I taught everything from preschool through high school level math at a learning center that was supplemental to regular school. The youngest I ever worked with was 2.5 and she was extremely mature. Typically students were at least 4 years old and by the time they got to middle or high school their lives had become so busy that they often wound up dropping the program. Usually by that point, they were several grade levels ahead anyways so at that point they're really just reaping the head start they'd sewn for themselves through years of previous supplemental work at the center.

We worked with helping absolute beginners in math by focusing on tactile, iconic, manipulative understanding of quantity, how to construct numerals, basic arithmetic algorithms, algebra, geometry, trig, and some calc and probability. We used puzzles and games as a "recess" of sorts which would break up the hour long weekly visit while keeping the kids learning and developing while they "get a break" and "get to play".

We also helped parents prepare their kids to attend our center before the kids were ready to attend our center through encouragement of the development of prerequisite abilities like discerning left from right, handwriting muscles, etc.

I taught math at a deep and connected level. Most school teachers only know the math they are supposed to teach, the math they expect their incoming students to have learned the year prior, and anything else they remember from their own educations. A good math teacher knows as much math as possible so when a 3rd grader asks "Why do I need to learn this?", the teacher can respond, "Well, when you get into high school and you learn about trigonometry, you're going to need this skill a lot. This particular concept we are studying applies to and that's why it's valuable. People get paid a lot of money to deal with those problems as their jobs. Does that make sense?"

A crappy teacher will say "I don't know" and move on, which, unfortunately, is what a lot of students get.

If you're curious to learn more about the center and the methods we used, I can tell you that I talked about kind of stuff on Episode 444 of Daniel Prince's Once Bitten podcast. It focuses more perhaps on teaching philosophy and the use of neurological profiling techniques to get better outcomes than it does on which math I taught but it's still related.