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Without reading the fine article except for searching for "calculus", I'll note that I've confirmed an accusation at the other end: the Common Core does not eve

by hga 13y ago

Without reading the fine article except for searching for "calculus", I'll note that I've confirmed an accusation at the other end: the Common Core does not even reach precalculus by the end of high school. No student in a school solely based on it will be taking AP Calculus, let alone be able to attend MIT or Caltech (the former requires you to be ready to learn the calculus, the latter demands you've already learned single variable calculus). Students interested in STEM majors, or anything needing serious math, will join the current legions who didn't learn (enough) math in high school taking remedial classes and be that much behind in graduating. Perhaps America has too many people in STEM careers; absent supplementation by school districts that e.g. already teach AP Calculus and don't want to stop, this will help fix that.... (Well, outside of the states rejecting it; it was implemented in my home state of Missouri without the input of the legislature, and they're about to zap it, joining another state who's name I forget.)

icolor 13y ago
Article only mentions that learning to teach the common core addition/division/multiplication/subtraction is as difficult as 'learning' calculus. I'm sure that the current common core level for math ends around Trigonometry.
- hga 13y ago
  You might, like I did, check out the online sources on this, from reports on a professor who was one of the drafters admitting it, to the official curriculum. It's enlightening.
kasey_junk 13y ago
AP Calculus has never been a standard part of the requirements for a high school diploma in any state in the union. Common Core did not change that. In fact Common Core has added to the requirements in math as it brought many states upwards to Trigonometry as a requirement. Remember, this curriculum is not for Advanced Placement, it's for common placement. No school is prevented from offering AP courses and they have quite a few incentives to do so.
tptacek 13y ago
The idea that Common Core prevents students from taking calculus is disputed: http://www.mindingthecampus.com/originals/2014/04/a_sorry_attack_on_the_common_c.html http://www.mindingthecampus.com/originals/2014/04/a_sorry_at... Further, a citation to Caltech's admission policy would be handy; I found sources directly disputing your claim (also in the context of Common Core), citing Caltech Math1a to rebut it.
- hga 13y ago
  Their Math1a uses Apostol as its textbook (http://www.math.caltech.edu/~2013-14/1term/ma001a/#text http://www.math.caltech.edu/~2013-14/1term/ma001a/#text). This is the classic proofs based text, in other schools what's commonly used for "honors calculus", including MIT but not with such a name. I suppose in theory a really mathematically adept student could start with it, but that's not what I remember any school I've looked into, including CalTech, requiring before you start it. The link you cited is just an attack on a particular contention; it's entirely unrelated to my examination of it, except second hand reports of it (some of the phases quoted are familiar) probably in part prompted mine.
  - ekm2 13y ago
    >Their Math1a uses Apostol as its textbook. Try Harvard's Math 55b.They hit you with Rudin freshman year.
- tzs 13y ago
  Academic preparation Caltech says you should have [1]: 4 years of math (including calculus) 1 year of physics 1 year of chemistry 3 years of English (4 years recommended) 1 year of U.S. history/government (waived for international students) They really want you to have calculus. From the admissions FAQ [3]: What if my high school does not offer Advanced Placement (AP) or International Baccalaureate (IB) courses? Many schools don't offer the AP or IB curricula. Regardless of the curriculum your school offers, we expect that you will have challenged yourself with demanding courses. The Caltech curriculum will require that you have completed rigorous courses in calculus and in physics. If these courses are not available in your high school, we strongly encourage you to take them at a local college or online. Here is Caltech's required first year math course [2]: --------- BEGIN QUOTE ----------- Ma 1 abc. Calculus of One and Several Variables and Linear Algebra. 9 units (4-0-5); first, second, third terms. Prerequisites: high-school algebra, trigonometry, and calculus. Special section of Ma 1 a, 12 units (5-0-7). Review of calculus. Complex numbers, Taylor polynomials, infinite series. Comprehensive presentation of linear algebra. Derivatives of vector functions, multiple integrals, line and path integrals, theorems of Green and Stokes. Ma 1 b, c is divided into two tracks: analytic and practical. Students will be given information helping them to choose a track at the end of the fall term. There will be a special section or sections of Ma 1 a for those students who, because of their background, require more calculus than is provided in the regular Ma 1 a sequence. These students will not learn series in Ma 1 a and will be required to take Ma 1 d. Instructors: Marx, Katz, Mantovan, Aschbacher, Ni, Kechris. Ma 1 d. Series. 5 units (2-0-3); second term only. Prerequisite: special section of Ma 1 a. This is a course intended for those students in the special calculus-intensive sections of Ma 1 a who did not have complex numbers, Taylor polynomials, and infinite series during Ma 1 a. It may not be taken by students who have passed the regular Ma 1 a. Instructor: Staff. ---------- END QUOTE ---------- Note: don't freak out over the unit numbers. Caltech's unit scale is different from that of most other schools. 1 unit corresponds to 1 hour of work per week, so a 9 unit course is one that should take 9 hours a week. The numbers in parentheses, such as (4-0-5) break it down by number of hours of lecture, number of hours of lab, and number of hours of outside preparation and homework. Ma1 does start with a "review of calculus", so you could probably do it without having had calculus in high school if you were really good, but it would be rough. [1] http://www.admissions.caltech.edu/applying/freshman http://www.admissions.caltech.edu/applying/freshman [2] http://catalog.caltech.edu/courses/listing/ma.html http://catalog.caltech.edu/courses/listing/ma.html [3] http://admissions.caltech.edu/uploads/File/general/FAQapplying.pdf http://admissions.caltech.edu/uploads/File/general/FAQapplyi...
groovy2shoes 13y ago
I was never particularly good at math. I also never took precalculus in high school. It was Algebra 2, Geometry, Discrete Math, and Statistics for me. I struggled a little with Calculus when I got to university, but managed to pass the class and got pretty good at it by the time I was in Multivariable Calculus. I know many people who were in the same situation. I don't think "precalculus" is requisite for learning calculus (I also never took any "prealgebra" and managed algebra just fine). I can't even imagine what a pre{calculus,algebra} course would possibly teach.
- maxerickson 13y ago
  They introduce some of the fundamental concepts of the later courses (and try to tie them into previous knowledge). In the U.S. system, they also serve as a review, I guess with the hope of shoring up knowledge that students were missing (but I think such an approach for math education is pretty optimistic; figuring out what they don't know and fixing that must be more valuable than just showing them things again).
- hga 13y ago
  Precalculus as I'm using it is a level of math, not a particular course (although there are of course courses with that title). In addition to what you learned in high school, assuming your Algebra II was like mine, plenty of analytic geometry, it would also include trigonometry. To do as well as you did, you obviously picked that up on your own, as did I. (While in theory I took a trig and further analytic geometry course in high school, followed by a semester of the calculus, the teacher flatly refused to teach anything, and trig at that level in that textbook was absolutely boring and unmotivated (e.g. didn't mention you needed it to do calculus on rotation including AC electricity); I only stayed in these automatic A courses so I'd have them on my transcript (I'd already taken my first go at the calculus in a summer course taught at a university before this, but focused most of my attention on a PDP-11/70 running UNIX(TM) Version 6, which ended up being infinitely more valuable (as it turned out, perhaps lifesaving; the introductory programming class that was my excuse for using it was easy, so I focused on UNIX(TM), Adventure and other games, wandering around the filesystem (very much like Adventure :-), software engineering, helping others debug their final class project, and using nroff for my class project which had more exposition on software engineering than code; included that in my college applications)). Expanding on maxerickson's comment, I gather formal precalculus courses also start teaching you about limits and stuff like that; since basic differentiation, especially speed and acceleration, is relatively simple, I'd hope it would teach an intro to that, which goes along nicely with the limits. It could also be a fancy name for a (further) analytic geometry course, and/or include trig motivated by the calculus vs., oh, surveying.

by hga 13y ago

icolor 13y ago

Article only mentions that learning to teach the common core addition/division/multiplication/subtraction is as difficult as 'learning' calculus. I'm sure that the current common core level for math ends around Trigonometry.

hga 13y ago
You might, like I did, check out the online sources on this, from reports on a professor who was one of the drafters admitting it, to the official curriculum. It's enlightening.

kasey_junk 13y ago

AP Calculus has never been a standard part of the requirements for a high school diploma in any state in the union. Common Core did not change that. In fact Common Core has added to the requirements in math as it brought many states upwards to Trigonometry as a requirement. Remember, this curriculum is not for Advanced Placement, it's for common placement. No school is prevented from offering AP courses and they have quite a few incentives to do so.

tptacek 13y ago

The idea that Common Core prevents students from taking calculus is disputed: http://www.mindingthecampus.com/originals/2014/04/a_sorry_attack_on_the_common_c.html http://www.mindingthecampus.com/originals/2014/04/a_sorry_at... Further, a citation to Caltech's admission policy would be handy; I found sources directly disputing your claim (also in the context of Common Core), citing Caltech Math1a to rebut it.

hga 13y ago
Their Math1a uses Apostol as its textbook (http://www.math.caltech.edu/~2013-14/1term/ma001a/#text http://www.math.caltech.edu/~2013-14/1term/ma001a/#text). This is the classic proofs based text, in other schools what's commonly used for "honors calculus", including MIT but not with such a name. I suppose in theory a really mathematically adept student could start with it, but that's not what I remember any school I've looked into, including CalTech, requiring before you start it. The link you cited is just an attack on a particular contention; it's entirely unrelated to my examination of it, except second hand reports of it (some of the phases quoted are familiar) probably in part prompted mine.
- ekm2 13y ago
  >Their Math1a uses Apostol as its textbook. Try Harvard's Math 55b.They hit you with Rudin freshman year.
tzs 13y ago
Academic preparation Caltech says you should have [1]: 4 years of math (including calculus) 1 year of physics 1 year of chemistry 3 years of English (4 years recommended) 1 year of U.S. history/government (waived for international students) They really want you to have calculus. From the admissions FAQ [3]: What if my high school does not offer Advanced Placement (AP) or International Baccalaureate (IB) courses? Many schools don't offer the AP or IB curricula. Regardless of the curriculum your school offers, we expect that you will have challenged yourself with demanding courses. The Caltech curriculum will require that you have completed rigorous courses in calculus and in physics. If these courses are not available in your high school, we strongly encourage you to take them at a local college or online. Here is Caltech's required first year math course [2]: --------- BEGIN QUOTE ----------- Ma 1 abc. Calculus of One and Several Variables and Linear Algebra. 9 units (4-0-5); first, second, third terms. Prerequisites: high-school algebra, trigonometry, and calculus. Special section of Ma 1 a, 12 units (5-0-7). Review of calculus. Complex numbers, Taylor polynomials, infinite series. Comprehensive presentation of linear algebra. Derivatives of vector functions, multiple integrals, line and path integrals, theorems of Green and Stokes. Ma 1 b, c is divided into two tracks: analytic and practical. Students will be given information helping them to choose a track at the end of the fall term. There will be a special section or sections of Ma 1 a for those students who, because of their background, require more calculus than is provided in the regular Ma 1 a sequence. These students will not learn series in Ma 1 a and will be required to take Ma 1 d. Instructors: Marx, Katz, Mantovan, Aschbacher, Ni, Kechris. Ma 1 d. Series. 5 units (2-0-3); second term only. Prerequisite: special section of Ma 1 a. This is a course intended for those students in the special calculus-intensive sections of Ma 1 a who did not have complex numbers, Taylor polynomials, and infinite series during Ma 1 a. It may not be taken by students who have passed the regular Ma 1 a. Instructor: Staff. ---------- END QUOTE ---------- Note: don't freak out over the unit numbers. Caltech's unit scale is different from that of most other schools. 1 unit corresponds to 1 hour of work per week, so a 9 unit course is one that should take 9 hours a week. The numbers in parentheses, such as (4-0-5) break it down by number of hours of lecture, number of hours of lab, and number of hours of outside preparation and homework. Ma1 does start with a "review of calculus", so you could probably do it without having had calculus in high school if you were really good, but it would be rough. [1] http://www.admissions.caltech.edu/applying/freshman http://www.admissions.caltech.edu/applying/freshman [2] http://catalog.caltech.edu/courses/listing/ma.html http://catalog.caltech.edu/courses/listing/ma.html [3] http://admissions.caltech.edu/uploads/File/general/FAQapplying.pdf http://admissions.caltech.edu/uploads/File/general/FAQapplyi...

groovy2shoes 13y ago

I was never particularly good at math. I also never took precalculus in high school. It was Algebra 2, Geometry, Discrete Math, and Statistics for me. I struggled a little with Calculus when I got to university, but managed to pass the class and got pretty good at it by the time I was in Multivariable Calculus. I know many people who were in the same situation. I don't think "precalculus" is requisite for learning calculus (I also never took any "prealgebra" and managed algebra just fine). I can't even imagine what a pre{calculus,algebra} course would possibly teach.

maxerickson 13y ago
They introduce some of the fundamental concepts of the later courses (and try to tie them into previous knowledge). In the U.S. system, they also serve as a review, I guess with the hope of shoring up knowledge that students were missing (but I think such an approach for math education is pretty optimistic; figuring out what they don't know and fixing that must be more valuable than just showing them things again).
hga 13y ago
Precalculus as I'm using it is a level of math, not a particular course (although there are of course courses with that title). In addition to what you learned in high school, assuming your Algebra II was like mine, plenty of analytic geometry, it would also include trigonometry. To do as well as you did, you obviously picked that up on your own, as did I. (While in theory I took a trig and further analytic geometry course in high school, followed by a semester of the calculus, the teacher flatly refused to teach anything, and trig at that level in that textbook was absolutely boring and unmotivated (e.g. didn't mention you needed it to do calculus on rotation including AC electricity); I only stayed in these automatic A courses so I'd have them on my transcript (I'd already taken my first go at the calculus in a summer course taught at a university before this, but focused most of my attention on a PDP-11/70 running UNIX(TM) Version 6, which ended up being infinitely more valuable (as it turned out, perhaps lifesaving; the introductory programming class that was my excuse for using it was easy, so I focused on UNIX(TM), Adventure and other games, wandering around the filesystem (very much like Adventure :-), software engineering, helping others debug their final class project, and using nroff for my class project which had more exposition on software engineering than code; included that in my college applications)). Expanding on maxerickson's comment, I gather formal precalculus courses also start teaching you about limits and stuff like that; since basic differentiation, especially speed and acceleration, is relatively simple, I'd hope it would teach an intro to that, which goes along nicely with the limits. It could also be a fancy name for a (further) analytic geometry course, and/or include trig motivated by the calculus vs., oh, surveying.