Anna Sfard - Module 4 - Mathematical objects, what they are скачать в хорошем качестве

Anna Sfard - Module 4 - Mathematical objects, what they are

Having defined mathematics as the activity of telling stories about mathematical objects, I ponder in this module about mathematical objects. These latter entities seem quite unlike those investigated in physics, biology or astronomy. The objects of the scientific discourses, just as those we encounter and talk about in our everyday life, can be experienced directly even before one is able to say anything about them. The case of mathematical objects is quite different. Numbers, functions and derivatives, unlike stones, stars and living creatures, do not wait for us out there to be seen, smelled, heard or felt. If so, what are these objects called mathematical (or MOs, for short), where we can find them and how we can get aware of them and their properties? This two-part module is devoted to all these questions. More specifically, in this module I will address the questions of what mathematical objects are and why we need them. According to the communitive answer to query 1, mathematical objects are discursive constructs, that is, a special form of speech that allows us to say more in less words. This position contrasts with the classical Platonic view, according to which the entities we talk about in mathematics are of a different ontological status than the talk itself (the latter plays the mere auxiliary role of a medium for describing the preexisting reality). Bibliography Sfard, A. (2000). Symbolizing mathematical reality into being: How mathematical discourse and mathematical objects create each other. In P. Cobb, E. Yackel, & K. McClain (Eds.) Symbolizing and communicating: perspectives on mathematical discourse, tools, and instructional design (pp. 37-98). Mahwah, NJ: Lawrence Erlbaum Associates. https://www.mathunion.org/fileadmin/I... Sfard, A. (2008). Chapter 6: Objects of mathematical discourse: What mathematizing is all about. In A. Sfard, Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge, UK: Cambridge University Press. https://www.mathunion.org/fileadmin/I...