According to commognitive conceptualization, development of mathematical thinking, whether historical or ontogenetic, requires periodic transitions to mathematical discourse incommensurable with the one that has been practiced so far. In this new discourse, some familiar mathematical words will be used in a new way. Historically, such discursive transformations were usually greeted with resistance and led to heated, centuries-long debates. Also for today’s learners, a discourse incommensurable with the one currently in use constitutes a source of much trouble. This is particularly true in those cases in which the change in the use of words occurs tacitly, leading to apparent paradoxes. In this paper, I argue that discourses of finite and infinite sets are mutually incommensurable, and thus the case of students grappling with Sierpiński triangle (ST) may lead to insights about ways in which learners act in the face of incommensurability. Here, possible sources of the confusion reported by the participants are identified with the help of specially designed discourse-analytic tools. It is shown that the students, imperceptibly to themselves, oscillate between the discourses of area-as-a-segment-of-a-plane and of area-as-a-number. The analysis is followed with discussion on theoretical, methodological and practical implications of this study.
|Journal||International Journal of Research in Undergraduate Mathematics Education|
|State||Accepted/In press - 2021|
Bibliographical noteFunding Information:
This special issue has been conceived at a workshop supported by the Israel Science Foundation under grant number 2821/19. The data described above and used in the papers in this special issue have been collected in the framework of research funded by the Israel Science Foundation under grant number 843/15. The author wishes to thank the Editors of this special issue for giving her the opportunity to engage with their work and have her own analytic take on their data.
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
- Meta-level learning
ASJC Scopus subject areas
- Mathematics (miscellaneous)