro.

    Google Scholar 

  • Lautert, S. L., Spinillo, A., & Correa, J. (2012). Children’s difficulties with division: An intervention study. Journal of Medicine and Medical Sciences, 1, 447–456.

    Google Scholar 

  • Leontiev, A. N. (1978). Activity, consciousness, personality. Englewood Cliffs, NJ: Prentice-Hall.

    Google Scholar 

  • Leung, S. S., & Silver, E. A. (1997). The role of task format, mathematics knowledge, and creative thinking on the arithmetic problem posing of prospective elementary school teachers. Mathematics Education Research Journal, 9(1), 5–24.

    Article  Google Scholar 

  • Lins, R. C. (1994). O modelo teórico dos campos semânticos: uma análise epistemológica da álgebra e do pensamento algébrico. Revista Dynamis, 1(7), 29–39.

    Google Scholar 

  • Lopes, A. C., & Magina, S. (2012). O xadrez e o estudante: uma relação que pode dar certo na resolução de problema matemáticos. In Anais do V Seminário Internacional de Pesquisa em Educação Matemática (pp. 1–20), Petrópolis, Rio de Janeiro.

    Google Scholar 

  • Lowrie, T. (2002). Young children posing problems: The influence of teacher intervention on the type of problems children pose. Mathematics Education Research Journal, 14(2), 87–98.

    Article  Google Scholar 

  • Magina, S. M. P., Spinillo, A. G., & Melo, L. M. (2015). As estratégias de estudantes dos anos iniciais na resolução de problema combinatório. In Anais do VI Seminário Internacional de Pesquisa em Educação Matemática (pp. 1–12), Pirenópolis, Goiás.

    Google Scholar 

  • Meaney, T. (2005). Mathematics as text. In A. Chronaki & I. M. Christiansen (Orgs.) Challenging perspectives on mathematics classroom communication. Connecticut: Information Age Publishing.

    Google Scholar 

  • Merlini, V., Santos, A., Teixeira, A. C., & Magina, S. M. P. (2015). Processo formativo centrado na escola: as reflexões da professora Maria. In Anais do VI Seminário Internacional de Pesquisa em Educação Matemática (p. 13), Pirenópolis, Goiás.

    Google Scholar 

  • Moro, M. L. F., & Soares, M. T. C. (2006). Níveis de raciocínio combinatório e produto cartesiano na escola fundamental. Revista Educação Matemática Pesquisa, 8(1), 99–124.

    Google Scholar 

  • Moschkovich, J. N. (2010). Language and mathematics education: Multiple perspectives and directions for research. Charlotte: Information Age Publishing.

    Google Scholar 

  • Oliveira, D. L., Albuquerque, L. C., & Gontijo, C. H. (2012). Criatividade matemática: alguns elementos na divisão de quadrados. In Anais do V Seminário Internacional de Pesquisa em Educação Matemática (pp. 1–19), Petrópolis, Rio de Janeiro.

    Google Scholar 

  • Onuchic, L. R., & Alevato, N. S. G. (2004). Novas reflexões sobre o ensino-aprendizagem de matemática através da resolução de problemas. In M. A. V. Bicudo & M. C. Borba (Orgs.), Educação matemática: Pesquisa em movimento (pp. 213–223). São Paulo: Cortez.

    Google Scholar 

  • Pires, C. M. C., Curi, E., Rabelllo, M., Pavanello, R., & Valente, W. R. (2003). Anais do II Seminário Internacional de Pesquisa em Educação Matemática. Sociedade Brasileira de Educação Matemática. São Paulo: Santos.

    Google Scholar 

  • Rabello, M., Lins, R., & Da Rocha Falcão. (2000). Processos cognitivos e linguísticos na Educação matemática. In T. M. Campos & C. M. C. Pires Anais do I Seminário Internacional de Pesquisa em Educação Matemática. Sociedade Brasileira de Educação Matemática (pp. 329–372). São Paulo: Serra Negra.

    Google Scholar 

  • Schön, D. (2000). Educando o Profissional Reflexivo: um novo design para o ensino e aprendizagem. Porto Alegre: Artes Médicas Sul.

    Google Scholar 

  • Sfard, A. (2008). Thinking as communicating. Cambridge University Press. Ebook.

    Google Scholar 

  • Sfard, A. (2012). Introduction: Developing mathematical discourse—Some insights from communicational research. International Journal of Educational Research, 51–52, 1–9.

    Article  Google Scholar 

  • Skovsmose, O. (2005). Foregrounds and politics of learning obstacles. For the Learning of Mathematics, 25(1), 4–10.

    Google Scholar 

  • Souza, E. R. R. de. (2015). Estruturas multiplicativas: Concepção de professor de Ensino Fundamental. Dissertação de Mestrado, Programa de Pós-Graduação em Educação Matemática, Universidade Estadual de Santa Cruz.

    Google Scholar 

  • Spinillo, A. G., & Lautert, S. (2006). Exploring the role played by the remainder in the solution of division problems. In Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 153–160).

    Google Scholar 

  • Spinillo, A. G., Lautert, S. L., Santos, E. M., & Silva, J. F. G. (2015). Uma análise de problemas do campo multiplicativo elaborados por professores do Ensino Fundamental I. In Anais do VI Seminário Internacional de Pesquisa em Educação Matemática (pp. 1–9), Pirenópolis, Goiás.

    Google Scholar 

  • Spinillo, A. G., & Silva, J. F. G. (2010). Making explicit the principles governing combinatorial reasoning: Does it help children to solve Cartesian product problems? In Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 216–224).

    Google Scholar 

  • Spinillo, A. G., Silva, J. F. G., & Lautert, S. L. (2016). Ensino e aprendizagem de conceitos matemáticos a partir da explicitação dos princípios invariantes. In J. A. de Castro Filho, M. Chagas, P. M. Barguil, D. L. Maia, & J. Lima (Orgs.), Matemática, cultura e tecnologia: perspectivas internacionais (pp. 35–48) Curitiba: CRV.

    Google Scholar 

  • Tardif, M. (2002). Saberes docentes e formação profissional. Petrópolis, Rio de Janeiro: Editora Vozes.

    Google Scholar 

  • Tomaz, V. S., & David, M. M. (2011). Classroom activity promoting students’ learning about the use of drawings in geometry. In Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 257–264).

    Google Scholar 

  • Torisu, E. M. (2012). Acompanhamento extraclasse e fortalecimento das crenças de autoeficácia matemática. In Anais do V Seminário Internacional de Pesquisa em Educação Matemática (pp. 1–22), Petrópolis, Rio de Janeiro.

    Google Scholar 

  • Vergnaud, G. (1983). Multiplicative structures. In R. Lesh & M. Landau (Eds.), Acquisitions of mathematics concepts and procedures (pp. 127–174). New York: Academic.

    Google Scholar 

  • Vergnaud, G. (1988). Multiplicative structures. In H. Hiebert & M. Behr (Eds.), Research agenda in mathematics education. Number concepts and operations in the middle grades (pp. 141–161). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Vergnaud, G. (1990). La théorie des champs conceptuels. Recherches en Didactique des Mathématiques, Grenoble, 10(23), 133–170.

    Google Scholar 

  • Vergnaud, G. (2003). A gênese dos campos conceituais. In E. Grossi (Org.). Por que ainda há quem não aprende? A teoria (pp. 21–60). Ed. Vozes, RJ: Petrópolis.

    Google Scholar 

  • Viana, O. A. (2012). A identificação de propriedades e a habilidade de planificação de figuras geométricas espaciais. In Anais do V Seminário Internacional de Pesquisa em Educação Matemática Petrópolis, Rio de Janeiro.

    Google Scholar 

  • Zunino, D. L. (1995). A matemática na escola: aqui e agora. Porto Alegre: Artes Médicas.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Carrião, A., Lautert, S.L., Spinillo, A.G. (2018). Cognitive and Linguistic Processes in Brazilian Mathematics Education: Theoretical Considerations and Educational Implications. In: Ribeiro, A., Healy, L., Borba, R., Fernandes, S. (eds) Mathematics Education in Brazil . Springer, Cham. https://doi.org/10.1007/978-3-319-93455-6_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-93455-6_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-93454-9

  • Online ISBN: 978-3-319-93455-6

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics