A Semiotic Analysis of Mediated Constructions of Quantity

Quantities are essential to students’ reasoning in mathematics and science. There is a continued need for research to explore the processes through which learners construct quantities involved in their reasoning. In this paper, we apply a semiotic perspective to analyze the case of a middle school student, Vicente, as he constructed quantities related to amounts of change of area in a dynamic task. We examine how Vicente’s reasoning became increasingly quantitative as he worked with artifacts. We first describe how Vicente constructed a semiotic chain supporting his quantification related to amounts of change of area. We highlight how artifacts from the situational context of a growing triangle supported his constructions. Then, we show how Vicente experienced semiotic interference as he connected his semiotic chain to new artifacts in a graphical context. In particular, he enhanced his signs related to amount of change of area to incorporate arbitrariness foundational to later smoothness. We discuss the implications of this work for future research applying semiotics to analyze quantitative reasoning.