... for the non-German population of the East there can be no type of school above the four-grade rudimentary school. The job of these schools should be confined to the teaching of counting (no higher than up to 500), the writing of one's name, and the teaching that God's commandment means obedience to the Germans, honesty, industry and politeness. Reading I do not consider essential.

She investigated the psychological process of forming clear and rigorous notions in geometry by the pupils.

The subject of the research - as Danuta Gierulanka wrote - emerged from her own professional experience, from everyday struggles with the craft of a mathematics teacher at school, motivating her to try to remedy the failures she experienced in working with students. It is a certain paradox - she stated at the beginning of her work in Kraków junior high schools - that mathematics, being a science of "the simplest, most transparent and harmonious structure", is in fact a particularly difficult school subject for the vast majority of students, and for some even hated. However, not every teacher, even if he or she is a so-called reflective teacher, undertakes scientific research to investigate the causes of his or her didactic difficulties and low effectiveness of teaching his or her subject.

Thus, for example, I will say that I have acquired the concept of a square if something has happened that can be described in outline more or less as follows: At first I had no idea what the word "square" meant. Thanks to certain procedures on the part of someone explaining the meaning of this name to me, i.e. pointing out in some direct or indirect way the object designated to me, I have reached such a state that I am able to do what I could not do before, namely, distinguish squares from non-squares, describe them, state their properties, construct them, and generally solve such problems concerning squares for the solution of which mechanical repetition of what was given to me as an explanation is not enough, but it is necessary to refer to some object that has become available to me; and in this case it is an object different from the words and actions of the person who taught me about it, but such an object to which these words and actions referred. In my experiences, however, I can precisely distinguish subjective moments of certainty, of a clear orientation towards something, of intellectual trust, moments that ultimately oppose decisively a certain sense of emptiness, uncertainty and instability that accompanied the first encounters with the name of the square in the initial stages of the described process. Despite the opposition of these subjective moments occurring in these extreme stages of the process, the transition from one to the other takes place rather gradually. I express the occurrence of moments characteristic of the final stage of the process by saying, for example: "I know, I understand what a square is."

Influenced by lectures and seminars conducted by Prof R Ingarden, in which I participated regularly since 1946, I was getting an even broader view of the philosophical problematics related to my psychological work. A problem in which I have taken stronger and stronger interest since 1948 is the problem of specificity of mathematics; in its solution I would see a natural complement of the work on acquiring geometrical notions. [This work] gave an idea - thanks to investigation of the course of suitable psychical thought processes - only about psychological sources of the paradoxical opposition between the fundamental clarity and comprehensibility of mathematics and the actual state of its being comprehended. To explain it fully it is necessary to realise what the specific character of mathematics, and of the cognitive means it employs, consists of. Seeing Cartesian mental intuition and what is called 'clara et distincta perceptio' as a cognitive activity typical for mathematics, I analysed this notion. ... Another kind of cognitive processes very relevant for mathematical cognition are processes of understanding. I have been concerned with the problems of understanding since 1951, conducting for 2 years research in the Laboratory of Experimental Psychology concerning primarily understanding of texts. With the subsidy from Scientific Pedagogical Society I conducted research parallel to this, concerning learning mathematics from textbooks, including analysis and criticism of school textbooks in geometry in use at that time. ... Because of the financial difficulties of the Scientific Pedagogical Society the research ceased, and the partial results obtained were not published; those concerning textbooks became obsolete when change occurred.

In her habilitation, Gierulanka addressed the problem of mathematical cognition as a philosopher, although she also used some previously collected psychological materials. ... Gierulanka analysed mathematical perception and deduction from the phenomenological standpoint and described attempts at systematisation and unification of mathematics. She did not consider reduction to set theory as true solution of the problem of unification of mathematics. She criticised Bourbakist mathematics, blaming it for, among other things, being arbitrary in constructing systems of axioms and making unnatural generalisations. However, she saw some possibilities for applying the notion of mathematical structure

I remember that weekly visits [by Roman Ingarden] to our home were always combined with scientific visits with Ms Gierulanka, who lived one floor below us. These were always connected. Ever since Ms Gierulanka moved into the same building, my Grandfather would go and spend an hour with her first, because they always had something to fix, discuss and plan.

Danuta Gierulanka was very attentive around Ingarden, planning, helping him out. I think it's worth mentioning that Ingarden's favourite hobby was developing photos. He simply liked taking pictures and having models to photograph. Not classic models, but for example ... Gierulanka.

Danuta Gierulanka was a great lecturer and a very clever head. She taught us psychology, but you know that Gierulanka had a master's degree in mathematics, a PhD in psychology and a habilitation in philosophy. These were really elaborate, well-prepared lectures with a certain analytical flair.

She retired with the sense of injustice: the programme of doctoral studies in university teaching for assistants in various academic disciplines was not launched and the university authorities did not show recognition of her work and achievements.