Poor high school AP calculus teaching tends to be exposed in lower AP scores – often too low to be allowed by the college to take advanced placement.
If the college allows a student with a 5 to take advanced placement, does it make sense automatically to assume that it is better to repeat, foregoing the opportunity to learn something new in the schedule space at the expensive college?
Also, no one seems to recommend students who take calculus BC in 11th grade to repeat single variable calculus when they take math at a local college in 12th grade.
My D had an A+ in AP Calc and a 5 on the AP exam. She took a bunch of online exams for Calc I from her college and decided that she was ready to start in Calc II. It was the right the decision for her.
Surprised that half of schools in the US have calculus. There are really a very small number of high schools that can address post Calculus in high school. Even at the nation’s top private schools, not all offer advanced math seen in college. MV, linear algebra and the rest are very atypical in high school. I’m not including kids who have taken college courses. Kids should not be held back by the curriculum but they are 95% of the time. And most schools are very inflexible ( and illogical) in their sequence.
And I cannot fathom a math kid thinking their high school Calc class was going to stand in for a Calc class at a major math program ( as many kids will be heading in this direction).
One complaint I have about how my district handles it is that the advanced path starts as they enter 6th grade, based on one test. This test is unfortunately not an “ability” test, but really based on advanced exposure to materials. So the kids who get advanced are ones whose parents are in-the-know and have prepped them (via Kumon or other homeschooling), and NOT necessarily the smartest/most talented at math. This then shakes out later when some of these kids who looked so smart in 5th grade because their parents had exposed them to the materials a grade or two ahead, then really end up middle of the pack or struggling. That’s fine, I guess, but the problem is this system misses all of the actually brilliant kids whose parents are not that type. It would be great if our town would allow later entry points to that path.
By the way, the parents who are “in-the-know” and do the Kumon prep or other parent-based teaching are not necessarily the more privileged families in my town, based on wealth. They are people who either had older children and saw what happens at the high school, or have a tight knit community of friends and relatives with older kids, etc. There are people who don’t hear about this process until it’s too late. Many younger families do not know about the impact of that one test, and they have no clue what is on that one test. Many families are not preparing for that test, while other families absolutely are. In my town, it is not associated with finances. Getting your kids prepped is free or cheap (or more money in the case of paying for Kumon), using resources at the library or Khan academy or other online freebies would be sufficient. However, I’d prefer to see a test that tests for aptitude more than exposure to math a year or two ahead.
My own kids were able to complete BC in high school, but you must take AB in 11th grade (no skipping straight to BC, and the BC class therefore is designed based on you already successfully completing AB). I believe our BC teacher then takes it to a great level, completing the “BC” curriculum before Christmas, and then doing more advanced math during senior spring. Every single one of his students in the past 5 years (that I’ve been watching) gets a “5” on the BC test. My children did not repeat calculus in college and were fully prepared to move to multivariate; I believe their friends did the same in college instead of repeating. I guess I have no problem with the 2 year calculus sequence at our high school because they seem to learn it so thoroughly and they all love the extra stuff he teaches senior spring—very cool projects etc. He’s a stellar, beloved teacher.
Anyway, I think this is a tough subject with so many pros & cons to different choices; I’ll leave it to the rest of you to solve!!
Lots of these colleges’ math departments allow advanced placement for high enough AP calculus scores, since frosh single variable calculus courses are service courses for many majors, rather than extra-rigorous proof based courses specifically for math majors.
Those who go on to major in math will prove calculus when they take real analysis.
With this type of system and a stellar teacher there should be no need to repeat calc.
Plus, not all students need to retake it anyway which is why I suggest checking out exams or placement tests at the different colleges. Some colleges have “lower level” calc courses that are essentially equivalent to AP. Others go more in depth even with covering the same topics. Some teachers are great. Others not so much. Some students naturally “get it” even with a not so great teacher. Others don’t. There are a ton of variables involved. If it matters for the major or needing a grade, 'tis best to be informed rather than thinking, “I did AP and got a good score, therefore I must be on par for the next class when I go to college.” Maybe, maybe not.
But then again I’m in favor of placement tests before entering each class in high school because I’ve seen kids do well grade-wise in Alg and not necessarily know the material well enough to move on IME.
@EmptyNestSoon2 you’d probably think I am one of those parents who exposed their kid to advanced materials early. And that would be true. But that’s because I had a kid who figured out multiplication at age four. He made his 5th grade French class poster on Pascal’s triangle. He read math theory books that I found hard going in middle school. He learned Visual Basic in 2nd grade. What was I supposed to do. Tell him to stop being interested in learning new things in math?
Math mom, ha ha, mine too ;-). Proved Pythagorean’s theorem to me in elementary school i think! I know my kiddos could have skipped many more grades in math—son was recommended to be “radically accelerated” I think the term was. I just had him skip one single grade, and then obviously ended up another year ahead in math. Clearly could have gone faster than that.
But as mentioned by someone up the thread, I think it was the OP, they weren’t talking about kids who are the outliers; the point of the thread was about the large group of “good students”. And looking at that group in my town, my point is that it isn’t clear that the naturally talented kids are the ones who end up on the accelerated track. Just the ones who are prepped at home. I blame the type of test they use to separate the kids—I don’t think it tests for ability/aptitude/intelligence/talent…I think it tests to see if you’ve been exposed to this slightly advanced math before. So I think they miss some amazing kids and I think they accept some more mediocre kids, purely based on exposure. Not how it should work in my opinion.
@mathmom Actually, your situation is the opposite of what appears to be the now-common situation. You are just following your kid’s lead in learning math, which is good and keeps him interested in math.
Unfortunately, lots of other parents push their kids to the +2 track when that may not be the best choice, as evidenced by high schools doing the two year AB-BC sequence, which may be too slow for your kid.
Sounds like SFUSD wants to push away the high-achieving kids of software engineers and the like.
The real problem is not the acceleration of kids who shouldn’t be accelerated (although this happens a lot), it’s rushing through algebra and the lack of variety in math classes. I actually think kids should start talking about algebra in elementary school, and in middle school they should become proficient in algebra. Now it’s taught so badly in many cases that kids don’t really understand what’s going on even though they can go through the motions and get a good grade. This makes them miserable in precalc and beyond. After algebra, why can’t they then in HS take discrete math, or a class on problem solving and proofs, or data science as suggested by Steven Levitt, or other math classes that could be a lot more fun?
This is typical public school nonsense, especially when they have a lot of high achieving students. At the private schools my son attended, they had Geometry in 8th grade and Calc 3 (diff eq) in the 1st semester of 12th grade. The final semester was for a math, science, or research elective.
My mother used to talk about how her Dad would do puzzle math with them in elementary school and then told her it was really basically algebra. My other kid was just on the regular plus one schedule - algebra in 8th grade. He mostly got B+'s because he couldn’t remember a formula for the life of him so would spend time on tests deriving the Pythagoreum theorem from scratch. Luckily that fabulous pre-calc teacher who covered the AB Calc material really got him and appreciated that he understood the material on a deeper level than most of his classmates.
My issue with math is that it’s often taught as memorization rather than concepts. Many intelligent kids can easily memorize, but without knowing the concepts they’re lost.
We’re so dependent upon calculators now that most kids even do things like x100 with a calculator. I once had an “average level” Alg 2 student argue with me that (-2)^2 was -4 because her calculator said it was. She had “forgotten” the parentheses and there was no real knowledge of the material.
Placement tests before each course would have a lot of concepts covered in a short period of time. It’s tough to memorize everything vs just the chapter one is doing at the time. We’d have a better idea if the student actually knows the material, just memorized it, or otherwise got the grade for it. (Some teachers more or less give grades due to their assessment being on numbers of kids who pass/fail. Or, HW can count enough to “pass,” but who did the HW - esp if tests weren’t great. Many tests now are also group tests - who knew the material in the group?)
“I am not a fan of sending middle school kids to a high school/college to take classes. Silly and emotionally awkward.”
We had kids as young as 5 th grade at the high school for math. (3 of the 4 I knew of were children of math/science professors at a highly regarded college). Also had several 6th graders go…they could walk 2 blocks to the HS and walk back). Based on very anecdotal evidence this was easier on girls than boys. Girls were fawned over by the “big girls”. Boys found it more awkward.
I believe the initial post said something about the few kids that are very capable would be able to accelerate.
Our district has Algebra 1, geometry, algebra 2, prec-calc, and then calc. So there are five courses. Most of the kids on the college prep track take algebra 1 in 8th grade. It is not clear to me how algebra 2 and precalc would be one course. Although I remember that my 11th grade class was algebra2-trig.
Our district allows either AB or BC calc, not both. The neighboring district puts kids into BC calc, but has them take the AB class. The AP tests are used for placement in some colleges, letting kids take a higher level of calculus or to place out if they aren’t math majors. Does a kid that gets a 5 on the BC test need to repeat Calc 1 in college?
Most kids who get a 5 on the BC test will not need to repeat Calc 1 in college. Some colleges offer intro Calc courses that are not aimed at any but the best mathematicians. So future math majors will take it, but it won’t even be in the stream of courses mere mortals take, even if they take a bunch of math courses.
In my kid’s college, no. She got 5 in Cal BC, as a freshman she takes Math54 (Linear Algebra and Differential equation). She is very well prepared apparently, thinks the least she will get is an A at this point.
We live in FL and they push the AP track even for kids where this isn’t appropriate. The normal track for high-achieving students through middle school is some advanced 6th grade math, then Alg 1 honors in 7th, followed by Alg 2/Geometry honors in 8th/9th grades. They flipped the order of Alg 2/Geo and then flipped it back while my girls went through so I can’t remember the order at this point. Pre-calc in 10th, Calc AB in 11th and BC in 12th or AP stats. Every year, we see posts from parents asking about Calc tutors for their children who had always been A students but were almost failing Calc. I believe the pass rate on the AP test is ~30% which to me shows that there are lots of kids taking the class who shouldn’t be.
That being said, my twin girls were fine because they were always ahead in math. They were ahead a year on that above progression starting in 6th grade, so they took Calc AB in 10th and Calc BC in 11th. One daughter just finished Calc 3 this past fall at our local college and got an A. We are fortunate enough to live close to UCF and she takes classes there through Dual Enrollment. She plans on taking linear algebra next semester and is also taking AP stats. My other daughter didn’t have room in her schedule to accommodate any classes at UCF so she’s taking AP stats only for math this year. There were probably about 5-6 students in their grade level who were also on this accelerated pathway and they were all fine.
Our school is large, approx 850 students per grade level, and we have one teacher dedicated to teaching Calculus and he is good. When my daughters were in 10th, they had a second Calc teacher and she was awful. I was lucky that my daughter who is stronger in math had her so she did just fine but she really appreciated having the better teacher the following year. They were both prepared well for college. The one taking classes at UCF received 5s on the AB and then the BC/AB subscore tests. The other received a 4 on AB and then 5s on BC/AB subscore. Seeing the material a second time and taking it more seriously the second time did help her. UCF requires that the students take math pretests to make sure they learned the material well enough to really bypass Calc 1&2 in college.
I’m always fascinated reading regional/state/school differences. Our district in OH was the opposite of @PPuggle 's experience. The middle school had 1 advanced class per subject for over 300 students. If you weren’t in the top 10% of test takers, you weren’t placed in the class. Her private HS also used placement test, teacher recommendations and no lower than a B+ to allow students into AP courses. It was very hard to be moved up.
