Dijkstra (the one who has a graph algorithm named after him, aside from being a really influential computer scientist in many ways) argued more or less exactly what you're arguing: that formal methods (that is, formally proving, mathematically, that your code will behave as it should) are the appropriate way to teach computer science/programming. His argument is basically that computer science is very hard applied math, and should be treated as such.

You might find https://www.cs.utexas.edu/users/EWD/transcriptions/EWD10xx/E... an interesting read, if you haven't read it before. There's been some interesting discussion of it on HN in the past, too.