Activity with Signs and Speaking About It

Exploring Students’ Mathematical Lines of Thought Regarding the Derivative

authored by: Annika M. Wille
Abstract: In order to participate proficiently in mathematical activity, a student needs to become fluent in both mathematical sign activity and speaking about the activity with signs. From the theoretical viewpoint of the philosophers Wittgenstein and Peirce, on the one hand, mathematics is seen as a sign game, while on the other hand experiments with signs allow for observable, communicable and describable reasoning. In this article, the focus is on the student’s sign activity and his or her speaking about it and the question of how they are intertwined. To that end, a method is presented to display the interplay of student’s activity with signs and speaking about it, and in particular, to reconstruct the student’s line of argumentation. This is applied to a case study where imaginary dialogues written by a class of grade 11 students on the topic “derivative” were analyzed.
External Organisation(s): Alpen-Adria-Universitat Klagenfurt (AAU)
Type: Article
Journal: International Journal of Science and Mathematics Education
Volume: 18
Pages: 1587-1611
No. of pages: 25
ISSN: 1571-0068
Publication date: 01.12.2020
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Education, General Mathematics
Electronic version(s): https://doi.org/10.1007/s10763-019-10024-1 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{8003c308b354496d98490bc095122793,
title = "Activity with Signs and Speaking About It: Exploring Students{\textquoteright} Mathematical Lines of Thought Regarding the Derivative",
abstract = "In order to participate proficiently in mathematical activity, a student needs to become fluent in both mathematical sign activity and speaking about the activity with signs. From the theoretical viewpoint of the philosophers Wittgenstein and Peirce, on the one hand, mathematics is seen as a sign game, while on the other hand experiments with signs allow for observable, communicable and describable reasoning. In this article, the focus is on the student{\textquoteright}s sign activity and his or her speaking about it and the question of how they are intertwined. To that end, a method is presented to display the interplay of student{\textquoteright}s activity with signs and speaking about it, and in particular, to reconstruct the student{\textquoteright}s line of argumentation. This is applied to a case study where imaginary dialogues written by a class of grade 11 students on the topic “derivative” were analyzed.",
keywords = "Calculus, Language and mathematics, Peirce, Semiotics, Wittgenstein",
author = "Wille, {Annika M.}",
note = "Funding Information: Open access funding provided by University of Klagenfurt",
year = "2020",
month = dec,
day = "1",
doi = "10.1007/s10763-019-10024-1",
language = "English",
volume = "18",
pages = "1587--1611",
journal = "International Journal of Science and Mathematics Education",
issn = "1571-0068",
publisher = "Springer Netherlands",
number = "8",
}