Most are fine but there is a small minority that just mimic and parrot their way through life having no understanding of why they do what they do. They only know how to solve problems that are exactly like problems they have seen before but the moment they run into one that is even a tiny bit novel they can not do it. And it is almost always students that failed to learn a very fundamental concept 5 to 10 years ago and have been limping along since then. The damage compounds because anything that is based on something they do not understand gets added to the pile of things they do not understand until eventually they end up asking for help.
I was a math tutor for a couple of years in college. It is difficult, but this can be corrected (assuming the student is willing to put in the work).
I had gaps in my knowledge when I started tutoring as well. Factoring polynomials was always a struggle for me. I would pretty much guess and check until I got it right, and that was good enough for me to pass all of the tests in high school. Of course, until I got to multivariate calculus and I needed to factor more complicated polynomials as part of a much bigger problem. As you said, it compounded. Did I learn my lesson? No. I bought a calculator with a CAS to do that part for me. But when I started tutoring, I felt that it was unfair to my students to not know how to do something correctly, so I forced myself to learn it properly.
Tutoring finally broke me.
Most are fine but there is a small minority that just mimic and parrot their way through life having no understanding of why they do what they do. They only know how to solve problems that are exactly like problems they have seen before but the moment they run into one that is even a tiny bit novel they can not do it. And it is almost always students that failed to learn a very fundamental concept 5 to 10 years ago and have been limping along since then. The damage compounds because anything that is based on something they do not understand gets added to the pile of things they do not understand until eventually they end up asking for help.
I was a math tutor for a couple of years in college. It is difficult, but this can be corrected (assuming the student is willing to put in the work).
I had gaps in my knowledge when I started tutoring as well. Factoring polynomials was always a struggle for me. I would pretty much guess and check until I got it right, and that was good enough for me to pass all of the tests in high school. Of course, until I got to multivariate calculus and I needed to factor more complicated polynomials as part of a much bigger problem. As you said, it compounded. Did I learn my lesson? No. I bought a calculator with a CAS to do that part for me. But when I started tutoring, I felt that it was unfair to my students to not know how to do something correctly, so I forced myself to learn it properly.