Case study comes ready and delimited, example clinical case. A research case will be initiated, explored so it needs to be delimited so as not to expand too much.
In my experience in research in mathematics teaching, understanding the specifics of a particular phenomenon in teaching and learning mathematics precedes the importance of the observed phenomenon in research in mathematics teaching.
Casuist-oriented teaching combines with the goal of developing a habitus of reflexive distancing. The extent to which reflexive distancing occurs could be illustrated by means of a case study for teaching. Ultimately, it is a question of scientific or methodological location. By a case study for teaching, I mean teaching sequences or examples from the classroom that are analysed in terms of, for example, an individual case.
With a research case I would (intuitively and associatively) rather expect a quantitative-empirical study, or at most a qualitative-empirical study. Psychoanalytic pedagogy, for example, works - like other pedagogies - with case vignettes and case studies. However, its approach is not primarily empirical. I would therefore make it dependent on the research paradigm on which the study is based. The reconstruction of a case could perhaps be called a research case. In both cases, the aim can be to better understand pedagogical action in the classroom. In doing so, to work out a casuistry from a theoretical and applied perspective and to go new innovative ways.
Not only difficult children and adolescents can entangle educators in confusing relationship constellations. A deeper understanding of the unsettling enactments of these pupils makes it possible to act more professionally and to initiate effective support steps. Case studies can show how instructional work can be designed in schools. The presentation of paradigmatic case studies can serve to develop pedagogy theoretically, which is why I would speak of research case in this case.
It would be easier for me to vote for a designation if I knew the article. You are welcome to send it to me.
Thanks for such a detailed reply. According to your elaboration, the teaching cases is my next target to publish with emerald case study journals in the area of family business.