In 2013, I found Marilyn Burns' "Math Reasoning Inventory" online. The "computerized" version was for sale, but there were questions on the site, and so I made a "do it by hand" adaptation based on the ideas. I also included some other conceptual questions that I liked.
There are tester's pages where the teacher/tester can keep track of how the student responds to each question, and there are student-facing files that I put in a binder so the student could see one question at a time. We made manipulatives for putting numbers in order and on number lines. These are Word documents.
I didn't get far with any of my postsecondary students. As was shown in the research "What Community College Developmental Mathematics Students Understand About Mathematics" by Stigler and Givven, student understanding of numbers in the context of math instruction is very limited.
Tester Pages - Algebra and Negative Numbers link fixed :)
Question Cards (to put into binder) for Whole Number Questions.
I'll see if I can find the question cards for the other ones -- if I made them!