On these forums, there seem to be two common pieces of conventional wisdom that get repeated often:
A. If the student does not complete calculus in high school, s/he will be “behind” in math. So parents of middle school kids need to do all they can to get their kids on the math track that leads to calculus in high school. Pushing even further ahead (calculus in 11th grade instead of 12th grade) is even more desirable.
B. A student with AP or IB credit for calculus that allows advanced placement in math (to a course more advanced than calculus 1) should start in calculus 1 in college, repeating his/her AP or IB credit regardless of AP or IB score or other indications of how well s/he knows the material.
Neither of the above really makes sense, but it is especially odd that both of these have become conventional wisdom, despite the contradiction between the two. If a student is good enough in math to take the more advanced track leading to calculus in high school, why would it make sense for him/her to repeat calculus as soon as s/he gets to college?
Maybe it’s just me, but I just as often see people countering this by reminding others that the “normal” math path is Alg 1 through Pre-calc in high school.
However, as I often say, the users on CC are not a representative subset of HS students (and their parents) targeting college. So while that’s the usual college-prep sequence, it’s not the usual honors sequence. So I think that @ucbalumnus statement A may be correct to students targeting top colleges (the calc in 12th grade part; I don’t agree with the calc 11th grade part unless that’s the students natural progression), it’s not valid for most US colleges.
Personally, I am not sure that there is a one-size-fits-most answer. It really depends on the kid.
My daughter didn’t get to calc in high school. She’s an engineer and graduated in 4 years. Took the calc 1,2,3 series in college, took the rest of the math in order. My nephew also didn’t take calc in high school, failed calc 1 so had to retake it in college. He wanted to stay on schedule so took calc 2 in the summer at a local university, and he too graduated on time.
I expect the seemingly conflicting advice relates to conventional forum wisdom about what the next level is looking for. That is, to get accepted to highly selective colleges, you need to take a huge number of AP classes during HS, including calculus. To get accepted to grad/professional/… school or to get a job you don’t need a huge number of rigorous courses like HS. Instead you need a ~4.0 GPA, and it’s easier to get that GPA by repeating calculus.
Note that I do not agree with either of the above statements. I did not repeat any of the math I took in HS including classes beyond calculus. There were advantages and disadvantages to this. As a general rule, I’d recommend that students take the school’s math placement exam (taking exam is mandatory at many highly selective colleges), and consider the math class the college recommends based on your score and background. Most colleges also have freshman counselors and/or placement officers for a more personalized approach and discussion.
Point 2 should is largely dependent on a student’s future career plans. If going on to something like med school or dental school, an solid A in a math/science course can be a nice start to their science GPA while they are trying to get a handle on gen chem or another weed out course…
Also while presumably AP calc should be sufficient to prepare you for Calc 2 anywhere (hence the whole idea of the college credit for qualifying exam), an incoming student may not actually be as ready as others who had taken Calc 1 in the same math department.
And some of us… did terrible in HS AP calc, but on repeat freshman year, managed to get an A. I was totally fine in math until I got to pre-calc, not being in the advanced track through junior high would have been a problem though.
The comparison is confounded by the fact that those with AP calculus credit (particularly with 5 scores) tend to be stronger math students than those without. So it is certainly possible that a college finds that AP 5 students do better in the more advanced math course than those who took calculus 1 (or 1 and 2) in college.
I would recommend that students with qualifying AP scores try the college’s old final exams of the courses to be skipped, if the college does not have its own placement testing for math courses more advanced than calculus 1.
There is a way to KNOW whether to repeat a class or not. A wise poster here, @ucbalumnus edified me so as to help my son make that exact decision. Get, and take, old tests of the class(es) the student is testing out of. If they do great, move on. If they struggle, repeat. A little rusty…brush up on something like Kahn and move on.
Students who blindly move forward may or may not be prepared, even with a 5 on the AP exam.
My son was invited into an honors section of Calc III. On the first exam, there were scores as low as the 30s. Every student in the section scored a 5 on the BC AP exam. Some were obviously prepared better than others for the next step in spite of the high AP score.
Moving forward has significant advantages. In his specific case, using the method above, he started ahead in both math and physics. Now in his last quarter of his 4th year, he’s mostly done with the course requirements for his masters in ME.
My oldest naturally tracked to AP calculus BC in 11th grade. He skipped 4th grade & 6th grade math. He did Algebra in 7th, Geo in 8th, and just kept going in the sequence. He is not applying to any selective schools, and he will likely take the standard classes for his bioengineering major. He is not in a rush, and he figures he needs a really good base for the much harder math to come. I wish he could have saved Calc for next year, but AP Stats didn’t fit his schedule this year, so he has to do it as a senior.
I think students who are ready should be allowed to progress through higher level math classes, past Calc, but should not be pushed. My daughter’s magnet school allowed students to advance, with some taking Algebra 1 in 6th grade. If they did well (B or better) they progressed to the next level, but if they passed with a C, they retook that class. The thinking was that they were better served by building a strong foundation in middle school, and a C did not represent such a strong foundation. They prefer students at her school to complete Algebra 1 as 8th graders, mainly because they have a STEM focus, and students are required to complete a significant number of math, science, and engineering courses (16 credits of 28 required for graduation). I can see a desire to take AP Calc along with Physic C, and to repeat it (and maybe Physics too) for an easy A, but not at the expense of a less solid foundation.
“I can see a desire to take AP Calc along with Physic C, and to repeat it (and maybe Physics too) for an easy A…”
There is no guarantee of this at the collegiate level. The tests are typically much longer, resulting in students needing to substantially quicken their problem solving pace. A student could easily end up wasting a quarter or semester, learning nothing new, while still not getting an A.
Except that it is not. In lowly California, nearly 60% of 8th graders take Alg 1. Add in the ~9% who take Alg 1 in 7th grade, and you have over 2/3rds of all students taking Alg I before HS.
In essence, just a little less than half of HS Frosh take Alg 1 (including repeaters for low scores in 8th grade).
@bluebayou The trend is reversing now with Common Core though. Our district now recommends that the majority of students take Integrated Math 1 (the equivalent of Alg1) in 9th grade. The requirements to qualify for Integrated Math 1 in 8th grade are much stricter than before.
The California situation with respect to starting algebra 1 in 8th grade is probably the legacy of a policy from about 1998 to 2013 to push all 8th grade students into algebra 1, apparently because placement in more advanced math courses was heavily influenced by race and SES*, in addition to actual achievement in math. Unfortunately, many students did fail and have to repeat algebra 1 in 9th grade. In some studies, such students had no greater rate of success in algebra 1 in 9th grade than those of otherwise similar achievement who did not take (and fail) algebra 1 in 8th grade, but those who failed and repeated tended to be less confident in math and less likely to be interested in math.
*In these forums, stories of unfair or apparently nonsensical middle school math placement policies are not that unusual. It would not be surprising if there were some correlation to race and SES in terms of which parents end up being better informed or connected in a way that helps their kids get into rationed spots in more advanced math courses.
I wish the choices could always be based on the student rather than being planned out as one of the many chess pieces in the big college admissions chess game. It’s a perfect move for some to accelerate and not backtrack or repeat, and not such a good move for others.
I am glad my daughter was recommended for Algebra I in 7th grade, and also glad that her college had a math placement test to help place her in the right level of math in her engineering program. She did not have to backtrack and did well. It was a perfect starting point for her.
Here are your choices: (assuming you are interested in STEM)
Get only to pre-calculus in HS. Then you are experiencing Calc for the first time in college. Many of your peers might have taken it in HS…so it will be more difficult for you. Also your peers may have gotten to Calc in HS…if you are a college, which student would you choose? the one on a (slightly) advanced math track?
Get to AB Calc (or Honors Calc). Maybe you do well, maybe not. Maybe you get a 5 on the AP exam, maybe you don’t. So if you take Calc again, then you are more prepared. Colleges don’t really look at AP scores in admissions, just your grades.
Get to anything more than Calc AB…BC, Multivariable, etc. If you do well in these, you are probably ready for more advanced math anyway.
So to me, if you want to major in STEM, and if you have the ability, I would try to get to Calc in HS so you are not disadvantaged in college.
As far as the second part is concerned if a student has had Calculus and beyond in HS I’d recommend taking a proof-based version of Calculus in college. Concepts will be repeated and helpful to already know but the skills learned in that kind of class will be beneficial throughout their life.
The majority of college-bound kids in our district end up in calculus in 12th grade - mostly in AB. For one of mine, he was able to skip the one semester of calc required for his major in college. For many top college, if calculus is offered in the HS, kids are expected to take it. That was true even back when I was in HS and took AP calc.
As to repeat Calc 1 in college, it really depends on the kid, the HS, the anticipated major and the college. In many cases it may make sense to re-take calc as the HS may not have prepared the kid well enough. A 5 on the AB test can be as low as about a 64%. A kid with a score at the level may not be prepared for college level calc 2.
@ucbalumnus Agree with you that the “conventional” wisdom doesn’t make sense, especially for #2. In fact, professors at South Carolina specifically recommend NOT taking Calc I or II if they have received satisfactory AP/IB/DE credit. They argue that Calc will be hard no matter how many times that you take it, and that retaking Calc I and II adds to the risk since students may not pay as much attention or take the course as seriously as they should. So much for the easy A!
At other schools that we visited, the professors qualified this recommendation by adding that the students should take their placement assessments to get a better picture or their preparation. None advocated retaking Calc I and II under all circumstances.