Has anyone tried to integrate Saxon math and Art of Problem Solving (AoPS)?

[stupidusername]

Hi everyone, I'm fairly new on this board so go easy on me!

 

I have a 10-year old homeschooled son (4th grader) who is cruising along in Saxon math.  He recently finished Saxon 7/6. He will finish Saxon 8/7 in the fall and Saxon Course 3 (the new book by Stephen Hake) by spring 2015 (i.e., by the end of fifth grade). If he keeps on whizzing along, I expect him to finish Algebra 1 and 2 in 6th grade, Advanced Math in 7th grade, and Calculus in 8th grade.

 

We are very happy with Saxon, but I see no reason for him to finish Calculus before entering high school. Because of that, I would like to introduce the Art of Problem Solving (AoPS) books into the mix. My hope and expectation is that the AoPS books will deepen his math, logic, and problem-solving skills. However, I don't know how the AoPS books fit in with the Saxon books.

 

Has anyone else tried to integrate these two curricula? If so, do you have any suggestions?

[wapiti]

I would: (1) drop Saxon and switch entirely to the AoPS standard sequence (that ought to slow him down :)), or (2) supplement with some of the various AoPS books that are outside of the standard sequence (e.g., Intro to Number Theory, Intro to Counting and Probability, Art of Problem Solving Vol. 1 and 2, the on-line Mathcounts class, etc.).  There's also the free on-line problem solving practice program, Alcumus.

 

I would NOT try to integrate the standard sequence AoPS books with Saxon.  I highly doubt that it's even possible due to the organization of Saxon, not to mention the long length of Saxon problem sets.

 

Eta, regardless of what program you're using, realize that as he gets further ahead of grade level and the math gets harder, he may not continue at the exact same pace that he is now.  I'd expect him to slow down some.

[Crimson Wife]

I agree with dropping Saxon and using either AOPS or perhaps the new Elements of Mathematics from eIMACS (courses 1-5 are available now and course 6 is supposed to be out soon). http://www.elementsofmathematics.com/

[EKS]

I also agree with dropping Saxon.  However, if you want to continue with it, I would run it behind AoPS so that AoPS is doing the initial concept development and Saxon is serving as review.

[Julie of KY]

On the other hand, some kids do better with the initial concepts presented with a text other than AoPS and then move deeper with AoPS.

 

I would vote first for going straight to AoPS and then decide if you need anything else (either before or after). If you understand the AoPS books, I see little reason for follow up with anything else.

 

I have one kid that devours the AoPS books and another that does better when the concepts are presented more piecewise with lots of drill. I then use AoPS to take it deeper.

[regentrude]

I would also not attempt to combine Saxon and AoPS - the disjointed incremental spiral nature of Saxon will not mesh with the mastery based stay-on-topic mode of AoPS.

AoPS is more than sufficient as a stand alone problem, will slow down your student if you do all challenge problems, and you have the extra topics which are not a typical part of the regular high school sequence.

One special aspect of AoPS is that it is discovery based. To take full advantage of this, I would not have the student learn the material before with another program - unless it was a student who did not learn well with a discovery based method.

[kiana]

I agree with everyone else who says that they'd TRY dropping the Saxon completely and going with AOPS. Unless he really needs the drill, the Saxon is going to be complete overkill.

 

If you really, really didn't want to do that, I'd look into supplementing with the AOPS problem solving books and the number theory/discrete math books, as well as some books from the IMACS elements of mathematics (which has also already been mentioned) rather than trying to do two complete curricula.

[Steppenwolf]

Also, I would not skip AOPS prealgebra: it consists of topics which are covered in more depth in the later AOPS courses: algebra, counting and probability, number theory, geometry. For topics that your child has already studied, try at least the challenge problems (at the end of each chapter). (Arguably, some places in AOPS prealgebra are more difficult than AOPS algebra - for a student who studies first the former, and then the latter.)

 

For determining the placement in AOPS, use pre- and post-tests (for each textbook or class) - those are good.

 

Definitely buy a solution manual for each textbook that you are going to use.

 

(And I agree with what the other posters above said.)

[stupidusername]

Thanks, everyone, for the feedback. As I said, we are quite happy with Saxon. I don't feel that the repetition is overkill. I think it reinforces what my son has learned, allowing him to develop mastery and automaticity.

 

I do, however, worry that he is not developing top-notch problem-solving skills. And, like I said above, I see no reason for him to zoom through a curriculum at such a rapid pace. Perhaps a more demanding textbook -- one that requires more time -- would be more appropriate.

 

I will take a look at the AoPS pre-Algebra book and see if it makes sense to switch. (I quickly looked at the AoPS Prealgebra placement test. I think my son will probably be able to get all of these right except maybe a couple of the word problems.)

[kiana]

When I said overkill, I meant that if you were doing AOPS, doing Saxon *as well* would be overkill.

[stupidusername]

Thank you for the clarification, Kiana. Sorry I misunderstood.

 

I gave my son the AoPS Prealgebra placement test this morning. The results were as I expected. He got all the computation problems right but missed three out of the four word problems. This reflects the strengths and weaknesses of the Saxon curriculum, i.e., he has solid computational skills but is poor at solving problems.

 

We will try AoPS Prealgebra for a week or two and see how it goes. I am anxious about switching because Saxon has worked well for us and we had gotten into a good routine.

[Dmmetler]

The Pre-algebra placement test is quite a bit easier than the pre-algebra book (which my DD finished this morning ;) ). For that matter, so is the Introduction to Algebra placement test. It's definitely a meaty curriculum. I will say that if your DS requires the Saxon-type spiral review, AOPS is much less explicit about it-previous concepts do come back, but they come back in the sense of being tools used to cover new problems, blended with other concepts. My DD used Mathletics a grade level behind as her incremental review (and for "easy math").

 

 

[kiana]

I will also add that: If your son finds AOPS *too* challenging (many students find going from a computational program to a more reasoning-based program challenging), another option to build reasoning and problem-solving skills would be supplementing Saxon's pre-algebra with Jousting Armadillos. If you chose to do this, I *would* keep working through the Saxon.

 

Not that you shouldn't try AOPS. Just that if it's too hard, JA would probably be a good transition. 

[Crimson Wife]

I agree with kiana about possibly wanting to start with an easier problem-solving supplement. Singapore Challenging Word Problems books 4 through 6 would get my vote. Don't let the low grade levels fool you- some of the problems in the 4th grade book are HARD!

[WinsomeCreek]

I looked into meshing the two books earlier in the year. *But* we are an AoPS family- my kids loathe Saxon and only use it because they are getting some official credit by doing so. The books really don't meld at all. It's great that you have something that works. On the other hand I sincerely believe you are shortchanging your kid if you don't at least try going for the depth and understanding offered by AoPS (or SM CWP or JA for ex). The placement test is not at all indicative of the challenge level of the text or class.

[stupidusername]

we are trying out AoPS preAlgebra. First lesson was today.  Very different from Saxon but so far so good. Thanks, everyone, for all the advice.

[stupidusername]

Day #2 with AoPS was a struggle. My son is clearly waaay outside his comfort zone.

 

An example:

 

Problem 1.25: What is the value of 1643 - 1994 - 1643?

 

For some reason, my son was unable to get this problem. He stared at it sadly for 5-10 minutes, at which point I finally gave him the answer and explained it to him.

 

This was not the only AoPS problem he struggled with.

 

Keep in mind: This a smart kid who was able to get all but three of the problems correct on the AoPS Prealgebra pre-test.

 

What do you make of his difficulties with this material? Is it evidence that he should go back to Saxon, where he is much more comfortable? Or, on the contrary, is it evidence of gaps in the Saxon curriculum that need to be addressed?

 

Thoughts?

 

[Crimson Wife]

on the contrary, is it evidence of gaps in the Saxon curriculum that need to be addressed?

 

Thoughts?

This would be my vote. That problem you listed wasn't a particularly difficult one. If he's having difficulty with something like that, I'd say he needs more problem-solving work. If AOPS is too difficult, do look into the Singapore CWP books.

 

ETA: The way I would handle that problem is grabbing some manipulatives and the - tiles from our Equate board game (it's like Scrabble only with math). I'd build something like red counting bear - blue counting bear - red counting bear and ask my student to solve the equation. Take away the two red bears and you're left with - blue bear.

[kiana]

I agree with Crimson Wife.

 

It MAY be evidence that he needs a gentler transition, but it's too early to tell.

 

However, rather than giving him the answer and explaining it to him, I would recommend giving hints.

 

For an example of this specific problem: I would start with 2 - 5 - 2, or something like that. Then 17 - 23 - 17. This way you can see if he can see what's going on when the numbers are simpler.

[wapiti]

I agree that this is just a sign that he needs to develop more problem-solving skills.  I wouldn't use the term "gap" with regard to Saxon because it's not really a sequence issue, but clearly there's a difference in the problem solving department, as one might expect.

 

I would expect there to be a transition period, perhaps even a lengthy one, and IMO that is absolutely ok.  I don't expect these skills to develop overnight.

 

I would start with leading questions in a socratic style (maybe have him write the problem on a white board, by itself), and then if that isn't enough, move on to more direct hints.  **It's ok to spend several minutes on a problem, even a "simple" one, just looking at it and considering things to try.  Patience, on both your parts, is important here, IMO**  (Even walk away for a minute, as in you "have to go do something," so that he can be alone with the problem, to think.)  For that particular problem, I'd say something like, "let's take a step back and look at the big picture here.  What do you notice about this problem that's interesting?"  I might also talk about looking for the "easy" way to solve the problem, easy meaning less-tedious calculation.  If all else fails, the full solution to the lesson problems is right there to walk through together.

 

Take your time helping him adjust in ch 1.  Be forewarned that ch 2 is one of the more challenging chapters.

 

Eta, you might also try having him watch the videos, ideally after he does the lesson problems but before the exercises.

[stupidusername]

Thanks, everyone. This is all really helpful. I appreciate the feedback and support!

[Dmmetler]

I will agree with what is said above-along with reassurance that it gets better. Most math books come out of the gate with significant review. AOPS doesn't. It comes out swinging, and if you're used to the start of a math book being easy and it getting harder, it's a bit daunting. Chapter 1 has some tough problems, and Chapter 2 makes a lot of people question AOPS.  I think it's a combination of both new concepts in many cases and just plain having to get used to AOPS.

 

After that point, it went much more smoothly for us. The first half of the book took about 6 months-the last half took 2 1/2-and the last chapter was completed in 2 days-one day for the chapter, one for the review problems and challengers (admittedly, it was raining and the internet was down, which meant DD couldn't go outside and work on her science stuff or go online and read herpetology journals, so her extra afternoon time was devoted to math, but still, given that there were sections in the early chapters that took nearly a week for a single section, that was pretty fast).

 

 

One thing that we did which helped a lot was to keep a "froggy book of formulas"-a collection of cards that DD copied every single formula, reminder, concept, and anything else interesting, which she'd then flip through and review as needed. It ended up being a BIG stack by the end of the book. And AOPS is one book we won't be selling this year-I want it on the shelf for reference next year.

 

 

 

[EndOfOrdinary]

Many kids do awesomely well with Saxon.  I was a total Saxon-style kid.  I loved knowing the expectations and then mastering them.  That is what I was good at.  Give me a process and I will not only know it, but then develop a way to make it my own in record time.  I would not have been a AoPS kid, because there is no process.  There was nothing for me to build off of.  Every action would have been a risk.  I had serious perfectionism issues and major insecurity with myself.  I could understand a concept if you explained it, then really get it.  However, I would not have been able to apply it myself without some guidance because I was too worried to try.

 

Your son sounds like he might be in the same place.  He is no less gifted.  Merely, he is not used to risk taking (and it quite possibly might not be in his nature).  To jump right in, have to get your hands dirty, and then maybe be wrong is paralyzing for some kids.  The most important thing is to not give him the answers.  Don't scar him, obviously.  The book is designed to be hard.   It is designed to place the solver outside their comfort zone and have them get uncomfortable for quite a while. It is not in any way about computation the way Saxon is.  It is about having to completely understand, rework, build, and then start over if it doesn't come out correctly.  No drill and kill.  No process.  Only you and your head.  That might be just a bit terrifying.

 

I second that by chapter 3, all is much, much better.  Chapter 2 kicked my son's butt.  That was a very good thing, though.  He needed a swift knock in the dirt.  It was the only way for him to realize that he needed to slow down and actually fight through the tough spots.  Otherwise, he would be fantastic at going through the motions, but never able to actually do anything with the math he was learning.  Life is problem solving, not computation.

[EndOfOrdinary]

The Pre-algebra placement test is quite a bit easier than the pre-algebra book (which my DD finished this morning ;) ). For that matter, so is the Introduction to Algebra placement test. It's definitely a meaty curriculum. I will say that if your DS requires the Saxon-type spiral review, AOPS is much less explicit about it-previous concepts do come back, but they come back in the sense of being tools used to cover new problems, blended with other concepts. My DD used Mathletics a grade level behind as her incremental review (and for "easy math").

 

Awesome!  I bet she feels pretty darn great about it! :hurray:

 

[WinsomeCreek]

Before starting AoPS we read this article:

http://www.artofproblemsolving.com/Resources/articles.php?page=hardproblems

 

I really recommend reading it together.

[boscopup]

I would expect to do a LOT of handholding those first couple chapters. I also would recommend learning how to question him to lead him to the answer, rather than telling him the answer. For example, in the problem you mentioned, I'd say, "What do you notice about those numbers?" Giving tiny hints but making him look and think and discover it himself works wonders.

 

I'll also ditto that Chapter 2 was a bear! The biggest problem for my 9 year old was the lack of experience with exponents. He understood them superficially, but didn't have them automatic. So when AoPS started throwing in stuff that goes well beyond a typical prealgebra book, he was :willy_nilly: . I pulled out a copy of Dolciani Prealgebra: An Accelerated Course (1985 - got it for $6 shipped off Amazon), and we did the exponent chapters in there. Dolciani was incredibly easy for my son after doing AoPS. Then we went back and finished Chapter 2 of AoPS, and lo and behold, my son was able to focus on the problem solving portion and get through the chapter. :D Then we got to Chapter 3, and he took off. He's in Chapter 5 now, and he's been working completely independently since Chapter 3. He had a few questions in the early part of Chapter 5 (he wasn't well versed in linear equations yet, though he's done them some). I thought maybe we'd need to pull out Dolciani again, but nope... He's doing fine. He'll do the Review and Challenge problems of Chapter 5 this week, and he's had no problem with the last few sections.

 

I agree with others that you *may* need to ease into problem solving with something like Singapore's CWP first. My son came from Singapore Standards Edition (which he was finding easy and boring by the end... even the CWP were no longer challenging him that much). Going from Saxon to AoPS, especially for a young child, is a leap. So expect lots of handholding if you continue, or use something else as a stepping stone to get there. It may end up a bad fit, but it's hard to tell until you've used it a good while (and gotten past Chapter 2 :tongue_smilie:). My son used to cry if he didn't immediately know how to solve a problem. AoPS has cured him of that!!! He now knows the feeling of thinking hard about a problem and then finally beating it on the 3rd try. :D

 

Also, something my son learned about AoPS is that the computation in the problems is usually really easy. So if you find yourself multiplying two 5-digit numbers, you're probably doing it wrong. ;) There is usually a really easy way to solve the problems, and that's what AoPS trains you to find. You have to be solid in your concepts to find it though.

[Sarah H]

I just want to say thank you to everyone who contributed to this thread, as I'm benefiting from reading it 8 years later! My firstborn is about to finish up AoPS' elementary curriculum, Beast Academy.  It's been a fantastic way for him to learn problem solving and math resilience with cartoon monsters.  I was trying to decide if we should switch to Saxon for the rest of middle and highschool, but I think the answer is NO after reading through this. He really understands the 'why' behind what he's already learned, and I don't want to give that chance up for someone who is lazy and always looking for the next shortcut.

*I* used Saxon for my entire homeschooled career. It was very thorough and my math SAT score got me out of any math in college. It also gave me an intense loathing for math that lasted for the next 20 years. That's why I gravitated to Beast Academy for my boys in the first place. On the other hand, my second child really struggles with the lack of handholding in the curriculum, so I might consider trying Saxon with him for a while to see if he enjoys it more. 

[SoCal_Bear]

This is an incredibly old thread. I would say Singpore Math or Rightstart Math could be options that are conceptual math curricula that you can look at. Beast is not for all students. I dislike how it is currently talked about in homeschooling circles. It's a niche math curriculum. I actually used both SM and BA  with my son.

Anyways, I will say if you are headed toward AOPS PA, it helps to know that the curriculum is designed so that you should not be about to solve more than 80% of the problems the first time through. Even the strongest of students. This is on purpose. Once my son understood this, he was a lot more ok that it is designed to force you to learn to rework and think through problems that you did not solve and develop problem solving stamina and the ability to try mutiple strategies and to learn from what didn't work. It is also supposed to frustrate you and force you to learn to work through that frustration.