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If your STEM-type child took Calculus in high school . . .


Carolyn in Ohio
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Dd completed the calculus sequence and other college math courses through dual enrollment.  She took a placement test and tested out of calculus.  She was ready and eager to move on.  I can understand pre-med students repeating it for an easy A or for others who want an easy transition, but otherwise (with the exception of some highly theoretical honors courses) it could be frustrating to do it all over again.  Assuming one of the usual calculus texts (for scientists, engineers & mathematicians) is used and the student does well, there shouldn't be a need to begin again.  That doesn't mean that dd doesn't sometimes think how much easier it would be to be taking calculus.

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Well, shoot, I think I was hoping for the opposite answer.  My plan for his senior year has always been to enroll ds in Calculus at the university (which he in all probability will attend)  through their PSEOP program (no cost ).  It would be the exact calculus class required for math/statistics majors. 

 

He has always done well in math (800 SAT) but the trig chapters in pre-calc (Chalkdust)  have been brutal.  I am worried that doing calculus for real college credit might end up backfiring and being a horrible experience. He has Aspergers. 

 

I can NOT teach calculus.  Pre-calc is my limit.  (Look - a math joke ;)  )

 

Carolyn

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Well, shoot, I think I was hoping for the opposite answer.  My plan for his senior year has always been to enroll ds in Calculus at the university (which he in all probability will attend)  through their PSEOP program (no cost ).  It would be the exact calculus class required for math/statistics majors. 

 

He has always done well in math (800 SAT) but the trig chapters in pre-calc (Chalkdust)  have been brutal.  I am worried that doing calculus for real college credit might end up backfiring and being a horrible experience. He has Aspergers. 

 

I can NOT teach calculus.  Pre-calc is my limit.  (Look - a math joke ;)  )

 

Carolyn

 

Do they offer pre-calculus?  If he really struggled with the trig, it might not be a bad idea to get a better foundation in that before moving onto calculus. 

 

I'd also check with the university whether just the (calculus) credit will transfer, or the grade as well and factor into his GPA.  

 

If you think he'd want to repeat the calculus course, there shouldn't be a reason why he can't if he takes it at another college.  Ask what his options would be if he took it at the university.

 

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It depends on the kid and the college.

 

My kids all took Calculus 1 and Calculus 2 in high school at a "public Ivy" 4-year college.

 

Three went on in math/science and had no problems at all with their higher-level classes.

 

One went to a small engineering school (Webb) that does not allow any transfer credits of any kind, so he had to start with Calculus 1 again. For him, the class had so many boat-related applications that the class was NOT review and he was glad he had to take it.

 

Be careful taking college classes in high school -- if he applies to grad school, he will need to send that transcript! College grades, even if taken in high school, will form part of his PERMANENT record.

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If you think he'd want to repeat the calculus course, there shouldn't be a reason why he can't if he takes it at another college.  Ask what his options would be if he took it at the university.

 

Some colleges have rules that if a course has already been passed (at any college) it cannot be repeated. 

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If he took calc through this program, it would be for real "permanent record" stuff.  If his placement test puts him in calc, I don't think they would let him take precalc. Plus, then he would have 2  years of pre-calc on his hs transcript.  I think my other option is to do calculus at home, through some online option.  Then see how it goes, and he could test out as a freshman if possible.  

 

Carolyn

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If he took calc through this program, it would be for real "permanent record" stuff.  If his placement test puts him in calc, I don't think they would let him take precalc. Plus, then he would have 2  years of pre-calc on his hs transcript.  I think my other option is to do calculus at home, through some online option.  Then see how it goes, and he could test out as a freshman if possible.  

 

Carolyn

 

Ask the school about that -- they frequently let students who feel unprepared drop down. Also check the "W" date -- if it's in the middle of the semester he could try, see how it goes, and then drop. 

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If he took calc through this program, it would be for real "permanent record" stuff.  If his placement test puts him in calc, I don't think they would let him take precalc. Plus, then he would have 2  years of pre-calc on his hs transcript.  I think my other option is to do calculus at home, through some online option.  Then see how it goes, and he could test out as a freshman if possible.  

 

Carolyn

 

I wouldn't worry about 2 yrs of pre-cal on his transcript.  You label yours pre-cal and the DE pre-cal course as Math ###, acronym for institution or name of institution written out.  That is not that unusual of a situation.

 

FWIW, I am the parent of an adult Aspie.  No way I would have wanted his first on campus experience to be anything other than successful.  My ds would have imprinted negative feelings on his memory forever and would never have let them go.  Ditto with positive ones.  I would much rather the positive feelings to be the dominate ones.  :)

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Well, shoot, I think I was hoping for the opposite answer.  My plan for his senior year has always been to enroll ds in Calculus at the university (which he in all probability will attend)  through their PSEOP program (no cost ).  It would be the exact calculus class required for math/statistics majors. 

 

He has always done well in math (800 SAT) but the trig chapters in pre-calc (Chalkdust)  have been brutal.  I am worried that doing calculus for real college credit might end up backfiring and being a horrible experience. He has Aspergers. 

 

I can NOT teach calculus.  Pre-calc is my limit.  (Look - a math joke ;)  )

 

Carolyn

 

I'm going to answer the OP's question below, but I need to comment on this first.  My two oldest did Chalkdust for high school math (Alg - Calc), and they found the Precalc book to be the most challenging of them all.  They thought chapters 10 and 11 (Analytic Geometry) were the hardest.

 

I kept telling them that if they mastered Precalc that Calc would be much easier.  They didn't believe me, but found it to be true.

 

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Did they repeat it in college, or place into the next class?  I have always heard that it's best to start a science sequence at the college, even if you have had an AP.  Is calculus the same way?  

 

Thank you!

Carolyn

 

Ds got a 5 on Calc AB, and Dd got a 5 on Calc BC.  Both went on to do very well in their math majors (they doubled with other majors).  Dd had to brush up on trig and 1st year calc using Khan Academy one weekend because she didn't take any math except a stats class between senior year of high school and her junior year of college.

 

Three caveats:

1.  Ymmv, especially if your student plans to take a very theoretical or accelerated Calc course in college.  For all other situations, you should be fine.

2. Many colleges, especially engineering schools, require a math placement test to be taken just before freshman fall semester begins, no matter what the student's score.  Be forewarned!  If your student forgets his/her calc over the summer, he/she will be taking Calc I!

3.  Many profs (especially at schools that do not require placement exams) have had bad experiences with students earning high scores on the Calc AP exams but not being prepared.  Dd was at a school like that, so she kept quiet about her AP credit.

 

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I placed out of the first semester of calc, but decided to take it anyway.  For me, it was a good choice.  The class was relatively easy, though I still had to put the work in, and I came out of it with a really strong grasp of the material, which served me very well in my engineering classes. 

I would talk to the school about pros and cons.  One point to consider is whether being "out of sequence" (by taking the second math class in the fall instead of in the spring) will create scheduling problems down the line, or whether enough kids are on that track that the opposite is the case.

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I placed out of the first semester of calc, but decided to take it anyway.  For me, it was a good choice.  The class was relatively easy, though I still had to put the work in, and I came out of it with a really strong grasp of the material, which served me very well in my engineering classes. 

 

I would talk to the school about pros and cons.  One point to consider is whether being "out of sequence" (by taking the second math class in the fall instead of in the spring) will create scheduling problems down the line, or whether enough kids are on that track that the opposite is the case.

 

This is what happened to me.  My advisor strongly recommended starting with Calculus I, and he was right. I found that their Calculus I had more detail and higher expectations after taking one semester in high school (rotten teacher) and then at a liberal arts school, although it was a relatively easy "A" for me. I struggled in Calculus II and was really glad I didn't start with that. I was also a new transfer student, and it was good to have a transition class versus starting out full bore. 

 

This was a small technical school where getting out of sequence meant far fewer options for registration.  They typically only offered one or two sections of out-of-sequence Calculus per semester.  Lots and lots of choices if you stayed in sequence (i.e. Calculus I, Calculus II, Calculus II, Differential Equations).

 

My oldest is headed towards a finance or accounting major, and I'm leaning towards having him repeat pre-calculus when he registers even though I'm guessing he'll place into calculus.  It won't slow his degree progress at all because he has credits in other areas covered by AP's/SAT II's, and he's been struggling of late with pre-calculus at home.  I had hoped to get in a little calculus this year, but getting pre-calculus down is more important to me.  Then he could do Pre-Calculus, Calculus I, Business Stats I, and Business Stats II over four semesters with no break in math.

 

So yes, there are situations where you might go "back."  Getting math solidly nailed down is important.

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I'm with everyone else and say it depends upon the school, the class, and the student.

 

The vast majority of students from our high school repeat Calc in college, but that's because our high school course, umm, lacks substance.  My public high school grad will be repeating Pre-Calc due to the "high" [sic] level of math our school offers.  He had As and one B in Pre-Calc in high school, but grades don't matter.  Understanding concepts does.

 

My two homeschooled through high school guys both did Calc at home (Chalkdust and Thinkwell respectively).  I had both repeat it at their colleges.  Oldest wishes he had saved the time and not repeated.  Middle is super glad he did.  (FWIW, Middle was far better at Calc in high school - Thinkwell is a more in depth and challenging course IMO).  Middle is also pre-med and the easy A was helpful for his GPA AND he goes to a Top 30 research U where the Calc classes are more in depth than oldest's LAC.  Others at middle's school who opted to skip Calc I told him they wished they hadn't as they ended up working their tails off to get a B in Calc II.  (Middle later also got an A in Calc II.)

 

Many schools offer math placement tests.  It's worth it to take those and gauge which course to take accordingly - and if pre-med - the easy A can be worth it even for a total repeat class.  In many colleges it is just a repeat of a basic AP course.  At others, there is more depth.

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My son's friends who have graduated high school and are in STEM majors at uni have all recommended he retake Calc 1.  The students in engineering programs who chose to move up to Calc 2 seem to be having the most difficult time and have stated they wish they would have started the sequence with Calc 1.  These are all students who have completed AP Calc A/B & B/C.

 

 

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So far, I've had 2 kids do the opposite of each other -- both took AP calc in high school.  One went right in to Calc 3 in college, the other started over at Calc 1.

 

I can see advantages to either path.  Skipping calc 1 and 2 frees up some time.  But going back and doing it over does seem to give a much firmer grasp on the material.

 

So the answer to the question may depend, in part, on how well the student needs to know it.  And whether they're going to pick up a lot of it in later courses anyway.

 

I did calc in high school but never got around to taking the AP test because by then I knew I was going to a college that wouldn't accept the credit.  I understood calc the 2nd time way better than I did the first time.  And every time I've had to tutor my kids through it, I've understood it even better.  So, with a good teacher, there might not be too much disadvantage to doing it over, except that it takes time.  Also, the student won't have bragging rights for being way smart -- but then, in our physics dept, the kids who skip calc because of AP credit don't seem to be significantly smarter/better prepared than those kids who didn't by the time they all graduate from college.

 

So I guess I wouldn't worry too much over the decision.  Whichever way the student goes is probably fine.

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At my son's school, they do placement on a case by case basis.  He took AP calc BC junior year and got a 5 on the exam.  Then he spent a year outside the US as an exchange student, and took a university course in discrete math, and a one semester CTY course in Linear Algebra.  He did not get A's in either.  After meeting with a math professor before freshman year (over the phone) he elected to take Honors Calculus 1.  It was an easy A but it also allowed him to pursue an Honors degree in math, which he ended up choosing as his major.  So it worked out OK.  He is glad he had the exposure to more advanced topics in high school, but he did not get a good, college-level exposure to Linear Algebra, and he found "real" calculus in college to be quite different from the AP treatment of the topic.

 

ETA: so IMO it depends.  I honestly think that any student other than a math major would not have benefitted from doing what ds did.

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Do they offer pre-calculus?  If he really struggled with the trig, it might not be a bad idea to get a better foundation in that before moving onto calculus. 

 

I'd also check with the university whether just the (calculus) credit will transfer, or the grade as well and factor into his GPA.  

How about just short course in Trig during the summer.  There are a few formal courses out there or just use Kahn Academy.  This student is smart he will get it on the second try!

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Well, shoot, I think I was hoping for the opposite answer.  My plan for his senior year has always been to enroll ds in Calculus at the university (which he in all probability will attend)  through their PSEOP program (no cost ).  It would be the exact calculus class required for math/statistics majors. 

 

He has always done well in math (800 SAT) but the trig chapters in pre-calc (Chalkdust)  have been brutal.  I am worried that doing calculus for real college credit might end up backfiring and being a horrible experience. He has Aspergers. 

 

Continue with your plan especially if DS will enroll at that same college!  Don't be discouraged, we all have some kind of disability or challenge area (we are human).  

 

[We have Engineers with Aspergers at work.  I only know this because my youngest son is autistic and I have studied a lot on that subject area.]

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How about just short course in Trig during the summer.  There are a few formal courses out there or just use Kahn Academy.  This student is smart he will get it on the second try!

 

A summer course is a great idea.  I wouldn't suggest it for new math material as the summer courses move incredibly fast, but if they offer pre-calculus or just trigonometry, that could be a great intro to the college and give him the confidence to begin calculus in the fall.  I would suggest going with your son and speaking with an advisor and maybe someone in the disabilities and/or math department.  They may have recommendations for him.

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A summer course is a great idea.  I wouldn't suggest it for new math material as the summer courses move incredibly fast, but if they offer pre-calculus or just trigonometry, that could be a great intro to the college and give him the confidence to begin calculus in the fall.  I would suggest going with your son and speaking with an advisor and maybe someone in the disabilities and/or math department.  They may have recommendations for him.

I meant to say a high school level or online Trig only class where the student seems to have issues.

I saw one once when I was poking around.

 

here are two:

http://www.time4learning.com/homeschool/curriculum/high_school_trigonometry.html

https://continue.utah.edu/noncredit/class/math_106_trigonometry

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My dd had to re-do calc at her technical college.  But, it was on a higher order of problems, techniques, depth of theory, etc.  Her school has various "grades" of calc offered: eg calc for engineers, calc for comp. sci., calc for math majors, calc for physical sci. majors, calc. for bio and chem majors.  She said it helped to have had calc. her sr. year in high school but, she did think that maybe having some statistics would have been more valuable, especially since it is often used in analyzing lab data....they offered a quick over view of what was necessary to do the lab reports but, she said she really would have liked to have had more background. 

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I wanted ds to take the calc for 2 reasons; The calculus, and the experience of a college class before full time college.  The calculus class would be the exact same class/course # required of math majors.

 

He may be better off taking another class through this program (maybe programming) and doing Derek Owens Calculus at home.  A one semester pace might be too much.  It would help if I understood the least bit about the differences between calc 1, 2, etc.  :)

 

thanks to all!

 

Carolyn

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  It would help if I understood the least bit about the differences between calc 1, 2, etc.   :)

 

Descriptions from different colleges  1)  2)  3)  4)

===================================

Calculus I

1)Introduction to calculus with an emphasis on understanding and problem solving. Concepts are presented graphically and numerically as well as algebraically. Elementary functions, their properties and uses in modeling; the key concepts of derivative and definite integral; techniques of differentiation, using the derivative to understand the behavior of functions; applications to optimization problems in physics, biology and economics. A graphing calculator is required for this course. We recommend the TI-83 or TI-84 models. Calculators that perform symbolic manipulations, such as the TI-89, NSpire CAS, or HP50g, cannot be used. 

2)Introduction to analytical geometry and calculus. Includes limits and continuity, derivatives, applications of the derivative, and integration.

3)Functions, limits, continuity, derivatives, implicit differentiation, related rates, maxima and minima, elementary transcendental functions, introduction to definite integral with applications to area and volumes of revolution.

4)This course provides an introduction to differentiation and its applications. Topics covered include: functions and their graphs, limits, continuity, differentiation, linear approximation, chain rule, min/max problems, and applications of derivatives. Recommended background: Algebra, trigonometry and analytic geometry. Although the course will make use of computers, no programming experience is assumed.

5) http://faculty.uml.edu/rbrent/131/F14syl.pdf

===================================

Calculus II

1)Techniques of symbolic and numerical integration, applications of the definite integral to geometry, physics, economics, and probability; differential equations from a numerical, graphical, and algebraic point of view; modeling using differential equations, approximations by Taylor series. A graphing calculator is required for this course.  We recommend the TI-83 or TI-84 models. Calculators that perform symbolic manipulations, such as the TI-89, NSpire CAS, or HP50g, cannot be used. 

2)Continuation of Calculus I. Includes techniques and applications of integration, numerical integration, improper integrals, separable integrals, separable differential equations, sequences, infinite series, and other related topics.

3)Techniques and applications of integration, polar coordinates, parametric equations, infinite sequences and series, vector functions and curves in space, functions of several variables, and partial derivatives.

4)This course provides an introduction to integration and its applications. Topics covered include: inverse trigonometric functions, Riemann sums, fundamental theorem of calculus, basic techniques of integration, volumes of revolution, arc length, exponential and logarithmic functions, and applications.

5) http://faculty.uml.edu/Jennifer_GonzalezZugasti/92.132/index_fall.html

===================================

Calculus III - AKA Vector Calculus 

1)Vectors, differential and integral calculus of several variables. 

2)Includes vectors in two and three dimensions, vector-valued functions, differentiation and integration of multivariable functions, and calculus of vector fields.

3)Multivariable Calculus and Matrix Algebra - Directional derivatives, maxima and minima, double integrals, line integrals, div and curl, and GreenĂ¢â‚¬â„¢s Theorem; matrix algebra and systems of linear equations, vectors and linear transformations in R^n, eigenvectors and eigenvalues, applications in engineering and science.

4)This course provides an introduction to series, parametric curves and vector algebra. Topics covered include: numerical methods, indeterminate forms, improper integrals, sequences, Taylor's theorem with remainder, convergence of series and power series, polar coordinates, parametric curves and vector algebra.

 

 

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Calc BC = Calc 1 + 2. 

Calc AB = roughly 2/3 of Calc 1 + 2. 

 

In High School (back in 1990) I got a 5 on the BC test.  That was my junior year of HS. I took no math my Senior year (Had maxxed out the school's offering) and tried to take Engineering Calculus III the next Spring in College. I bombed.

 

I would have done MUCH better either not skipping math somehow. Or (more likely) Retaking Calculus II. I think I'd have been fine not retaking Calculus 1 but it was too much of a jump. And I had an EXCELLENT teacher for Calculus in HS.

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Thanks for all the help.

 

So then, what in the world is the difference between calc and AP calc?  

 

Carolyn

 

Any course with "AP" in front of it has to have the syllabus approved by College Board (who owns AP and its tests).

 

The content can be identical and you can even take the AP test without an approved course, but you can't put AP on the transcript without that approval of the syllabus.

 

When my guy self-studied for some tests we listed them on his transcript as Stats w/AP test score = 5.  I could not call his course AP Stats even though we used the same book most courses use, etc, and he got his 5 on the test.

 

Some students take an approved course and opt not to take the test.  They could list AP Stats, but if a college were looking for scores, they wouldn't have one and the grade alone would not be accepted for credit.  Test scores alone are accepted by many (not all) colleges for credit.

 

I have seen no real reason a homeschooler needs an official AP course.  There are plenty of reasons why many homeschoolers want to have comparable coursework and/or take the tests though.

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In High School (back in 1990) I got a 5 on the BC test.  That was my junior year of HS. I took no math my Senior year (Had maxxed out the school's offering) and tried to take Engineering Calculus III the next Spring in College. I bombed.

 

I would have done MUCH better either not skipping math somehow. Or (more likely) Retaking Calculus II. I think I'd have been fine not retaking Calculus 1 but it was too much of a jump. And I had an EXCELLENT teacher for Calculus in HS.

 

Taking a year and a half off causes you to lose a lot of skill. 

 

BTW, I'm not saying that a student shouldn't repeat a level -- just that BC covers calc 1 + 2.

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My two took Calculus at the local liberal arts college and aced the class.  Neither felt the need to repeat it.  One is going into biology so he doesn't need nearly as much a math focus.  My other kid is going into Physics and has not yet taken the next course in the series.  But so far, K has not had any trouble with the advanced physics classes using the calculus already learned. 

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At Georgia Tech, Calc 2 covers linear algebra and multivariable calculus, neither of which are covered in BC.

Several engineering colleges do things like this. You can usually tell by looking at the AP credit page. Georgia Tech only gives credit for Calc I even if you make a 5 on BC test (since obviously the BC test doesn't cover the content of Calc II).

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Our middle boy will have Calc 1 taught by my husband who has a math degree. We have recommended that he still take calc 1 again due to college professors also teaching it in a more applied manner and more depth, but also because the usual math and science rotation for STEM students begins with Calc 1 and the related science coursework. Getting into the rotation and staying on that schedule, not trying to jump ahead and then ending up either overwhelmed or unable to get into the next math or science in the sequence because it is offered every other semester so then there is a gap in learning which can lead to being a little rusty on specific skill sets.

 

Most of the STEM oriented schools my guys have interviewed at were willing to give credit for community college Calc 1 or AP, but weren't thrilled about the students going into the next level because so many did poorly. However, they indicated that most of the freshmen who transferred Calc 1 from four year universities and LAC's here in Michigan do just fine in Calc 2.

 

We have a boy who will make it through Calc 2 before graduation. We've really wrestled with the best path for him as a budding robotics engineer. He will probably take Calc 1 his junior year with DH, then again from one of University of Michigan regional campuses because the class sizes are so much smaller and with DH as his go to tutor if he needs assistance followed by Calc 2 from the extension campus. Since this particular extension campus is a full STEM school that has tons of math and science degrees, we think the rigor will be enough that he can then go to Calc 3 his freshman year so long as the cycle will match up so that he doesn't sit around waiting for classes he needs. We don't want math skills going stale. Otherwise, he may end up repeating a math, and that's okay because there isn't anything bad about making an easy to earn A.

 

For the most part, whatever the dean of the department over the major recommends is best to follow since they've "seen it all" so to speak.

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Ds took Calc 1 at CC, then started in Calc 2 at STEM school.  Had I known that the school would register him for Chemistry, Physics, and Computer Science in addition to Calc his first semester, I would have suggested Calc 1 instead of Calc 2.

 

 

 

It depends on the kid and the college.

 

Yep.

 

older son: took calculus at ps, grade 11 --> BC exam score 4; wanted to repeat Calc 1 his freshman year at his college, because it had been over a year since he'd had calc, and he felt he hadn't really mastered it anyway (confirmed by his AP score). Ironically, this took multiple visits to his academic & honors advisors for him to get this Calc 1 re-do approved, since he had placed into Calc 2, but didn't qualify for Calc 1 (!), as his ACT score (placing him into Calc 1 and out of precalc) was too old -- by one day -- during class signups at orientation.

 

He re-took Calc 1 and was glad he did; he had a good basis for Calc 2 the following semester, and as with Sue's son, his other classes -- chemistry, engineering, etc. -- plus adjusting to college life and being far from home, were enough challenges for his first semester!

 

My younger son is taking upper-division math his freshman year in college and loving it. He is different from his older brother, though. :) Oh, and he just declared his math major. :)

 

 

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At Georgia Tech, Calc 2 covers linear algebra and multivariable calculus, neither of which are covered in BC.

 

You are totally correct that GA tech's calculus is accelerated beyond most standard calculus courses. This is why they say on their website that you can't transfer in calc 2 unless you've also taken linear algebra. This is non-standard. 

 

I keep editing this because I can't get it to sound right. I'm just intending it as a general guideline -- not as a 'covers everything in every class everywhere'. Clearly there's going to be some differences in coverage and this is exactly why I believe I said early on (unless someone else had said it earlier and better) that at a large research university with a talented student body it would be beneficial to repeat calculus because the coverage would probably be deeper and more thorough. But it will cover everything in an average calc 2 class. 

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You are totally correct that GA tech's calculus is accelerated beyond most standard calculus courses. This is why they say on their website that you can't transfer in calc 2 unless you've also taken linear algebra. This is non-standard. 

 

I keep editing this because I can't get it to sound right. I'm just intending it as a general guideline -- not as a 'covers everything in every class everywhere'. Clearly there's going to be some differences in coverage and this is exactly why I believe I said early on (unless someone else had said it earlier and better) that at a large research university with a talented student body it would be beneficial to repeat calculus because the coverage would probably be deeper and more thorough. But it will cover everything in an average calc 2 class. 

FYI - MIT also follows a different pattern as well from the

 

Calc 1

Calc 2

Calc 3

Differential Equations 

 

course sequence that most Engineering schools follow.  

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Sometimes you do not have a choice in which class to take no matter what you test into because of scheduling issues. My daughter tested into Calc 3, but she needed to take the honors version to meet her honors program requirements. However, the honors 3 calculus class conflicted with the intro class for her major. She did fine in Calc 1 and 2. 

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I personally think it's silly to repeat AP classes in college UNLESS the student is going to a phenomenally awesome college in that particular field. So, if they go to MIT or Harvey Mudd for engineering, sure, repeat physics . ..  but no, don't repeat biology or history . . . 

 

FWIW, when my dad went to MIT in the 60s, he had to self-teach Calculus the summer before entering since his high school hadn't offered it, but MIT expected it upon entrance. He apparently did just fine, even having to self-teach the entirety of Calculus. 

 

If they are going to a solid state school or another "good" school, I wouldn't repeat any coursework unless the student is weak.

 

I took all the AP credits I could use when I went to college, and I took the engineering-sequence calculus, skipping the one semester I'd tested out of with AP, and still got As no problem.

 

My dd will skip the first two semesters of Calculus based on her AP Calc score, and she'll skip plenty of other courses, too. I'm sure she'll do just great.

 

IME, a great AP class can be just as good or better than a college class. If my kid wasn't confident for some reason, sure, they could consider repeating . . . But, I suggest they dive in and try. I expect most kids would do just fine. 

 

The 40+ college credits my dd will enter with based AP and CLEP tests will allow her to get her MS (after the BS) in the same time she'd just get the BS if she didn't use the credits. Plus, it'd mean wasting 40 credit hours repeating elementary material instead of plunging on in to her areas of interest. 

 

All that said, I will encourage dd to register for 15 or 16 credits, to allow her the possibility of dropping any one course while still maintaining full time status. That is a nice insurance policy in case any course is over her head. 

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