A minor success in programming seeming to help with math: VPython (
vpython.org) makes it easy to write programs that generate navigable
real-time 3D animations, and in the Matter & Interactions curriculum
thousands of college students every semester write VPython programs to
model physical systems, to visualize fields in 3D, etc. VPython does vector
algebra, which lets students write computations in vector notation,
handling vectors as unitary objects rather than conceiving of vectors only
in terms of components (or worse yet, in terms of sines and cosines). Most
of a VPython program is written coordinate-free and component-free. After
the introduction of VPython we observed that average students at NCSU had a
better understanding of and facility with vectors than did very strong
students at CMU before the introduction of VPython. (It may also have
helped that at about the same time we also introduced a vector notation
found in some calculus textbooks, <x,y,z>, that seems to promote the idea
of regarding a vector as a single thing.)
An interesting side comment is that in necessarily brief AAPT conference
workshops on VPython, it was common to see physicists finding it difficult
to conceive of a computation in terms of vectors rather than in terms of
components.