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Investigating the Dynamics of Knowledge Acquisition in Learning Using Differential Equations
Abstract:A mathematical model for knowledge acquisition in teaching and learning is proposed. In this study we adopt the mathematical model that is normally used for disease modelling into teaching and learning. We derive mathematical conditions which facilitate knowledge acquisition. This study compares the effects of dropping out of the course at early stages with later stages of learning. The study also investigates effect of individual interaction and learning from other sources to facilitate learning. The study fits actual data to a general mathematical model using Matlab ODE45 and lsqnonlin to obtain a unique mathematical model that can be used to predict knowledge acquisition. The data used in this study was obtained from the tutorial test results for mathematics 2 students from the Central University of Technology, Free State, South Africa in the department of Mathematical and Physical Sciences. The study confirms already known results that increasing dropout rates and forgetting taught concepts reduce the population of knowledgeable students. Increasing teaching contacts and access to other learning materials facilitate knowledge acquisition. The effect of increasing dropout rates is more enhanced in the later stages of learning than earlier stages. The study opens up a new direction in further investigations in teaching and learning using differential equations.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1316670Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 394
 D. Kuhn, M. Garcia-Milla, A. Zohar, C. Anderson, S. H. White, D. Klahr, S. M. Carver, Stratergies of knowledge acquisition, Monographs of the Society for Research in Child Development, 60, 1-157, (1995).
 J. E. R. Staddon, Adaptive behaviour and learning, Cambridge University Press, London, ISBN: 0521 256992 (1983).
 M. Woda (2010). Effective Knowledge Acquisition by Means of Teaching Strategies, Computational Intelligence and Modern Heuristics, Al-Dahoud Ali (Ed.), ISBN: 978-953-7619-28-2, InTech, Available from: http://www.intechopen.com/books/computational-intelligence-and -modern-heuristics/effective-knowledgeacquisition-by-means-of-teachingstrategies.
 N. Spaull, J. Kotze, Starting behind and staying behind in South Africa- The case of insurmountable learning deficits in mathematics, Int. J. Educational Development, 41 (2015) 13-24.
 M. Latseka, The Illusion of Education in South Africa, Clin Microbiol Infect, 5th World Conference on Educational Sciences - WCES 2013, Procedia - Social and Behavioural Sciences 116 ( 2014 ) 4864 4869.
 H. Venkat, N. Spaull, What do we know about primary teachers’ mathematical content knowledge in South Africa? An analysis of SACMEQ 2007, Int. J. Educational Development, 41 (2015) 121-130.
 N. Spaull, Poverty and privilege: Primary school inequality in South Africa 2013, International Journal of Educational Development, 33 (2013) 436447.
 M. Murray, Factors affecting graduation and student dropout rates at the University of KwaZulu-Natal, South African Journal of Science, 2014;110(11/12), Art. 2014-0008. 6 pages, http://dx.doi.org/10.1590/sajs.2014/20140008.
 J. Dewey (1897). My pedagogic creed. In J. Dewey and A. W. Small, Teachers manuals (No.25). New York, NY: E. L. Kellogg and Co..
 C. G. Mooney (2000). Theories of childhood: An introduction to Dewey, Montessori, Erikson, Piaget, and Vygotsky. St. Paul, MN: Redleaf Press.
 L. S. Vygotsky (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press. (Original work published in 1934).
 T.E. Mabila, S.E. Malatje, A. Addo-Bediako, M.M.M. Kazeni, S.S. Mathabatha, The role of foundation programmes in science education: The UNIFY programme at the University of Limpopo, South Africa, International Journal of Educational Development, 26, (2006) 295304.
 W. R. Derrick, P. van den Driessche, A disease transmission model in a nonconstant population, Journal of Mathematical Biology, 31 (1993) 495-512.
 W. O Kermac, A.G. MxKendrick, Proceedings of the Royal Society of London Series A In Mathematical and Physical Character , 15, 700-721, (1927).