Reply to How can precalc be an AP class?

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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]Not all states have 4 years obligatory math in high school. For example California only has 2 years mandatory, which is why precalculus could be a university class.[/quote]

But wouldn't it be considered remedial? There are college English classes that cover the absolute basics of grammar and composition,  and they're zero-level classes, whereas "Introductory Composition" is 101[/quote]

All the scoffing is a little ridiculous, elitist and parochial, all at once. The educational requirements are varied across the 50 states not everything is the same as in your neck of the woods.

It would not be remedial, but if course it will not count as a requirement for science and engineering majors. It will count for some other majors like humanities, and frankly you don’t need to take calculus for comparative literature or marketing.

If UC Berkeley has a precalculus course and gives credit to it, it’s good enough as an AP from some random high school. It’s up there with all lower division courses like calculus, multi, Lin alg, etc.
https://math.berkeley.edu/courses/overview/lowerdivcourses/math32

Another benefit is in an age of grade inflation and lax standards there some attempt at an independent evaluation, which I welcome. [/quote]
But the AP precalc exam is watered down. It only tests on the first three units of AP Precalc, which is roughly 2/3 Algebra 2 content. The exam does not cover the more challenging aspects of precalc.[/quote]

Check the Berkeley precalculus, it’s the same as what’s on the AP exam.

College Board doesn’t have to do the most challenging course or the most in depth, probably there are honors precalculus classes that are better.

The student should choose whatever makes the most sense to them. [/quote]
Berkeley's course appears to cover even less content than the watered down AP Precalc exam; no polar functions. Berkeley's course is just a validation of Algebra 2 skills. The SAT does the same thing. But, since the UC no longer considers SAT scores, they appear to need an alternative way to do the same thing.

Berkeley's course name for precalc is interesting. Math 32. Generally, math courses are ordered sequentially in order of difficulty. But calculus is Math 1 at Berkeley. So their options were to label Precalc as Math 0 or give it a higher number. They opted for the latter even though it is incongruous with the ordering of other courses. [/quote]

There's always kids that need remedial courses in college. Their HS didn't offer good coursework, they struggle on some subjects etc. But we used to just call it remedial, now that term is disfavored.[/quote]

[b]It isn’t remedial, there’s only two years of math required in high school in California [/b]so a student could be done after geometry. Most take 4 years, however given that the UC system serves a large number of California residents, it makes sense to offer precalculus.

Those classes were never called remedial. They are just called the same as they would be in high school, ie algebra geometry etc. Students that need to take them most often go through the CC, where precalculus can be transferred to UC, but algebra and geometry can’t.

It has always been like that, it has nothing to do with SAT, or anything else.[/quote]

That doesn't mean it's not remedial -- admitting students who don't have the standard college prep background doesn't mean college graduation standards have been lowered, it just means that kids who might not have been admitted previously will be given more help to catch up. That's a good thing, but it doesn't make precalc a college-level course.

I mean, you can argue that if it's taught in college, it's by definition a college-level course, but in that case, you're abandoning standards entire rather than being flexible in how students meet them.[/quote]

Then you don’t know what remedial is. Not only Precalculus is offered at a university, it also counts towards a degree. Remedial courses don’t earn credit.

You’re writing from the viewpoint of someone intending to major in stem, not everyone follows this path. Whatever you think the standard college prep background is, it’s just too narrow.

AP Precalculus is in the same category as AP Physics 1, 2. It’s not good for a stem degree but it satisfies requirements for other degrees (eg nursing). You wouldn’t say AP Physics is remedial.[/quote]
DP. Then why put students intending to go on to BC calculus into AP Precalculus? [/quote]

Who is putting them where? They can choose among courses their school offers.

If the school only offers AP Precalculus and you’re not happy, then talk to the math department, although I’m not sure what the issue is. AP Precalculus is an ok preparation for BC. [/quote]
Local districts have eliminated honors precalc, opting instead to put honors students into AP Precalc and exclude non-honors students from it. AP Precalc was not designed just to prepare students for calculus since it was assumed that most students taking it would be in 12th grade. As such, the course takes an applied approach and has students spend time running regressions, which are not needed for AP Calc. In contrast, it excludes series and sigma notation which are needed for BC. And, if teachers follow the AP Precalc pacing, there won't be adequate time to cover introductory calculus in the second semester. Honors precalc was better preparation for BC Calc.[/quote]

Why would they teach Calculus in the precalculus class? Honors students should be able to handle BC in two semesters, not in three like you’re suggesting. Tens of thousands of students do it every year and get a 5 on the exam.

The series prerequisite for Calculus BC is very basic and it’s covered in Algebra. You don’t need that much time for the summation notation.

Precalculus is not supposed to be optimized for giving the maximum edge to students taking BC. Vectors and matrices are still worthwhile for Physics for example.

To be honest all the hand wringing about AP precalculus is a little silly. Its a fine preparation for BC, at least according to published prerequisites.

https://secure-media.collegeboard.org/digitalServices/pdf/ap/ap-course-overviews/ap-calculus-bc-course-overview.pdf
[/quote]
The standard for decades has been to begin teaching high school BC calculus in spring semester of precalculus. That is how honors precalculus was taught in local districts here prior to AP Precalc. Another PP on this thread noted that that is their district's current policy. BC becomes more rushed if you don't since it covers more content than AB. Why slow down honors students in precalculus by having them run regressions? Two thirds of the AP Precalc exam is effectively Algebra 2. Advanced students don't need that much time for Algebra 2 content; they can do a short Algebra 2 review and then move on to vectors and matrices and then on to calculus.[/quote]

It’s clear you don’t know what you’re talking about. Link to some evidence that there are honors precalculus classes that do BC in the second semester. Some course description, a catalogue, a syllabus, anything.

AP precalculus is what the vast majority of precalculus (honors) classes cover. Occasionally you’d see more combinatorics, but it’s a minor thing, and it fits better in Statistics anyway.

It’s just bizarre to complain there not enough calculus in precalculus, one full semester, none the less.[/quote]
Prior to the introduction of AP Precalc, there were many districts that began calculus in spring semester precalculus because they found it maximizes student success in BC.

Loudoun LCPS: https://sites.google.com/lcps.org/lcpsprogramofstudies2023-2024/hs-mathematics-courses
Mathematical Analysis H: (Honors Precalc)  "Mathematical Analysis also includes an introduction to calculus topics including limits and continuity; the derivative of functions of a single variable; the first and second derivative tests; and curve sketching."

Fairfax FCPS 2022: https://westfieldhs.fcps.edu/sites/default/files/media/inline-files/FINAL%20Westfield%20HS%20Course%20Catalog%202021-22%20.pdf  
Precalculus with Trigonometry Honors "The course also includes the study of limits, continuity, maximum and minimum points and values, definition and properties of the derivative, rules of differentiation, equations of tangent lines to polynomial functions, infinite limits, and partial fractions"

Arlington APS old precalc course: https://catalog.apsva.us/sites/default/files/pdf/class/pre-calculus-trigonometry-1115.pdf
Pre-Calculus/Trigonometry  "Other major areas include a study of analytic geometry, parametric equations, polar coordinates, sequences and series, discrete mathematics, vectors, matrices, and an introduction to limits and derivatives."

Charlottesville City  https://s3.amazonaws.com/scschoolfiles/3437/2023-2024_program_of_studies.pdf
Precalculus Honors  "Students study functions, trigonometry, discrete mathematics, data analysis, analytic geometry, limits, and an introduction to calculus"[/quote]

One of the classes isn’t called precalculus, but math analysis. One of them is called “AP Precalculus” so it looks like there’s some freedom to include the extra topics. Another one is not offered anymore etc.

Limits, asymptotes, maxima and minima are part of the precalculus curriculum, although the depth of treatment will vary.

I’ll give you that the derivatives are in calculus, doesn’t really add up to a semester of classes, and I don’t see the point of including it in a precalculus class if the same material is repeated in AP Calculus. It makes more sense to do precalculus specific topics like conics and combinatorics which are missing.

By this logic during the last semester of BC one should start multivariable, then at the end of it, do differential equations etc.[/quote]
Math Analysis is LCPS's honors precalculus course. The name stems from state standards. LCPS also offers AP Precalc but Math Analysis is more rigorous. LCPS is one of the few districts locally to retain an honors MA/precalc option although some students have to access it virtually.

Districts don't repeat the calculus content covered in precalc. Wherever they end in precalc is the jumping off point for BC the following fall. Students have been more successful with spreading BC content over the full year plus part of spring semester precalculus. It makes more sense to spend the extra time going deeper into calculus than treading water in AP Precalc's extended Algebra 2 review. For instance, AP Precalc assumes students have no prior exposure to logs, however, honors students have already covered those in Algebra 2. AP Precalc with Unit Four is a solid precalculus course for many students. However, it falls short of the honors precalculus/math analysis courses that BC-bound students were taking previously.[/quote]

The AP Calculus classes will repeat the material or at least review it because they must conform to the college board guidelines for the class.

I don’t see the benefit of rushing through the curriculum so there’s more time for calculus. A class isn’t honors because you cover material from the one next in sequence like honors precalculus is precalculus + calculus, honors algebra 2 is algebra 2 + Precalculus etc. It should be honors because it goes deeper in the topics compared to the regular class.

AP Precalculus makes the class more uniform across the country, which is welcomed in my view.[/quote]
They're not rushing through the earlier curriculum. Algebra 2 has been combined with Trig for advanced students successfully for many years, which opens up space in precalc to begin calculus. It's only in recent years that math reformers are trying to slow down acceleration, pulling out trig from algebra 2 and now putting students in more heterogenous precalc. Many BC students will use their BC credit to enter multivariable and above in their first year of college; for them, it makes sense to build a strong foundation in calculus. [/quote]

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