Marian Mazur, “Źle z matematyki” (‘Trouble with Mathematics’), the weekly Argumenty 1966, no. 36 (430), pp. 5 and 10.
Why teach mathematics to everyone if many educated people get by without it once they have left school? Mazur answers that the school should provide tools for describing change and for making sensible choices, and alongside them the fundamentals of statistics together with a distrust of numbers, because mathematics has its limits. Calculation carries the truth of the input data over to the result but does not create it: a correct calculation based on false data yields falsehood in a tidy form, while data that are true but incomplete can be used to justify opposite conclusions.
The common justification that school mathematics teaches reasoning is, in the author's view, a myth: a typical problem is settled by a single apt trick that cannot be transferred to another case. The curriculum he proposes instead proceeds from the general to the particular and takes in problems of organisation (schedules, algorithms, graph theory) and of optimisation, that is, of choice under limited resources. It begins with the concept of a function and with the graph, which can be drawn and read even when all that is known about a phenomenon is in which direction and how fast it is changing — and this opens the way to qualitative analysis. Differentiation and integration he reduces to the rate of growth and the summing of increments, that is, to concepts present in almost every press article on the economy. Less room would go to drills in taking logarithms and in trigonometric transformations, and using tables would no longer be forbidden.
For the few candidates for studies in the sciences and engineering, the author proposes a separate solution: a preparatory year at the university, with a faster pace and better teachers, which would replace competitive entrance examinations and take a load off the school.
The theme of decisions under limited means is developed in Cybernetyka a zarządzanie (‘Cybernetics and Management’, 1969), and the question of whether data agree with reality can — in our reading — be described in the language of Jakościowa teoria informacji (‘A Qualitative Theory of Information’, 1970), in which the concepts of the original and the image appear.