Pivotal to me and my math reality was one important teacher. Her name was Mrs. Boyd an algebra teacher in the Tift County school system she was the dreaded reality of arrival into the 7th grade. Her class was considered legendarily hard.
And it was hard for me, at first. She liked to give lots of homework including word problems. And I remember laboring over the weekend with a particularly long set. I think it was over a hundred. And something weird happened at some point, and suddenly every single one of them seemed easy.
I saw a pattern. Zipped through the rest of them, and suddenly algebra was ok. And I think there is something to having kids just do algebra, with as much instruction as you can of course, until they reach that magic moment. As I think it's just a matter of doing enough until the patterns emerge.
And then I felt myself to be in a different position in class and considered now with detached fascination as my classmates continued to struggle. One of my favorite memories was when I noticed a neat trick that would make a particular bit of algebra even easier. Mrs. Boyd listened to me, and if I remember correctly, put her finger to her lips, and called me to her desk.
She told me that was good but it might confuse the others.
It was like I was part of a special club. I could see it in her eyes. We were in the know.