Development of substitution thinking

Pupils expect teacher guidance on how to calculate and are less interested in why the task is solved in such a way. If we accede to this way of teaching, our pupils will become users, who will see each part of mathematics as a single entity. They will learn the various procedures by heart and thus will lose the overview of more complex tasks and will not be able to transform the unknown task to a familiar one. The primary objective of teaching mathematics is to develop pupils' thinking. It is to develop and improve pupils' thinking during mathematics lessons and not just burden their memory. If the pupil succeeds in fully developing their thinking by using substitution, he or she gets the upper perspective in solving mathematical tasks. He is aware of the fact that on the basis of the task solution in the maths lesson, he can solve many other tasks with the right approach. Developed substitutional thinking is not just the use of substitution; it is basically a way of thinking, of how to find the ways to a solution of the specified tasks. This way of thinking is based on mathematical freedom.