One thing I see on occasion is the concept of "cool math" in action. By "cool math" I mean the idea that making the classroom more fun and pop-culture oriented makes math itself more fun and thus more accessible. In a sense it's sort of true: for people who are brought up in systems that teach math with the expectation that it will be used in some way (eg; engineering, stats, financial math, chemistry, physics) making the learning process more fun makes it easier to digest the complicated material. And if you get the pop-culture references or like the same stuff (music, movies, etc.) as your classmates, that's always nice. But all of that is contingent on the system your brought up in.
There are other systems out there. And within those systems, there are other definitions of "cool", and the students aren't necessarily (if at all) expected to use math or science in their lives after they complete just enough math to graduate high school and/or some certificate programme. I, myself, come from such a system. (As and aside, I realize I'm old enough to be a parent to some of my classmates [in some systems, anyway], and as such there's an argument to be made that it's an age gap. I argue somethings are universal and education is one of them).
In our system, a teacher in grades K-12 isn't/wasn't just a teacher: they were a social worker. They had to educate while also looking for signs of abuse, malnourishment, exceptionally poor hygiene, and teaching kids HOW to learn (in absence of active help outside of school) while teaching them WHAT they had to learn. In mathematical jargon, we might call that a knot. It becomes an issue of priority: basic skills and social care over in depth understanding of subject matter and the accompanying variety of subject matter.. For example: until my 20's, I honestly thought physics and astrophysics were the same thing. If you were a physicist, you studied space and that's it. My knowledge of physics was limited to what I read in my "grandparent's" National Geographic collection, and I guess astrophysics is the sexy branch of physics according to NatGeo. I digress... Any how, none of that is an indictment on the teachers ability to teach (note difference between "ability" and "desire"): A teacher is a teacher, not a miracle worker and you just can't expect an inner-city/urban teacher to be able to give the same clarity to subjects like math when it's hard enough having to teach almost every kid in the classroom how to write while trying to ignore that their best (we hope) efforts don't stop the bruises or the growling stomachs or the unwashed clothes.or the lack of outside help. In some places this cycle literally goes from K-12.
So how do you make math (and thus the STEM careers good K-12 math education opens doors to) accessible to the youth coming out of the broken system? Good question. Complicated, multifaceted answer. . It takes time, interdisciplinary co-operation, willingness on the part of members of both system-types, and serious revision of societal prejudices, motivations, and intentions. I can only speak with confidence in a few areas, one being math from an outsiders viewpoint. Recently I attended a seminar up at Reed College in PDX (a great conference, ps, and thanks to the Reed College Math Crew for putting it on) and overheard a conversation/argument on set theoretical based math education VS. a more visual approach. There's good and bad arguments for both sides. But I think one problem lies within the fact that nobody was talking about marrying the two.. Good pictures make good set theory more easily understandable. Say you have a pre-algebra class and you're telling the seeds "x+3=y, solve for y" or some such. Half the class stopped caring when you said "Good morning", the other half stopped caring when you said "x". Saying "This is important, you have to learn it" isn't going to inspire kids who've been barely getting by in math since 1st grade (I myself graduated high school having completed the minimal amount of math after having failed the 2nd semester of high school geometry). The change, the accessibility, the personalization of math has to come at the earliest levels. possible.. A teacher coming from a suburban background and a decent-to-good educational background coming into an "urban" (worst euphemism ever) school system is going to have a difficult time adjusting to the new culture they're now immersed in. All of the LotR references in the world aren't going to help you guys relate.. Saying "OK, now say you're a rapper and you want to add up the money you made...." is going to get you made fun of, possibly sued, possibly slapped, and most definitely "tuned-out" status. So maybe it's not about relating, but more about empathy and willingness on the teachers part to become in-tune with the culture that surrounds them. To give extra effort to be part of these kids lives in a way that can guide them to understanding through context of not just what math is, but where higher levels of math take you.
To give the math context, you have to give the kids context to math. "X is apples, Y is oranges" isn't context. It's a grocery list. "Urban" kids like science-y stuff too.. So you go around the room and spend a day (or more) relating math to things they're interested in. "You like electronics/apps/techno-doohikeies/car engines (applied math)? Well, you have to know about graphs...". Instant intro to combinatories/graph theory/engineering/physics. And graph theory is a fairly intuitive and visual way to understand...wait for it... sets and their theory. Some kids like space, so you give an intuitive, interest-piquing glimpse into geometry and relativity and such. Kids like sci-fi, and machine learning can be a fairly interesting idea to kids. Some kids won't ever "get" math because it's not their skill set (no matter what system you're a part of). The might be lawyers or doctors or who knows. But the point is identifying the kids who have the capacity by giving them a chance and a frame of reference....an understandable context to their identified strengths.....that can't be achieved without an empathy for the world and system these children and young adults live in.