The second author deals with mathematical instruction in common, as by this time computers were still not present in schools. It is Walther Lietzmann: Die Methodik des mathematischen Unterrichts (Methodology of Mathematical Instruction), Quelle & Meyer Heidelberg 1951, p. 9:
"The development of the opinions on the goals of calculating instruction is reflected by its history. Until 17th century it nearly totally emphasized practical purposes. The pupil was instructed how to do:
"Machs also - und kumpt recht" (Do it this way - and will come right) the Bamberg Rechenbuch of 1483 tells. Why this way should be gone stayed unanswered. So calculating was a handicraft, taught and learned as all the others. Teaching was dressing, instructing was swotting rules. Such a unilateral emphasis of the material principle has occasionally persisted into the 19th century.
We may say - or at least hope - that nowadays this kind of calculating instruction has died out. The reversal began in the 18^th century, decisive by the working of Pestalozzi. There was the new intention to form intelligence by calculating. Insight to the system of mathematical rules is not less important than knowledge and skill in execution. Thus the development of visual and logical qualifications became the main duty of mathematical education. Not rarely this formal principle was exaggerated, to teach more about the principles than to train the student's ability to use them properly. Gradually by time came an even balance between the formal and the material principle. Harnisch, Diesterweg and Hentschel should be mentioned."

move on