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I grew up in a culture like that, too, but I still struggled with algebra, in spite of working hard on it every night. I don't think the same person who does well in engineering will also do well with music performance or speaking a foreign language. Most people (allowing for a few exceptional individuals) will be better at one or two of those, out of three (not to mention other fields). There's definitely something to be said for starting kids out young with skill acquisition. Still, some kids who are raised bilingually go on to master other languages easily, some don't. And being exposed to music early doesn't mean you'll have a gift for it.
It would be interesting to do some studies on these questions. Does early ear training result in a facility for music? Does that mean that tone deafness could be eliminated with early ear training? Good questions.
The Suzuki method of music training emphasizes early exposure to music. The idea is that children can pick up music similar to how they pick up their native language. Children begin instruction as early as two years old, and the initial focus is on playing by ear rather than reading notation.
The one caveat is that care must be taken to master each of the building blocks (algebra, trig, etc) before proceeding to the next level. If you start trying to take on the next level before you have an intuitive understanding of the prerequisites, it will get confusing quickly.
I'm going to make a point that this is where American education falls down.
The Suzuki method of music training emphasizes early exposure to music. The idea is that children can pick up music similar to how they pick up their native language. Children begin instruction as early as two years old, and the initial focus is on playing by ear rather than reading notation.
I wish the Suzuki method had been around when I was a kid! My music teachers all complained that I played too much by ear, not by the notes! But your post doesn't answer the question re: whether early exposure to music and ear training can override tone deafness, and whether all kids respond to the method with the same level of progress. It would be good to do a study of Suzuki-trained kids, to see if they universally handle music more skillfully, or if some quit or lag behind others.
Someone of reasonable intellect can eventually learn anything. But that is not the program. In these difficult majors a specific amount of work or learning must be accomplished in a limited amount of time. Many simply cannot learn that fast. So no they cannot do the program. Engineering is somewhat different from many fields. Those that do well with engineering in major projects are able to merge their basic engineering training with gifted creative interpretations that either contain or reduce cost or limit risk or yield totally new creations.
1) Math really isn't a homogeneous pool of knowledge, but a set of discrete skills. Someone can be great at calculus, but lousy at matrices, or vice versa.
Math is a language, more or less, so it's not that different from the possibility someone could be great at vocab (or creative writing) but lousy at grammar.
So I think some of why people struggle with math is that we take a very linear approach to instruction, some of which builds upon skills learned prior, but not entirely. They might be fantastic at a particular area in math, but they're unlikely to get there if they struggle with topics earlier in the curricular order.
2) In many cases I think people struggle significantly with "how" we teach. Math is often taught purely as rote memorization in the U.S. - that approach will work for some and not for others. Historically the small percent of the population that learned math did it in the context of solving problems, not the abstract labor of learning for the sake of unclear future application.
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You're not bad at math, you're just lazy.
