This paper tries to clarify the way in which our theoretical model relates to teaching practice in response to questions about how the model could potentially be applied. The theoretical model introduces an extension of Jean Piaget’s general law of cognition to explaining the difference between algorithmic thinking and computational thinking by adequately locating the latter in the specificities of the subject instructing a computer. The teaching practice consists on activities introducing programming in high school mathematics courses. These are organised in a functional programming course to high school mathematics teachers and didactic instances in which the teachers teach their students to program solutions to mathematics problems.

Through examples we explain how the model helps teachers in finding a meaning of the popular and controversial expression “computational thinking”. The goal of the didactic instances is to educate students in thinking algorithmically and computationally.