Competencies in Mathematical Modelling Tasks: An Error Analysis
Hanti Kotze 1  
More details
Hide details
University of Johannesburg, Johannesburg, SOUTH AFRICA
Hanti Kotze   

University of Johannesburg, Johannesburg, SOUTH AFRICA
Online publish date: 2018-06-02
Publish date: 2018-06-02
EURASIA J. Math., Sci Tech. Ed 2018;14(8):em1567
This paper aimed to investigate the type of modelling task that may elicit competencies that are more aligned with demands from the biomedical technology industry. The inquiry identified strengths and weaknesses in students’ modelling competencies by analysing errors in two types of modelling tasks: atomistic and holistic. By using subtasks, errors could be identified according to the Newman error categories and compared with six modelling competencies according to the framework of Blum and Leiß. First-year biomedical technology students at a South African university made more errors in interpreting, validating and presenting, these being modelling competencies required to convert mathematical results to real-world results. The findings indicated that competencies embedded in atomistic tasks are more relevant to workplace demands in the local setting than those elicited in holistic modelling tasks. The implications for classroom practices are discussed.
Blomhøj. M., & Jensen, T. H. (2003). Developing mathematical modelling competence: conceptual clarification and educational planning. Teaching Mathematics and its Applications, 22(3), 123–140.
Blum, W., & Leiß, D. (2007). How do students and teachers deal with modelling problems? In C. Haines, P. Galbraith, W. Blum, & S. Kahn (Eds.), Mathematical modelling: Education, Engineering and Economics – ICTMA 12 (pp. 222–231). Chichester: Horwood Publishing.
Freudenthal, H. (1991). Revisiting mathematics education. Dordrecht: Kluwer Academic Publishers.
Gainsburg, J. (2013). Learning to model in engineering. Mathematical Thinking and Learning, 15(4), 259–290.
Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. ZDM Mathematics Education, 28(2), 143–162.
Gravemeijer, K., Stephan, M., Julie, C., Lin, F., & Ohtani, M. (2017). What mathematics education may prepare students for the society of the future? International Journal of Science and Mathematics Education, 15, 105–123.
Harris, T. R., Bransford, J. D., & Brophy, S. P. (2002). Roles for learning sciences and learning technologies in biomedical engineering education: a review of recent advances. Annual Review of Biomedical Engineering, 4, 29–48.
Huang, Q. R. (2007). Competencies for graduate curricula in health, medical and biomedical informatics: a framework. Health Informatics Journal, 13(2), 89–103.
Humphrey, J. D., Coté, G. L., Walton, J. R., Meininger, G. A., & Laine, G. A. (2005). A new paradigm for graduate research and training in the biomedical sciences and engineering. Advances in Physiology Education, 29(2), 98–102.
Khan, T., Desjardins, J., Reba, M., Breazel, E., & Viktorova, I. (2013). Quantitative methods in biomedical applications: creative inquiry and digital-learning environments to engage and mentor STEM students in mathematics. In J. Rychtář, R. Shivaji, S. Gupta, & M. Chhetri (Eds.), Topics from the 8th annual UNCG regional mathematics and statistics conference, Springer Proceedings in Mathematics and Statistics 64 (pp. 15–24). New York: Springer.
Kotze, H., Jacobs, G., & Spangenberg, E. (2015). Attitudes of biomedical technology students towards mathematical modelling. Proceedings of the ISTE International Conference on Mathematics, Science and Technology Education, 25 – 29 October, Mopani Camp, Kruger National Park, South Africa, 136-148.
Lave, J. (1996). Teaching, as learning, in practice. Mind, Culture, and Activity, 3(3), 149–164.
Magjarevic, R., Lackovic, I., Bliznakov, Z., & Pallikarakis, N. (2010). Challenges of the biomedical engineering education in Europe. Proceedings of the 32nd Annual International Conference of the IEEE EMBS, Buenos Aires, Argentina, August 31 – September 4, 2959-2962.
Makonye, J. P. (2011). Learner mathematical errors in introductory differential calculus tasks: a study of misconceptions in the senior school certificate examinations (PhD thesis), University of Johannesburg, Johannesburg, South Africa.
Mantas, J., Ammenwerth, E., Demiris, G., Hasman, A., Haux, R., Hersh, W., Hovenga, E., Lun, K. C., Marin, H. Martin-Sanchez, F., & Wright, G. (2010). International Medical Informatics Association (IMIA) on education in health and medical informatics – 1st revision. Methods of Information in Medicine, 49(2), 105–120.
Newman, M. A. (1977). An analysis of sixth-grade pupils’ errors on written mathematical tasks. Victorian Institute for Educational Research Bulletin, 39, 31–43.
Schoenfeld, A. (2001). Reflections on an impoverished education. In L.A. Steen (Ed.), Mathematics and democracy: the case for a quantitative literacy (pp. 49–54). National Council on Education and the Disciplines.
Schraw, G. (2013). Conceptual integration and measurement of epistemological and ontological beliefs in educational research, Review article, Hindawi Publishing Corporation ISRN Education, Volume 2013, Article ID 327680.
Stoddart, T., Abrams, R., Gasper, E., & Canaday, D. (2000). Concept maps as assessment in science inquiry learning - a report of methodology. International Journal of Science Education, 22(12), 1221–1246.
University of Johannesburg (2017). Faculty of Science, Doornfontein campus, Rules and regulations for undergraduate programmes. Retrieved from
Van den Heuvel-Panhuizen, M. (2005). The role of contexts in assessments. For the Learning of Mathematics, 25(2), 2–9.
Wijaya, A., van den Heuvel-Panhuizen, M., Doorman, M., & Robitzsch, A. (2014). Difficulties in solving context-based PISA mathematics tasks: an analysis of students’ errors. The Mathematics Enthusiast, 11(3), 555–584.