From the perspective of cultural theory of objectification (Radford, 2006, 2014), and under a microgenetic approach, a multimodal analysis of the thought process occurred during the implementation of a set of three tasks which promote the development of the object mathematical derived is performed, from a variational and geometric view. The analysis found the emergence of various semiotic means (gestural, verbal, kinesthetic, writings, alphanumeric) that were coordinated and complemented during segments of activity, and showed the formation of semiotic nodes rating momentum and narrowing the space referential.