At our kids’ school, the teacher for multivariable calc has a PhD in math from MIT. Our S has been lucky to have him starting with a newly developed trig/precal modeling class that he loved. The calc BC class that he’s in right with the same teacher is a flipped classroom with very different problems than the other BC class. I do not have an extensive math background, so I can’t elaborate.
We live in a part of the country with no math circles, little high tech, and a low-ranked state flagship, which is sparsely populated. So, if our school offers this curriculum, I’d imagine this must be happening in more metropolitan areas all around the country.
Our S has no idea what he’s going to study (10th grader) but, hopefully, although it sounds like he’ll have to retake math beyond BC, it will give him a good foundation for whatever he goes into if it’s math-related.
This is true, but probably about three quarters of high school students attend high schools which offer calculus. The universe of all high schools includes schools with small populations of low performing students like reform/continuation schools and juvenile hall schools which are much less likely to offer advanced courses like calculus.
“Also, linear algebra courses may come in computational-oriented and theory/proof-oriented versions; math majors may be required to take the latter after or instead of the former.”
My second year college student is taking Linear at St. Andrews and a high school friend at a college here asked what software they are using. She was puzzled. “We aren’t using software” The other student was also puzzled. “How are you crunching all these big matrices without software?” She said “Um, I’m using pencil and paper to prove that a particular operation is or is not part of an eigenspace.”
It’s like they are in different classes altogether.
Also- this kid is a classic example of a math late bloomer. Didn’t love math in high school. Started at the bottom with the equivalent of Calc 1 in first semester of university. Currently receiving a 20!!! in a proof based Linear class based on midterm and problem sets. (grade scale is out of 20)
Sometimes it is not about how fast you get there, but just that you do get there.
http://www.olin.edu/content/what-were-looking/ says “If you plan to apply to Olin, you should make sure that you are on track to complete courses in calculus and physics by the time you finish high school. (It’s OK if you are taking them during your senior year; many students do!)” and does not mention that the calculus has to be BC or equivalent.
The kids come in to the schools at all different levels of math. My kid graduated in May with a math degree from Harvard. They skipped the lower division math classes. There were actually four math majors in the class of 2018 that skipped the lower division math classes. One kid was so bright that he went directly into graduate level math at Harvard. I think of the four only one is in grad school in math now. Interesting.
MV Calc and Linear Algebra are basic underclassmen foundation math classes. They are not the type of high level math classes that only a PhD can understand well and teach adequately. This relates to why offering them is becoming increasingly common at HSs in wealthier areas. Both the local public and private where I most often interview applicants to a HYPSM college offer post BC calc math, and most students I interview take such classes, including ones who struggle more with STEM and plan to major in a non-STEM field and athletes who have been in contact with coaches.
Instead I’d expect the quality of the teaching largely depends on more subjective criteria such as able to explain the material clearly, able to make students interested/enthusiastic, taking extra time to assist students who are struggling with the material, etc. I took MV calculus at a SUNY while in HS. A grad student without an advanced degree taught the class, and I thought he was an excellent teacher. He seemed very enthusiastic to be teaching and wasn’t at all burnt out. He clearly explained the material, engaged students, was charismatic with jokes, etc. I used him for one of my LORs, which had a similar style.
Next semester, I had a regular tenured professor at SUNY for Linear Algebra with a PhD. In contrast, this was probably the worst teacher I’ve ever had beyond a HS level. Few in the class had a clue what he was mumbling about when he was writing on the board, after which he would immediately leave. He gave the impression that he just didn’t care. Students who bothered to attend class would regularly make fun of his teaching style before and after he arrived. By the end of the class, only 3 students had a grade average high enough to qualify to take the final. If the class had been offered in my HS instead, I’d expect any of the regular HS math teachers would have done a far better job.
DS19 will be going into university having completed AP Chemistry, AP Physics 1, and AP Calculus BC. The recommendation of faculty at the various universities we toured all recommended repeating the courses in first year and not accepting credit for them if they are necessary for your major. Engineering programs as a general rule will not give transfer credit for AP courses. As a caveat I will say that grade 12 Calculus is a prerequisite for all the programs he is applying to and is part of our provincial high school university stream curriculum. As a result AP Calc BC is at most 1 year accelerated (but not exactly as there are topics covered in our grade 12 calculus curriculum that are not covered in AP Calculus BC). DS tells me that AP Physics 1 isn’t actually all that different from our grade 12 university track Physics course. What students here don’t have access to is dual enrolment at the university level so AP Calc BC/IB Math HL is as far as they can go while in high school and most schools don’t offer AP/IB courses.
It depends on the school @gwnorth. My DD skipped Calc I and some students even skipped Calc II. She also is in the honors program which combines the first year engineering class with physics, instead of a separate physics course. She took Physics C in high school and her school did accept her AP credit for both E&M and Mechanics towards graduation credits. The one credit she did not take was for AP chem as her intended major is chem e and her advisor told her not too. She’s finding her college course to be very straight forward.
While teachers with a BS in math should be able to teach multivariable or linear algebra, such classes are never offered in our district because classes need at least 25 students in order to be offered. This is also the reason that the AP Physics C classes are never offered despite being in the list of classes students can request.
We typically have ~2-5 students per graduating class who have wanted these sorts of classes. S17 got 14 students to request AP Physics C one year–still not enough.
But, the local high schools have many students who take classes at the local community college and several students per grade who end up taking classes at the local UC campus.
Most US universities will allow advanced placement and subject credit in math for high enough scores on the AP calculus exam (though “high enough” may be 5 at some universities), even for engineering majors. AP chemistry is also often accepted for advanced placement and/or subject credit. AP physics 1 (not calculus based) is generally not accepted for engineering majors, since engineering majors need calculus based physics.
Whether a student should take advanced placement from AP credit can often be answered in a more informed way by having the student try the university’s old final exam of the course(s) that are allowed to be skipped.
Taking math beyond calculus BC at a college makes more sense than taking it at a high school, since transfer credit is possible with a college course.
Calculus-based physics is also more advantageous to take at a college, particularly when getting to the E&M part, which in colleges commonly has multivariable calculus as a corequisite (unlike AP physics C E&M). Due to the lesser math intensity of AP physics C compared to many colleges’ calculus-based physics courses, AP physics C may not be as well accepted for advanced placement.
not necessarily, ucb. math and physics classes at our high school are taught at a higher level, and have frankly much smarter students, than the comparative classes at the local community college. It is quite possible for high schools to offer excellent foundation in higher level math, particularly if there is a critical mass of students ready for those courses.
This is a topic I’ve been thinking about recently as credit or placement in college becomes more important for my senior who has taken many math, science, and CS courses beyond AP level. These have been high level and much higher level than the college courses he took before high school, but one school he’s applying to stated they would only accept AP or college credit. Sometimes, the high school courses have been rigorous, taught by a PhD and proof-based in math. There are plenty of math classes he’d like to take to make repetition unappealing. How to most colleges handle all these kids coming in with beyond-AP credit? Which colleges have placement tests beyond the basic courses to allow students to show mastery of a subject and be placed appropriately?
This you have to check each college (or math department) for whether it has placement testing for students that advanced in the subject. Be aware that the department of the student’s major would also have to accept the placement testing results, if it is different from the department of the subject in question (e.g. if the student wants to major in physics, the physics department needs to accept math placement results from the math department to exempt the student from lower level math requirements).
Even having scored 5’s on BC, AP Chem and AP Spanish, often, as was the case with my kid, the university also required taking a placement exam in each topic. Additionally as a freshman taking MV Calc, the class required a separate AB/BC test in order to pass the MV Calc class specifically. FWIW.