Skip to main content
  • Dossier “Mathematical e-learning”
  • Article
  • Open access
  • Published:

A Knowledge-Skill-Competencies e-Learning Model in Mathematics

Conocimientos, destrezas y competencias: un modelo para aprender matemáticas en un entorno virtual


This paper concerns modelling competence in mathematics in an e-learning environment. Competence is something complex, which goes beyond the cognitive level, and involves meta-cognitive and non-cognitive factors. It requires students to master knowledge and skills and at least some measurable abilities, which Niss calls ‘competencies’. We present a model that exploits the innovative technological features of the IWT platform to define a personalised learning experience allowing students to increase their competence in mathematics. It is based on knowledge and skills representations by means of a graph metaphor, and on a theoretical framework for modelling competence.


Este trabajo se centra en la competencia matemática en un entorno de aprendizaje virtual. La competencia es algo complejo, que trasciende el nivel cognitivo, e implica factores metacognitivos y no cognitivos. Exige de los estudiantes su dominio sobre conocimientos y destrezas y, por lo menos, sobre algunas capacidades medibles, a las que Niss llama «competencias específicas» [competencies]. El modelo que presentamos utiliza las innovadoras características tecnológicas de la plataforma IWT para definir una experiencia de aprendizaje personalizado que permite a los estudiantes aumentar su competencia en matemáticas. Se basa en la representación de conocimientos y destrezas mediante metáforas gráficas y en un marco teórico para modelar la competencia.


  • ALBANO, G. (2011a). “Knowledge, Skills, Competencies: a Model for Mathematics E-Learning”. In: R. Kwan; C. McNaught; P. Tsang; F. L. Wang; K. C. Li (eds). Enhancing Learning Through Technology: International Conference, ICT 2011, Hong Kong, July 11–13. Proceedings (Communications in Computer and Information Science). CCIS 177. ISBN: 978-3-642-22382-2. Springer Heidelberg. Pages 214–225.

    Google Scholar 

  • ALBANO, G. (2011b). “Mathematics education: teaching and learning opportunities in blended learning”. In: A. Juan; A. Huertas; S. Trenholm; C. Steegmann (eds). Teaching Mathematics Online: Emergent Technologies and Methodologies [in press].

  • ALBANO, G.; FERRARI, P. L. (2008). “Integrating technology and research in mathematics education: the case of e-learning”. In: F. J. García-Peñalvo (ed.): Advances in E-Learning: Experiences and Methodologies. IGI Global. Pages 132–148.

  • ALBANO, G.; GAETA, M.; RITROVATO, P. (2007). “IWT: an innovative solution for AGS e-Learning model” International Journal of Knowledge and Learning. Vol. 3, No 2/3, pages 209–224.

    Article  Google Scholar 

  • ARZARELLO, F.; ROBUTTI, O. (2002). Matematica. Brescia: La Scuola.

    Google Scholar 

  • ASIALA, M.; BROWN, A.; DEVRIES, D. [et al.] (1996). “A Framework for Research and Curriculum Development in Undergraduate Mathematics Education”. CBMS Issues in Mathematics Education. Vol. 6.

  • D’AMORE, B. (2000) “La complessità dell’educazione e della costruzione dei saperi”. Riforma e didattica. No 4, pages 35–40.

  • GAETA, M.; ORCIUOLI, F.; RITROVATO, P. (2009) “Advanced Ontology Management System for Personalised e-Learning”. Knowledge-Based Systems. Special issue. Vol. 22, Iss. 4, pages 292–301.

    Article  Google Scholar 

  • GODINO, J. (2002). “Competencia y comprensión matemática: ¿Qué son y cómo se consiguen?”. Uno. Vol. 8, No 29, pages 9–19.

    Google Scholar 

  • NISS, M. (2003). “Mathematical competencies and the learning of mathematics: The Danish KOM project” In: A. Gagatsis; S. Papastavridis (eds). Proceedings of the 3rd Mediterranean Conference on Mathematical Education. Athens: Hellenic Mathematical Society. Pages 115–124.

    Google Scholar 

  • OECD (2009). PISA 2009 Assessment Framework — Key Competencies in Reading, Mathematics and Science. [Accessed: 28 January 2011]. <>

  • SKEMP, R. (1976). “Relational understanding and instrumental understanding”. Mathematics Teaching. No 77, pages 20–26.

  • WEINERT, F. (2001). “Concept of competence: a conceptual clarification”. In: D. Rychen; L. Salgenik (eds). Defining and electing key competencies. Seattle, Toronto, Bern, Göttingen: Hogrefe & Huber Publishers.

    Google Scholar 

  • WILEY, D. A. (2000). “Connecting learning objects to instructional design theory: A definition, a metaphor, and a taxonomy”. In: D.A. Wiley (ed.). The Instructional Use of Learning Objects. [Accessed: 18 February 2010]. <>

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Giovannina Albano.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and permissions

About this article

Cite this article

Albano, G. A Knowledge-Skill-Competencies e-Learning Model in Mathematics. Revista de Universidad y Sociedad del Conocimiento 9, 306–319 (2012).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


Palabras clave