Full Idea
According to the structuralist, mathematicians study the concepts (objects of study) such as variable, greater, real, add, similar, infinite set, which are one level of abstraction up from prima facie base objects such as numbers, shapes and lines.
Gist of Idea
Structuralist says maths concerns concepts about base objects, not base objects themselves
Source
Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.1)
Book Reference
Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.82
A Reaction
This still seems to imply an ontology in which numbers, shapes and lines exist. I would have thought you could eliminate the 'base objects', and just say that the concepts are one level of abstraction up from the physical world.