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>And over the last couple of decades, there’s been a rapid but uneven growth of students taking AP Calculus in high school. Low-income students are much less li

>And over the last couple of decades, there’s been a rapid but uneven growth of students taking AP Calculus in high school. Low-income students are much less likely to attend schools that offer AP Calculus—and then they often end up in freshman calculus at college sitting next to lots of well-off students who have already taken the equivalent of freshman calculus in high school. Complete anecdote here, but I did not take AP Calculus in high school. Many of my Calculus I classmates had taken AP Calculus in high school. However, taking AP Calculus in high school did not seem to provide them any advantages, in fact it seemed to disadvantage them. The issue was that they had learned the various formulas for derivatives, etc but had not gotten a deep appreciation for limits. At the college level, understanding and appreciating the concept of limits was much more important than memorizing formulas ( IIRC they actually provided the formulas for you during the test). Many of the students who had taken AP were frustrated when the problems were not amenable to a blind application of formulas, and required deeper understanding of limits.

sct202 7y ago
If they were in Cal 1 and had taken AP Calc, they probably didn't do particularly well on the AP test or they would have tested out.
- brewdad 7y ago
  Some schools give generic credits but still require freshman students to take the "core" classes there. I'm pretty sure (it's been a few years) I got 6 credit hours towards graduation but still had to take Calc I and Freshman English. I did avoid having to take college level Spanish but I don't think I got any credit hours for it.
  - scarecrowbob 7y ago
    Well, when I was a student I tested out of the 2 freshman comp classes. When I was teaching Freshman Comp, it was routine for folks to test out of one or both. I dunno if that was a great idea, given the skills I was seeing on display from the students who had done that, but personally I did get the credit and was able to avoid the class.
- scarecrowbob 7y ago
  Not necessarily... my son started a mechanical engineering program about 2 weeks ago, and the recommendation from the school was to take Calc at the college even if the student had passed the AP test. I understand their interests in that, but I also feel like even if my son had done better on the AP test I'd have encouraged him to follow that advice, given how much of the following curriculum relied on that base.
  - logfromblammo 7y ago
    I got the same advice when I got to college with my heaping pile of AP and IB test credits. In retrospect, I should have focused solely on my major, eschewed the double minor and "honors" classes, and graduated in six semesters of very light study. Instead, I took some chemistry classes that I already technically had a double-cover of test credits for. If the kid got a 5 on the AP test, no college should ever be telling them to take the course anyway. If they got a 4, that advice should be rare, and confined to classes on the degree track. Maybe if they squeaked by with a 3, and somewhat important to the major, that might be good advice, depending on the student. Otherwise, if the institution does not have confidence in the test, it shouldn't be granting credit for it!
    - scarecrowbob 7y ago
      " Otherwise, if the institution does not have confidence in the test, it shouldn't be granting credit for it! " Having taught at the expensive and prestigious institution in question, I can say that there may be a gap between what the institution has faith in and what the instructors experience. I mean, yeah, if it's a class outside of your major then sure. My son (and I, when I went) skipped freshman comp. I encourage my son to get through via whatever means is easiest, and in his case, I believe it's getting some extra time in the seat in a calc class.
      - logfromblammo 7y ago
        If there is a gap between "the institution" and "the instructors", that is a problem large enough to overwhelm any problems that may exist in standardized testing. The motive of an instructor is presumably to ensure that, by the end of a course, every student will be adequately prepared to meet a minimum standard of knowledge, regardless of their preparedness prior to the beginning of the course (subject to prerequisites). At a wider scope, the instructor, as a member of an instructional department, is also motivated to progress students towards possession of a total body of knowledge deemed adequate by their peers to either practice in the field, or continue on to a more intense program of academic study. The institution is motivated to collect tuition, receive grants, accumulate prestige, and pester alumni to support goals that are not necessarily academic in nature. The only instructional goal is to produce graduates that will not embarrass the institution. The student is motivated primarily to get a degree that is their admission ticket to a broad swath of jobs otherwise unavailable to anyone without a degree. They are motivated secondarily to actually learn about subjects that interest them personally. The student's sole reason to take SAT, ACT, AP, IB, CLEP, &cetera is because the academic institutions reward those passing test scores. The principle in play is that it should not be necessary to instruct any person that already has the knowledge. If the standardized tests are insufficient to establish that, the instructors should then be applying the same methods they use on students that have taken their courses, on prospective students that have not, and only recommend taking a course that would otherwise not be required by the institution, when it can be shown that the standardized test signaled a false positive. That is, a passing score on the test should not automatically grant credit, but should allow a brief interview with a professor that teaches the relevant course, who can then determine by any means they care to use whether or not the student already possesses the knowledge to pass. If too many false positives are found, the institution can then revise its treatment of the test scores.
- makerofspoons 7y ago
  My university thought so poorly of the AP Calc exams that they didn't let engineering majors test out of their applied calculus courses.
rongenre 7y ago
Yeah that was my experience too. I did a lot of calculus in high school, but it was.. High School Calculus, and I was definitely good at doing high school plug-and-chug math. College math is entirely different and I think the arrogance from the former worked against me. In retrospect I should have just taken actual college classes.
- mattmcknight 7y ago
  My high school AP Calc BC was good and prepared me for both getting a 5 on the exam and the subsequent classes. Letting high schoolers take college courses should be much more of a thing than it currently is. There is some dual enrollment, but we have a situation where there are large number of students ready for college courses at the beginning of high school. The local Basis Independent school has all students take AP World History in 8th grade. We have a thing called "high school" that is completely unstandardized. How someone as smart as Paul Tough really believes that GPA from one school can be compared to GPA from another is beyond me.
TrackerFF 7y ago
When I took our equivalent to AP calculus, it was basically just plug'n chug - not a whole lot of conceptual or intuitive learning. Hell, I didn't even learn the definition of the derivative until first year at college, using limits. Should be noted though, that this was long before the advent of youtube and all the excellent learning channels / resources you have today. So much of the math and physics would have been a breeze given the tools and options we have to day.
- m_ke 7y ago
  That's because most high school math teachers in america don't know calculus and have a poor understanding of basic math concepts. I had a few math classes with students from the teachers college while getting my math degree and they were consistently the worst performing students.
- stallmanite 7y ago
  Re: YouTube it really is amazing. I got an engineering degree circa 2004 and am not proud to say have only recently finally grasped many concepts that I “learned” and was tested on back then. (Esp in mathematics) The quality of educational materials on YouTube is exceptional.
zwieback 7y ago
Interesting - my daughters both took Calculus in high school and they spent a lot of time on limits prior to learning the rote mechanics of derivatives. I was surprised by that - after 30 years of practice using derivatives I'd sort of forgotten the basics and was pleasantly suprised to see how in-depth the curriculum at our high school is. Having said that - the big problem is that in high school it's really hard to appreciate what good calculus is, whether you understand it or not. Once you're a practicing scientist or engineer it becomes obvious.
- noobiemcfoob 7y ago
  My high school calculus class was similar. I remember spending so much time on limits that our introduction to derivatives was to "invent" derivatives as a last question on our limits exam.
noobiemcfoob 7y ago
Anecdata vs. Anecdata: My high school calculus course (AP Calc BC, so college Calc I and II) was phenomenal. It let me jump into Calc III at college and get an A+. Ideas that there is a huge difference in high school vs. college math is more that there is a huge difference in math teachers and course expectations.

sct202 7y ago

If they were in Cal 1 and had taken AP Calc, they probably didn't do particularly well on the AP test or they would have tested out.

brewdad 7y ago
Some schools give generic credits but still require freshman students to take the "core" classes there. I'm pretty sure (it's been a few years) I got 6 credit hours towards graduation but still had to take Calc I and Freshman English. I did avoid having to take college level Spanish but I don't think I got any credit hours for it.
- scarecrowbob 7y ago
  Well, when I was a student I tested out of the 2 freshman comp classes. When I was teaching Freshman Comp, it was routine for folks to test out of one or both. I dunno if that was a great idea, given the skills I was seeing on display from the students who had done that, but personally I did get the credit and was able to avoid the class.
scarecrowbob 7y ago
Not necessarily... my son started a mechanical engineering program about 2 weeks ago, and the recommendation from the school was to take Calc at the college even if the student had passed the AP test. I understand their interests in that, but I also feel like even if my son had done better on the AP test I'd have encouraged him to follow that advice, given how much of the following curriculum relied on that base.
- logfromblammo 7y ago
  I got the same advice when I got to college with my heaping pile of AP and IB test credits. In retrospect, I should have focused solely on my major, eschewed the double minor and "honors" classes, and graduated in six semesters of very light study. Instead, I took some chemistry classes that I already technically had a double-cover of test credits for. If the kid got a 5 on the AP test, no college should ever be telling them to take the course anyway. If they got a 4, that advice should be rare, and confined to classes on the degree track. Maybe if they squeaked by with a 3, and somewhat important to the major, that might be good advice, depending on the student. Otherwise, if the institution does not have confidence in the test, it shouldn't be granting credit for it!
  - scarecrowbob 7y ago
    " Otherwise, if the institution does not have confidence in the test, it shouldn't be granting credit for it! " Having taught at the expensive and prestigious institution in question, I can say that there may be a gap between what the institution has faith in and what the instructors experience. I mean, yeah, if it's a class outside of your major then sure. My son (and I, when I went) skipped freshman comp. I encourage my son to get through via whatever means is easiest, and in his case, I believe it's getting some extra time in the seat in a calc class.
    - logfromblammo 7y ago
      If there is a gap between "the institution" and "the instructors", that is a problem large enough to overwhelm any problems that may exist in standardized testing. The motive of an instructor is presumably to ensure that, by the end of a course, every student will be adequately prepared to meet a minimum standard of knowledge, regardless of their preparedness prior to the beginning of the course (subject to prerequisites). At a wider scope, the instructor, as a member of an instructional department, is also motivated to progress students towards possession of a total body of knowledge deemed adequate by their peers to either practice in the field, or continue on to a more intense program of academic study. The institution is motivated to collect tuition, receive grants, accumulate prestige, and pester alumni to support goals that are not necessarily academic in nature. The only instructional goal is to produce graduates that will not embarrass the institution. The student is motivated primarily to get a degree that is their admission ticket to a broad swath of jobs otherwise unavailable to anyone without a degree. They are motivated secondarily to actually learn about subjects that interest them personally. The student's sole reason to take SAT, ACT, AP, IB, CLEP, &cetera is because the academic institutions reward those passing test scores. The principle in play is that it should not be necessary to instruct any person that already has the knowledge. If the standardized tests are insufficient to establish that, the instructors should then be applying the same methods they use on students that have taken their courses, on prospective students that have not, and only recommend taking a course that would otherwise not be required by the institution, when it can be shown that the standardized test signaled a false positive. That is, a passing score on the test should not automatically grant credit, but should allow a brief interview with a professor that teaches the relevant course, who can then determine by any means they care to use whether or not the student already possesses the knowledge to pass. If too many false positives are found, the institution can then revise its treatment of the test scores.
makerofspoons 7y ago
My university thought so poorly of the AP Calc exams that they didn't let engineering majors test out of their applied calculus courses.

rongenre 7y ago

Yeah that was my experience too. I did a lot of calculus in high school, but it was.. High School Calculus, and I was definitely good at doing high school plug-and-chug math. College math is entirely different and I think the arrogance from the former worked against me. In retrospect I should have just taken actual college classes.

mattmcknight 7y ago
My high school AP Calc BC was good and prepared me for both getting a 5 on the exam and the subsequent classes. Letting high schoolers take college courses should be much more of a thing than it currently is. There is some dual enrollment, but we have a situation where there are large number of students ready for college courses at the beginning of high school. The local Basis Independent school has all students take AP World History in 8th grade. We have a thing called "high school" that is completely unstandardized. How someone as smart as Paul Tough really believes that GPA from one school can be compared to GPA from another is beyond me.

TrackerFF 7y ago

When I took our equivalent to AP calculus, it was basically just plug'n chug - not a whole lot of conceptual or intuitive learning. Hell, I didn't even learn the definition of the derivative until first year at college, using limits. Should be noted though, that this was long before the advent of youtube and all the excellent learning channels / resources you have today. So much of the math and physics would have been a breeze given the tools and options we have to day.

m_ke 7y ago
That's because most high school math teachers in america don't know calculus and have a poor understanding of basic math concepts. I had a few math classes with students from the teachers college while getting my math degree and they were consistently the worst performing students.
stallmanite 7y ago
Re: YouTube it really is amazing. I got an engineering degree circa 2004 and am not proud to say have only recently finally grasped many concepts that I “learned” and was tested on back then. (Esp in mathematics) The quality of educational materials on YouTube is exceptional.

zwieback 7y ago

Interesting - my daughters both took Calculus in high school and they spent a lot of time on limits prior to learning the rote mechanics of derivatives. I was surprised by that - after 30 years of practice using derivatives I'd sort of forgotten the basics and was pleasantly suprised to see how in-depth the curriculum at our high school is. Having said that - the big problem is that in high school it's really hard to appreciate what good calculus is, whether you understand it or not. Once you're a practicing scientist or engineer it becomes obvious.

noobiemcfoob 7y ago
My high school calculus class was similar. I remember spending so much time on limits that our introduction to derivatives was to "invent" derivatives as a last question on our limits exam.

noobiemcfoob 7y ago

Anecdata vs. Anecdata: My high school calculus course (AP Calc BC, so college Calc I and II) was phenomenal. It let me jump into Calc III at college and get an A+. Ideas that there is a huge difference in high school vs. college math is more that there is a huge difference in math teachers and course expectations.