Pre-service teachers’ knowledge on elementary geometry concepts

Angela Couto, Isabel Vale


This text is based on a research, which is still in progress, whose main objective is to identify and understand what are the main difficulties of future mathematics teachers of basic education are, regarding their content knowledge in geometry in the context of the curricular unit of Geometry during their undergraduate degree. We chose a qualitative approach in the form of case study, in which data collection was done through observation, interviews, a diverse set of tasks, a diagnostic test and other documents. This paper focuses on the test given to prospective teachers at the beginning of the course. The preliminary analysis of the data points to a weak performance of pre-service teachers in the test issues addressing elementary knowledge of Geometry.


elementary concepts of geometry, initial teacher training, geometrical knowledge

Full Text:



Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215-241.

Ball, D., Bass, H., Sleep, L. & Thames, M. (2007). A theory of mathematical knowledge for teaching [CD-ROM]. Proceedings of the 15th ICMI Studdy. The Professional Education and development of Teachers of mathematics. Águas de Lindóia, Brasil, 15-21 may 2005. UNESP.

Battista, M. T. (2007). The development of geometry and spatial thinking. In Frank K. Lester, Jr. (Ed.). Second Handbook of Research on Mathematics Teaching and Learning (pp. 843-908). Reston: NCTM.

Battista, M. & Clements, D. (2002). Using spatial imagery in geometric reasoning. In D. L. Chambers (Ed.), Putting research into practice in the elementary grades (pp. 174-178). Reston: NCTM.

Braumman, C. (2004). A matemática e diferentes modelos de formação. In A. Borralho, C. Monteiro & R. Espadeiro (Orgs.), A matemática na formação do professor (pp. 75-82). Lisboa: Secção de Educação e Matemática da Sociedade Portuguesa de Ciências da Educação.

Bullough, R., Jr. & Gitlin, A. (2001). Becoming a student of teaching: Methodologies for exploring self and school context. (2.a ed.). London: Routledge Falmer.

Burger, W. & Shaughnessy, J. (1986). Characterizing the van Hiele levels of development in geometry. Journal of Research in Mathematics Education, 17, 31- 48.

Duval, R. (1998). Geometry from a cognitive point of view. In C. Mammana & V. Villani (Eds.). Perspectives on the Teaching of Geometry for the 21st Century, 29- 83. Dordrecht: Kluwer Academic Publishers.

Gomes, M. (2003). Um estudo sobre o conhecimento matemático de (futuros) professores do 1.o ciclo. O problema dos conceitos fundamentais em Geometria. Tese de doutoramento. Universidade do Minho, Braga, Portugal.

Gutierrez, A., Jaime, A. & Fortuny, J. M. (1991). An alternative paradigm to evaluate the acquisition of the van Hiele levels. Journal of Research in Mathematics Education, 22, 237-251.

Hill, H. C., Sleep, L. Lewis, J. M. & Ball, D. L. (2007). Assessing teachers mathematical knowledge: What knowledge matters and what evidence count. In Frank K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 111-156). Charlotte: Information Age Publishing.

Jaime, A. & Gutierrez, A. (1994). A model of test design to assess the van Hiele levels. Proceedings of the 18th PME Conference, 3, 41-48.

Jones, K. (2000). Teacher knowledge and professional development in Geometry. Proceedings of the British Society for Research into Learning Mathematics, 20 (3), 109-114.

Korthagen, F., Kessels, J., Koster, B., Lagerwerf, B. & Wubbels, T. (2001). Linking practice and theory: The pedagogy of realistic teacher education. Mahwah, NJ: Lawrence Erlbaum Associates.

Loughran, J. (2006). Developing a pedagogy of teacher education: Understanding teaching and learning about teaching. London: Routledge.

teaching and learning about teaching. London: Routledge.

Ma, L. (1999). Knowing and teaching mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah: Lawrence Erlbaum Associates.

Ministério da Educação (2007). Currículo nacional do ensino básico. Lisboa: ME, DGIDC-DEB. Acedido em maio 20, 2013, em

Ministério da Educação e Ciência (2013). Programa e metas curriculares de matemática do ensino básico. Lisboa: MEC, DGIDC-DEB. Acedido em maio 20, 2013, em

National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston: NCTM.

National Council of Teachers of Mathematics. (2009). Focus in high school mathematics: Reasoning and sense making. Reston: NCTM.

Oliveira, H. & Cyrino, M. (2011). A formação inicial de professores de matemática em Portugal e no Brasil: Narrativas de vulnerabilidade e agência. Interacções, 18, 104-130.

Oliveira, H. & Hannula, M. (2008). Individual prospective mathematics teachers: studies on their professional growth. In T. Wood (Series Editor) & K. Krainer (Volume Editors), International Handbook of Mathematics Teacher Education, 3 (pp. 13-34). Rotterdam: Sense Publishers.

Ponte, J. (2006). Os desafios do processo de Bolonha para a formação inicial de professores. Revista de Educação, XIV (1), 19-35.

Ponte, J. & Chapman, O. (2008). Preservice mathematics teacher ́s knowledge and development. In L. English (Ed.), Handbook of International Research in Mathematics Education (2nd ed.) (pp. 223-261). Mahwah, NJ: Lawrence Erlbaum Associates.

Saads, S. & Davis, G. (1997). Spatial abilities, van Hiele levels and language use in three dimensional geometry. In E. Pehkonen (Ed.), Proceedings of the 21st Conference of the International Group for the Psychology of Mathematics Education, 4 (pp. 104-111).

Segall, A. (2002). Disturbing practice: Reading teacher education as text. New York: Peter Lang.

Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15 (2), 4-14.

Vale, I. (2002). Didáctica da matemática e formação inicial de professores num contexto de resolução de problemas e de materiais manipuláveis. Tese de doutoramento, Universidade de Aveiro. Lisboa: APM.

Vale, I. & Barbosa, A. (2009). Padrões. Múltiplas perspectivas e contextos em educação matemática. Viana do Castelo: ESEIPVC.

Veloso, E. (2008). Notas sobre o ensino da geometria. Há vida para além dos prismas, paralelepípedos, cubos, esferas, cilindros e cones. Educação e Matemática, 96, 18-19.

Wu, H. (1999). Professional development of mathematics teachers. American Mathematical Society, 46 (5), 535-542.

Categories: 2014, Articles, Mathematics Education

Tags: , ,

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: