Question about AP Calculus BC

[annabanana1992]

My son has two years left of high school and has just completed pre-calc. He is signed up to take a online calculus course next year that is not an AP class, and the syllabus would not necessarily prepare him to take the AP test. We don't have flexibility with this class. He has to take it for a diploma requirement. My question is, then, would it be odd to take an official AP Calculus BC class the following year? Would that seem strange on a college transcript?

 

Thanks!

[StephanieZ]

That would sound strange to me, but I don't really know. I'd try to make the second year of Calculus sound different. Maybe call the first class Intro.to Calculus and the second class an offical BC Calc or simply Advanced Calculus. Seems like it might be really boring. Calculus is calculus to a large degree. I'd consider having your son use a prep book to practice some AP tests and cover any minor gaps, then take the exam if he is testing well on the practice tests. If the required course really doesn't come close to good prep for the exam, then redo it the following year with some different name. Otherwise, he'll be free to take stats or an advanced math senior year.

[kiana]

That would sound strange to me, but I don't really know. I'd try to make the second year of Calculus sound different. Maybe call the first class Intro.to Calculus and the second class an offical BC Calc or simply Advanced Calculus. Seems like it might be really boring. Calculus is calculus to a large degree. I'd consider having your son use a prep book to practice some AP tests and cover any minor gaps, then take the exam if he is testing well on the practice tests. If the required course really doesn't come close to good prep for the exam, then redo it the following year with some different name. Otherwise, he'll be free to take stats or an advanced math senior year.

 

 

This really varies. I have seen a fair number of students come in and take my precalculus or calculus class who were very upset at having to take it, when they claimed they had had calculus in high school.

 

They had never really done limits, and strongly resented having to do work with the limit definition of the derivative (which is what explains why it works).

 

They had no idea what the derivative was or how to apply any of the derivatives they loved taking. They knew that there was this magical thing called "the derivative" and how to get it (on polynomials), but not what to do with it once they had it.

 

They had no recollection of anything involving trigonometric functions, products/quotients/compositions of functions, or indeed anything more difficult than a polynomial.

 

In short, there were tremendous gaps in their knowledge, made worse by their refusal to learn anything that hadn't been in their high school (non-AP) calculus course, because "I already took this course".

 

Even at the university level, there are different levels of calculus, and someone who took applied calculus would not be prepared for engineering calculus.

 

OP: I would ask the teacher of the online course how it compares to the BC calc syllabus. A lot of non-AP courses don't even cover the full AB syllabus, and it is not at all uncommon at high schools to do either intro to calculus and then calc BC, or calc AB and then calc BC. I would strongly consider the teacher's advice.

[regentrude]

That would sound strange to me, but I don't really know. I'd try to make the second year of Calculus sound different. Maybe call the first class Intro.to Calculus and the second class an offical BC Calc or simply Advanced Calculus. Seems like it might be really boring. Calculus is calculus to a large degree. I'd consider having your son use a prep book to practice some AP tests and cover any minor gaps, then take the exam if he is testing well on the practice tests. If the required course really doesn't come close to good prep for the exam, then redo it the following year with some different name. Otherwise, he'll be free to take stats or an advanced math senior year.

 

 

I do not agree that "calculus is calculus" and that it would be boring. It really depends on the level of the class. As kiana already pointed out, many high school calculus classes barely scratch the surface and do not incorporate a deep enough conceptual background, but teach calculus as a series of tricks for computing derivatives and simple integrals (there are no cooking recipes for hard integrals, those have to be puzzled out by trial and error and lots of experience)

Single variable calculus at our university is taught as a two semester sequence of five hour courses, it is a very intense and difficult class and would easily be worth two years of high school credit.

 

OP: I do not think that two years of calculus would be a bad idea. I second the recommendation to consult the instructor; the class may cover enough material that your son may be able to simply self-study for the test at the end of the year. If that is not the case, take a second year and go deeper. IN addition tomore theory, you can spend a lot of time on integration techniques (there is some tricky stuff there) and applications in physics, or do an intro into differetial equations... I think giving it a different name may be wise, but I strongly disagree that two years of calculus have to be "boring".

[annabanana1992]

Kiana,

 

Thank you! I did speak with the instructor who did indicate that the course would not cover all of the topics in the AP syllabus nor would it prepare the typical student to apply to concepts learned in a varied way in order to do well on the AB test. That's when I got the idea to do the official BC class the next year as we would really like for him to sit for an AP test.

[Caroline]

That would sound strange to me, but I don't really know. I'd try to make the second year of Calculus sound different. Maybe call the first class Intro.to Calculus and the second class an offical BC Calc or simply Advanced Calculus. Seems like it might be really boring. Calculus is calculus to a large degree. I'd consider having your son use a prep book to practice some AP tests and cover any minor gaps, then take the exam if he is testing well on the practice tests. If the required course really doesn't come close to good prep for the exam, then redo it the following year with some different name. Otherwise, he'll be free to take stats or an advanced math senior year.

 

 

Lots of students take a year of AB Calc and then a year of BC Calc. That is not strange or unheard of at all. Lots of students take a regular calc class and then one of the AP Calc classes. Not strange at all.

[snowbeltmom]

 

Lots of students take a year of AB Calc and then a year of BC Calc. That is not strange or unheard of at all. Lots of students take a regular calc class and then one of the AP Calc classes. Not strange at all.

 

:iagree:

 

This is how it is done in my neck of the woods as well. In fact, at most schools in my area, the AB Calc class is a pre-requisite for the AP Calc BC class.

[kiana]

Kiana,

 

Thank you! I did speak with the instructor who did indicate that the course would not cover all of the topics in the AP syllabus nor would it prepare the typical student to apply to concepts learned in a varied way in order to do well on the AB test. That's when I got the idea to do the official BC class the next year as we would really like for him to sit for an AP test.

 

 

I think that given what the instructor has said, the best course would be to have one year of Intro to Calculus and one year of Calculus BC.

[StephanieZ]

Wow, I stand corrected! I had no idea that people offered Calculus classes that were so superficial. I guess I shouldn't be surprised since it happens in most/all other areas of study! It seems so bizarre to me to offer an advanced class but then just scratch the surface of it. Ah, well, the dumbing down of class content shouldn't be shocking anymore. :( Sounds to me like it would not be strange at all to have two years of Calculus on a transcript! Just name them differently so the second is clearly more advanced, and it sounds like you won't raise any eyebrows. :)

[annabanana1992]

Thanks everybody! I think we have a plan!

[plansrme]

Wow, I stand corrected! I had no idea that people offered Calculus classes that were so superficial. I guess I shouldn't be surprised since it happens in most/all other areas of study! It seems so bizarre to me to offer an advanced class but then just scratch the surface of it. Ah, well, the dumbing down of class content shouldn't be shocking anymore. :( Sounds to me like it would not be strange at all to have two years of Calculus on a transcript! Just name them differently so the second is clearly more advanced, and it sounds like you won't raise any eyebrows. :)

 

 

This is a bizarre statement to me. Aren't you implying that calculus should ALL be covered in one year? That there is only one year's worth of material that can be called "Calculus"? I think it is most common for schools to teach Calc AB and Calc BC in two years, but that hardly means they are only scratching the surface: there is a lot to calculus. My daughter took AB as a homeschooler, then BC in a STEM magnet, where it was a full credit. She will take Calc 2 and 3 through Georgia Tech for her sophomore and junior years. That is a lot of calculus, and I cannot imagine the schedule that would cover that in one year! She will end up with four years' of calculus on her transcript and 5s on both AP exams. I am confident that no college is going to think that is strange or question the depth of her math education.

[Caroline]

This is a bizarre statement to me. Aren't you implying that calculus should ALL be covered in one year? That there is only one year's worth of material that can be called "Calculus"? I think it is most common for schools to teach Calc AB and Calc BC in two years, but that hardly means they are only scratching the surface: there is a lot to calculus. My daughter took AB as a homeschooler, then BC in a STEM magnet, where it was a full credit. She will take Calc 2 and 3 through Georgia Tech for her sophomore and junior years. That is a lot of calculus, and I cannot imagine the schedule that would cover that in one year! She will end up with four years' of calculus on her transcript and 5s on both AP exams. I am confident that no college is going to think that is strange or question the depth of her math education.

 

 

Just because I have facilitated the GA Tech Distance Calculus program before, are you sure she won't be taking 2 and 3 the same year? Or are you splitting it on purpose? My students have always done 2 in the fall and 3 in the spring.

 

And I agree that no college is going to question the depth of her math education. I have seen GA Tech Distance Calc students go to many different universities and the calc always transfers. There is no way all of that could be scheduled in one year. (If you are comfortable, could you pm me the name of your dd's school? I met some great young women from a STEM school at a Girl Scout event, and it made me think of your dd.)

[plansrme]

Just because I have facilitated the GA Tech Distance Calculus program before, are you sure she won't be taking 2 and 3 the same year? Or are you splitting it on purpose? My students have always done 2 in the fall and 3 in the spring.

 

And I agree that no college is going to question the depth of her math education. I have seen GA Tech Distance Calc students go to many different universities and the calc always transfers. There is no way all of that could be scheduled in one year. (If you are comfortable, could you pm me the name of your dd's school? I met some great young women from a STEM school at a Girl Scout event, and it made me think of your dd.)

 

 

No, you are correct that it is in one year. It just counts as two credits because of the block scheduling, which just seemed like more detail than necessary. And technically (as you no doubt know), she has not been admitted yet--we find out in mid-July, but she is confident of a 5 on the BC exam, and her SAT math score was plenty high, so she is not sweating too much. I will be relieved, of course, to see that "admitted" status so she doesn't get shunted into what we jokingly refer as the slacker math track in her program: multivariable calculus at her high school. I am glad to hear the calc will be easy to transfer. I have assumed it would be--it's GA Tech, not a random community college, but good to know for sure. Thanks!

[StephanieZ]

 

 

This is a bizarre statement to me. Aren't you implying that calculus should ALL be covered in one year? That there is only one year's worth of material that can be called "Calculus"? I think it is most common for schools to teach Calc AB and Calc BC in two years, but that hardly means they are only scratching the surface: there is a lot to calculus. My daughter took AB as a homeschooler, then BC in a STEM magnet, where it was a full credit. She will take Calc 2 and 3 through Georgia Tech for her sophomore and junior years. That is a lot of calculus, and I cannot imagine the schedule that would cover that in one year! She will end up with four years' of calculus on her transcript and 5s on both AP exams. I am confident that no college is going to think that is strange or question the depth of her math education.

 

 

Ummm, you bolded where I said that it would NOT be strange to have two years of Calc on a transcript. Indeed, when I was in high school, I, along with many peers, went from precalc to BC calc. Others, who were less mathy, went from precalc to AB calc. No one back then took AB and also BC. I hear you that this is now done. Thus, I said before that I stood corrected and that apparently no one would now look askance at this.

 

My familiarity with basic Calculus is as a three semester sequence. Thus, A, B, and C in the AP designations. I can see that being spread into two years. Four seems quite a bit overdone IMHO. There are many fields of math, so unless these additional years of Calculus are something beyond the traditional three semester sequence done in colleges, then I would wonder why someone didn't study something else rather than Calculus for years and years. It would be like putting Physics on a transcript over and over . . . I would think that you would want to be sure to show in the transcript that each year was a unique topic and not simply a rehashing of the same intro physics materials. So, if your child has two or more years of Calculus or two or more years of Physics, then I would just suggest being sure to title the courses uniquely to show either a progression in difficulty or a unique subset of topics for each course.

 

Fwiw, AoPS teaches one Calculus course, in about 25 weeks, and from what I understand, it more than prepares kids for acing the BC exam. My dd will be doing this in the coming year. There are also plenty of kids who similarly master the materials with other courses and texts in two or three semesters.

 

So, yes, I would personally think it a bit concerning that a capable math student took two, three, or more full years to master what others master in a shorter period of time. I can see with public schools it taking two full years for some kids, and obviously that is happening a good bit. More than two years would certainly make me wonder at the quality of the courses or the caliber of the student. It would just make me wonder what the problem was. If the student were applying to an engineering or other STEM field, I would not want that question to hang unanswered in my child's application packet.

[Jen in NY]

So, yes, I would personally think it a bit concerning that a capable math student took two, three, or more full years to master what others master in a shorter period of time.

 

I think previous posters are suggesting that if a student finishes CalcBC there are more calculus classes to be had that are above and beyond anything covered in the AP program. The student could go on to those classes, put them on a transcript with a course description that differentiates between "APCalC" of any flavor and something more advanced, and admissions offices would understand the distinction. (This was never my problem, as I barely finished trig. Happily, dd#2 will have this issue to wrestle with. :laugh: )

[StephanieZ]

 

I think previous posters are suggesting that if a student finishes CalcBC there are more calculus classes to be had that are above and beyond anything covered in the AP program. The student could go on to those classes, put them on a transcript with a course description that differentiates between "APCalC" of any flavor and something more advanced, and admissions offices would understand the distinction. (This was never my problem, as I barely finished trig. Happily, dd#2 will have this issue to wrestle with. :laugh: )

 

Why yes, of course. Multivariate calculus, etc. Heck, I am sure there are phds whose research interests are in calc. I was generally responding to the op's inquiry about a year of high school calculus leading up to an ap calculus class, etc. I presume that anyone who knows enough about calculus to be beyond ap level calculus won't be looking for MY advice on it, lol.

[Julie in MN]

My oldest son took "calculus" from the beginning 3 times, even though he got A's in all 3.

 

First he took "calculus" at his high school in 11th, then he took calculus in 12th at the community college, starting at the beginning again (took it 2 semesters), and so both were on his high school transcript but clearly one was at a high school and one at a college. He then took calculus -- starting at the beginning again -- at School of Mines because he wanted to follow the traditional freshmen sequence in his college of choice and wanted to learn it "their way" -- he expected each teacher would have something new for him to learn.

 

No one ever batted an eye and he was a valued student with good scholarships and such. He also stayed with his program and finished in 4 years, unlike many of his compatriots.

 

If you have an admission counselor at a multidisciplinary college who doesn't know anything about math, then I might worry that you'd have to find someone above that person to talk to. However, any math or science university would likely feel this is a good student, especially if his grades and his test scores confirmed his abilities.

 

Julie

[kiana]

A, B, and C in the AP designations actually refer to quarters -- that's why AB usually gives one semester and BC may give two. AB is the first 2/3 of a one-year sequence and BC is the full sequence. This of course refers to university.

[mathwonk]

I think it would be fine. There are many different courses called calculus. In high school there are AB and BC and so on, and they seem only to mean that the BC is a little harder than the AB. When i got these students in college they had almost never seen any proofs or any of the reasoning that I expected and so AB, BC or whatever they all needed pretty much to start from scratch. I could essentially not tell the difference between students with high school AP background and those with no calculus at all. Indeed I would much prefer my students had a good solid precalculus preparation than to have calculus as would most other professors I know.\

 

I measured these AP courses by the tests they inspired. The AB tests I saw had no proofs at all. The BC tests had maybe one proof question at the end of the test. But at Stanford, my son's class had 100% proofs on the tests. Where does one prepare for such a class? Certainly not in a typical AP class.

 

What we look for even in a state college calculus class is a familiarity with algebra and geometry and some trig. We would like our students to know that r is a root of a polynomial if and only if (X-r) is a factor. And that the only rational roots r/s in lowest terms, of a polynomial with integer coefficients has r dividing the constant term and s dividing the lead term.

 

We would also,like our students to know the sine and cosine of angles of 30, 60, 45, and 90 degrees, We essentially never get any of this.

 

High school courses are taught by high school teachers, usually with at most a math major in college. College courses are often taught by professional research mathematicians, and as such are on an entirely different level. But you never know, as the proliferation of AP classes in high school has flooded college with so many poorly prepared students that many college courses have also been dumbed down to the level that will accommodate them.

 

My apologies for this rant as your students are probably in the small percentage of those who do have everything we would like but who go away to the better colleges and we never see them at state college.

 

But it never hurts to take as many classes as challenge you and teach you, no matter what their names are.

 

if you want to see how many different varieties of calculus there are, look at books like Calculus made easy, by Silvanus P. Thompson, Calculus and analytic geometry by George B. Thomas, Lectures on Freshman Calculus, by Cruse and Granberg, Calculus by Michael Spivak, Calculus by Tom Apostol, Differential and Integral Calculus by Richard Courant, Calculus by Joseph Kitchen, or if you want to know what advanced freshmen took at Harvard in 1965, look at Advanced Calculus by Loomis and Sternberg....... This ludicrously abstract book was used in a class that actually had mostly freshmen enrolled.

 

http://www.math.harvard.edu/~shlomo/docs/Advanced_Calculus.pdf

[Arcadia]

We would also,like our students to know the sine and cosine of angles of 30, 60, 45, and 90 degrees, We essentially never get any of this.

 

To be honest, I was supposed to memorise the above in 9th grade. However I just draw one right angled triangle with 30 deg, 60 deg, 90 deg (half an equilateral) and one isosceles right angled triangle. Then just use Pythagoras Theorem to calculate the unknown side. That way I have the sine, cosine and tangent for 30 deg, 45 deg, 60 deg and 90 deg without having to memorise.

 

ETA:

I guess there is also the do so many practise questions until you unintentionally remember way.

[mathwonk]

yes! When I use the word "know:" it never means "memorize mindlessly". So it did not dawn on me that there was any other way to "know" this other than the Pythagorean theorem.

[eumyang]

I'm very late to the thread, but I wanted to comment on these:

 

My familiarity with basic Calculus is as a three semester sequence. Thus, A, B, and C in the AP designations.

A, B, and C in the AP designations actually refer to quarters -- that's why AB usually gives one semester and BC may give two. AB is the first 2/3 of a one-year sequence and BC is the full sequence. This of course refers to university.

 

My understanding is that the A, B and C actually refers to groups of topics within Single-Variable calculus.

A - precalculus

B - differential and integral calculus

C - techniques of integration, infinite series

 

A couple of high schools, I recall, would use these letters in their courses, and for multivariable calculus, they would use the letter D (ie. "Calculus D").  But this is not an offical CB designation, obviously (there is no AP exam in multivariable calculus).

 

[kiana]

I'm very late to the thread, but I wanted to comment on these:

 

 

My understanding is that the A, B and C actually refers to groups of topics within Single-Variable calculus.

A - precalculus

B - differential and integral calculus

C - techniques of integration, infinite series

 

A couple of high schools, I recall, would use these letters in their courses, and for multivariable calculus, they would use the letter D (ie. "Calculus D").  But this is not an offical CB designation, obviously (there is no AP exam in multivariable calculus).

 

I have more commonly seen:

 

Calculus A - differential.

Calculus B - integral.

Calculus C - sequences, series, advanced integration.

 

Precalculus is usually separate but sometimes a review is included in A -- but it is not usually the sole topic.

 

Examples:

http://www.nuvhs.org/Academics/NUVHSCourses/CalculusABC.html

http://www.rit.edu/~w-sms/calculus.html

http://catalog.njit.edu/courses/math.php

http://sb.cc.stonybrook.edu/bulletin/current/courses/mat/

http://epgy.stanford.edu/schools/EPTM/index.html

[Brad S]

I came across this thread as I was looking for information about calculus texts for a high schooler.  Excellent threads like these maintain their relevance, and I think that some folks new to the High School Forum in the past 2-3 years might find this thread interesting.  Thanks to all the posters here.  Some follow-up confirming some of mathwonk's statement (which I already knew was true having run calculus help sessions many moons ago).

 

... I could essentially not tell the difference between students with high school AP background and those with no calculus at all. Indeed I would much prefer my students had a good solid precalculus preparation than to have calculus as would most other professors I know.

I measured these AP courses by the tests they inspired. The AB tests I saw had no proofs at all. The BC tests had maybe one proof question at the end of the test. But at Stanford, my son's class had 100% proofs on the tests. Where does one prepare for such a class? Certainly not in a typical AP class.

What we look for even in a state college calculus class is a familiarity with algebra and geometry and some trig. We would like our students to know that r is a root of a polynomial if and only if (X-r) is a factor. And that the only rational roots r/s in lowest terms, of a polynomial with integer coefficients has r dividing the constant term and s dividing the lead term.

We would also,like our students to know the sine and cosine of angles of 30, 60, 45, and 90 degrees, We essentially never get any of this.

High school courses are taught by high school teachers, usually with at most a math major in college. College courses are often taught by professional research mathematicians, and as such are on an entirely different level. But you never know, as the proliferation of AP classes in high school has flooded college with so many poorly prepared students that many college courses have also been dumbed down to the level that will accommodate them.

My apologies for this rant as your students are probably in the small percentage of those who do have everything we would like but who go away to the better colleges and we never see them at state college.

But it never hurts to take as many classes as challenge you and teach you, no matter what their names are. ...

 

The Mathematical Association of America put out a report in 2015 which said much of the same about the desired preparation for calculus and beyond in college, including in the Preface, p. vi, esp. paragraphs 3-5.

 

ETA: link

Edited April 15, 2016 by Brad S

[vonfirmath]

My son has two years left of high school and has just completed pre-calc. He is signed up to take a online calculus course next year that is not an AP class, and the syllabus would not necessarily prepare him to take the AP test. We don't have flexibility with this class. He has to take it for a diploma requirement. My question is, then, would it be odd to take an official AP Calculus BC class the following year? Would that seem strange on a college transcript?

 

Thanks!

 

I do not think so.  Esp considering at our HS (graduated 1991) some kids took AP Calculus AB and then came back and took BC the next year (You can jump right to BC. But the BC after AB gives more practice at calculus)

 

You could think of it as they took a Introductory Calculus course, really enjoyed it. And decided to go deeper in depth so they could take the AP test.

Edited April 15, 2016 by vonfirmath

[Arcadia]

I do not think so.  Esp considering at our HS (graduated 1991) some kids took AP Calculus AB and then came back and took BC the next year

 

OP's son would be finishing 12th grade now :lol:

I do agree with you that Calc AB followed by Calc BC the next year is not unusual.

 

ETA:

There are updates though

 

"We’re excited to announce updates to the AP Calculus AB and BC courses and exams, taking effect in the 2016-17 school year

.....

No topics will be removed from the AP Calculus program, and the following topics will be added:

• L’Hospital’s Rule will be included in AP Calculus AB.
• The limit comparison test, absolute and conditional convergence, and the alternating series error bound will be added to AP Calculus BC."

https://advancesinap.collegeboard.org/stem/calculus

 

 

 

Edited April 15, 2016 by Arcadia