Anna Sfard - Module 5 - Mathematical objects, how we construct them скачать в хорошем качестве

Anna Sfard - Module 5 - Mathematical objects, how we construct them

Having described mathematical objects as discursive constructs, that is, as a special form of speech that allows us to say more in less words, I will ask in this module how these constructs come into being. More specifically, a close look will be given to objectification - the process of constructing mathematical objects. This process, its causes and its mechanisms, will be discussed as it occurs on the historical and ontogenetic levels. In both cases, three basic discursive transformations will be identified: those of saming, reifying and encapsulating. A distinction will be made between primary (unnamed) and discursive objects, and also between concrete and abstract objects. In the end, the question will be asked about the main challenges mathematics students face while faced with the task of constructing a new mathematical object. Bibliography Nachlieli, T., & Tabach, M. (2012). Growing mathematical objects in the classroom – the case of function. International Journal of Educational Research, 51-52, 1-27. https://www.mathunion.org/fileadmin/I... Sfard, A. (2015). Metaphors in mathematical thinking and in research on mathematical thinking: a prop or a trap? In F. Caluori, H. Linneweber-Lammerskitten, & C. Streit (Eds.), Beiträge zum Mathematikunterricht (pp. 42-49). Münster: WTM-Verlag. https://www.mathunion.org/fileadmin/I...