A hard adjustment for parents/educators who were raised as I was on traditional algorithms. Of course, understanding the rule for multiplying fractions DOES NOT mean students should use this to get the result.
Teaching conceptually is fundamental to the Mathematical Practice Standards of the Common Core. BUT this should be BALANCED with traditional methods. Current thinking is that the way we learned may be far more efficient but it leads one to think of math as just a set of meaningless rules. Kind of like a "black box." I see the need for both.
After watching this MathCast you'll probably conclude this is way too confusing for students not to mention adults! Just remember, some of that confusion results from sloppy drawings and carelessly worded explanations. I'm definitely guilty of both!
Watch "SHOWING one-third of three-fourths vs Traditional" on YouTube - https://www.youtube.com/watch?v=8vtce4rz9dE&feature=youtube_gdata_player