![]() ![]() The second part presents an analysis method together with a study which was carried out in a grade 11 school class and takes up the research questions stated at the end of the theoretical part. ![]() The process of establishing these connections in an explanation (see RQ 2). The connections a student establishes between mathematical signs, between verbal terms, or between signs and terms (see RQ 1). Afterwards, these considerations are related to the subject area of “derivative”, which leads to specific research questions regarding: This article is divided into two parts: In the first part Wittgenstein’s view of mathematics is presented and referenced to Peirce’s theory of signs with an emphasis on connections between mathematical sign activity and speaking about this activity. In particular, studies mention that one difficulty in understanding the derivative is that various other terms need to have been learned beforehand, such as “function”, “limit”, and “difference quotient” (e.g. Ferrini-Mundy & Graham 1991 Orton, 1983 Rasmussen et al. Students exhibit various difficulties in learning calculus (e.g. In other countries, like Austria, it is already part of the school curriculum in grades 11 and 12. In some countries, calculus is only taught at college or university. Therefore, how a student uses mathematical signs in an explanation on this topic is particularly interesting. In complex subjects, as with the topic of “derivative”, sign activity and speaking about it are linked to each other in various ways. Neither one nor the other can be dispensed with. From this perspective, in order to participate more and fully in mathematical social practice, a learner needs to become fluent in mathematical sign activity and in addition this sign activity needs to be linked to speaking about the sign activity. The ways in which mathematical activity, sign activity and speaking about sign activity intertwine will be elaborated upon below. Additionally, speaking about sign activity is also inevitable within mathematical reasoning. Therefore, these signs are not only a means but are objects of mathematical activity as well. Furthermore, the meaning of these signs arises from the use of the signs, thus, largely from activity with the signs. Dörfler, 2016), where sign activity is seen as a central and inevitable part of mathematical activity. In this article, mathematical signs will be considered from the perspective of Wittgenstein and Peirce (cf. In the literature, the role of mathematical signs, such as symbols, terms, equations and graphs, often is described as a means for mathematical activity, for example to serve as representations for abstract mathematical objects (e.g. It is precisely this linkage that is the focus of this article by means of examples of students’ explanations and reasoning regarding the derivative. Sign activity and speaking about sign activity are both part of mathematical activity.
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