Math sequences for college-bound AL?

[Brittany1116]

My 10 year old is about 1/4 way through Saxon Algebra 1. He will likely be in a STEM field, probably engineering. What is a good plan for math from now til graduation? After Algebra and Geometry, I will be outsourcing teaching. 

[Dmmetler]

Mine was in a similar position. We moved to AoPS at Pre algebra. (Books and at home. DH has a graduate degree in math and I’m certified as a math teacher, so we felt fairly confident, and my kids has never liked online math). We did AoPS through Pre-cal and then moved to college math classes. Mine is majoring in bio, so we focused on the math needed there, through Calculus and statistics. All told, my kid graduated at 16 with 8 post Algebra 1 math classes.

[Slache]

My plan is what Dmmetler did. It's really what makes the most sense to me.

[wendyroo]

I was/am very wary of what (AOPS's) Richard Rusczyk calls The Calculus Trap, so we are going deep and wide rather than all steam ahead plowing through the typical sequence.

My oldest was ready for prealgebra in 4th (having finished Math Mammoth and Hands on Equations including the fantastic word problem book), so did Zaccaro's Becoming a Problem Solving Genius and then AOPS prealgebra (I will not use this with younger children).

Next, in 5th, he did Zaccaro's Real World Algebra, and then AOPS Algebra (I will not use this with younger children) and a mix of other resources such as Zaccaro's 25 Real Life Math Investigations That Will Astound Teachers and Students, Make it Real Learning Activities (available on the Math Mammoth site) and University of Waterloo math circle materials.

In 6th he did James Tanton's Great Course: The Power of Mathematical Visualization (We both LOVED this). He liked James Tanton so much, that I used his Geometry Great Course plus AOPS Alcumus to get DS through geometry which he is not a huge fan of. Also during that year he did AOPS Intro to Counting and Probability (just the book, not the class) and more University of Waterloo math circle investigations.

This year he is in 7th and is doing Algebra 2 using the Foerster book. Plus more University of Waterloo and lots of independent study with Numberphile, Veritasium, and Vi Hart math videos.

Next year is Precalc...probably. He is deciding between using Foerster on our own again, Math without Borders or Derek Owens.
- Or, he could do AOPS Intermediate Counting & Probability and/or Number Theory. He is not a huge AOPS fan, so I doubt he will choose this option.
- Alternatively, he could stay busy with Great Courses like Magic Numbers: Hannah Fry's Mysterious World of Maths, The Secret Life of Chaos, Mathematical Brain Teasers and Logic Puzzles, Prove It: The Art of Mathematical Argument, Mind-Bending Math: Riddles and Paradoxes, etc. If he chooses this path, I will have him also work on Alcumus weekly to keep his skills sharp.

Once he is ready for Calculus, we might start dual enrollment classes, but we also might use MIT OCW classes. MIT is my alma mater, so even if I don't remember everything, I can pull out my old notes and give him any help he might need.

[daijobu]

To keep his skills fresh I might supplement with some math contests either for real if he enjoys that sort of thing, or just at home just for practice.   He might enjoy doing old MathCounts, AMC and Math Kangaroo.  You can find  old exams for free on the AoPS website, or for sale at the contest websites.   

[Brittany1116]

Thank you all for replies. This is a great springboard because he is my first child and I haven't made any plans yet beyond middle school. I know nothing of advanced mathematics, and very little about my options aside from the few curricula we have used so far. He doesn't love math but he excels at it and will need it. 

[8filltheheart]

I have a 26 yos who was similar. He completed MUS alg and geometry at 10. His sequence was to follow that with

• Foerster's alg 1 ((way more complex problems than MUS)
• Geometry (Alexander and Koeberlein)
• Foerster's alg 2/trig and AoPS Intro to Counting and Probability 
• AoPS intermediate alg
• AoPS precal
• AoPS cal

After he took the AP cal BC exam, he dual enrolled  at a 4 yr U for

• multivariable cal
• DiffEQ
• linear alg
• DiffEQ 2

He decided he loved physics more than math. He ended up DEing for

• university physics 1&2
• physical mechanics 1&2
• modern physics.

My current 6th grader is about 3/4 of the way through Foerster's after completing MUS alg and geo last yr. I have no clue whether she will want to pursue math like her brother. They have a sister who was at a similar place but stopped a cal 1. She loved languages and literature and that became her focus. (She ended up with degrees in Russian and French and is currently working on her master's in library and information sciences.)  Only she will decide.

Edited February 14, 2022 by 8filltheheart

[SeaConquest]

My oldest has done:

Math Mammoth (too many problems)

Singapore Intensive Practice and Challenging Word Problems (better than MM for him)

Beast Academy (starting at book 3 when they came out -- he did books 3 and 4 with me, then went to AoPS Academy for BA 5)

AoPS Pre-A at the Academy

AoPS Algebra I with part of Intro CP at the Academy

AoPS Intro NT (online)

AoPS Geometry (online)

AoPS Intermediate Algebra (online)

AoPS Pre-Calculus (online) -- current course

Going forward, his path is likely to be something like this:

8th SOHS Single Variable Calculus

9th SOHS Multi Variable Calculus

10th SOHS Linear Algebra & Differential Equations

11th SOHS Modern Algebra & Real Analysis

12th SOHS Discrete Math & Complex Analysis

My youngest did Singapore and then went into Beast with their 2nd grade books. 

[SDMomof3]

My ds14 is similar to your dc. He excels at math, but not passionate about it. His passion is computer science. Here are the classes he has taken 

AoPS Intro to Number Theory

AoPS Algebra

AoPS Intro to counting and Probability 

AoPS geometry

AoPS intermediate algebra

AoPS intermediate counting and Probability 

AoPS PreCalc 

AoPS intermediate number theory

AoPS calculus 

He is dual enrolled taking calculus 3 and Linear Algebra this year. He will take calculus multi variable and vector calculus and finish lower division math in 9th grade.

For 10-12 grades, he will take upper division applied mathematics required for Computer Science and Engineering classes like calculus-base probability and Statistics, applied Linear Algebra, discrete math and graph theory.

 

Edited February 17, 2022 by SDMomof3

[Shoes+Ships+SealingWax]

I have a few different paths sketched out for DS9, depending upon whether or not he becomes interested in UNT’s summer or residential programs. Unless he decides to double-up we shouldn’t “run out” of AOPS before he graduates. 

Option 1

• AOPS PreA 
• AOPS Intro to Algebra
• AOPS Intro to CP & Intro to NT
• AOPS Intro Geometry 
• AOPS Inter Algebra 
• AOPS Inter CP & Inter NT
• AOPS PreCal
• AOPS Calculus

Option 2

• AOPS PreA 
• AOPS Intro to Algebra
• AOPS Intro CP & Intro Number Theory (Summer: SMI Algebra)
• AOPS Inter Algebra (Summer: SMI Algebra 2)
• AOPS Intro Geometry (Summer: SMI Geometry)
• AOPS PreCal (Summer: SMI PreCal)
• AOPS Inter CP or Inter NT
• AOPS Calculus 

Option 3

• AOPS PreA 
• AOPS Intro to Algebra (Summer: SMI Algebra)
• AOPS Intro Geometry (Summer: SMI Geometry)
• AOPS Inter Algebra (Summer: SMI Algebra 2)
• AOPS PreCal (Summer: SMI PreCal)
• AOPS Calculus 
• UNT TAMS 
• UNT TAMS 

Edited February 15, 2022 by Shoes+Ships+SealingWax

[wendyroo]

12 minutes ago, Shoes+Ships+SealingWax said:

I have a few different paths sketched out for DS9, depending upon whether or not he becomes interested in UNT’s summer or residential programs. Unless he decides to double-up we shouldn’t “run out” of AOPS before he graduates. 

Option 1

• AOPS PreA 
• AOPS Intro to Algebra
• AOPS Intro to CP & Intro to NT
• AOPS Intro Geometry 
• AOPS Inter Algebra 
• AOPS Inter CP & Inter NT
• AOPS PreCal
• AOPS Calculus

Option 2

• AOPS PreA 
• AOPS Intro to Algebra
• AOPS Intro CP & Intro Number Theory (Summer: SMI Algebra)
• AOPS Inter Algebra (Summer: SMI Algebra 2)
• AOPS Intro Geometry (Summer: SMI Geometry)
• AOPS PreCal (Summer: SMI PreCal)
• AOPS Inter CP or Inter NT
• AOPS Calculus 

Option 3

• AOPS PreA 
• AOPS Intro to Algebra (Summer: SMI Algebra)
• AOPS Intro Geometry (Summer: SMI Geometry)
• AOPS Inter Algebra (Summer: SMI Algebra 2)
• AOPS PreCal (Summer: SMI PreCal)
• AOPS Calculus 
• UNT TAMS 
• UNT TAMS 

Something to be aware of...sometimes AOPS just really isn't a good fit even for a really mathy kid.

If you search the boards you can find a number of kids that were very gifted and accelerated math students who could not stand AOPS books or classes.

My oldest would fit into this category. He did AOPS Prealgebra and part of Algebra (just with the books), but he hated them, he didn't learn from them, and they almost killed his love of math. I have never signed him up for the classes because 1) they are only offered at one time (mostly) and it would never work for him and 2) I don't like they they move so, so quickly and skip so much of the content in the books.

I had always planned to use AOPS for most of his math journey, and I ended up scrambling to come up with different plans.

[Shoes+Ships+SealingWax]

46 minutes ago, wendyroo said:

Something to be aware of...sometimes AOPS just really isn't a good fit even for a really mathy kid.

Oh, absolutely! I have a list of back-up curricula to try if AOPS stops suiting him at one point or another, but these are Plans A-C 😅

[SoCal_Bear]

We use AOPS but we don't use it via the online text based courses. Not my son's cup of tea. He likes live with interactive with video. Anyways, we opted for WTMA AOPS classes. They don't move as fast. I'm ok with it not being as deep because we do other math over the summer plus he is part of the local math circle which does a lot of competition math. He will do AOPS Pre-Calc this fall. I don't need math to be so compressed and take up as much time because his others that have a heavy work load. Science takes up a lot more time than math because of his involvement with Science Olympiad. Plus we need time for Latin and Chinese.

[Brittany1116]

@wendyroo when you say you will not use AOPS alg etc with younger kids, are you saying just because of your younger kids' needs or that there is something about it that doesn't mesh with kids of a certain age? 

Full disclosure, I was a big fish in a small pond. Got the top grade in every class for all of middle and high but math was not my forte. I did 2 years of Alg in HS and a year of Geo, then college algebra. Somehow always made an A but I was no math prodigy. I literally do not know what many of these math course terms are.

This kid understands things so easily. I rarely have to explain concepts. He just keeps trucking along. 

I read the 2014 thread about mixing Saxon and AOPS. I see the consensus is to nix Sax and adopt AOPS, but... the videos seem like they could easily be added to our Saxon lessons to round out the learning. Plus, the whole *insert man into teacher role somewhere because preteen boys* thing helps. 

Edited February 16, 2022 by Brittany1116

[wendyroo]

7 hours ago, Brittany1116 said:

@wendyroo when you say you will not use AOPS alg etc with younger kids, are you saying just because of your younger kids' needs or that there is something about it that doesn't mesh with kids of a certain age? 

Full disclosure, I was a big fish in a small pond. Got the top grade in every class for all of middle and high but math was not my forte. I did 2 years of Alg in HS and a year of Geo, then college algebra. Somehow always made an A but I was no math prodigy. I literally do not know what many of these math course terms are.

This kid understands things so easily. I rarely have to explain concepts. He just keeps trucking along. 

I read the 2014 thread about mixing Saxon and AOPS. I see the consensus is to nix Sax and adopt AOPS, but... the videos seem like they could easily be added to our Saxon lessons to round out the learning. Plus, the whole *insert man into teacher role somewhere because preteen boys* thing helps. 

I am not completely ruling out AOPS books for my younger kids...but I am going into that stage with a much clearer understanding that AOPS materials really aren't the right fit for all mathy kids.

My oldest went into AOPS Prealgebra with a thorough understanding of prealgebra already (having done Math Mammoth 7 which is their prealgebra level, plus Hands on Equations and Zaccaro's Real World Algebra). There was almost no new math in AOPS Prealgebra for him to learn, which in hindsight was really good, because he learns almost nothing from AOPS books.

For him, it is really a mismatch with how AOPS teaches...or doesn't teach. It is supposed to be discovery learning, and kids are pretty much left to their own devices. This is what I wrote in a previous thread about DS working in an AOPS book:

Quote

 

He starts by reading the teaching at the beginning of a section...except that many of the sections don't have any teaching at all. Then he works the problems. One of his downfalls is that if he gets the problems correct he is very resistant to reading the solutions, but I think reading the book's solutions would be very helpful to him. OTOH, the book's solutions look dense and overwhelming with a lot of text for him to slog through (language is not his strong suit), and even I often find them very confusing, so I understand why he shies away from them.

Then he moves on to the exercises. He gets about the first half correct and the second half wrong. But, we've experimented, and if I have him do the exercises before reading the teaching or working the problems, he still gets about the first half correct and the second half wrong...so that is all knowledge he came in with, and AOPS hasn't really taught him anything he did not already know.

He reworks the exercises he got wrong. He gets a few more of them correct. For any that are still incorrect, I look in the solution manual to see if I can pinpoint what might be leading him astray. It is incredibly difficult for me to guide him because there is very little instruction I can have him re-read and I never know which of the example problems might be of help to him for any particular exercise. So we often spend a while searching YouTube and google for any tutorials or worked examples that might help (completely defeating the discovery method and a very inefficient way to cobble together instruction). Eventually we give up on the last couple problems and read the solution manual...which sometimes prompts a eureka moment, but sometimes still leaves us baffled.

I am very much looking forward to next year. Algebra 2 is in my mathematical wheelhouse (more so that C&P which I never took), and Foerster will actually teach Peter the concepts he needs to know and then build up his skills with challenging problems that require him to use the concepts in unique, non-formulaic ways.

 

And another thread:

Quote

 

What I sense is that AOPS is teaching him to beat his head against the wall, give a sigh of relief when he finally accidentally hits the magic brick that unlocks the right answer, and then give a sigh of frustration because he still has no clue why that is the right answer and therefore knows that the next problem and the next and all the rest of them are going to be just as incomprehensible. There never is an "aha" moment, but rather just a "thank God that one is over" moment before despairing starting up the next one.

Realistically, the AOPS book taught him very, very little. So, the problems that he already knew how to do, or that were just a baby step of challenge above what he could already do, were great. But lacking any meaningful instruction (at least in any form that he could connect with), the more difficult problems were just torture that he "got through" with little understanding or growth.

 

And another:

Quote

That seems to be the theme of the AOPS books (or at least how Peter perceives it):
      Here are a bunch of hard problems which you will either intuitively understand and be able to solve, or not. It not, we will show off our slick way of solving them, not so much to gradually building up your skills and intuition, but more to prove that we are smarter than you.

Peter made it through Prealgebra in about 18 months (from 8 years old to 9.5), and at the time I felt it was painful but also somewhat worthwhile in that it did really help him learn to work from a textbook and gradually how to show his work. BUT, that was because he wasn't actually having to learn any new math at the time. We bailed half-way through the Algebra book because he wasn't learning algebra from it. Then we tried one more time a couple years later because he wanted to learn counting and probability and there were not many good resources available. But this is what I wrote after that venture:

Quote

 

Peter did work through AOPS Counting and Probability this past year. And I think it was good conceptual material that isn't often covered at this level.

OTOH, he hated it. He LOVES math; he thinks and breathes and adores math, and yet he dreaded that AOPS book. And now he says that math is "bland" and "confusing". When I asked him what additional subject he wanted to add to his schedule this week (we are ramping up to the full fall lineup), he chose history over math. Huh? He hates history and has almost always delighted in the whole plethora of math resources we have used.

The last time he was down in the dumps about math was when he finished AOPS pre-algebra and started AOPS algebra. It got so severe then that I switched him to a different algebra. This time, though, we soldiered on because there wasn't another good C&P resource. But I'm not sure I made the right choice. He is just so turned off and disheartened by math right now, and I lay most of the blame on the AOPS style of textbook.

I do think they are a good repository of problems, but I can just use Alcumus for that. That is what we did for Geometry. I chose a couple strong, interesting, conceptual, but straight-forward, explicitly taught geometry resources. Throughout the year I also had him work through the Alcumus geometry sections to ensure that he was tackling more challenging, rigorous problems that forced him to integrate concepts and think outside the box.

 

This year he has worked through Foerster Algebra 2 with trig...and, no, it is probably not quite as rigorous was AOPS, but Peter is back to enjoying and being confident about math. He is back to playing with math for fun. That is worth a lot to me. So from now on we will only do AOPS books at his request and even then I will proactively pair them with other, more traditional books/resources on the subject that can actually teach Peter the material.

[prairiewindmomma]

My oldest absolutely despised AOPS. I've talked about it a bit on the boards.

He decided to go the Calc route because that was his jam--the usual sequence up including advanced multivariable calculus, vector calculus,  applied linear algebra, etc. I think he did rings & fields & discrete stuff somewhere in the mix.  He officially graduated high school after vector calculus and linear algebra I think. I can't remember because my teaching and grading work ended after Calculus 2. I made a conscious decision to step back and just let him thumb the university coursework catalog and pick what appealed to him. I let him play and explore without having him really plan for a graduation sequence in a major while he was in high school. It was still cheaper than private school tuition and way more rewarding for him. 

 

[Brittany1116]

Sounds like AOPS is love it or hate it. Is everyone hating it for the same reasons? I looked up the sample pages from PA and Alg, watched some videos. It doesn't look wildly different at those levels from Saxon A1 except that Saxon has far more practice questions. I wonder what I am missing. I think I am getting a bit of FOMO just from seeing AOPS so widely recommended. 

[Brittany1116]

When I say I don't understand terms, I mean Number Theory and Discrete Math etc. I never went past basic 3 courses so I have no clue what any of those mean or what is a reasonable order.

[daijobu]

40 minutes ago, Brittany1116 said:

Sounds like AOPS is love it or hate it. Is everyone hating it for the same reasons? I looked up the sample pages from PA and Alg, watched some videos. It doesn't look wildly different at those levels from Saxon A1 except that Saxon has far more practice questions. I wonder what I am missing. I think I am getting a bit of FOMO just from seeing AOPS so widely recommended. 

 

Generally the problem sets are shorter, but more challenging.  You may start with some basic problems, but then they are throwing stuff at the student from left field, and they must solve using the material from the chapter, but in a novel situation.  Many of the problems are lifted directly from math contests. 

 

[wendyroo]

42 minutes ago, Brittany1116 said:

Sounds like AOPS is love it or hate it. Is everyone hating it for the same reasons? I looked up the sample pages from PA and Alg, watched some videos. It doesn't look wildly different at those levels from Saxon A1 except that Saxon has far more practice questions. I wonder what I am missing. I think I am getting a bit of FOMO just from seeing AOPS so widely recommended. 

I've never used Saxon, so I looked up a sample.

Then I looked up a sample of the AOPS Algebra book.

The biggest difference is that in the Saxon sample, pages 4 and 5 (labeled textbook pages 239-240) are teaching the student how to do a certain type of problem. And then there are exercises that test if the student can solve the type of problems they were just taught to solve (and obviously a lot of review since that is Saxon's jam).

In the AOPS sample, the entire teaching portion of the section is "We’ve seen thus far that solving basic problems involving functions is typically a matter of substitution and solving equations. The same is true as the problems get more challenging." That's it. And then they set you loose to solve problems that you have never been taught to solve.

For some kids, this approach will work well. They will struggle with the problems, either solve them or not, not get disheartened, read through the solutions, learn something new, and then lather, rinse, and repeat through the rest of the problems. Then they will move on to the exercises...but realize that even those won't really look like the previous problems. They will all be novel and ask the student to apply the new information (that they may or may not have learned through discovery by doing the previous problems) in unique ways that they may have never seen before.

Plus, realistically, AOPS is much, much harder than Saxon. I have two engineering degrees from MIT. Nothing in the Saxon sample even made me think twice; all of the problems are incredibly straight-forward. There were many, many problems in the AOPS Prealgebra that I had to think deeply about and actually put work into because they are approaching "easy" prealgebra concepts in very unique, convoluted ways.

[Brittany1116]

Thank you. I suppose the AOPS looked pretty similiar because the portions I saw are basically the same exact work we are doing now. Maybe my brain jumped from contrast mode to comparison mode. 

[Shoes+Ships+SealingWax]

4 hours ago, wendyroo said:

I have two engineering degrees from MIT. Nothing in the Saxon sample even made me think twice; all of the problems are incredibly straight-forward. There were many, many problems in the AOPS Prealgebra that I had to think deeply about and actually put work into…

This makes me feel much better about working ahead of DS in PreA & having the occasional “Crap - I thought I was good at this stuff! 😬” moment! Lol

[SeaConquest]

Wendy,

Having not worked through the AoPS courses (beyond Beast) with Sacha, I really appreciate you taking the time to explain all of this. I like to think of myself as fairly good at math, but I know that there is no way that I would be able to learn math in the way that you explained it here. I would love to work on AoPS problems, because I enjoy challenging problems, but to *learn* the math from the outset this way, without the benefit of a live teacher to walk me through it? Yeah, no. I can really see now why even some very mathy kids would struggle with this method and why Sacha is now asking me for more explicit (and live) instruction. I can also see why this method may also be a very poor fit for my younger DS, who while very good at math, struggles with frustration tolerance, anxiety, perfectionism, and confidence issues that older DS doesn't. So again, thank you. This is very very helpful.

Not to completely change the subject, but does anyone have a rigorous book or videos they recommend to go along with AoPS pre-calculus that has more explicit instruction? I think Sacha could benefit from some supplemental materials and practice.  I might cross-post this on the high school board as well. Thanks in advance. 

Edited February 17, 2022 by SeaConquest

[wendyroo]

1 hour ago, SeaConquest said:

Wendy,

Having not worked through the AoPS courses (beyond Beast) with Sacha, I really appreciate you taking the time to explain all of this. I like to think of myself as fairly good at math, but I know that there is no way that I would be able to learn math in the way that you explained it here. I would love to work on AoPS problems, because I enjoy challenging problems, but to *learn* the math from the outset this way, without the benefit of a live teacher to walk me through it? Yeah, no. I can really see now why even some very mathy kids would struggle with this method and why Sacha is now asking me for more explicit (and live) instruction. I can also see why this method may also be a very poor fit for my younger DS, who while very good at math, struggles with frustration tolerance, anxiety, perfectionism, and confidence issues that older DS doesn't. So again, thank you. This is very very helpful.

Not to completely change the subject, but does anyone have a rigorous book or videos they recommend to go along with AoPS pre-calculus that has more explicit instruction? I think Sacha could benefit from some supplemental materials and practice.  I might cross-post this on the high school board as well. Thanks in advance. 

We have liked ProfRobBob videos. We haven't watched PreCalc (that is what Peter is doing next year), but Peter has watched some of his Algebra 2 videos when he needed clarification on a topic.

I've also really liked Foerster's Algebra 2 book, so I will be purchasing his PreCalc text for next year even if that doesn't end up being Peter's math spine.

There is also a Great Courses series called Mathematics Describing the Real World: Precalculus and Trigonometry. It doesn't look awe-inspiring or particularly rigorous, but the lectures I have previewed seem clear, straightforward, understandable, and well-illustrated. The instructor did not keep me on the edge of my seat or anything, but he also didn't put me to sleep. There are small sets of problems (with solutions) in the course guide, but they look to just check for basic understanding.

[daijobu]

9 hours ago, SeaConquest said:

 

Not to completely change the subject, but does anyone have a rigorous book or videos they recommend to go along with AoPS pre-calculus that has more explicit instruction? I think Sacha could benefit from some supplemental materials and practice.  I might cross-post this on the high school board as well. Thanks in advance. 

3blue1brown has a series of excellent videos about vectors and matrices that I have my AoPS precalculus students watch.