A phenomenographic study on profession-oriented modelling of the concepts of derivative and integral in the Turkish military academy, and the instructors and cadets views

The derivation and integral, which comprise the content of mathematics I and II in TMA (Turkish Military Academy), are also high school senior grade concepts. Cadets have fundamental knowledge of these concepts, all of which are the basics of the courses studied by senior classes. This paper aims to study the teaching of concepts through profession oriented real life modeling and their effects on teaching in line with the viewpoints of instructors and cadets. The participants of this research are the cadets, Mathematics instructors teaching 1st grade, and those teaching senior classes, which require Mathematics I and II as prerequisites. In this respect, some issues posing problems have been qualitatively examined: whether derivative and integral concepts in the Turkish Military Academy Math I and II courses provide sufficient fundamentals and meet the prerequisites of the senior class courses, the effects of real life modelings on teaching of mathematics, and the effects of profession-oriented real life modeling on teaching the courses to be followed in the upper classes. Data have been collected and analyzed in accordance with phenomenographic techniques, and the results obtained have shown that cadets have difficulty in expressing the subjects relating to economy and life mathematically, and that such applications are necessary to learn how they will confront the concepts of derivative and integral in near future and how much of it they will need in such a case. Depending on the data acquired, the researcher has made some suggestions such as allocating more time for the examples to encourage mathematical modeling, and attaching more importance to units of limit, integral, and derivative in lower educational institutions for a good restructuring