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Your mistake is in believing that you have a "natural" understanding of math. You don't. You have an idiosyncratic way of understanding it, and as your own example shows, it was not superior to the formalism learned by your peers.

The elementary operations of arithmetic, like the ordinary digital operations of our feet and hands can -- and should -- be reduced to sub-cortical processes at an early age, so that they can be applied to difficult conceptual problems without effort.

The Common Core arithmetic approach is like trying to teach people to use a computer who don't know how to type. They focus so much on finding the letters on the keyboard that their conceptual path through accomplishing a task is quickly lost in details that aren't really part of the problem domain. It's not really necessary that everyone learn to touch type, just that they know where the letters are without thinking.

Conceptual and mental arithmetic can always be returned to at a later phase without any danger that the student will be so mired in methodology that he won't be able to grasp concepts; in fact the connection will be easier, as your peers who could easily learn advanced mathematics while you struggled with it proves.

Common Core is just the latest phase in a disastrous educationist program that has been going on since the catastrophe called "New Math" was introduced in 1963. Each time the approach of teaching math concepts before formalism and drill has been tried it has been abandoned in favor of the traditional method. Each time the educationists refuse to understand that they really do not understand how people learn math. After each failure they regroup and introduce a New-New Math that is even sillier than before. The sad fact is that most educationists are mathematically innumerate, and therefore unqualified to teach the subject -- even to children -- themselves.

I am pretty good at math and I remember doing nothing but drills in math while in grades 1-3. Grade 1 we learned to count, grade 2 flash cards in addition and subtraction. everyday flash cards. Grade 3 flash cards in multiplication (1-12). By the time I hit 4th grade I had addition, subtraction and multiplication nailed. In the forth grade we move on to adding/subtracting columns and multiplying larger numbers.

You are absolutely, correct pound in the basics at a young age. I feel sorry for kids that hit grade school after 1980 or so. They are not being educated in a proper fashion.

Your mistake is in believing that you have a "natural" understanding of math.

Can't speak for Monitor, but I did not actually say that I had a natural understanding of Math. I only claimed that about arithmetic and numbers. Start throwing the Greek alphabet in there and I fall back a bit in the pack of my peer group of graduate engineers. That stuff was only "easy" for a very gifted few.