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bnbacademy

How much math is necessary for STEM major?

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We have a decision to make... and would like your input.  Ds is currently taking Algebra 1, doing very well, so... we had been looking into stepping things up by taking Geometry online simultaneously.  The school's math options 9-12  include: Algebra 1, Geometry, Algebra 2, pre-Calculus, AP Calculus.  

 

On current schedule, ds would take Alg 1, Geometry, Alg 2, pre-Calc by 12th grade.

OR, if we hurry and start an online Geometry class, he would reach AP Calc by 12th grade. However, this would mean summer school.

 

What do STEM majors need or maybe the ? is: what do STEM colleges look for?  Would they even give him credit for AP Calculus or would they want him to take Calculus at their college anyway?  Do colleges look at classes or at GPA? He could take Honors math from here on out, including Honors Geometry, which would help a GPA.

 

Trying to decide if it is worth/ necessary to spend the $500  and the time for this class or not...?

 

He likes math and is good at math. He had Algebra already, just wanted to give him a boost by repeating Algebra to start high school and he didn't do great on the placement test. However, he is doing very well in current Alg 1 (currently has 97% grade).

 

TIA,

 

 

 

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First, I think it is very good you chose to repeat Algebra. I teach math and science at an alternative school. If algebra is shaky, the later courses really fall apart. A student needs to be solid at each level of math, especially those students considering STEM. 

 

The answer to your question depends on which STEM degree and which university applied to. 

 

I know the unstated requirements for 2 schools competitive universities in my state. These are not the requirements listed on their websites, but the profile of student they actually accept. Both schools state on their websites an expectation that a student will have 4 credits of math. One school says this will include Algebra 2 and the other says Precalc. However, what they accept is quite different:

1. Large state university with nationally recognized engineering program. I just visited this school with my dd. The admissions officer told a group of visiting potential applicants that if they are not taking calculus (and doing well) their senior year they will not be admitted to the engineering program. They might be able to apply to the school of arts and science and major in something like physics, math or chemistry, but I am not sure. 

2. Small state liberal arts school (a public ivy and my alma mater). An article in my alumni magazine specifically stated that all admitted applicants had completed at least Calculus AB. All admitted applicants--that surprised me. By virtue of my volunteer work in sports programs, I happen to know quite a few kids who applied and attended this school and they all had calculus in high school, so  I have not met anyone in recent years who appears to be an exception to the claim, but it still surprised me. That would include people who are seeking to study Art History, English and Latin. I have a STEM degree from this school, so I took a lot more math when I arrived on campus.

 

My state has quite of few other less competitive schools that offer engineering and I would expect just about all schools to offer degrees like Comp Sci, Math, Physics, Chem. These other schools may not be so demanding of applicants. I haven't gotten into the nitty gritty of a lot of schools yet. I just happen to know what's happening at the two highly competitive programs I described. 

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Credit for AP is usually (except at top tier schools) given when the student scores a 4 or 5 on the AP exam, not for simply taking the AP course.  It is beneficial if the student had an introduction to calculus in high school, but not essential.

 

I teach physics at a STEM university which is the top engineering school in our state. Most students take calculus 1 here, some have AP credit. It does not really matter whether they had calc in high school. Placement is done by placement test (and some student with AP Calc credit place into remedial trigonometry).

It is infinitely more important that they had a rock solid algebra preparation. The students who struggle in my calculus based physics courses because of math do so not because of a lack of calculus, but because of an insufficient mastery of algebra. I would never encourage rushing just to get to calculus; it is far more important to have solid algebra. I know I am repeating myself, but I can not stress this enough.

 

As far as GPA and classes: it all depends on the school how good you have to be to get in. There are schools that admit 85% of applicants and some that admit 7%.

 

FWIW, my DD will have had calculus in high school, but we specifically want her to retake calculus at the university because we consider it extremely beneficial, and hence did not bother with the AP.

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I forgot to say, but regentrude pretty much did, at both the schools I wrote about, even though they are expecting to see calculus on a transcript, with a good grade (and good grades in all math courses), students typically repeat calculus at the university, even students who took the AP exam and would be awarded credit. 

 

Many top tier universities are expecting to see calculus on a transcript. My dd's high school has math beyond calculus. They offer linear algebra or multivariable calculus(alternating years) for students who have finished the calculus sequence. So, it's not that unexpected that top tier universities have come to expect it. However, all that math is meaningless on the transcript if the student has rushed through and not understood basic principals. I see a lot of kids who have memorized formulas with no understanding where such formulas came from. These students become more and more limited in their ability to apply math over time and will not do well in a STEM program. 

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I know physics majors who only made it through Algebra 2 while in high school.  They just took pre-calc and calc once they got to college.

 

Getting through pre-Calc in high school is often where kids end up.  At a really high falutin school (like MIT) you might have a leg up in admissions if you'd finished calculus and had AP credit from the test.  Maybe.  I'm only saying that because a lot of the other applicants probably would too.  (Actually, it wouldn't be a leg up.  It would just be entering the pack.  Although, from having met some MIT students recently, I'm less convinced that MIT students are all the mythology thinks they are.  They just seem to be, well, college students.)

 

But at most schools, it seems steady, solid progress through the math sequence is what colleges are looking for.  And, yes, there are a certain number of colleges that won't take the Calc AP credit.  Some won't even take credit from other colleges (MIT used to be in this category.  Haven't checked recently.)

 

Doing Calc in high school (and getting credit for it -- either AP or dual enrollment) might free up a class or two at college if it's not one of the colleges that insist kids retake it.  That would be the big advantage of doing it in high school.

 

However, as Regentrude has said, doing calc twice may be a good thing.  A lot of kids may benefit from another pass through.  If they intend to do a major that uses calculus concepts heavily, knowing it better will make the student's life a lot easier.

 

Keep in mind, though, that Algebra 1 is often fairly easy, compared to the later math courses.  It's difficult to plan based on how a student does in that class.  Although a student may be breezing ahead at this point, don't get fixated on getting through calc if it means skimping on the rest of the sequence to keep on schedule. 

 

Also, I suspect a lot of kids would benefit from delaying calc and doing it in college, just because it gives the brain a bit more time to mature. (Or repeating it)

 

So, if it were me, no, I wouldn't rush through it, unless the student was really begging for more.

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I'm always puzzled by the advice that students should repeat calculus at college. I think it depends on the college and the student, but folks shouldn't assume that repeating calculus is routine or customary.

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I'm always puzzled by the advice that students should repeat calculus at college. I think it depends on the college and the student, but folks shouldn't assume that repeating calculus is routine or customary.

 

The reason I consider repeating calculus very beneficial is that a second pass through allows the student a deeper appreciation of the underlying concepts if he has mastered the procedural aspect.

During the first calculus course, students are typically taught procedure: they learn to take derivatives, find minima and maxima, calculate integrals of certain functions, maybe learn a few integration tricks if it is a strong course. That is what most traditional calculus courses (and certainly the textbooks I have seen) focus on. The students emerge with a reasonable ability to perform these actions, but usually lack the insight into the concepts of, for example, epsilon-delta proofs, or the understanding how to set up integrals to describe physical situations. Do not get me started on the inability of students after two semesters of college calculus to set up an integral for the electric field of a line charge! Once they are given the integral, they can evaluate it, but the conceptual insight is missing and hence they can not apply their calculus. The majority of the students in our engineering physics course (for which calculus 2 is a prerequisite) struggle with this aspect.

Why? Because calculus is a tough course, and the students who take it for the first time focus their time and energy on managing the procedures. That's pretty much all they are able to, even with a large time investment.  A student who, in contrast, has already mastered the procedural side during high school, will be able to appreciate the conceptual aspects of his college calculus course and go much farther than a student who has to focus a lot of time and effort on solving the homework problems.

 

Btw, during my time at the university, I found that repeating pretty much ANY conceptually difficult subject is highly beneficial. I did that several times, by working through a textbook over the summer preceeding the course (for classical mechanics) or by auditing a course a semester before I was supposed to be taking it (quantum mechanics). The gain in deeper understanding from a repeat, especially if it uses a different textbook/instructor/approach is very valuable.

ETA: Students who found it beneficial to put this extra effort in were not the ones who needed the second go to barely hang on, but the smartest students in our year. My near genius DH self-studied the entire math sequence before university and swears that it was extremely useful to take the courses and that he got far more out of it with the previous knowledge that he would have otherwise.

 

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Both older boys did different tracks for high school and neither had a problem with their engineering coursework.  DS1 went through Calculus 1 at CC as a dual enrolled high school student.  He had to retake the course at the state uni because it was not considered equivalent.  It was broader but the uni. course was deeper.  Uni course is 4 semesters long, CC course is a 3 semester sequence.

 

DS2 took precalculus and statistics at the CC as a dual enrolled student.  He went straight into Calculus 1 at the university.  He's doing fine.

 

For our state university, there were no issues with their high school math sequences.

 

For private universities - who knows?

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I'm always puzzled by the advice that students should repeat calculus at college. I think it depends on the college and the student, but folks shouldn't assume that repeating calculus is routine or customary.

 

I agree completely.  I would think it is student dependent and how they were taught and how well learned the material the first time through.   Both of my sons would (have) detested having to repeat cal. 

 

My oldest had zero problems continuing forward with math and his engineering courses.   He was one of the strongest students in his program.

 

Our youngest ds has continually had the highest grade in every subsequent math course he has taken.   He goes to professors' offices and has conversations with them about proofs, etc not gone over in class.    He has had at least 2 math professors tell him that he is the strongest math student they have encountered in their careers.   He would go crazy having to go back to cal 1 and repeat it.   As a matter of fact, I think he would eliminate any college that required him to do so.

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I'm always puzzled by the advice that students should repeat calculus at college. I think it depends on the college and the student, but folks shouldn't assume that repeating calculus is routine or customary.

 

As always, it depends on the caliber of the student and the depth of the courses.

 

I personally did retake Calc 1 (the version for math majors) at my state engineering U due to the test out exam being scheduled for a time slot when I had a class and not knowing it was ok to negotiate a different time (secretary didn't volunteer that & I was too new to have any idea). Total waste of time, other than learning how to take an exam in a large room full of noisy people with profs walking around. The prof read the text to us. Couldn't even come up with his own examples. Skipped the meaty stuff.  Total disappointment.

 

I am seeing a number of schools that ds2 is looking at who state up front that a CC version taken on a high school campus is not going to be accepted.  However, the fine print as always is that test out is available. We do supplement his CC class; the majority of proofs have been omitted and roughly half the students are memorizers so its a slog for the teacher, butthe material is there for the reading (which ds does while the review is going on).  Older students we know are reporting different experiences...the difference really seems to be that the memorizers are having difficulty; the thinkers are doing fine wherever they've landed with the CC Calc 1 & 2 background...that includes Math majors at Schools like NYU and Columbia.

 

Students doubling in high school usually double Geometry and Algebra 2, not Algebra 1. 

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I'm always puzzled by the advice that students should repeat calculus at college. I think it depends on the college and the student, but folks shouldn't assume that repeating calculus is routine or customary.

 

Many students who do well in an AP course have memorized how to do various types of problems. They often don't know the material well enough to apply it in engineering or physics, even when they've gotten a 4 or 5 on the AP exam. 

 

Another pass through the material allows the students to really get the mathematical understanding of why. 

 

In real life the formula you need is not given, and the answers to the odd problems are not in the back of the book. 

 

This is not that much different than the WTM approach of having students going through the history cycle three times. If you've never had history before it's really hard to understand original documents (like the magna carta or the US Constitution) without the hooks and internal timeline a student has developed by studying and beginning to understand the time period of these document previously. 

 

A student who did decently through calculus in a high school AP knows how to solve a problem that is set up or when given most of the details needed to organize set up. A second pass gives the student a chance to understand the whys and see where he can apply it. If you didn't really understand calculus the first time, you probably won't get to the deeper understanding the second time.

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Honestly, I understand some universities not transfering credit from other schools. 

 

In my work with online high school classes, it's pretty obvious what passes for algebra is some states is prealgebra elsewhere. I've seen precalculus courses (year long full credit courses) that never got to material beyond what my dd covered in her honors algebra 2 class. 

 

When I was in college I took multivariable calc in summer school at a univ near my home. I transferred the credits. My classmates used the same text and covered a lot more material ( my summer class cut off 4 chapters). That really bit me in the butt in my upper level chem and physics classes I took the next school year. I thought I was getting ahead but I had to make up a lot on my own. 

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Typically, anyone going in to STEM needs calculus in high school. I saw a statistic a while ago on those who already had calculus and those who did not and the chances they would succeed in a STEM major. It was very low for those who did not.

 

That being said, there are exceptions. My son is at a small private LAC that I do not think is that strong in the STEM areas. They do focus on pre-med people (premeds do not need as much math). For my son, a computer science major, a lot of those students start with calculus 1, so not a big deal. However, if your STEM major student goes to a college that is strong in STEM, or any engineering school at all, he really needs to have the calculus 1 out of the way at minimum.

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Many students who do well in an AP course have memorized how to do various types of problems. They often don't know the material well enough to apply it in engineering or physics, even when they've gotten a 4 or 5 on the AP exam. 

 

Another pass through the material allows the students to really get the mathematical understanding of why. 

 

In real life the formula you need is not given, and the answers to the odd problems are not in the back of the book. 

 

This is not that much different than the WTM approach of having students going through the history cycle three times. If you've never had history before it's really hard to understand original documents (like the magna carta or the US Constitution) without the hooks and internal timeline a student has developed by studying and beginning to understand the time period of these document previously. 

 

A student who did decently through calculus in a high school AP knows how to solve a problem that is set up or when given most of the details needed to organize set up. A second pass gives the student a chance to understand the whys and see where he can apply it. If you didn't really understand calculus the first time, you probably won't get to the deeper understanding the second time.

 

I still think this is an over generalization.  Maybe some....but is it really "many"???  Nor do I really agree with the math/history comparison.

 

FWIW, you might want to look into AoPS cal course.  It is definitely not memorizing how to solve problems.

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I know physics majors who only made it through Algebra 2 while in high school.  They just took pre-calc and calc once they got to college.

 

 

This could put a physics major 1 or more yrs behind for graduation.   Depending on the university, some pre-cal courses are split into pre-cal 1 and pre-cal 2. Physics majors are expected to start with university physics (cal based physics)--any physics lower than cal physics won't count toward their degree.  Again, depending on the university, some universities have cal as pre-req, not a co-req.   So that could put them at least 3 semesters behind. 

 

While it is doable, students would need to be aware that their 4 yr degree just got bumped up to more than that.   When courses are on the pre-req level, it really impacts the ability to take courses.

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I still think this is an over generalization.  Maybe some....but is it really "many"???  Nor do I really agree with the math/history comparison.

 

FWIW, you might want to look into AoPS cal course.  It is definitely not memorizing how to solve problems.

 

Sure, whatever... I have a STEM degree from a competitive school and through my online classes a get to see what is happening for students coming from a variety of school districts using a variety of curriculum across the country. In general math instruction is in a sorry state and higher math instruction is worse. Yes, there are a few students who do not need the repeat, but that is the exception not the rule for students pursuing STEM. It you got a 5 on the AP calc exam and you aren't pursuing STEM then I would say just take the credit and get further ahead in your major, because calc is not foundational to your major. If calc is foundational to your major you need to be careful about skipping the calc course at your university. 

 

You might want to consider Regentrude's posts carefully, since she has first hand experience at the University level. 

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. If calc is foundational to your major you need to be careful about skipping the calc course at your university.

 

You might want to consider Regentrude's posts carefully, since she has first hand experience at the University level.

My oldest ds graduated from our homeschool and is now a chemical engineer. Our youngest ds is 17, made a 5 on the AP exam in 10th grade and has already taken multi-var cal, diffEQ 1, is finishing linear alg in a couple of weeks....all taken at universities with the highest grade in the classes. If you had read my previous response in this thread, you would see that this ds actually goes and talks to his professors about proofs not discussed in class.

 

That was my pt. Not all students are plug and chug students. There are students that really know what they are doing. Our youngest ds has gone to multiple academic camps full of students equal in strength (or greater) to him in math. They are out there. That is why the suggestion should be student dependent.

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My oldest ds graduated from our homeschool and is now a chemical engineer. Our youngest ds is 17, made a 5 on the AP exam in 10th grade and has already taken multi-var cal, diffEQ 1, is finishing linear alg in a couple of weeks....all taken at universities with the highest grade in the classes. If you had read my previous response in this thread, you would see that this ds actually goes and talks to his professors about proofs not discussed in class and 2 have told him that he is the strongest math student they have encountered in their careers.

 

That was my pt. Not all students are plug and chug students. There are students that really know what they are doing. Our youngest ds has gone to multiple academic camps full of students equal in strength (or greater) to him in math. They are out there. That is why the suggestion should be student dependent.

 

Glad it worked out for you. Your family does not represent a majority sample of STEM majors. The kids in your son's camps don't represent a majority of STEM majors.

 

The majority of engineering and physics programs I've seen recommend repeating and the reason is not so the university can make money on the course. Again, look at Regentrude's posts since she is working at the university level. 

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Stanford has a special honors calculus track that has a prerequisite of a "5" on the AP Calc BC exam. It is designed for prospective math majors and very strong STEM students. I get the impression it's designed for the kids who were on the math competition circuit in high school. DH, who got a "5" on the AP exam but never did super-well with competition math, just took the regular STEM math track and that was sufficient for his electrical engineering degree. I took the lowest level calculus track and that was fine for pre-med/biology but it wouldn't have sufficed for engineering or physics.

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Miriam, even more important than whether he gets to calculus or not, is that he take the honors math classes.  It's not only from the point of view of how it will look on the transcript, it's that that level will be needed to do well and not struggle in the higher math.   I can see a him being accepted as a STEM major with pre-calculus, but I think it would be unlikely if he did it with non-honors level courses.   The colleges will know that the honors math courses were available for your son, and that he chose not to take them.  As for doubling up with geometry, only if he's got the time in his schedule so that his algebra work and other courses won't be adversely affected.  Mastering math is more important than rushing to a certain level.  He should also consider honors level science courses if he's able as chemistry and physics will allow him to apply what he's learned.

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"we had been looking into stepping things up by taking Geometry online simultaneously."

 

IMHO doing the 2 subjects, concurrently, is not a good idea. Better for the student to be able to concentrate on one subject at a time.

 

As "regentdude" and other PPs have written, it is urgent that the material be understood, correctly and completely, and that one can apply it.

 

Getting into Engineering school is one thing. Graduating is another thing. 

 

 

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Miriam, even more important than whether he gets to calculus or not, is that he take the honors math classes.  It's not only from the point of view of how it will look on the transcript, it's that that level will be needed to do well and not struggle in the higher math.   I can see a him being accepted as a STEM major with pre-calculus, but I think it would be unlikely if he did it with non-honors level courses.   The colleges will know that the honors math courses were available for your son, and that he chose not to take them.  As for doubling up with geometry, only if he's got the time in his schedule so that his algebra work and other courses won't be adversely affected.  Mastering math is more important than rushing to a certain level.  He should also consider honors level science courses if he's able as chemistry and physics will allow him to apply what he's learned.

 

I'm also a STEM professor (math/computer science), and I agree with this.  The depth of math is so much more important than rushing to calculus.  I actually dropped calculus in high school (jerk teacher), and did a liberal arts program for two years before switching majors and schools.  I studied my math over the summer using a used pre-calculus book, and placed solidly into Calculus I at all-tech school.  I had no problems at all from there. I know though that I had top-notch math in high school.

 

I have one who is interested in civil engineering and had to repeat Algebra I twice (8th and 9th grade).  We took Algebra II slowly, and are now taking our time in Geometry.  I want understanding and depth more than anything.  I think we'll probably get some calculus in, but I'm not stressing about it. This kid got a perfect score on the Stanford Test's math portion last year and did great on the PSAT as a 10th grader despite being "behind" for a kid with STEM leanings.

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Miriam, even more important than whether he gets to calculus or not, is that he take the honors math classes.  It's not only from the point of view of how it will look on the transcript, it's that that level will be needed to do well and not struggle in the higher math.   I can see a him being accepted as a STEM major with pre-calculus, but I think it would be unlikely if he did it with non-honors level courses.   The colleges will know that the honors math courses were available for your son, and that he chose not to take them.  As for doubling up with geometry, only if he's got the time in his schedule so that his algebra work and other courses won't be adversely affected.  Mastering math is more important than rushing to a certain level.  He should also consider honors level science courses if he's able as chemistry and physics will allow him to apply what he's learned.

 

Yes, he will be taking all Honors math and others from here on out. We semi-chose a repeat of Algebra 1 to strengthen what he already knows. Now we are paying for it, by having to add in Geometry somewhere. Starting now will probably mean summer school... not my preferred goal. I want him to have open doors by college, so trying to plan now.

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Yes, he will be taking all Honors math and others from here on out. We semi-chose a repeat of Algebraen' 1 to strengthen what he already knows. Now we are paying for it, by having to add in Geometry somewhere. Starting now will probably mean summer school... not my preferred goal. I want him to have open doors by college, so trying to plan now.

 

While I don't know your son as you do, from what you've shared here, I would be inclined to keep geometry for next year and supplement, both this year and next, with more in depth honors level algebra I, so he can make a smooth transition into algebra 2 in his junior year.   You haven't mentioned what STEM field he's interested in, or what he wants to do about math.  Does he want to take geometry over the summer?

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While I don't know your son as you do, from what you've shared here, I would be inclined to keep geometry for next year and supplement, both this year and next, with more in depth honors level algebra I, so he can make a smooth transition into algebra 2 in his junior year.   You haven't mentioned what STEM field he's interested in, or what he wants to do about math.  Does he want to take geometry over the summer?

 

He is a high school freshman, so he does not know what future major he wants. He has always been very good at math, not genius, but proficient. He will take all Honors in math from next year on. At the start, from a homeschool education, I did not know how he would do in math or in high school. As it turns out, he has adjusted splendidly; all teachers like him and his study habits. All recommend Honors/AP as available in all classes. 

 

I am leaning toward online Geometry because I know he could do it.  Right now, the $500 seems like a lot, but probably cheaper in the long run, than taking a future class from CC.  I think that he will end up a STEM major because he likes math and science.

 

Yes, he is the one pushing for the online Geometry, even if it is thru summer. His current Alg 1 class is mixed 8th + 9th graders, so he says he wants to move up to a math class of his grade peers.

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As he's the one asking to do the geometry, then I think it would be money well spent.  At the same time, even though algebra is usually reviewed a bit during geometry, I'd suggest that he work with a teacher at his school to find out what's covered in honors algebra I so he's ready for next year.  If there's not much difference, then maybe working with Kahn online or something which allows him to try more challenging problems may be enough.  

 

As for career, few know what they want to do in 9th grade, but I just thought it would help to know if he's thinking of something in biology, which is lighter in math, or engineering or other more math intensive careers.   Sounds like he'll be on the right path with the honors and AP courses.   It also sounds like you gave him a great foundation with homeschooling.  :001_smile:

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Glad it worked out for you. Your family does not represent a majority sample of STEM majors. The kids in your son's camps don't represent a majority of STEM majors.

 

The majority of engineering and physics programs I've seen recommend repeating and the reason is not so the university can make money on the course. Again, look at Regentrude's posts since she is working at the university level. 

 

This was our experience, as well.  Yes, there are a few 4.0 graduates who live and breathe math, and they could be bored.  Those who enjoyed AOPS calc at home might be bored.  The other 99.9% probably would benefit from doing calc more than once, or at least spending solid time in the basics leading up to calc (either of the options the OP proposes).

 

My oldest is 29 now, so I checked the current status of his degree (Petroleum Engineering at CSM) and they still have Calc 1 on track for first year (undergrad flow chart link here  http://petroleum.mines.edu/undergraduate_program.html ).  I have no idea whether incoming freshmen typically have had calc 1 already (their website only requires trig but suggests more http://www.mines.edu/NewFreshmen ).  However, it would seem doubtful that they all have mastered it, based on their flow chart.

 

My ds went to a poor public high school, chose not to take honors anything.  He stood out for other reasons, I guess -- he had a couple of honors and extras in junior high, he had a community college A in calc, and he also tested well in math.  Although, the ACT doesn't include calc -- in fact, testing well is sometimes a challenge for calc students because they may be out of the habit on some of the more basic math. 

 

My son took calc 1 as a freshman and still graduated in 4 years, and did well enough that he was hired before he graduated.  He had taken calc1 at his high school (I think that one was independent study), and then again at the community college, so he was actually taking calc 1 for the third time in his major.  That's not the norm, I know.  But he wanted to be fully a part of his freshman class.  And one of the benefits for him was having an easy calc1 class to start out.  He is a good student but not probably up to the 8Fills level, as he probably was off doing other hobbies when he could have been chatting math (although he was a tutor, etc).  My son felt each calc teacher had something different to offer him.  My youngest son has had three different college math professors so far and now realizes they are all over the board in teaching methods and teaching ability.

 

Oldest does still feel the topic was worthy of repetition, since he needs it in his career.  I look at it as lives depend on his work being done well.  Of course, if he was genius level and bored, it would have been a waste of time.  But for him, even though he was/is a good student, it wasn't.

 

The boys we saw drop out of his school, or who took 5-6 years to graduate, did not do so because they wasted a semester on calc 1.  They typically did so because they just didn't like doing (or couldn't do) all that math every day, in the sciences as well as the maths.  I think perhaps making calc 1 an easy class that first semester might even be encouraging.

 

Julie

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The reason I consider repeating calculus very beneficial is that a second pass through allows the student a deeper appreciation of the underlying concepts if he has mastered the procedural aspect.

During the first calculus course, students are typically taught procedure: they learn to take derivatives, find minima and maxima, calculate integrals of certain functions, maybe learn a few integration tricks if it is a strong course. That is what most traditional calculus courses (and certainly the textbooks I have seen) focus on. The students emerge with a reasonable ability to perform these actions, but usually lack the insight into the concepts of, for example, epsilon-delta proofs, or the understanding how to set up integrals to describe physical situations. Do not get me started on the inability of students after two semesters of college calculus to set up an integral for the electric field of a line charge! Once they are given the integral, they can evaluate it, but the conceptual insight is missing and hence they can not apply their calculus. The majority of the students in our engineering physics course (for which calculus 2 is a prerequisite) struggle with this aspect.

Why? Because calculus is a tough course, and the students who take it for the first time focus their time and energy on managing the procedures. That's pretty much all they are able to, even with a large time investment.  A student who, in contrast, has already mastered the procedural side during high school, will be able to appreciate the conceptual aspects of his college calculus course and go much farther than a student who has to focus a lot of time and effort on solving the homework problems.

 

Btw, during my time at the university, I found that repeating pretty much ANY conceptually difficult subject is highly beneficial. I did that several times, by working through a textbook over the summer preceeding the course (for classical mechanics) or by auditing a course a semester before I was supposed to be taking it (quantum mechanics). The gain in deeper understanding from a repeat, especially if it uses a different textbook/instructor/approach is very valuable.

ETA: Students who found it beneficial to put this extra effort in were not the ones who needed the second go to barely hang on, but the smartest students in our year. My near genius DH self-studied the entire math sequence before university and swears that it was extremely useful to take the courses and that he got far more out of it with the previous knowledge that he would have otherwise.

 

I absolutely agree with regentrude and her dh, 100%, both from my own experience and that as a college math professor. IMO, even the strongest students benefit very much from repeating calculus with a text such as Apostol or Spivak. I took AP math in high school, earned my 5, and self-studied a lot from Schaum's outlines before college (the only thing I could find in my small town's bookstore!).  I got to U Rochester, where I signed up for Honors Calculus on the advice of my freshman advisor. At first I was disappointed that he thought I should repeat calculus, but later realized the wisdom of that decision. We used Apostol, and I started to understand what math REALLY is. I credit that course sequence with making my success in a math PhD program possible. Sometimes what worked well is only really evident in retrospect!

 

Currently, I'm studying calculus based physics using MIT's online classes on EdX. This is AFTER already teaching calc-based physics twice in the past few years with no problem, using Resnick & Halliday. But...I'm amazed every week at how much MORE I'm learning from Walter Lewin. There is always more depth, more connections, more fun :)

 

Stanford has a special honors calculus track that has a prerequisite of a "5" on the AP Calc BC exam. It is designed for prospective math majors and very strong STEM students. I get the impression it's designed for the kids who were on the math competition circuit in high school. DH, who got a "5" on the AP exam but never did super-well with competition math, just took the regular STEM math track and that was sufficient for his electrical engineering degree. I took the lowest level calculus track and that was fine for pre-med/biology but it wouldn't have sufficed for engineering or physics.

 

My daughter took that Math 51-2-3 Honor sequence which counts as multivariable calculus, differential equations, and linear algebra. Here's the first quarter's (11-week) syllabus. Dd earned a 5 in Calc BC in 10th grade, with *plenty* of post calculus math while still at home. In fact, she had all those classes (multi, diff eq, lin alg) with me, and I chose rigorous texts and worked her hard, LOL. But she learned so.much.more in college, & at such a deeper level! This kind of course can help future mathematicians & physicists get a terrific grounding in theory, work through all the intricacies that are usually glossed over in a typical class, and more importantly, make connections between various fields of math. Good stuff!!

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That the majority of Calc I classes are not adequately preparing students to go on into higher math is a condemnation of the current state of education and an indicator of the lowering of standards.

 

I'm genuinely shocked / surprised that repeating a class is considered the norm. Wow. How sad.

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That the majority of Calc I classes are not adequately preparing students to go on into higher math is a condemnation of the current state of education and an indicator of the lowering of standards.

 

I'm genuinely shocked / surprised that repeating a class is considered the norm. Wow. How sad.

 

 

Inclusion is the norm now in many places.  Honors/AP/IB courses are not. So, a student who is taking Calc 1 at the high school will not be offered an honors version in many many districts ...that will have to wait until they get to college.

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I do agree with the people who said it should be student-dependent and also college-dependent. If a true honors class is not available (for example, if the student is at a middling state university, or a community college), the college course may go into no more depth than the high school course did. Some students really shut down in frustration when sitting through a course that's taught with the same book as they had the last time they took the course. I am not saying that this is the most mature outlook - as a matter of fact, it is not. But I know for a fact that when I took calculus, in a summer program for high school students, that had I repeated it at the university I ended up attending they would have used the same book, the same number of problems, and the same difficulty of problems. I would have found this immensely frustrating.

 

I do think repeating it is a good idea in a lot of cases and should be strongly considered.

 

That the majority of Calc I classes are not adequately preparing students to go on into higher math is a condemnation of the current state of education and an indicator of the lowering of standards.

I'm genuinely shocked / surprised that repeating a class is considered the norm. Wow. How sad.

I don't understand why repeating high school calculus at the university level is so sad. After all, we have high school chemistry and college chemistry. This has a lot more to do with how difficult it is for most students to really understand calculus at a higher level than purely mechanistic plug-and-chug than it does to do with anything else. The same thing happens with highly abstract classes such as modern algebra - *most* students struggle mightily with that on their first pass, and then when they retake it at a somewhat higher level in graduate school, understand it on a far deeper level.

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An entire course can be geared toward maximizing a student's score on the AP exam. Being able to do well on an AP exam does not mean a student knows how to apply calculus beyond problems in a textbook. A STEM student needs go into an engineering or physics lab and know how to apply calculus as a tool. College calculus courses geared to STEM majors are going to provide more depth than a high school AP course. I am not sure why anyone would find that surprising. 

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An entire course can be geared toward maximizing a student's score on the AP exam. Being able to do well on an AP exam does not mean a student knows how to apply calculus beyond problems in a textbook. A STEM student needs go into an engineering or physics lab and know how to apply calculus as a tool. College calculus courses geared to STEM majors are going to provide more depth than a high school AP course. I am not sure why anyone would find that surprising. 

 

AoPS is one cal course that doesn't teach to the AP.   The course prepares a student to do well on the AP, but they have to do quite a bit of study in addition to the course in order to know how to do the FRQs and for my ds, the calculator questions, etc.  

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My daughter took that Math 51-2-3 Honor sequence which counts as multivariable calculus, differential equations, and linear algebra. Here's the first quarter's (11-week) syllabus. Dd earned a 5 in Calc BC in 10th grade, with *plenty* of post calculus math while still at home. In fact, she had all those classes (multi, diff eq, lin alg) with me, and I chose rigorous texts and worked her hard, LOL. But she learned so.much.more in college, & at such a deeper level! This kind of course can help future mathematicians & physicists get a terrific grounding in theory, work through all the intricacies that are usually glossed over in a typical class, and more importantly, make connections between various fields of math. Good stuff!!

 

Kathy, was this her first math course at Stanford or did she repeat cal 1 and 2 first?    If she didn't, do you think she would have needed to or would have benefited from repeating those 2 courses?

 

FWIW, I asked ds if he would be willing to go all the way back to cal 1 and he said no way.   He said he would be willing to do course like what you have linked, but not all the way back to 1.  (though, the places that are looking like real possibilities for him are not going to be on par with Stanford's level of study.)  BTW, I tried to get him to not take math next semester and he was completely indignant.  ;)  I'm sure you can appreciate this (I can't!!)....he said he cannot imagine ever not taking a math.   It is looking like he might have to forfeit his 2nd physics course for the math course unless he can somehow get the university to approve him taking 3 courses instead of only 2.  No way I would have guessed he'd choose a math over 2 physics.   Silly me for even suggesting it!!!

 

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Kathy, was this her first math course at Stanford or did she repeat cal 1 and 2 first?    If she didn't, do you think she would have needed to or would have benefited from repeating those 2 courses?

 

FWIW, I asked ds if he would be willing to go all the way back to cal 1 and he said no way.   He said he would be willing to do course like what you have linked, but not all the way back to 1.  (though, the places that are looking like real possibilities for him are not going to be on par with Stanford's level of study.)  BTW, I tried to get him to not take math next semester and he was completely indignant.  ;)  I'm sure you can appreciate this (I can't!!)....he said he cannot imagine ever not taking a math.   It is looking like he might have to forfeit his 2nd physics course for the math course unless he can somehow get the university to approve him taking 3 courses instead of only 2.  No way I would have guessed he'd choose a math over 2 physics.   Silly me for even suggesting it!!!

 

 

Yes, this sequence was what she studied freshman year, and that's the norm for honors math students at Stanford. They only require Calc BC as a prereq, & they build from there. The class also weaves in some real analysis lectures, which is really grown-up calculus. So what they end up teaching is very similar to the Apostol Calculus texts...

 

To be clear, I wouldn't recommend that this type of kid go back and repeat a standard calculus course from a text such as Stewart for a second go-round. That could be boring for some kids. But if the more in-depth theoretical class is available, then yes, I'd recommend taking a serious look.

 

And I totally agree with your ds! Happiness requires learning new math... :D

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Kathy, thank you for explaining the level of calculus you were suggesting be "repeated".  As you said, I couldn't imagine some repeating at the Larson or Stewart level, but doing a truly in depth proof based course could make sense.

 

ETA:  In looking quickly at the syllabus, it seems not to be Calc 1 and 2 at all, but an analysis of Calc 3 and Linear Algebra.  That would be the logical progression for someone who has completed Calc BC or Calc 1 and 2.

 

 

I'm not sure why so many consider AP to be superior to community college courses.  As I think has become apparent, the AP courses taught at many high schools are in no way comparable to what is taught in a true college class.  I know the quality of community college courses, and instructors, does vary, but with a good community college, everything we've seen so far suggests that a calculus course for STEM majors at the community college is comparable to that which is taught at the state universities.  As has been noted, some of these professors have taught at both levels and verify this.  I've also noticed that some are talking about college courses taught at the high school by high school teachers when comparing the college course taken in high school with one taken at a university.   I think it would be very rare to find one of these of equal quality and rigor. 

 

 

Edited to correct the calculus texts ... I had physics on the mind.  lol

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I'm not sure why so many consider AP to be superior to community college courses.  As I think has become apparent, the AP courses taught at many high schools are in no way comparable to what is taught in a true college class.  I know the quality of community college courses, and instructors, does vary, but with a good community college, everything we've seen so far suggests that a calculus course for STEM majors at the community college is comparable to that which is taught at the state universities.  As has been noted, some of these professors have taught at both levels and verify this.  I've also noticed that some are talking about college courses taught at the high school by high school teachers when comparing the college course taken in high school with one taken at a university.   I think it would be very rare to find one of these of equal quality and rigor. 

 

My local cc has coordinated one of it's math sequences with the most competitive engineering school in our state. They have a direct transfer program set up. They  first coordinated the math courses over 30 years ago, the direct transfer program was set up over 10 years ago. I don't think the partnership would have continued if the cc was not sending prepared students. 

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I'm not sure why so many consider AP to be superior to community college courses.  As I think has become apparent, the AP courses taught at many high schools are in no way comparable to what is taught in a true college class.  I know the quality of community college courses, and instructors, does vary, but with a good community college, everything we've seen so far suggests that a calculus course for STEM majors at the community college is comparable to that which is taught at the state universities.  As has been noted, some of these professors have taught at both levels and verify this.  I've also noticed that some are talking about college courses taught at the high school by high school teachers when comparing the college course taken in high school with one taken at a university.   I think it would be very rare to find one of these of equal quality and rigor. 

 

The quality difference varies by location. 

 

In my area, the CC Math courses taught at the high school are identical to the ones taught on the CC campus. I know, I have a nephew in one and a son in the other.  We've compared notes, syllabi, and assignments for College Alg thru Calc 1.  Not surprising considering son's high school teacher teaches on both campuses. The CC course in both locations will transfer to the state engineering school.

 

Now, in some subjects other than math, AP is indeed superior to CC here.  Partly that is because of the type of student that takes the course, partly the teacher, partly the course objectives. In my area, the top students take AP in humanities, the next level down CC. 

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This could put a physics major 1 or more yrs behind for graduation.   Depending on the university, some pre-cal courses are split into pre-cal 1 and pre-cal 2. Physics majors are expected to start with university physics (cal based physics)--any physics lower than cal physics won't count toward their degree.  Again, depending on the university, some universities have cal as pre-req, not a co-req.   So that could put them at least 3 semesters behind. 

 

While it is doable, students would need to be aware that their 4 yr degree just got bumped up to more than that.   When courses are on the pre-req level, it really impacts the ability to take courses.

 

The physics major in our dept can be done in 3 years, so it is possible to enter with only the Alg 2.  Chem generally gets taken in the senior year by the physics majors, so there's just a bit of readjusting -- doing chem the first year, then intro physics the 2nd.

 

It may not be the easiest way to pull it off, but it can be done.  They often have to double up on a lot of hard courses the last year, and it may mean the student doesn't have the room to take a couple more specialized courses at the end, but if their intent is to go into engineering, it often isn't a big deal that they skipped a couple esoteric physics courses.  If they're going on into physics grad school, they can just pick up the more advanced courses then.  (One person I know who only entered with Alg 2 is graduating with a physics BA, not a BS.)

 

It wouldn't be what I'd advise, but I wanted to point out that it is doable.  If a student really wants to do physics, but is coming from a weak math background, all is not necessarily lost.  Finishing high school with a good solid Alg 2 background might be better than blasting through a lot of classes and doing poorly in them.

 

We do have a calc co-req, not a pre-req.  I've seen it done both ways.  Frankly, I think the pre-req is just overkill.  Freshman physics just doesn't delve that deep into calculus, least not the first semester.  And it can be handled so that the students learn the little calc they need in the first few weeks of the semester.

 

On repeating calculus:  My daughter did the AP route and got dropped into college calc 3 her senior of high school.  For her, this was ok, as she's pretty math-brilliant, but it was a STEEP curve getting up to speed for calc 3 after only having done the BC AP test.  She was only taking 3 courses at the time, and one was pretty much a gut course, so she had the time to do it.  I'm not sure how that would work out for a student who was just starting freshman yr at college with a full load.  She probably could have struggled through it, maybe not got a great grade, and gone on with life, but I suspect there would be a fair amount of calc she hadn't really internalized.  -- so she essentially did repeat calc 1 and 2, but she did it while getting through calc 3.  Not the easiest thing to do.

 

Some of this will depend on the varying levels of calc courses, though.  Some schools do start out calc 1 pretty gently, so a student who had done the BC test might not really get much out of it.  Problem is, there might be no way to know that without actually taking the course.

 

I think one has to decide what would be the worst case scenario -- being bored in a class and wasting a credit, or finding out the AP course of the cc course wasn't up to snuff and now you've got to do a lot of catch up.

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We do have a calc co-req, not a pre-req.  I've seen it done both ways.  Frankly, I think the pre-req is just overkill.  Freshman physics just doesn't delve that deep into calculus, least not the first semester.  And it can be handled so that the students learn the little calc they need in the first few weeks of the semester.

 

It is actually a hen-egg problem. The reason there is so little calculus in a typical physics course in this country is that the students do not have enough math.

The biggest problem is the second semester with electricity and magnetism. For this, even a prerequisite of calc 1 for the first and calc 2 for the second semester physics class would be falling short, since students should actually be familiar with multivariable calculus when they begin e&m. Otherwise, Gauss' and Faraday's laws remain black boxes where students can solve only extreme simple symmetric problems without a full understanding of what exactly it is they are doing, and a standard course never gets to Maxwell's equations in differential form.

But even in the first semester, even with a calc 1 prerequisite, interesting topics have to be omitted that are  included in the starred (i.e. optional) textbook sections: non-constant acceleration, velocity dependent forces (beyond a simple calculation of the terminal speed), Coriolis force... all the cool stuff.

I realize that at US universities it is not possible to impose a calc 3 prerequisite for e&m, for scheduling reasons, because that would cause to much of a delay for students taking physics. This does, however, diminish the depth of instruction that is possible. When I studied physics back home, all university bound students had differential and integral calculus at high school, so the first semester of math was a quick repeat of calc 1 and 2 at university level and a coverage of multivariable integration while taking calculus based physics semester 1. The second math semester started with vector calculus in time for having it available to express Maxwell's equations in differential form in the e&m course taken concurrently. Something that sadly can not be done here. 

I believe the reason that standard physics texts/classes do not contain much calculus is simply that students have not been taught enough calculus; otherwise one might be able to teach more complex material.

 

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There's a pair of textbooks, by Andrew Rex and Martin Jackson, that I've always wanted to get my hands on. They covered integrated physics and calculus, volumes 1 + 2 - starting assuming the student had had either calc AB or calc 1, and taught, in two semesters, integral calculus, multivariable calculus, mechanics, and E and M. The calculus was taught and then immediately applied in the physics class to continue the learning.

 

It didn't seem to catch on -- for one thing, it requires extremely close coordination, it doesn't allow for students whose schedules don't permit them to take calc and physics in the same semester (like biochem majors) -- but I always thought it was a great idea for engineering and physics majors.

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Is it this series? http://www.amazon.com/Integrated-Physics-Calculus-Volume-1/dp/0201473968

 

That looks very intriguing. I've been self-educating E&M in order to help my kids with Science Olympiad as I managed to avoid taking physics both in high school and college (having to take physics next was the straw that broke the camel's back in terms of my dropping out of the pre-med track).

 

Right now I'm working through Hewitt's "Conceptual Physics" and I have copies of Young & Gellar's algebra-based "College Physics" and Giancoli's calculus-based "Physics for Scientists & Engineers". But given that it's been almost two decades since I took calculus, I have to wonder if this Rex & Martin series might be a better choice after the Young & Geller.

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Yes.

 

If you can score a cheap copy, it certainly wouldn't hurt as a supplement. It would at least answer the question you might have, when reading through the calculus text, of "What the ^%("^(£^£^$ is this technique good for anyway?!"

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There's a pair of textbooks, by Andrew Rex and Martin Jackson, that I've always wanted to get my hands on. They covered integrated physics and calculus, volumes 1 + 2 - starting assuming the student had had either calc AB or calc 1, and taught, in two semesters, integral calculus, multivariable calculus, mechanics, and E and M. The calculus was taught and then immediately applied in the physics class to continue the learning.

 

It didn't seem to catch on -- for one thing, it requires extremely close coordination, it doesn't allow for students whose schedules don't permit them to take calc and physics in the same semester (like biochem majors) -- but I always thought it was a great idea for engineering and physics majors.

 

Does anyone have any thoughts on the British approach. As I understand it, Mechanics is integrated at the A-level in math. How beneficial is this for either math or physics majors?

 

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It may not be the easiest way to pull it off, but it can be done.  They often have to double up on a lot of hard courses the last year, and it may mean the student doesn't have the room to take a couple more specialized courses at the end, but if their intent is to go into engineering, it often isn't a big deal that they skipped a couple esoteric physics courses.

 

......... finding out the AP course of the cc course wasn't up to snuff and now you've got to do a lot of catch up.

 

I actually don't understand the logic of the bolded.   It might not be a big deal to skip a couple of esoteric physics courses, but I have never seen an engineering program that didn't expect engineering students to start off with calculus.  Engineering students will definitely be off cycle for their engineering sequence courses (which are heavily pre-req based) if they entered with only an alg 2 background.   I'm not saying students can't do it, but they certainly will be unlikely to achieve an engineering degree in 4 yrs.

 

Here is a link to a flow chart for mechanical engineering which shows how all the courses flow for the 4 yr plan with the pre-reqs.   http://www.me.vt.edu/_files/pdf_Path2013-2014.pdf  VT apparently requires cal 2 as a co-req for physics 1.

 

FWIW......another option that is really not discussed in general is neither AP nor CC through a local university.   Obviously that isn't an option for everyone since you have to live near one, but it alternative beyond AP and CC.

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All of our sons are going into STEM majors. All will have calculus 1 in high school and two will have calculus 2. Eldest boy will repeat Calc 1 in college on the recommendation of every Computer Science advisor we have talked to at our college visits. I am willing to admit that while we are no slouches here in our math abilities and dh majored in math in college, the reality is that he will be taken into greater depth in college and we consider high school calculus classes, even AP's, to be nothing more than preparatory and not worthy of skipping the prerequisite in college.

 

Additionally, while many, many universities and LAC's will list pre-calculus as their admission's requirement - even some stating only Algebra 2, that is for general admission only and certainly does not take into consideration  merit aid.  While ds could get admitted to his top choice school on pre-calc only, and possibly even his comp sci major, he wouldn't get scholarships and he would be behind many of the other students who will have had calculus 1. Middle boy also could get into biology and environmental science on pre-calculus only, however not only does he need merit aid, in order to be considered for research positions, he needs to be in the top echelon of his class and that means at least calc 1. He's an excellent mathematician and will be through calc 2 in high school however, we will have him take calc 2 again at the university.

 

No matter what the major, do not look at the general admission's requirements for the university or LAC. What might get an acceptance letter, may not get one into the department of choice and most certainly the competition is stiffer for scholarships than it is for general admissions. Even dd, five years ago, could have been admitted to many decent universities on algebra 2 and a 25 composite on the ACT, but the nursing department of her top choice required pre-calculus and a 27 in the math section of the ACT and minimum composite of 27.  She well topped out the necessary requirements, but unfortunately many friends of hers who thought they were heading off to BSRN's in nursing, or pre-pharma, chemistry, etc. were in for rude awakenings when their high school guidance counselors told them they only had to meet the college's general admission's requirements and to go ahead and have a fun, easy, laid back senior year. Bad, bad, advice.

 

Faith

 

 

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All of our sons are going into STEM majors. All will have calculus 1 in high school and two will have calculus 2. Eldest boy will repeat Calc 1 in college on the recommendation of every Computer Science advisor we have talked to at our college visits. I am willing to admit that while we are no slouches here in our math abilities and dh majored in math in college, the reality is that he will be taken into greater depth in college and we consider high school calculus classes, even AP's, to be nothing more than preparatory and not worthy of skipping the prerequisite in college.

 

Additionally, while many, many universities and LAC's will list pre-calculus as their admission's requirement - even some stating only Algebra 2, that is for general admission only and certainly does not take into consideration  merit aid.  While ds could get admitted to his top choice school on pre-calc only, and possibly even his comp sci major, he wouldn't get scholarships and he would be behind many of the other students who will have had calculus 1. Middle boy also could get into biology and environmental science on pre-calculus only, however not only does he need merit aid, in order to be considered for research positions, he needs to be in the top echelon of his class and that means at least calc 1. He's an excellent mathematician and will be through calc 2 in high school however, we will have him take calc 2 again at the university.

 

No matter what the major, do not look at the general admission's requirements for the university or LAC. What might get an acceptance letter, may not get one into the department of choice and most certainly the competition is stiffer for scholarships than it is for general admissions. Even dd, five years ago, could have been admitted to many decent universities on algebra 2 and a 25 composite on the ACT, but the nursing department of her top choice required pre-calculus and a 27 in the math section of the ACT and minimum composite of 27.  She well topped out the necessary requirements, but unfortunately many friends of hers who thought they were heading off to BSRN's in nursing, or pre-pharma, chemistry, etc. were in for rude awakenings when their high school guidance counselors told them they only had to meet the college's general admission's requirements and to go ahead and have a fun, easy, laid back senior year. Bad, bad, advice.

 

Faith

 

Absolutely agree.   I can't imagine what engineering dept would accept a student with only alg 2.   Acceptance into the university and acceptance into a dept are 2 different things.   Then add in getting into a specific major.   W/in the engineering dept there are going to be levels of competitive acceptance. 

 

I agree that students need to be rock solid in alg (heck, all of my kids I have had take alg 1 twice) and we should never rush through math.   But, I do honestly wonder about setting our kids up for unrealistic expectations or for failure. 

 

This thread has mentioned multiple different scenarios.  1- repeating cal at the university, 2-only getting through pre-cal in high school, 3-only getting through alg 2 and starting pre-cal at the university level.   Those are all very different and not really even comparable.   For those that think students should repeat cal at the university, do you believe that students that arrive only having completed pre-cal and place into cal are going to be at a disadvantage to students that repeat cal?   I am just being honest when I say that I believe kids arriving with only alg 2 are at a serious disadvantage as a STEM major and are probably far less likely to complete a STEM degree.

 

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This thread has mentioned multiple different scenarios.  1- repeating cal at the university, 2-only getting through pre-cal in high school, 3-only getting through alg 2 and starting pre-cal at the university level.   Those are all very different and not really even comparable.   For those that think students should repeat cal at the university, do you believe that students that arrive only having completed pre-cal and place into cal are going to be at a disadvantage to students that repeat cal?   I am just being honest when I say that I believe kids arriving with only alg 2 are at a serious disadvantage as a STEM major and are probably far less likely to complete a STEM degree.

 

In my calculus classes, it is definitely an advantage to have seen the material before IF the algebra skills are solid. I have had students with solid algebra skills who had never seen calculus before do very well, but in general, they need to do more work and often are the solid B students. I have also had students who took "calculus" in high school fail my calculus class at the university because their algebra skills were weak. I say "calculus" because apparently the only things that they learned were how to differentiate polynomials and L'Hospital's rule.

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