I think one thing that really helped me understand math in a computational sense the 3rd or 4th time around was the aid of online homework/study guides (eg; MyMathLab from Pearson), where the step by step interactive aspect helped me build more confidence and understanding. It was easier to see patterns in the problems when I could work on them and view the step-by-step examples when I got tripped up. I've never actively used the Khan Academy site, but it also seems to have the emphasis on a step by step understanding. I think either of these can be great gateways to more advanced online applications and resources (eg; Mathlets for visualization, MIT's Open Course Ware for students/people interested in more advanced subject matter).
I think having these types of programmes (which is to say, the online programmes and resources) opens doors not only to availability of information, but also availability of help in understanding the information. In cases where teachers/tutors are sometimes overwhelmed or unable (or just as often unwilling) to help some or any students, these types of programmes offer a sort of "equalization" where differences in privilege and influences such as prejudice and other "face-to-face" discriminatory mindsets are less....well, influential. It hasn't been uncommon for me (and others, I'm absolutely sure) to be met with skepticism of my abilities/desire to learn math/science from teachers and/or tutors based on...who knows.. (That's that lack of empathy and understanding, I guess).
In the class room, I'll give an example of what I mean by using the intuitive concept of graph theory to open doors to higher level maths. We all know and hate the classic problem "if R and J are leaving from C and O respectively, who will reach N first?"This is where the teacher can draw a graph and explain how bus maps, subway maps, airplane destination maps etc. are types of graphs. This is where you show students how you can "take apart the segments" and compare them to each other. This is an intuitive intro to topology. And all of this is an excellent way to start in with "..and these are major areas of research in math."
I think another good way to open understanding math is comparing it to language in the classroom. To set up an equation "3x=y" and then compare it to a sentence "the (blank) is (blank)". Show how blanks 1 and 2 are really no different than x and y. "The (dog) is (human)" doesn't make sense., just as "3 times 2 equals 0" doesn't make sense.. Math is the language of science, after all, and this is a way of showing how important it is to be familiar with that language if the student has intentions of being in a STEM-related field (or any field that requires more advanced math).
Obviously the "equalizers" only equalize so much: STEM jobs don't come from messing around with OCW and MML and Wikipedia and all of that. That's where the mentality/empathy aspect comes in to play (and I'm neither a sociologist or a psychologist so I can't give any solutions there).
Just a rambling rant.