I am reposting this very nice explanation of the difference between teaching algorithms versus teaching conceptual understanding. The author is Sam Otten from The University of Missouri, and is responding to a viral post by a dad earlier this year (that I commented in in my May 16th post). The context is within the Common Core, but the issue is common to any math teacher no matter if you are in a Common Core state or not:

https://www.youtube.com/watch?v=dmybO35F_EI