Abstract In this research, we consider the “subject” in mathematics as a “sign”―in Peirce’s semiotics―that directs our attention to different things, and we expose its evolutional development in a mathematics class from the perspective of its ontological status. We analyzed subjects through a lesson using the square root in the 9th grade while comparing them with Euler’s mathematical activity in “Analysin Infinitorum” from the viewpoint of Peirce’s “ten classes of signs.” The results highlighted the following points.
First, we described the evolutional development of subjects in a mathematics class and Euler’s mathematical activity using the ten classes of signs. Because both cases are similar in that the subjects develop almost evolutionarily in the order of the classes, it may be inferred that the mathematics class has a structure similar to Euler’s mathematical activity. Second, both cases, however, have a different point. In the mathematics class, there is occasion for the class to change from “legisign (sign as law)” to “sinsign (individual sign).” In other words, the subject in mathematics exists within the classes, including the sinsign, without existing for many members when the sign is appeared under the law or concept which exists for only some members in the mathematics class.
