Our study was designed to identify a learning trajectory for the accumulation function as it learned with multiple representational technology based artifact. Thirteen pairs of 17-year-old students were asked to explain the connections between multiple-linked representations and to conjecture about the mathematical relationship embedded in the artifact. The study was guided by the semiotic mediation theory and the theory of knowledge objectification. We include two rounds of analysis: one to detect mathematical elements involved in learning the accumulation function, another to identify the progression process of learning the accumulation function. The data analysis identified four phases in the processes of objectification along which we suggest a trajectory for learning the accumulation function concept.