Speaking from my own experience, this is never the case among the teachers I work with or the teachers my children have had. It is true, yes that teachers are stretched too thin, and yes, testing does take a lot of time...however, I can say that I am consistently checking to make sure my students know what they are doing...after school, over email, and during classes. I'm not trying to say that what you are describing doesn't happen, just that it's not happening everywhere - and that it doesn't apply to every teacher.
New math practices and strategies are based on research for what helps students learn best and what helps them become critical thinkers. Again, not everything is a fit with everyone - but alternate strategies are very useful to a lot of kids.
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