Algebra 2 and PreCalc however were very similar for me. If you’re a strong Math student you *might * get away with skipping one.
I agree that a second opinion (perhaps via the SAT subject tests) might be worth doing just to make sure the OP really has covered the math well enough to jump ahead. It makes me sad not to see people take a full year of proof based geometry, but I realize you aren’t going to find that in many high schools these days.
A good geometry book (even though it skimps on proofs) is Harold Jacobs. A review here: http://www.mathmammoth.com/complete/harold_jacobs_geometry.php
It’s very common in our high school for students to take pre-calc in the summer. All of our precalc teachers finish the curriculum before the end of the year. The one my younger son had started teaching Calculus in January!
My son has a friend who “skipped” Geometry and Precalculus. He got the Geometry book in 7th grade while taking Alg 1. He did the work for both classes and too the final for Geometry at the end of the year. I guess they agreed to put his final grade on the transcript, because he is going to UC Berkeley next year.
I think he just skipped Precalc. But Trig identities are covered in Alg II for our HS, and he must have learned the other topics on his own.
I self studied almost all of these, and at a very good district too. Not sure if they’d allow it today.
OP’s post is kind of confusing as he/she said he took Alg 1 and then self studied for a “couple of years”, not months. If he self learned geometry and Alg 2, no reason not jump to Calc. But what grade is he/she in and why were no math classes taken the last few years? Or is this a home schooled kid going to community college or returning to HS?
Many helpful posts here. Now I know what is skippable in the math sequence, none or all depending on one’s situations and ability. But I hope we don’t have pressure locally for my non mathy kid to skip any. I do wonder however if one skips many, does that mean he/she takes college math afterward in a local college or online, e.g., in the case of @HCollegeAlum?
I remember a math teacher said if students want more math they can read Euclid’s Elements, etc. Do students need to skip courses to learn more?
@eiholi Nope, I went through the material on my own. I had taken a short geometry mini-class a year before , but it covered different material
One of my kids skipped Alg 2 as part of significant subject acceleration in elem and middle school. He had extraordinary Alg1 and Geometry teachers (was at a specialized math/science program starting in 6th grade) who went way beyond the usual curriculum. He was fine (and majored in math at a top program). Noone questioned the lack of Alg 2 on his transcript.
My other S had honors Alg1 in a specialized humanities program and was woefully unprepared for Alg 2 at his IB program. Got Jacobs Algebra to help him fill in the gaps, but the experience soured him on math, even though his college board scores indicated he had excellent skills.
The Art of Problem Solving site is a good way to assess one’s knowledge (as opposed to checking off a skills list). We were confident that if S1 had any gaps in his learning, he and his teachers would identify it and address it quickly. But his teachers were amazing and used to kids who learned quickly and deeply. @eiholi, S1’s school offered Differential Equations, Multivariable Calc, calc-based Stat, Linear Algebra and Complex Analysis (proof-based). S was glad not to have to schlep to the flagship for math, though he had friends who did for 300 and 400-level classes. We liked that he could take interesting math courses with students his age.
Proof-based geometry is important as a basis for higher level analysis courses required of math majors. I will say geometry is also very handy for quilters!
If I understand this correctly, the OP has taken a placement test at a local college, and placed out of their algebra course into precalculus, and the OP’s high school wants to recognize this exam and place him/her in its own precalculus course?
I have a number of concerns about this. First is the question of what courses the community college may or may not have between algebra and precalculus, i.e., there may be none. College curricula at the pre-calc level are typically designed to be remedial, with the goal being to prepare students for calculus (and/or their respective majors) as quickly and efficiently as possible. A reasonably solid background in high school mathematics is usually presumed, so an average student who does reasonably well with basic algebra will often be seen as “ready” for precalculus.
Indeed, if the goal is to get to calculus as quickly as possible, and one believes that purpose of a mathematics course is to fill one’s head with “facts,” then pretty much any course in the high school curriculum can be covered in a few months of “systematic self-study.” If, on the other hand, one wants to truly learn a subject, then it’s better to have as rich as possible an experience with it, which includes developing an ability to talk about it fluently with one’s peers. Several have suggested enriching your study with something like Art of Problem Solving, rather than racing through the curriculum – I think this is a great idea.
On that note, I simply do not understand this need to accelerate, particularly with wonderful resources like AoPS available. Having taught many students at the college level who raced through high school math, I can say that accelerating their curriculum was appropriate for vanishingly few of them (maybe a handful in decades of teaching). Many of them (and this is at an elite liberal arts college) barely even understand fractions and decimals, let alone trigonometry, so they would have been much better served by a deeper understanding of the basics rather than acceleration for its own sake (or, worse, for college admissions’ sake).
Although I have “Liked” mathprofdad’s post just above, I do have some reservations about it, depending on how math is taught in the local school and what alternatives might be available.
I am sure that there are other contributors to CC who have witnessed a surfeit of art projects, posters, and construction projects in their children’s math classes. I think art is enriching and worth studying and practicing in itself; but I became rather tired of art requirements distributed across the curriculum. Great for a student who enjoys art projects and is good at it–but time-consuming and peripheral to the understanding of mathematics for a student who understands math easily.
Also, many high schools have eliminated proof-based geometry from the curriculum, on the grounds that it is too difficult for students to grasp. Back when I was in high school, I think virtually all geometry courses were proof-based.
AoPS is a great resource. I am not sure how its learning experience runs for a student who would like to supplement non-proof high school geometry with proof-based geometry, and does not have a math prof dad. Does anyone have experience with that?
An interested parent can help - the socratic nature of the lesson problems easily lends itself to parent and student working through the problems together, in my opinion, even if the parent doesn’t know any more than the student about what to do next. Plus, the lesson problem solutions are immediately available if parent and student are stuck.
The text might be difficult to use as a supplement. It would probably be easier to work through the text sequentially on a schedule independent of what is happening at school.
Alcumus is a great, free resource as well, a logistically easy way to add problem solving, although that may not help with learning to write proofs. A student would get better feedback on proof writing by taking the online course although it is quite challenging.
S1 went to HCSSiM one summer, which was all about deriving proofs. They used the IBL method, which his college also used in analysis and advanced algebra courses. There are a number of other summer math programs (most pricier than HCSSiM and Mathily), some of which focus on the math competitions, others which dive deep and do interesting stuff. S was not into the math competitions, preferring the CS ones instead. One of his HS math teachers (MV and Complex Analysis) assigned homework that came from UMich, Dartmouth, UMD and other top schools (alums would return and give him interesting materials). We could see the school’s name and course number on the assignment. Stat was the AP Stat curriculum plus a lot of other topics, calc-based and taught in one semester.
This was a public selective admit STEM program with extraordinary results over decades. The neighborhood HS didn’t offer this kind of stuff. We were beyond fortunate to have had that kind of opportunity available for him.
We liked Jacob’s Algebra and Geometry books as a good supplement for filling S2’s gaps. The geometry book does a lot of proof work, IIRC. The Algebra book was an Alg I text back in he good old days; we got a LOT of use out of it when S2, like many of his classmates, discovered they didn’t have a good foundation in Alg 1. In our experience, in the rush to accelerate kids into Algebra early, the course was heavily watered down. It came back to bite them in Alg II/Functions. We heard it from both kids’ teachers.
If the OP is looking at majoring in math, he would be FAR better served to go deep and not rush. A lot of math majors switch majors when the going gets theoretical and proof-driven.
That’s indeed a good program and I wish we had it here. On the other hand, I like the low pressure in my area (Midwest) where middle school kids can still goof around in the summer. It seems we aren’t worse off college admissions wise (on test scores wise) than on either coasts.
Resources are abundant nowadays. But I too would like to hear their outside of school enrichment experience, especially without much time commitment. It feels weird kids aren’t challenged enough at school and need to waste their out of school time learning. But where we live is where we live (glad not on the coasts).
My D does AoPS at home by herself, with a single mom that does not know anything about math. She is S L O W with it, but only does it for her personal desire. No math competition. She does what she is interested in. She did not care to do the geometry. No interest in advancing in math at school. Our school is low pressure regular high school in West Texas.
My S didn’t do AoPS or summer enrichment (except one summer at HCSSiM). He spent his free time programming and teaching himself interesting stuff. Because the public magnet programs offered such good opportunities, there was no pressure for us to find ways to challenge him (like CTY, Davidson, and other math programs). We didn’t bother.
OTOH, it can be hard to live in an academic hothouse. One of my kids ignored the pressure; the other felt like he could never live up to it. My nieces and nephews who live in other parts of the country envied the programs, but were largely unburdened by the academic arms race. That has real value, too.