Gregorio C. Sablan, CNMI Congressional Delegate, got it right. “Pre-algebra” starts early, or should.
At Broadwater Elementary School in Helena, Montana, algebra starts in second grade, where students learn the basics behind mathematical theory and reasoning to prepare them for high-level math classes in middle and high school.
Elementary math is supposed to prepare students for high-level math classes is middle and high school. Students should not need a dedicated pre-algebra class. When I was a kid, pre-algebra did not exist. Now it is part of every school's math course line-up. The author of a pre-algebra text wants students to build math reasoning skills.
But that doesn't always happen. Many teachers treat pre-algebra as a last chance for students to get those elementary math procedures down pat. Problem is, a student can be A+ in procedures and still not get algebra. In fact, students who are competent with procedure often believe they are good at math. It's not their fault. Our education system has been telling them for years that grades equal understanding. So if they get a good grade in math, naturally they conclude they are good at math.
Math has been misnamed. What passes for math in schools is often non-math. “Carry the one” is not a mathematical explanation. Students get good grades in non-math believing it's math. No wonder algebra is such a shock. Math reasoning skills actually matter in algebra.
Still a student with a good memory can get by, at least until they meet a new math monster, calculus. However, since middle and high school math also fail to teach math reasoning, students get to take pre-calculus, another relatively recent addition to course offerings. Without a major change of emphasis, pre-calculus prepares students no better for calculus than pre-algebra prepared them for algebra.
By now pre-calculus students have so internalized non-math that they complain to the instructor, “Just tell us how to get the answer. We don't want to know why.”