re: (Not Common Core)-- Why are they teaching math this way?

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If I were FORCED to do math that way from the beginning, I would have struggled. My teachers were always understanding of the fact that there were many different ways to solve a problem and didn't always have to go by the book. These methods of teaching are indeed forcing you to learning by the book.

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What you are describing is an issue with poor teaching practices, not methodology. A teacher should teach multiple methods, but accept work done by a student in a way that makes the most sense to them. Unfortunately, most teachers are ill-equipped to facilitate this.