These are incompatible, which is what I am saying and the parent above my comment is also saying.
>> simple multiplication tables (and similar)
If you fail to memorize these, you can derive the answer using your fallback to addition, which you've been shown how to do. In Common Core textbooks and in the class my oldest is in, these are assumed facts. Breaking down how to derive multiplication and division is at least a failure of the teacher in the class, if not the methodology, though I suspect the teacher is pretty good.
Common Core relies on a lot of memorization and pattern matching. This is fine, and good for everyday use. It is not learning it from first principles, which makes it hard when your pattern matching engine isn't working properly.
Both methods should be taught in an integrated fashion. I support Common Core - and have for a long time - as an adjunct. Not as the primary method of teaching math. Most kids will find Common Core easier, I'll readily admit that. It also has better carryover to everyday use, as I've already admitted. But it lacks rigor.
>> Back in the 90s, when I was in school, I don't recall this kind of rigor in math at all until I got to Calc 2
We're likely the same age. My arithmetic classes were far more rigorous than most of my mathematics classes beyond that up until Linear Algebra.
>> solve problems
These are incompatible, which is what I am saying and the parent above my comment is also saying.
>> simple multiplication tables (and similar)
If you fail to memorize these, you can derive the answer using your fallback to addition, which you've been shown how to do. In Common Core textbooks and in the class my oldest is in, these are assumed facts. Breaking down how to derive multiplication and division is at least a failure of the teacher in the class, if not the methodology, though I suspect the teacher is pretty good.
Common Core relies on a lot of memorization and pattern matching. This is fine, and good for everyday use. It is not learning it from first principles, which makes it hard when your pattern matching engine isn't working properly.
Both methods should be taught in an integrated fashion. I support Common Core - and have for a long time - as an adjunct. Not as the primary method of teaching math. Most kids will find Common Core easier, I'll readily admit that. It also has better carryover to everyday use, as I've already admitted. But it lacks rigor.
>> Back in the 90s, when I was in school, I don't recall this kind of rigor in math at all until I got to Calc 2
We're likely the same age. My arithmetic classes were far more rigorous than most of my mathematics classes beyond that up until Linear Algebra.