Several times I’ve posted our son’s experience trying to jump ahead in math at Choate but will repeat for those who are new(er) to this forum and because this question comes up every year.
Our son loved math and was dying to get to calculus as fast as he could. He took algebra II at our local CC the summer before BS, earned an A, and passed Choate’s placement test for entering the math stream at a higher level, but the math dept. seriously advised against it as they felt that their algebra II course was foundational for their upper math curriculum. They gave him the option, but the gravity of their advice to enter at algebra II caused him to do so. He was a bit bored the first few weeks, but as the pace picked up and his teacher began to teach a methodology for analyzing, problem-solving, organizing, presenting, and participating in a Choate math classroom, he did not feel advanced toward the end of the course and was very glad he “repeated.”
I will emphasize: Do not discount the part about learning how to participate in a BS math classroom. You will NOT be memorizing formulas. You will be taught first to clearly understand the problem you are trying to solve. You will learn to think mathematically about approaches to solving the problem without delving first into any formulaic toolkit. After that, you will learn some methods for crafting solutions. You will understand and own how to derive formulas so that you will know not only which to apply but also why, the same way a carpenter knows when to use a hammer over a saw. I remember one Parents Weekend watching three kids go to the board and correctly solve the same problem three different ways. The rest of the class time was spent discussing those various approaches and why each worked. Very different from the match-the-equation-pattern-to-the-one-right-formula method I was taught in school.
It’s far more important that a student learn to think like this than at what level math course s/he starts or ends. There are no prizes for accelerating in math. Generally, you can trust the BS to place each student into the stream at the right point and expertly guide their progression. On the few occasions they get it wrong, they should be quick and happy to adjust. It is perfectly OK to reach out to the teacher and/or head of the math department to get their advice on your concerns. It serves no one for a student to be in the wrong class.