This is something I've been pondering quite a bit recently. It is my firm belief that mathematical skill and general numeracy are actually a small subset of abs

This is something I've been pondering quite a bit recently. It is my firm belief that mathematical skill and general numeracy are actually a small subset of abstract thought. Am I wrong in thinking that school math is the closest to deliberate training in abstract reasoning that one would find in public education? Abstract reasoning, intuition, and creativity, to me, represent the underpinnings of software engineering, and really, most engineering and science, but are taught more by osmosis along side the unintuitive often boring mechanics of subjects. The difference between a good engineer of any sort and one that 'just knows the formulas' is the ability to fluently manipulate and reason with symbols and effects that don't necessarily have any relation or simple metaphor in the tangible world. And taking it further, creativity and intuition beyond dull calculation are the crucial art behind choosing the right hypothesis to investigate. Essentially, learning to 'see' in this non-spacial space of relations. When I'm doing system engineering work, I don't think in terms of X Gb/s throughput and Y FLOPS... (until later at least) but in my mind I have a model of the information and data structures clicking and buzzing, like watching the gears of a clock, and I sort of visualize working with this, playing with changes. It wouldn't surprise me of most knowledge workers arrive have similar mental models of their own. But what I have observed is that people who have trouble with mathematics or coding aren't primed at all to 'see' abstractions in their minds eye. This skill takes years to cultivate, but, it seems that its cultivation is left entirely to chance by orthodox STEM education. I was just thinking that this sort of thing could be approached a lot more deliberately and could yield very broad positive results in STEM teaching.