i wish I had a magic wand, a perfect solution....the WAY!
It would be so much easier....
Remediation is a matter of understanding the student, It's a matter of knowing how best he/she/ze will see the concept most clearly.
I've known teenagers for whom subraction still makes no sense. Division, fraction and number sense confusion is so common as to assume that it's confusion should be expected.
I love my kids, but I ache that I cannot possibly help all of them have experiences to clarify all the misconceptions, never mind successfully develop a full understanding of all the current grade level standards as well.
I do know that disruption and sleeping as well as not doing the work is definitely positively correlated to not participating, not doing homework and not answering questions in math class.
Motivation is a killer for students. Often-times a student's home life can make our best efforts feel like standing still. We are not alone in this, the students feel it as well.
It's true that math is sequential, and it builds upon itself. It's also true that many of our students memorize steps, not understanding the why. The good news is that continuing to build basic skills and remediating misconceptions does slot in lost concepts and I've seen students with that "ah-ha" look in their eyes.
6th through 8th graders have learned the 4 basic arithmetic operations, they need opportunities to hone these skills and practice them. My 6th graders practice divisibility, factor trees, do kenken, review vocabulary and skip-count (to practice multiples/multiplication and learn to see linear/arithmetic progression, though I don't share the motivation with them).
My 8th graders need to better explain their thinking (yes, Mathematical Practice #3, construct viable arguments - I'm looking at you). They need to work on being better at showing their work/thinking so that in time they can be better at those explanations.