In my own personal experience in teaching linear algebra, where many students encounter abstract ideas for the first time, I find that most students have trouble consolidating observations from concrete examples into understanding of abstract ideas.
Very often, after giving many examples, students understood the examples very well, but they can't say anything beyond that.
Take the concept of subspace, for example: Many students can know 5 examples of subspaces of vector spaces very well, yet cannot answer the most basic question about any subspace they have not studied. E.g., "if we have a set of functions in the vector space of continuous functions over [a,b], how can we check if this set form a subspace?"
I wonder if this a common problem: Are any empirical studies or observations derived from large samples on how well average undergraduate students can learn abstract concepts through concrete examples.