If this is important to you, it would suggest that larger schools or those with larger departments in the desired major may be preferable over smaller ones for reach and likely/safety schools. A larger school or department may be more likely to offer several variants of a core course (e.g. honors versus regular) or different in-major electives for students of different academic strength, while a small school or department may only have the resources to offer courses targeted to its middle range of students. Of course, inspection of actual course offerings to check whether this is the case at any given school or department is preferable over making assumptions based on size.
Note that there are also schools or departments where the rigor level is higher than one might assume based on admission selectivity, and schools or departments where the opposite is the case.
The most interesting thing about your son is that he seems authentic and passionate. Heās self-studying for a bunch of APs so he can have a chance at Oxford and he thinks itās fun. He watches videos on math. And heās not doing this because he wants to be some highly-compensated financial analyst with a 7-figure portfolio by the time heās 30. Heās doing this because he finds math interesting and loves the engagement of the mind.
He also seems authentic in part because he doesnāt seem to be gunning for whatever a publisher said are the top schools. Heās looking for the right programs, the right fit. But he surfs and cooks for the homeless and seems as though heās a real person with genuine interests.
Your sonās story is not the common kind that is found on CC (or common anywhere, Iād guess) and thus itās interesting.
Thank you for this! Having never taken higher math courses, I appreciate this breakdown as I really know nothing about higher math (even if there is nuance in whether some areas have applied leanings or not).
I would highly recommend that your son self study or take a mathematical writing course if he will be starting college in mid to upper level math courses. My son has found that college math courses are much more proof oriented than his high school calculus courses. He was lucky to have a mathematical writing freshmen seminar last summer which gave him an advantage over some classmates who had a tougher time learning that skill while also trying to learn linear algebra and discrete math.
I think a lot of people hit a wall in math and once that happens it becomes hard to get good grades. However, before you get to that point it can be relatively easy (and not much work) to excel. Where that limit is depends on ability and it may not be obvious at HS - you can enjoy math enough to think youāll major in it, and only find out your limits in college.
Yes, that makes sense. Do you feel that is very math specific, or maybe the general trajectory of so called āgiftedā individuals?
(I have relatives who have worked with gifted young people - the āhitting a wall in collegeā happens quite frequently, and often times with not so great outcomes, as it can be quite a shock to the system and even the entire sense of identity. What you wrote reminded me of that.)
Just out of curiosity - what did your daughter pivot to?
Hahahaha - Iāll happily do that, however I have zero idea what Iāll glean from it. (I just had the image of us wielding a tape measure to figure out the depth of a department.)
She is a ballet dancer (BFA). But double majored in environmental studies.
My impression is that itās harder to hit a wall in understanding in most arts and social sciences, where itās about incrementally learning more material and writing more sophisticated analysis. But there are plenty of people who feel that (for example) quantum mechanics is too much of an intellectual leap from what they had done before in math and physics.
However, hitting a wall in terms of everything having been relatively easy in high school and finding that in college a lot more organization and focus is needed is not unique to a particular subject.
Oh, a ballet dancer! Not an easy calling - but very fulfilling if it is your passion, Iāve been told.
Hm - yes and no, I would say. There is a level of ātalentā in some things that no matter of hard work can replace, I do believe that. I once met a professor for creative writing - she is department head of a very prestigious university and an incredible teacher. She did and does inspire countless very successful writers and helped them to unlock their gifts, she is mentioned in numerous interviews and dedications as a life changer . However, her own writing, although technically excellent, never managed to convince. It is really interesting: she was very diligent in her writing, did get published, but her work lacked a voiceā¦
Thank you for your perspective @AustenNut, very interesting. That is a very accurate description of my kid.
Your sonās story is not the common kind that is found on CC (or common anywhere, Iād guess) and thus itās interesting.
To be honest, I read the descriptions of the kids here and am in total awe. Mind blown, very intimidating. Most of them seem to be in an entirely different league than any kid I know, including mine.
One of the reasons we are so keen on identifying non-reach schoolsā¦
Unfortunately, that can be hard to do from a prospective studentās point of view. Within the major, probably the best one can do is find someone with knowledge of the major subject and ask them to review syllabi and old exams from some of the courses. But these things are not always easily available.
But also note that rigor can extend to general education requirements. Some colleges have more general education requirements than others, and the required rigor may vary (e.g. āphysics for poetsā type courses may be allowed at one college, but not another, to fulfill a general education science requirement). The individual student may also find some types of general education requirements especially rigorous but find others not too difficult even if taking more rigorous course options in them.
If the student needs to take a foreign language for a college general education requirement, French, German, and Russian may be useful for reading math research papers (math PhD programs commonly require a reading knowledge of one of these languages).
Have you read the āApplying Sidewaysā post from MIT? Your son sounds like heās definitely following those principles without having read the article, which also is an indication of some great parenting, in my opinion. Although people whoāve seen a number of my posts know that always stress building a list heavy on schools with likelier admissions, I definitely think that your son should throw his hat in the ring for some tougher admits if he thinks itād be a good fit. I doubt Iām the only one who would find his story compelling.
Adding to what @ucbalumnus has said, Iād suggest the following steps when comparing colleges for their rigors:
Start with general education, and more importantly, the major-specific requirements. Does one college have fewer requirements in terms of breadth and/or depth?
Take a close look at the required courses. Search online for course syllabi in previous years. Compare the materials covered, the textbooks, the recommended readings, the handouts, the problem sets, the exams, etc.
Figure out all the electives in the major your son is interested in taking. Do the same comparisons between colleges.
If you need help comparing specific courses, you can post in forums like this and Iām sure someone will be able to help.
You will note that when looking at student profiles for academically broad, highly selective schools, the 25th percentile math SAT score will register at 700 or higher. Since this includes students who will major in all fields, including humanities and fine arts, you might infer that students who choose math majors at these schools represent an especially rarefied group with respect to their aptitude for quantitative fields. From this group of highly selective schools, smaller, relatively academically homogeneous colleges may be still more likely to attract students of relatively similar abilities and interests to their math departments.
Good morning from AP bootcamp, otherwise known as spring break Flash cards abound.
AustenNut, thank you for the MIT article, which we read with interest!
The idealistic side of me hopes this is true - the more realistic (ok, call it cynical) side thinks, sure, thatās how colleges want to imagine themselves to be - but when the pedal hits the medal I donāt believe thatās how they act. It just makes a lot more sense for any college to take the olympic medalist in whatever than the āsidewaysā kid - the one they can immediately output to their pr material, the other one not so much. But, who knowsā¦
Aw, thank you for the compliment. I of course think the kiddo is great (kind of comes with the mom label, right?) but I have no idea how he looks on the other side of a screen. I do know that we both find this process highly absurd. I think at the beginning of it all we thought there would be a small lesser known school somewhere that the math kids tell each other about and all go to. But we are finding it to be a bit more complicatedā¦
From this group of highly selective schools, smaller, relatively academically homogeneous colleges may be still more likely to attract students of relatively similar abilities and interests to their math departments.
Yes, thatās kind of been my thinking, this makes sense to me. One of the reasons Iāve encouraged my son to look at small, highly selective schools. Downside: who says he will be one of the selected?
Itās a real head scratcherā¦
SAT math is probably not that great a predictor for math major math, except in a negative sense. That is, doing poorly on SAT math suggests that the student is unlikely to do well on math major math, but doing well on SAT math does not mean that the student will do well on math major math.
However, smaller generalized schools often have smaller math departments, so there is a greater risk of upper level course offerings being too limited the smaller the school and department get. It is better to check the actual offerings of upper level (and graduate level if desired) math courses.
Larger schools (particularly state flagships) may be more likely to have varying levels of courses (e.g. honors versus regular courses) to accommodate a range of students that they may admit, although that should be checked specifically at each school. A smaller school may not have enough students and the ends of its distribution of academic strength to offer courses for other than the middle of its range. Hence, larger schools may be better as safeties and reaches.
This goes way back to your original post, but I think multivariable calculus would make the best choice of these three topics. Your son could then take linear algebra as a first-year college student. This can be characterized as the gateway course into true college mathematics.
(I just had the image of us wielding a tape measure to figure out the depth of a department.)
Flash cards abound.