[haphazardeous]

This depends on how people learn and perceive information. If I hadn't learnt programming before I was taught Maths and Calculus, I probably wouldn't have understood some of the basics like Functions, Matrixes and Series etc or it would have taken me quite a while to grasp the idea.

For me Maths is boring. It's abstract and you don't have any interaction whereas programming is more fun for me. I never truly understood some of the physical and mathematical concepts I was taught in school and uni until I came across programming/software development problems that are solved with those and only then I realised how useful they can be.

[DamnYuppie]

I also find Math studies by themselves to be quite boring, at least that is how I perceived it for most of my education. Yet I had one teacher who worked really hard to show how Calculus is applied in reality. He made all of his homework and test's real world problem solving oriented. He was also a part time scout for the Seattle Mariners and he would do all of his in class examples using either base ball or real estate. This really helped me put into context many of the concepts and the multitude of ways they can be applied, not to mention it was a really exciting and enjoyable class.

After experiencing that I saw Math in a new light. I simply wish that my K-12 education was more directed to the applicability of many of the concepts we learned as I believe it would have made the subject not only much more approachable but enjoyable.

[vog]

Indeed, programming something is a great trick to get a deeper understanding of it. It means writing everythin down to the details that even a dumb machine can understand it.

I guess this is like understanding something better by explaining it to others. Just that this "other person" is a machine. It is also well-known that it even helps to explain it to your own, by writing it down. For example, PG noted that in the introduction of http://paulgraham.com/writing44.html

[pjmlp]

It is a very personal thing how each one learns, of course.

On my case, the tools provided by abstract math and CS (algorithms, data structures, calculus) allow me to think outside of the box and quickly adapt to any programming language.