[milspec]

Standard algorithms are standard for very good reasons. They are 100% reliable and at least reasonably fast, if not the fastest.

Failure to learn the standard algorithms impedes progress. You are unlikely to do well in the next course if you are slow and can't handle numerous cases.

Learning alternate algorithms is great... once you have the standard algorithms down solid and are ready to prove equivalence.

[keithpeter]

Concrete illustrations based on things in your world -> procedural methods (your algorithms) -> formal proof seems to work in my teaching of basic maths to adults.

Have a look at the sample chapter from David Tall's book...

https://homepages.warwick.ac.uk/staff/David.Tall/themes/thre...