Teaching in Software Applications: A Single Robust Built-In Command versus Sequence of More Elementary Commands

We investigate several exercises from the two fundamental disciplines of applied mathematics. We process the exercises in the software applications Maple and MATLAB: the exercises in Maple are from numerical analysis and the exercises in MATLAB are from statistics. For each example, we provide two ways of solution (not two different solutions) and try to explore their advantages and disadvantages for teaching students of university technical fields (undergraduate level). We pit solutions against each other: the first way of solution uses pre-prepared functions (robust built-in commands) for fundamental methods of given disciplines; in the second way of solution we have to “program” these methods by using sequences of fundamental commands. In the process, we theoretically establish parameter of education that needs to be carefully balanced for students’ success. However, we are not only thinking about how well the students pass the subject if we use this or that way of solution. We also want to reflect on what we expect and what it is expected that students should learn. Which of the ways will provide them with a more “suitable” type of education for their further development? It seems that with advancing technologies (constantly expanding computing power, the current boom in AI) some of our positions about teaching in software applications need to be re -evaluated – is it really so, or is it just an illusion and the fundamental practices remain valid and they just adapt to new environments? Specifically, for us: Is it still necessary to understand what applications do, or is it enough to remember how to interpret their various outputs? Finally, let us note that we also pay attention to how challenging it is, even for us teachers, to find out what a given robust command actually calculates.