Visual tricks like dot patterns are how I do basic arithmetic operations, too.
Count me among those who
eventually got automaticity with most math facts-- but there are a few that just won't stick.
My calculation speed is nearly fast enough that most people no longer
notice this about me, and I did get a terminal degree in a physical science, math notwithstanding, so it pays to remember that "Math" isn't the same thing as "Arithmetic."
Also-- what
is it with the modern notion that ALL teaching tools/methods/models have to work for ALL students, anyway? DD hated manipulatives, so I didn't force the issue. I love number lines and other visual methods, but she hates them. I figure that as long as we can both do the math reasonably accurately, this is just not a big deal.
Here is one thing that got me to some increased automaticity with arithmetic-- working with money and learning "counting on" to give change back in retail work as a teen. It's a quirky skill that you don't use all that much elsewhere, but it was a sort of alternative stealth pathway to holding onto math facts for me. Weird but true.
