Most of the time, student fail to solve a problem simply because they do not know what to do.
Then, when they have a vague idea of what they have to achieve, they do not necessary are able to use/understand mathematic symbols.
I've made a document that could permit to know the "level" of a student according to his math symbol comprehension.
These are 58 questions that DO NOT REQUIRE advanced PROCESSING. It's direct application and student is NOT required to THINK.
All questions are multiple choice (5) and choices are offered so student can't logically deduce the answer from the answer of another question.
These are also some answers that appear to be right if you misunderstand a symbol.
Like confusing "(4!)!" and "4!!" or "²3" and "3²", etc.
Math symbolism is really important since it can help you for formalism then isomorphism and advanced analysis.
The answers are not given since question are trivial for a teacher.