Application of Markov Chain to the ACE Teaching Style of Mathematics

The APOS instructional treatment of mathematics, introduced in the USA during the1990's by Ed Dubinsky and his collaborators, states that the teaching of mathematics should be based on helping students to develop the proper mental structures for learning mathematics. The ACE teaching style is the pedagogical approach of the APOS theory with the help of computers. Here a Markov Chain model is developed on the components of the ACE cycle on the purpose of studying mathematically its flow-diagram. This leads to a measure evaluating the student difficulties in learning mathematics. Examples are also presented on teaching the graphical representation of the derivative illustrating the applicability and usefulness of our model.