Strategies of Number Sense in Pre-service Secondary Mathematics Teachers

  • Rut Almeida
  • Alicia Bruno
  • Josefa Perdomo-Díaz


This paper presents some results of an investigation on the number sense of a group of pre-service secondary teachers from Spain. The objective of this research was to analyze students’ use of strategies associated to number sense and compare them with those obtained in a previous study with pre-service primary teachers in Taiwan, (Yang, Reys & Reys, International Journal of Science and Mathematics Education, 7, 383–403, 2009). Pre-service secondary teachers showed lower success than pre-service primary teachers in a number sense test. Nevertheless, these last based their reasoning mainly on rules and algorithms, while pre-service secondary teachers used more strategies of number sense. In an attempt to delve into the low success shown by of Spanish pre-service secondary teachers, some students were interviewed. Those interviews showed that a deeper work on number sense in the training of these students is needed.


Number sense Pre-service secondary teachers Pre-service primary teachers Strategies Degree in mathematics 



This research is supported by the project EDU2011-29324: Modelos de competencia formal y cognitiva en pensamineto numérico y algebraico de alumnos de Primaria, de Secundaria y de profesorado de Primaria en formación. Ministerio de Ciencias e Innovación. Madrid. Funding from FONDECYT 3140597 project and PIA-CONICYT Basal Funds for Centers of Excellence Project BF0003 are gratefully acknowledged. Chile.


  1. Alajmi, H. & Reys, R. (2007). Examining eighth grade Kuwaiti students’ recognition and interpretation of reasonable answers. International Journal of Science and Mathematics Education, 8, 117–139.CrossRefGoogle Scholar
  2. Almeida, R, Bruno, A. & Perdomo-Díaz, J. (2014). Estrategias de sentido numérico en estudiantes del grado en matemáticas [Strategies of Number Sense in Mathematics Degree Students]. Enseñanza de las Ciencias, 32(2), 9-34.Google Scholar
  3. Alsawaie, O. N. (2011). Number sense-based strategies used by high-achieving sixth grade students who experienced reform textbooks. International Journal of Science and Mathematics Education, 10, 1071–1097.CrossRefGoogle Scholar
  4. Australian Education Council (1990). A national statement on mathematics for Australian schools. Carlton, Australia: Curriculum Corporation.Google Scholar
  5. Dowker, A., Flood, A., Griffiths, H., Harris, L. & Hook, L. (1996). Estimation strategies of four groups. Mathematical Cognition, 2(2), 113–135.CrossRefGoogle Scholar
  6. Ghazali, M., Othman, A. R., Alias, R. & Saleh, F. (2010). Development of teaching models for effective teaching of number sense in the Malaysian primary schools. Procedia Social and Behavioral Sciences, 8, 344–350.CrossRefGoogle Scholar
  7. Greeno, J. G. (1991). Number sense as situated knowing in a conceptual domain. Journal for Research in Mathematics Education, 22(3), 170–218.CrossRefGoogle Scholar
  8. Markovits, Z. & Sowder, J. (1994). Developing number sense: An intervention study in grade 7. Journal for Research in Mathematics Education, 25(1), 4–29.CrossRefGoogle Scholar
  9. McIntosh, A., Reys, B.J. & Reys, R.E. (1992). A proposed framework for examining basic number sense. For the learning of mathematics, 12(3), 2–8. Google Scholar
  10. Mohamed, M. & Johnny, J. (2010). Investigating number sense among students. Procedia Social and Behavioral Sciences, 8, 317–324.CrossRefGoogle Scholar
  11. National Council of Teachers of Mathematics (2000). Principles and standars for school mathematics. Reston, VA: Author.Google Scholar
  12. Real Decreto 1631/2006, de 29 de diciembre, por el que se establecen las enseñanzas mínimas correspondientes a la Educación Secundaria Obligatoria [establishing core curriculum for compulsory Secondary Education]. BOE nº5, España, viernes 5 de enero de 2007.Google Scholar
  13. Reys, B. J. & Yang, D. C. (1998). Relationship between computational performance and number sense among sixth and eighth grade students in Taiwan. Journal for Research in Mathematics Education, 29(2), 225–237.CrossRefGoogle Scholar
  14. Sengul, S. & Gulbagci, H. (2012). An investigation of 5th grade Turkish students’ performance in number sense on the topic of decimal numbers. Procedia Social and Behavioral Sciences, 46, 2289–2293.CrossRefGoogle Scholar
  15. Sowder, J. (1992). Estimation and number sense. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 245–275). New York, NY: MacMillan.Google Scholar
  16. Tsao, Y. (2004). Exploring the connections among number sense, mental computation performance, and the written computation performance of primary pre-service school teachers. Journal of College Teaching and Learning, 1(12), 71–90.Google Scholar
  17. Veloo, P. K. (2010). The development of number sense and mental computation proficiencies: An intervention study with secondary one students in Brunei Darussalam. Dunedin, New Zealand: Doctor Ph. University of Otago.Google Scholar
  18. Yang, D.C., Hsu, C.J. & Huang, M.C. (2004). A study of teaching and learning number sense for sixth grade students in Taiwan. International Journal of Science and Mathematics Education, 2, 407-430.Google Scholar
  19. Yang, D. C. (2005). Number sense strategies used by 6th grade students in Taiwan. Educational Studies, 31(3), 317–333.CrossRefGoogle Scholar
  20. Yang, D. C., Reys, R. & Reys, B. J. (2009). Number sense strategies used by pre-service teachers in Taiwan. International Journal of Science and Mathematics Education, 7, 383–403.CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media B.V. 2015

Authors and Affiliations

  • Rut Almeida
    • 1
  • Alicia Bruno
    • 1
  • Josefa Perdomo-Díaz
    • 2
  1. 1.University of La LagunaLa Laguna (Tenerife)Spain
  2. 2.Centro de Modelamiento Matemático y Centro de Investigación Avanzada en Educación, University of ChileSantiago de ChileChile

Personalised recommendations