The main argument of this chapter is that cognitive semiotics will allow us to articulate a semiotics of science where philosophical and didactic aspects of scientific discourse can be investigated from a theoretical as well as an empirical perspective. More specifically the focus will be on two selected problems of graph and model comprehension in science education within reaction kinetics in physical chemistry: similarities between graphs misapprehended as images can confuse students, and image-schematic metaphorical interpretations of graphs can support model misconceptions. To understand didactic problems of this kind we need a semiotic analysis of science as a discourse.