AOPS and LOF together?

[abba12]

As you can tell by my signature, I am no where even close to needing this stuff yet, however I LOVE researching these things, and I have a friend who is interested in self-teaching some higher math, so I wanted to make some recommendations.I am also interested for myself, going back over some higher level work.

 

I have loved Life of Fred since I discovered it 5 years ago, and wished I was taught with it. I love the concept and I do think it  could be used as a stand alone curriculum, however, I know one of the biggest problems people have with it is a lack of thorough explanation for struggling students and a lack of practice questions.

 

I have just recently discovered Art of Problem Solving and it looks fabulous, now I can't decide whether I wish I was taught with LOF or AOPS :) I LOVE the idea of walking through a problem you couldn't solve as a way of teaching, as opposed to trying to understand a meaningless formula and then apply it.

 

I got to thinking, would LOF and AOPS complement each other for a complete, thorough high school math education? I see flaws in both systems, as there is in any, but it looks as if they both seem to address what the other lacks, and in less time than a normal math curriculum, since they limit their practice problems and use alternative teaching methods.

 

But would there be too much overlap? I hate busywork, I see no reason to spend an hour on math when I only need to spend a half hour and would hate to do the same thing twice by using two 'complete' curriculum, even though both are listed as being used commonly as supplements. 

 

So, does anyone do this? Would it be redundant, or a great 'alternative' math course?

[JanetC]

First, my biases: I have one kid doing LOF and one doing AOPS right now, and my philosophy on curriculum is "less is more."

 

My LOF kid loves the stories and playfulness of LOF. My AOPS kid thinks that stuff gets in the way of the math. My LOF kid likes "warm fuzzies". My AOPS kid enjoys challenges and acceots that when she has to bang her head against the wall a few times it really sinks in. I bought AOPS first, for the older one who is now in LOF. It did not work for her at all. When it didn't work out, I thought about selling it, but it was sitting on my bookshelf when the younger one finished prealgebra early and needed something to fill out the rest of the school year. She was hooked, in a where-has-this-been-all-my-life sort of way.

 

If you attempt to do both of these at once, you may find that your student find your student loves one and hates the other, because the approaches are night and day. These particular books are going to be hard to correlate because they both are written for the chapters to be done in order, not to be skipped around.

 

And, yes, whenever you do two whole textbooks, it's redundant. I definitely believe that "less is more." When you do need a supplement, just get a drill book (I used Aplus math by Rong Yang since I had it on the shelf, but for LOF Algebra, there is the Zillions of problems book). Don't start a whole new textbook.

 

With quirky texts like these, it's best to try them with your DC to see how they work. For either LOF or AOPS, it's only going to work if the approach fits the kid. Because of AOPS reputation as "the very best", some parents maybe try to force a square peg into a round hole a bit harder than they should.

[regentrude]

I have been using AoPS from Intro to Algebra through Calculus, for grades ranging from 6th through 11th. It is a stand-alone curriculum and more than sufficient for a high school math education; it covers more material and in more depth than any other curriculum. For a student for whom AoPS is a good fit, I see no need to add anything else: the student will already spend more time on math than with another curriculum, and further additions would be busy work.

For a student for whom AoPS is not a good fit, LOF may be a great resource. But I see no benefit in piling yet another math curriculum on a student who is already going above and beyond by using AoPS.

 

 

 

I got to thinking, would LOF and AOPS complement each other for a complete, thorough high school math education? I see flaws in both systems, as there is in any, but it looks as if they both seem to address what the other lacks, and in less time than a normal math curriculum, since they limit their practice problems and use alternative teaching methods.

 

Huh? AoPS most definitely does not take less time than another curriculum. If anything, it takes more time, because it covers more material and the problems are a lot harder. It is geared towards students who are strong in math and who would not be adequately challenged with a traditional curriculum. The amount of practice problems is not "limited"; there is plenty of practice for mastery, as much as needed for a student from the target audience (gifted math students, who do not need the drill&kill other curricula may contain). Spending less time is a complete illusion. There are practice problems that take 30-60 minutes for one problem because the student has to THINK.

 

I have trouble understanding why you would think AoPS is not "complete" and would need supplementing.

[Julie of KY]

AoPS is a complete curriculum. I'm not sure of anyone that calls any of their books a supplement. Kids that do well with AoPS don't need the extra practice of LOF - they might like the storyline, but AoPS already goes farther and deeper than LOF. While AoPS has fewer total problems, they take much more time to solve and generally more time is spent in an AoPS text compared to a standard text of the same subject.

[Sebastian (a lady)]

AoPS is a complete curriculum. I'm not sure of anyone that calls any of their books a supplement. Kids that do well with AoPS don't need the extra practice of LOF - they might like the storyline, but AoPS already goes farther and deeper than LOF. While AoPS has fewer total problems, they take much more time to solve and generally more time is spent in an AoPS text compared to a standard text of the same subject.

 

I could see possibly using the Art of Problem Solving, Vol. 1 - The Basics or Vol. 2 - Beyond as supplements to another curriculum.  Or using Alcumus problems as an expansion of another curriculum. 

 

As others have pointed out, the small number of problems in each section don't correspond to a smaller amount of time spent on math.  I did on occasion revert to an old Dolciani algebra text when I felt that my kids hadn't really understood or mastered a concept.  So for example, when I saw that they were struggling with quadratics in AoPS, we went back and spent a couple weeks reviewing polynomial multiplication from several angles.  But I think just doubling up on curriculum across the board is probably going to frustrate more than help.

[Sebastian (a lady)]

As you can tell by my signature, I am no where even close to needing this stuff yet, however I LOVE researching these things, and I have a friend who is interested in self-teaching some higher math, so I wanted to make some recommendations.I am also interested for myself, going back over some higher level work.

 

I have loved Life of Fred since I discovered it 5 years ago, and wished I was taught with it. I love the concept and I do think it  could be used as a stand alone curriculum, however, I know one of the biggest problems people have with it is a lack of thorough explanation for struggling students and a lack of practice questions.

 

I have just recently discovered Art of Problem Solving and it looks fabulous, now I can't decide whether I wish I was taught with LOF or AOPS :) I LOVE the idea of walking through a problem you couldn't solve as a way of teaching, as opposed to trying to understand a meaningless formula and then apply it.

 

I got to thinking, would LOF and AOPS complement each other for a complete, thorough high school math education? I see flaws in both systems, as there is in any, but it looks as if they both seem to address what the other lacks, and in less time than a normal math curriculum, since they limit their practice problems and use alternative teaching methods.

 

But would there be too much overlap? I hate busywork, I see no reason to spend an hour on math when I only need to spend a half hour and would hate to do the same thing twice by using two 'complete' curriculum, even though both are listed as being used commonly as supplements. 

 

So, does anyone do this? Would it be redundant, or a great 'alternative' math course?

 

BTW, I would very much endorse the possibility of working through AoPS yourself.  I learned more about how algebra worked by going through the chapters ahead of my kids than I had in all of high school and college math.

[abba12]

Thanks! I saw the lack of drill and kill and automatically assumed it would be quicker to complete. I was quite mathy in school, however, due to certain circumstances (I said I was a homeschooler, I never said my mum was a good homeschool teacher) I never went past geometry.  

 

Damn, so now I have to choose between two great curriculum. Well at least I have a while to figure out their learning styles! I'm just not sure which one to recommend to my friend or for myself. Being in Australia, it isn't as simple to buy one, and then sell it and buy the other if it doesn't work. I always feel like I/my DC will miss out on something if I have to pick one over the other, because they're both wonderful.

[regentrude]

Damn, so now I have to choose between two great curriculum. Well at least I have a while to figure out their learning styles! I'm just not sure which one to recommend to my friend or for myself. Being in Australia, it isn't as simple to buy one, and then sell it and buy the other if it doesn't work. I always feel like I/my DC will miss out on something if I have to pick one over the other, because they're both wonderful.

 

I think it will very likely be that only one of them is a good fit for a particular child, because they are extremely different. You will see how your kids develop, and it should be rather obvious which will fit (if any!).

 

I have chosen AoPS and never looked back. I want this level of conceptual depth and challenging problems and the style of explanations. My kids prefer the math plain and simple and find it intrinsically interesting and fun, without the need for a cutesy story and pictures.  LOF would drive them nuts, and I do not think they miss out on anything.

For different kids, AoPS might be a disaster, and they might love to have their math wrapped in the LOF story.

 

For your friend:

AoPS is discovery based: the student is presented with problems to solve first, and the new concept, which he should discover while he is solving the problems, is discussed afterwards. If your friend does well with such an approach and is willing to spend time on puzzling over difficult problems and genuinely enjoys math, AoPS is  a good fit. OTOH, if your friend prefers direct instruction and is not interested in delving this deeply into the concepts, AoPS is not suitable.

Look at the previews on the website; they have sample chapters.

[Dmmetler]

My DD did LOF Pre-algebra last year, and we're going to try AOPS Pre-A as our primary math, with LOF for "fun reading" This year. She loves Fred, but she's also very into contest math, and I believe she will do well with AOPS, so I'm hoping that giving her the freedom to work through LOF on her own along with the fun, tough problems of AOPS will be a good fit for her, either simultaneously ( and not worrying about completing an AOPS book in a year) or alternating. If she were a high school student, I would make her go with one or the other, but since she's very accelerated in math, slowing down and doing multiple programs isn't a bad thing for her IMO, and I like the idea of having the contest-type math in one place instead of piecing it together from multiple resources online.

[8filltheheart]

I'm going to completely agree with Regentrude and Julie in that AoPS does not need any supplementation and is definitely superior in developing the theoretical understanding behind mathematical concepts.   I am also biased against LOF and do not believe it is superior in mathematical instruction in any way other than the author figured out how to weave math instruction into a story format.   There are better math programs out there that actually teach the mathematical concepts better than LOF, imo.   (Not a popular opinion on this forum, but still my view. ;) )

 

The fundamental question you need to ask yourself and your friend is how do you learn and what approach will work better for you individually.    Do you  need direct instruction, step-by-step, leading to the big picture on how to solve the problems or do you learn better with big picture instruction and filling in the details on your own?

 

I'm copying and pasting an old reply (several yrs old.   When I wrote this reply when my ds was in 9th grade (he is now a senior) and he had only completed through pre-cal.  Now he has finished AoPS through cal and is taking math at the local university.   My dd whom I mention did not end up liking AoPS's approach at all.   She is a strong math student (took alg 1 in 7th, geo in 8th, and is currently in alg 2 in 9th).   She much prefers direct step-by-step instruction.)   The reply below is describing the difference between Foerster (traditional instruction, but strong text with excellent real world application problems....much better text than LOF, imo) and AoPS.

 

Foerster teaches the details that lead to the big picture. AoPS gives the big picture and leaves the student to fill in the details.

 

My ds that thinks mathematically sees patterns which he likes to then dissect in order to find their relationships. He "fills in the details on his own." Quoting him, "Not only [does AoPS] expect you to develop the little points through guided practice, they expect you to assimilate the information to see the big picture in order to allow you to truly understand the concepts that you are learning."

I do NOT think that way with math. I need to be taught the details in order to completely understand the big picture. Once I understand what I am being taught, I can think things over and make the connections in order to "own it." I am watching my dd and I know she does not think like my ds (only my oldest ds (so far) seems to think the same way he does). I do not know for sure how she will end up doing with AoPS, but I am very cognizant of their different thought processes and I have a gut feeling that she is going to want (and perhaps need) the details.

 

AoPS is absolutely fantastic and I am so thrilled for my ds that he finally has something to use that appreciates how he processes math. I just know that not all people think that way.

A couple of other thoughts about the 2. AoPS is much heavier in theory. Foerster is much heavier in application. I have spent a LOT of time thinking about this b/c my oldest used Foerster and will be graduating from college with a degree in chemical engineering. My 9th grader used Foerster for alg 1-alg2 (I didn't know about AoPS back then) and he has used AoPS for alg 3, intro to counting and probability, and pre-cal.

My 9th grader's understanding of math definitely surpasses anything that my oldest ever approached. He dwells in math theory. He loves it. However, w/in the AoPS books, there is very little in the way of real life application problems (now ds gets those but not from AoPS). Foerster has more real life application problems any other math program I have seen. My oldest had zero problem in his college math/science/engineering courses b/c he knows how to solve problems.

 

I just wanted to post this b/c while we love AoPS and my ds absolutely thrived using their texts, they are definitely not for everyone.    They were written for gifted math students and not for the avg math student.   Just reading through the books is not the same as actually using them to learn math that you do not know how to do.   The problems are challenging and require time to think through vs. simplysitting down and solving.   My ds took the classes through their online courses, so I am not sure what problems came from the text and what problems were the challenge problem sets from class, but he had problems where a single problem might have taken him 2 hrs to finally solve.   This is not an approach that all individuals are going to want to take.

[StephanieZ]

I agree with the chorus. :) AoPS is time consuming, definitely not quick. (LoF is pretty quick, though, IME. Certainly seems quick compared to AoPS, lol)

 

Having happily used both, I definitely think AoPS is the top of the bunch. If it is a feasible fit for you and your child, go for AoPS for sure. If it doesn't work out, LoF certainly has a lot to offer. 

 

AoPS is 100% standalone. No need for supplementing anything that AoPS does, IME. 

 

LoF is solid. If you use LoF as a primary curriculum, you can always add single courses (or switch tracks) from AoPS at any time. You could add C&P, or Number Theory, or whatever. My eldest switched to AoPS for Alg 3 after some time with LoF (Geom & Adv. Alg), and she'd done beautifully with AoPS for Alg 3, now finishing PreCalc, and enrolled for Calc this fall. So, she is evidence that you don't HAVE to be on AoPS from the get go in order to benefit from it. :) Now, however, that we know how truly astonishing and amazing AoPS is, I wouldn't want my kids to miss out on any of it. :) So, my youngest is on the AoPS train from day 1. :)

 

 

[dhudson]

My ds uses AoPS as his main math curriculum but reads LOF as a fun supplement. He also watches Khan Academy and reads other math books for fun.

 

I don't think you have to give up LOF but could use it for fun summer math. Just make sure you let them know what their main math curriculum is. The older AoPS gets, the longer it takes in a day.