Without numeracy, math just does not happen.... At conferences I often hear teachers discuss the problem of students hitting High School without the basic skills - cannot add fractions, cannot do integers, etc. Quickly the conversation often leads to a comment like "I can't teach fractions, I don't have time." This is when I know we will probably are going to have a "discussion."
The way I view my job is to take each student on their individual journey, that means differentiation. It means starting with fractions or integers if that is where the student is at. And lets think about it - how can a student who can't handle fractions with numbers handle abstract fractions - if they cannot add 1 1/2 + 3 1/3 without a calculator how can they handle a/b + c/(b+1)????
But you can't give a ton of class time -- that I do agree with. You always review some, but then there needs to be a student accountability system to help them get it. What I mean is - we, the teachers, need to find a way to make sure the students learn -- and remember grades are not a motivator -- unless it is the choice between an F and D (and even that does not always work). And we also know simple giving Fs does not make students learn.
They need to be pushed, encouraged, coherised, whatever - our job is to get them the skills and make sure they still know them years later so they can use in college math, or in their career. That takes a team effort at a recursive curriculum. Half my Algebra 1 grade is 8th grade and down material. Half my Geometry grade is Algebra 1 & down, and so on.
But my thoughts now are focused on the student who does not have numeracy. Those students, the ones who are truly focused on learning, become tremendously frustrated. They understand algebra, the idea of balancing equations - but rarely get the correct answer. They try check, try, check,..... Come in and ask - they will have 10 problems, 8 they cannot get the solution for, and all 8 have mistakes like -12 - 4 = 8 or -2*3 = 6.
So we cannot move on, in a school, in a class, or in a lesson without making numeracy as necessity....