Better would be for the incoming frosh to try the college’s old final exams for calculus 1 and 2 to check their knowledge relative to the college’s standards before making this placement decision in a more informed way.
Actually my son, at Tufts not an Ivy, discovered that grades do matter. There were a number of internships and study abroad programs that required a 3.5 GPA - his was 3.499999 at the end of sophomore year when he ran into this issue. After straight A’s on his year abroad and better grades in Arabic as a senior - he got over that critical 3.5 mark. For this kid I got the impression college was more work because there was so much more reading, but except for Arabic, it was not that much more difficult than high school had been.
Older son found some of the college grading seemed arbitrary to him and while in high school he got A’s in non-STEM courses, in college he just didn’t bother. I remember seeing one paper he left out in his room which had the comment “This would have been an A paper if you had handed it in on time.” That B+ did not hold him back from getting the CS job he wanted. 
Totally agree with @lvvcsf ‘s daughter’s approach to improve the grade in the college. How much the issue here is responsible by the student not being able to adjust to the college’s way of learning? Freshman daughter was a national AP scholar (taken at least 8 AP tests with average of >4+ scores) but did lousily in one of her STEM class in 1st semester in a highly selective college. D blamed the class material and way the class was taught. She wanted to play the same trick on us during the Spring break when reporting one of her STEM class’ grade was trending from C to D. Using analyzing skilled learned 20 some years ago from a rolling-enrollment college, I was able to help her realizing (or maybe a threatening voice on that if she did not get her act together she had to repeat it or start to pack home and go to a CC instead) that she had not worked as diligent as she did in high school (not pre-read, taking notes, review the test material, review the test results…). Basically applying the same method as what Ivvcsf’s daughter did, she was able to pull that class from C- to a final B in just 40 days after Spring break.
One thing I’ve found is that HS and the college can use same textbook in different ways. A high school student can master the material and ace the class by doing the home work sections where the problem is simply stated and the student just need to practice the formula and solve the problem with correct answer to a certain familiarity; in college, the student should study the sections that are real life application of the equations and issues that could have multiple solutions or sequence of solutions that connect multiple chapters (usually the review section of several chapter (quarter review).
Second thing I’ve found is that colleges, especially the highly selective ones, really want the students to discover what they are really good at, instead of just working hard. There are students who are just naturally good at subjects (for example, the two STEM classes my D took) without much effort; whereas, my D has taken a sophomore level foreign language (not a native speaker) in her 1st semester and junior level in her 2nd semester, and going to take senior level classes in her sophomore year. It seems to me the system is set up like in a free market that efficiency and effective is achieved through an invisible hand that through good and bad grades that students eventually find their proper career path in which they can be best performing and enjoying without working to death to be successful. Otherwise, everyone would want to be in a STEM major, and soon the acceleration of the boom-and-bust industry cycle will plague the nation and globe like the 90’s and early 2000’s.
We are only discussing GPA here. If median is 3.8 for UMich, which is not in the top tier of T14, and if you are not an URM or have top LSAT score then 3.8 is what would be needed.
There are few high schools where you can be top math students outside of that high school and participating in national level level math competitions, but struggle in your own math classes as As are very stingy. Those classes have other kids who are IMO, USAMO level and kick your butt.
Plenty of students do not switch majors when they get a few Bs, nor do most highly selective colleges expect them to. Instead many have special programs to help students who are struggling be successful and stay in the major. This is especially true for underrepresented groups, such as women and minorities in tech. You actually see the type of boom/bust major selection you describe at many highly selective colleges that allow students to easily switch back and forth between majors. Some examples about num of Stanford undergrads with different majors over time is below. You can view more at http://stanfordvisualized.darkmirage.com/ (only goes to 2014)
CS
1993 – 76 students
2001 – 250 students (peak just after start of dot com crash)
2006 – 129 students (still feeling effects of dot com crash)
2014 – 574 students (became Stanford’s most popular major in 2012 and still is today, with continued increasing enrollment)
Econ
1998 – 515 students (stock market boom, by far Stanford’s most popular major)
2001 – 187 students (post stock market crash, no longer Stanford’s most popular major)
History
1965 – 647 students (boom during Vietnam, by far Stanford’s most popular major)
1981 – 121 students
1991 – 287 students (boom during end of Soviet Union and end of cold war era)
2014 – 84 students
Perhaps true, but that’s not what your earlier post said.
[QUOTE=""]
Better would be for the incoming frosh to try the college's old final exams for calculus 1 and 2 to check their ?>>knowledge relative to the college's standards before making this placement decision in a more informed way
[/QUOTE]
Trying the old final exam is a great idea.
We were specifically talking about Engineering majors who still need to take: MultiVar,Differential Equations, Partial Differential and possibly Linear Algebra. His roomate retook Calc 2 and got a B after a 5 on the BC exam, but he never felt he had a full grasp of the material.
As S20 discovered in “Higher Math/Proofs” and “Real Analysis”, AP Calc does not prepare you in any way for theory. AP Calc is Plug&Chug.
In his college, you would need to take Calc 1&2 honors to get into theory. The regular Calc engineering sequence is like AP, but with harder exams and a faster pace.
If the professor teaching the course changes, taking old exams can be a waste of time at an Ivy.
Math academia at many schools including those at many of the Ivies unfortunately continues to be a very sexist group
Most college calculus courses are not proof/theory oriented, which is the reason why many college math departments offer an introduction to proofs type of course or suggest taking a less difficult proof/theory oriented math course before taking a harder one like real analysis.
The standard* frosh level single variable calculus should have a well defined set of learning goals and expectations that all instructors at a given college should adhere to, so even if the instructor is different, the old final exams should be a reasonable way of testing one’s knowledge to the expectations at that college, especially for the purpose of whether to use AP credit to skip the course if allowed to do so.
*As opposed to an honors course, or an easier calculus for business majors course.
Maybe. Maybe not. For many colleges, including some Ivy League colleges, Calc 1 and 2 classes have a common final exam, so a change in instructor may not impact the final exam content.
Or you could just take the college’s math placement exam. Math placement exams are mandatory for freshman at HYSM and most similarly selective colleges I am familiar with that offer several math sequences. I believe they are optional at P.
@bluebayou : this is what I said, “To get into a top 14 law school one needs 3.8+ GPA.” I could have added, “Unless you have some special hooks (like race, high LSAT scores, great internships, connections).” Unfortunately, most applicants are fairly ordinary, but they look at lower percentile and think they may have a chance.
@Data10 yes Math placement exam is optional at Princeton. My D just signed up for the proof based version of Calc 3. No APs offered at her high school but she had the equivalent of Calc 3 at Penn - they call it Calc 2 there.
My two cents: (1) A significant number of students who do poorly do so because they fail to put in the same effort in college that they did in high school, or else their high school did not require as much effort as it should have for that 4.0 so they have poor habits; and (2) many professors are just plain lousy teachers, often accompanying a complete indifference to the quality of their teaching. Don’t underweight #2–professors are neither hired nor promoted on their teaching ability, and it often shows.
Some of my worst teachers back in the day, were the most “respected” in their field. Their research knowledge didn’t translate well into the classroom. My daughter got the same advice over and over from students at various universities - go to every recitation and every TA study sessions/office hours.
Universities have different starting points as @Dolemite explained. Calc 1 content at university #1 may be Calc 2 for a student at university #2 even-though both schools are top tier. Results of math placement exam along with AP scores are a great indicator. I understand that no one passes the Chem exam. Every university seems to have one department that ensures students are critical thinkers during freshman year.
Incoming students are also paired with student orientation peer advisers in their specific major. These students have terrific advice for first semester scheduling especially recommended sections and AP credit. They know which course sections are a repeat of the AP curriculum and which courses added to their foundation.
Although core courses are often listed in the College of Arts and Science, the Engineering School may have inserted depth into the major recommended/required sections of math, physics and chem. Honestly, I was shocked that an entering CBE and an ME would not use their AP credits for chemistry (the CBE or the ME) and Mechanics C (the ME). We quickly learned that the AP and college class section course curriculum are not aligned.
Had our children chosen to attend other engineering programs (examples in our area WPI, RPI, Northeastern), they would have taken the many AP credits and either graduated early or used the open semesters to get a master’s degree. Their current core is a struggle and an incredible foundation. I’m happy to see that they are able to take one major specific course during freshman and sophomore years. It was drudgery to wait until junior year (back in the day) and I’m not sure that we had enough exposure to ensure we selected the best major.
Also, if you have a choice take the course with the good teachers not the famous names.
Perhaps not at research Us, but at LACs teaching ability is very important. Students at D’s school can’t see their grades until they’ve filled out the evaluation for their professors (which is obviously anonymous, but required of all students - goes to the dept not the prof).
There aren’t recitations or TAs, but there are definitely office hours, which D learned after a semester to go to very regularly. The first semester she thought she could just go to class and do the work and study and do well. Since then she brings lunch to her prof’s offices, her homework, her questions, her study sheets, whatever. And her grades show the difference in that approach.
She’s abroad at the moment at a large research uni and has found the difference striking. Now there are recitations and TAs, and she definitely goes, but she misses her home college academically. It’s confirmed that she made the right choice, for her.
I guess my dad is the exception. He has gotten numerous international awards for his research, but he’s also gotten a lot of teaching awards and was named one of the best teachers at UT. I had him for two classes, and I concur! He was very clear and helped his students succeed.