I'm an engineer; but this astounded me. Let me see if I understood this correctly. A college degreed adult, does not understand math well enough to teach a 6th grade student, in a manner that was different than before? Am I missing something?
My reaction is pretty straight forward - you have an incompetent Math teacher. The basic rules of Algebra, Mathematics and Geometry have not changed. If your teacher cannot grasp a different way to present Mathematics, Algebra and Geometry - I'd say the problem isn't with the ciriculmn, it's with an incompetent teacher who should have her Math teaching certificat revoked before she does more damage to her students.
I have a Master of Arts degree in Psychology. I took required courses in Statistics for both my undergraduate and graduate degrees (six courses in all that involved Statistics). I passed all but one of those classes with an A (the other was a B. I missed an A by just a few points). I use Statistics in my profession daily. My son-in-law is in IT. He not only works on the hardware, but he writes software. He took required mathematics courses, and passed them all with high grades. Neither one of us were able to make heads or tails of the math homework from the new curriculum. I do not believe it is because WE are incompetent. I have talked with other teachers at varying grade levels who were also extremely disappointed in the new curriculum they were forced to use, and were having a hard time understanding. The problem isn't the competence of the teachers, but of the individuals who wrote the text books.