Somebody asked if there’s anything in AP comparable to the extended essay and it was worth mentioning that’s it’s possible to get college credit for that work and gave MIT as an example. Is MIT is dumb for giving credit for it? Doesn’t matter, they just do. Most schools don’t, a few ones do like CalStateSLO, UC Santa Cuz give some credit or a way to fulfill writing requirements. It’s mostly inconsequential, anyways. MIT majors also have unrestricted electives that can use the AP credits including capstone. |
Do you have any basics for your claims? The squeeze theorem takes 5 minutes to demonstrate. http://educ.jmu.edu/~ohmx/squeeze_proof.pdf Calc BC crams 2 semesters of college courses into one HS year, so obviously it can only do so superficially without proving the theorems, right? |
With AP credit, a student can take one fewer semester-class each year and still graduate on time. It's an insurance policy for students who can't keep up with the MIT workload. |
Link to the syllabus of IB Math HL. They don’t teach a single theorem in Calculus, even the fundamental theorem of Calculus is listed as “Enrichment”. You can also see that only 55 hours of teaching are dedicated to Calculus topics. https://holyheart.ca/wp-content/uploads/2019/06/Mathematics-Analysis-and-Approaches-Guide-first-assessment-2021.pdf A list of Calculus theorems taught in AP: Squeeze Theorem Intermediate Value Theorem Mean Value Theorem Extreme Value Theorem Fundamental Theorem of Calculus Theorems and proofs are a fundamental part of teaching mathematics. They are not really helpful for the test, but provide an understanding on the why and how things work the way they do. It also shows the mindset of the teaching, do you prove L’Hopital and differentiation rules or just give them as a recipe to follow, aka rote memorization and teaching to the test, accusations that are often used by IB cheerleaders to characterize AP classes. Even community college calculus is better than what’s in IB AA Math. They can be hit and miss, but some that go even beyond the AP curriculum although the homework, exams and grading tend to be easier. |
There are also programs for Masters degree right after the Bachelor’s in one year by taking graduate level courses. Some students choose to use the AP credit for electives so they can get their Bachelor and Master degrees within four years, which in my view is the best use of non-restricted AP credit. You can use up to 48 credits, but since MIT doesn’t give credit to math and science APs it pays to take APs in humanities, social sciences and foreign language. You only need five APs to cover the non restricted electives, which could be a combination English, Spanish, History and the Capstone. Since many MIT students are not that strong in humanities, it may be easier for them to do the capstone if they choose a math or science topic, compared to for example AP English Literature. |
That depends on the local high school and teacher. College board gives a lot more latitude on course content and organization than IB. You don’t need to teach a prescribed syllabus, you only need to pass the course audit. Magnets generally teach the real deal college level. Two semesters for Calculus 1 and 2 is standard, that wouldn’t be considered crammed. Supposedly AP is for students that can handle college classes in high school, not for ones that need a watered down, in between, course version. The truth is that it varies, that’s why we have AP Calculus AB, which is about 3/4 of Calculus BC, or AP Statistics which is taught over one year in high school but over one semester in college. The redeeming quality is that the AP classes align well with college classes and its easy to decide what you’ve mastered and what to take next. IB HL AA suffers from the same shortcomings and more, not really a college class, but a mix of advanced and basic topics put together under the same label. Sometimes you see it getting credit for a combination of Calculus 1 and/or Statistics, but it’s not comparable with either. Occasionally you see people jumping straight into Multivariable after HL AA which is ill advised. |
The truth is that fewer and fewer of the most highly competitive colleges give credit for AP or IBD work in this century. Kids are probably better off focusing on what they're actually learning in high school than the prospect of getting college credit to save you some dough on tuition. AP curriculum has its own shortcomings. IBD language exams are much tougher to ace than AP language exams. There's no multiple choice with IBD and the exams stress advanced speaking and listening skills to a much greater extent than AP (because it's a European curriculum). If you want your kid to score high on an IBD language exam, even at the SL, you probably need to ensure that they land in full immersion environments for weeks during high school summers. If you don't speak the language consistently at home, plan ahead, save up, pay. |
The proof is only 5 minutes if you already introduced the delta epsilon formal definition of a limit. With absolute certainty that part is not in the IB curriculum. |
Come on, you're really splitting hairs here, given that far more MCPS students take advanced humanities and IBD language than Maths AA HL. The toughest IBD math is OK and there's considerable merit to Diploma studies for hundreds of high performers in the county.
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The VAST majority of students taking AP classes will not go to MIT. Why use this school as an example? |
Why are you solely focused on math? Most high level IB courses are not math nor do they have any review components. If the kid is learning more and enjoys the subject then they are happy to be in the second year of the course. My child loves the HL history class for example. They are not “missing out” on any of the other history courses because they are in the one they want. |
Epsilon-delta is specifically excluded from AP calculus https://apcentral.collegeboard.org/media/pdf/ap-calculus-ab-bc-course-and-exam-description-errata-sheet.pdf Anyway, it doesn't matter. By any reasonable engineering (non pure math) standard, epsilon delta doesn't matter. Even Liebniz and Newton didn't need episilon-delta to prove anything. Insisting on epsilon-delta for well-behaved normal functions is just fetishism. |
Even MIT doesn't use epsilon-delta in its definition of limit or proof of trig derivatives.
https://youtu.be/kCPVBl953eY?si=Qg67lEG7iQpkd74H Lec 1-3 Calculus, whether it's IB, AP, or MIT, is a different class from Real Analysis |
Top math students in IB take Calc BC as the first year of IB Math HL anyway. |
IB and AP foreign language exams have similar format, with multiple choice, essay, and listening and speaking components. |