Computational structuralism has been presented by [Halbach-Horsten 2005] and [Quinon-Zdanowski 2007] as a particular type of structuralism with respect to the structure of natural numbers. It has even been claimed that this approach can solve problems of traditional structuralism. Computational structuralism has been considered to be structuralism, because, according to this view, arithmetic is about the structure of natural numbers. The individual elements of this structure are defined in terms of dependence upon this structure. There is, however, an important consequence of computational structuralism which distinguishes this approach from traditional structuralism, and which begs the question of its ‘structuralist’ character. Computational structuralists claim that natural numbers are precisely those objects that people use for counting and computing. In order to provide an account of what computations are, without using the notion of the natural number, computational structuralists find themselves constrained to define computations on strings of characters: computations are manipulation of symbols with syntactic structure. An obvious consequence of this definition is that numbers are objects having necessarily an internal structure, and hence in the result, it is not only a 'structure' of the internal relationship between elements of a model that is important, but also the inner structure of those elements, the reference to which is avoided in classical structuralism. Furthermore, in order to determine the identity between numbers from different recursively isomorphic models, computational structuralists need to determine criteria for acceptable notations. I am going to address these issues in my presentation.