I've seen both sides of this in my kids. My oldest was not required to memorize math facts (it wasn't a state math standard at the time) and just finished her freshman year in college. She will be the first to tell you that not having those facts memorized handicapped her in math--to the point that she didn't have the math skills necessary to get an A in college chemistry which was required for her to stand a chance at acceptance in the dental hygiene program. She did place into college-level math as a freshman and passed the ONE college math class required for graduation during her first quarter in college (she attends a state university in Washington State) so she isn't terrible at math. 
 
My younger daughter, however, had a 2nd and 3rd grade teacher who required memorization of math facts (addition, subtraction, mulitplication and division). In addition, because of that memorization, she was put in an advanced math class in 4th grade, took 6th grade math in 5th, 8th grade math in 6th and has been two years ahead since then. She will be able to take both AP Calculus AB and BC in high school. I credit her 2nd and 3rd grade teacher for her success in math.  
 
I as an expert at paper writing service theessayservice.org think memorization of the basic math facts is instrumental in students being able to succeed in higher-level math and to be able to carry-on the mathematical conversations you mentioned in your post. I also think students need to be taught standard algorithms that work EVERY time because with the "discovery" type math you seem to highly regard, students could end up with a method they developed on their own being stuck in their head even though it does not produce the correct answer EVERY time they use it.  
 
In Washington State, the "discovery" method has been in use for over a decade. My older daughter is a victim of it and my younger daughter escaped most of it becaues she was in advanced math classes with traditional math teachers from second grade on. My younger daughter will have EVERY field open to her that she wishes to pursue in college while my older daughter is now limited in the fields she can pursue because she was not given the tools she needs to succeed when she was in elementary school.  
 
BTW, in "discovery" classrooms kids who know math get very frustrated because they are forced to teach math to the kids around them.