Skip to main content

Advertisement

SpringerLink
Log in

The growing gap between colombian education policy, official claims and classroom realities: insights from mathematics teachers' conceptions of beginning algebra and its teaching purpose

  • Published:
International Journal of Science and Mathematics Education Aims and scope Submit manuscript

Abstract

Since 1994 when the General Law of Education was issued, educational authorities have been claiming that Colombia has embarked on an educational revolution [‘La revolución educativa’ (n.d.). From the Colombian Ministry of Education website: http://www.mineducacion.gov.co. Retrieved 23 Nov 2004] where schools have curricular autonomy, and are to improve the quality of education by attending to the needs of the communities they serve. Teachers are urged to engage in a continuous process of constructing the curriculum which is to be anchored in the fundamental aim of educating critical citizens. The findings of this study carried out with the participation of 13 mathematics teachers with a range of teaching experiences and from different schools in Bogotá, show a totally different picture. Instead, for the teaching of school algebra, teachers emphasised the purpose of training pupils in the manipulation of symbolic expressions, as the prerequisite knowledge for the next school mathematics level and ultimately for the External Examination. I offer explanations for the identified gap and argue for the crucial need to create conditions for change at the education systemic level and for the actual empowerment of teachers.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Agudelo-Valderrama, C. (1996). Improving mathematics education in Colombian schools: ‘Mathematics for all’. International Journal of Educational Development, 16(1), 15–26.

    Google Scholar 

  • Agudelo-Valderrama, C. (2000). Una innovación curricular que enfoca el proceso de transición entre el trabajo aritmético y el algebraico. Tunja: Universidad Pedagógica y Tecnológica de Colombia.

  • Agudelo-Valderrama, C. (2001).Challenging the teaching-learning patterns in elementary algebra: A Colombian case. Paper presented at the 12th ICMI Study: The Future of the Teaching and Learning of Algebra. University of Melbourne: Australia.

  • Agudelo-Valderrama, C. (2002). Promoción del pensamiento algebraico en la escuela primaria: Una propuesta que cobra sentido de acuerdo con nuestras concepciones sobre el conocimiento matemático. Aula Urbana No. 37, pp 18–19. Bogotá: Magazín IDEP.

  • Agudelo-Valderrama, C. (2004). Explanations of Attitudes to Change: Colombian Mathematics Teachers’ Conceptions of their Own Teaching Practices of Beginning Algebra. Unpublished PhD thesis, Monash University, Melbourne, Australia.

  • Agudelo-Valderrama, C. & Clarke, B. (2005) The challenges of mathematics teacher change in the Colombian context: The power of institutional practices. Paper presented at the 15th ICMI Study: The Education and Professional Development of Teachers of Mathematics. Águas de Lindóia. Brazil.

  • Banks, J.A. (2001). Citizenship education and diversity. Journal of Teacher Education, 52(1), 1–11.

    Article  Google Scholar 

  • Bishop, A.J. (1988). Mathematical enculturation. Dordrecht: Kluwer Academic.

    Google Scholar 

  • Catelblanco, B. (Ed.) (1994). General law of education (Ley General de la Educación). Bogotá: Editorial Publicitaria.

  • Cobb, P., Wood, T., Yackel, E. & McNeal, B. (1992). Characteristics of classroom mathematics traditions: An iteractional analysis. America Educational Research Journal, 29(3), 573–604.

    Article  Google Scholar 

  • Cooney, T.J. (2001). Considering the paradoxes, perils and purposes of conceptualizing teacher development. In F. Lin & T.J. Cooney (Eds.), Making sense of mathematics teacher education (pp. 9–31). Dordrecht: Kluwer Academic.

    Google Scholar 

  • Díaz, C., Solarte, E. & Arce, J. (1997). Colombia. In D.F. Robitaille (Ed.), National contexts for mathematics and science education. An encyclopaedia of the education systems participating in TIMSS (pp. 82–90). Vancouver: Pacific Educational.

    Google Scholar 

  • Doerr, H. (2004). Teachers' knowledge and the teaching of algebra. In K. Stacey, H. Chick & M. Kendal (Eds.), The future of the teaching and learning of algebra: The 12th ICMI study. Dordrecht: Kluwer Academic.

    Google Scholar 

  • Ernest, P. (1989). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 13–33.

    Google Scholar 

  • Ernest, P. (1991). The philosophy of mathematics education. London: Falmer.

    Google Scholar 

  • Freire, P. (1985). The politics of education: Culture, power and liberation. Basingstoke: MacMillan.

    Google Scholar 

  • Gates, P. & Vistro-Yu, C. (2003). Is mathematics for all? In A.J. Bishop, M.A. Clements, C. Keitel, J. Kilpatrick & F.K. Leung (Eds.), Second international handbook of mathematics education (pp. 31–73). Dordrecht: Kluwer Academic.

    Google Scholar 

  • Gómez-Campo, V. (1998). Estándares educativos (a propósito del TIMSS): Nueva política curricular y calidad de la formación de docentes en Colombia. Revista de Estudios en Educación, 1(1), 94–110.

    Google Scholar 

  • González, M. & Pedroza, G. (1999). Reflexiones sobre aspectos claves del algebra escolar. Revista EMA – Investigación e innovación en educación matemática, 5(1), 87–91.

    Google Scholar 

  • Gregg, J. (1995). The tensions and contradictions of the school mathematics tradition. Journal for Research in Mathematics Education, 26(5), 442–466.

    Article  Google Scholar 

  • Gutstein, E. (2003). Teaching and learning mathematics for social justice in an urban, Latino school. Journal for Research in Mathematics Education, 34(1), 37–73.

    Article  Google Scholar 

  • Jones, B.O. (1981). Strategies for teaching in a technologically oriented society. In Magill, S. (Ed.), Changing education in a changing society: Implications for teacher education (pp. 11–16). Australia: The Australian Association of Principals of Colleges of Teacher Education.

    Google Scholar 

  • Kaput, J.J. & Blanton, M. (2001). Algebrafying the elementary mathematics experience. Part I: Transforming tasks structures. In H. Chick, K. Stacey, J. Vincent & J. Vincent (Eds.), Proceedings of the 12th ICMI study: The future of the teaching and learning of algebra, vol. 1 (pp. 344–351). Melbourne: University of Melbourne.

    Google Scholar 

  • Kieran, C. (1992). The learning and teaching of school algebra. In D.A. Grows (Ed.), Handbook of research on mathematics teaching and learning. New York: McMillan.

    Google Scholar 

  • Kieran, C. (2004). Algebraic thinking in the early grades: What is it? The Mathematics Educator, 18(1), 139–151.

    Google Scholar 

  • Kieran, C., Boileau, A. & Garaçon, M. (1996). Introducing algebra by means of a technology-supported, functional approach. In N. Bednarz, C. Kieran & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 257–294). Dordrecht: Kluwer Academic.

    Google Scholar 

  • Kincheloe, J.L. (1993). Toward a critical politics of teacher education: Mapping the postmodern. Westport, Connecticut: Bergin & Garvey.

    Google Scholar 

  • Lave, J. & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge: Cambridge University Press.

    Google Scholar 

  • Leder, G. & Forgasz, H. (2002). Measuring mathematical beliefs and their impact on the learning of mathematics: A new approach. In G. Leder, E. Pehkonen & G. Törner (Eds.), Beliefs; a hidden variable in mathematics education? (pp. 95–114). Dordrecht: Kluwer Academic.

    Google Scholar 

  • Lerman, S. (1990). Alternative perspectives of the nature of mathematics and their influence on the teaching of mathematics. British Educational Research Journal, 16(1), 53–62.

    Article  Google Scholar 

  • Lubienski, S.T. (2003). Celebrating diversity and denying disparities: A critical assessment. Educational Researcher, 38(8), 30–38.

    Article  Google Scholar 

  • Manouchehri, A. (1998). Mathematics curriculum reform and teachers: What are the dilemmas? Journal of Teacher Education, 49(4), 276–286.

    Article  Google Scholar 

  • Mason, J.H. (1999). Incitación al Estudiante para que Use su Capacidad Natural de Expresar Generalidad: Las Secuencias de Tunja. Revista EMA, 4(3), 232–246.

    Google Scholar 

  • Mason, J., Graham, A., Pimm, D. & Gowar, N. (1985). Routs to algebra/roots of algebra. UK: Open University Press (Milton Keynes).

    Google Scholar 

  • McLeod, D.B. (1992). Research on affect in mathematics education: A reconceptualization. In D.A. Grows (Ed.), Handbook of research on mathematics teaching and learning (pp. 575–596). New York: McMillan.

    Google Scholar 

  • Mellin-Olsen, S. (1987). The Politics of mathematics education. Dordrecht: Kluwer Academic.

    Google Scholar 

  • MEN (1996). Resolución 2343: Lineamientos generales de los procesos curriculares e indicadores de logro para el ciclo básico educativo escolar. Bogotá: Ministerio de Educación Nacional.

    Google Scholar 

  • MEN (1998). Matemáticas – Lineamientos curriculares. Bogotá: Ministerio de Educación Nacional.

    Google Scholar 

  • Mockus, A. (1985). La reforma curricular y el magisterio. Educación y Cultura, 4(1), 65–68.

    Google Scholar 

  • NCTM (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Niño, J. (1998). El proceso de acreditación universitaria. El caso de las Facultades de Educación. Bogotá: Ministerio de Educación Nacional.

    Google Scholar 

  • Pehkonen, E. & Furinghetti, F. (2001). Towards a common characterization of beliefs and conceptions. Proceedings of the 25th Annual Conference of the International group for the Psychology of Mathematics Education. Uthrech. The Netherlands.

  • Povey, H. (2002). Promoting social justice in and through the mathematics curriculum: Exploring the connections with epistemologies of mathematics. Mathematics Education Research Journal, 14(3), 190–201.

    Google Scholar 

  • Raymond, A. (1997). Inconsistency between a beginning elementary school teacher's mathematics beliefs and teaching practice. Journal for Research in Mathematics Education, 28(5), 550–576.

    Article  Google Scholar 

  • Richardson, V. & Placier, P. (2001). Teacher change. In V. Richardson (Ed.), Handbook of research on teaching (pp. 905–947). Washington, D.C.: American Educational Research Association.

    Google Scholar 

  • Roberts, R.E. (2002). A study of the cognitive and affective characteristics of high and low achievers in year 10 algebra. PhD thesis, Queensland University of Technology.

  • Robitaille, D. & Dirks, M. (1982). Models for the mathematics curriculum. Learning of Mathematics, 2(3), 3–19.

    Google Scholar 

  • Smith III, D. (1996). Efficacy and teaching mathematics by telling: A challenge for reform. Journal for Research in Mathematics Education, 27(4), 387–402.

    Article  Google Scholar 

  • Steen, L.A. (1999). Does everybody need to study algebra? In B. Moses (Ed.), Algebraic thinking grades K-12: Readings from NCTM's school journal and other publications (pp. 49–51). Reston, VA: NCTM.

    Google Scholar 

  • Sutherland, R. (1991). Some unanswered questions on the teaching and learning of algebra. Learning of Mathematics, 11(3), 40–46.

    Google Scholar 

  • Thompson, A. (1992). Teachers' beliefs and conceptions: A synthesis of the research. In D.A. Grows (Ed.), Handbook of research on mathematics teaching and learning (pp. 127–146). New York: McMillan.

    Google Scholar 

  • Woodrow, D. (2003). Mathematics, mathematics education and economic conditions. In A.J. Bishop, M.A. Clements, C. Keitel, J. Kilpatrick & F.K. Leung (Eds.), Second international handbook of mathematics education (pp. 9–30). Dordrecht: Kluwer Academic.

    Google Scholar 

  • Yackel, E., Cobb, P. & Wood, T. (1992). Instructional development and assessment from a socioconstructivist perspective. In G. Leder (Ed.), Assessment and learning mathematics (pp. 63–82). Melbourne, Australia: Australian Council for Educational Research.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. F. of Education, Monash University, Melbourne, Victoria, 3168, Australia

    Cecilia Agudelo-Valderrama

Authors
  1. Cecilia Agudelo-Valderrama
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cecilia Agudelo-Valderrama.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Agudelo-Valderrama, C. The growing gap between colombian education policy, official claims and classroom realities: insights from mathematics teachers' conceptions of beginning algebra and its teaching purpose. Int J Sci Math Educ 4, 513–544 (2006). https://doi.org/10.1007/s10763-005-9021-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10763-005-9021-8

Key Words

Search

Navigation