This study interprets the change of the ontological status of “subjects,” which have a tripled structure consisting of a semiotic object, interpretant, and media. The study was carried out during a series of secondary school mathematics lessons from the embodiment perspective including embodied acts and language use. The authors presented the dynamic “zig-zag” phenomena of the semiotic classes, analyzed from the semiotic perspective, and assumed that perceptual media affected individual and collective activity in the classroom. Hence, we adopted the embodiment theory to make sense of the phenomena because it might prepare us for useful, detailed interpretations.
Embodiment theory has at least two theoretical assumptions concerning complementary analytical methodology: (1) “subjects” could exist through embodied actions with perceptual media, and (2) the way to deal with “subjects” is language use. These metaphorical expressions are based on some prior discussions about possible roots of embodied mathematics. In recent mathematics education research, the metaphorical approach is one of the most familiar and strongest methods to analyze the multimodal nature of human mathematics. Gesture appears to be an important factor to form mathematical meaning during mathematical communication. Thus, we developed the analytical framework under the above two assumptions.
Through embodiment analysis, we could identify several typical metaphors, such as “a magnitude relation between numbers is a segment.” In addition, we could establish that the segment metaphor might create a foundation for students to understand an approximation value of a square root. Finally, we identified whether students could recognize isomorphism among various media or not as the critical factor under the special “zigzag” phenomena.
