This study tries to clarify students’ states and processes in connecting the representations and the situation of function through analyzing the interviews with two eight grade’s students in terms of the semiotic perspective, in particular in view of the gestures.
First, we examined the meaning of signs as well as the difficulties in dealing with the signs. Then, we set our research frameworks focused on two roles of gesture: generalization and conceptual blending. As a result of analysis, we got the following findings regarding the students’ difficulties and the roles of the students’ gestures in reading the meaning of the situation in terms of the representations of function.
◦ The students had their difficulties in transforming from one representation to the other one with their understanding of the situation. In particular, their difficulties were related to the understanding of quantity-per-unit which was showed as the gradient of the graph of the linear function and the coefficient of x in the expression.
◦ It was suggested that there are several roles of gesture in connecting the students’ recognitions of the representations and the situation of function: Making the referent explicit, focusing the correspondence between two components of the situation, enriching the image of the motion and change of the situation, giving their conceptions of function a sense of reality, finding the regularity with their rhythmic actions, facilitating their conceptual blending through making one representation realistic, and becoming the further tool for understanding the related phenomenon.
