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.
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