AoPS study approach

[ThomasT]

Our daughter will be finishing Pre-Algebra. She did every problems in the book by herself with essentially no support. It takes her almost a year to finish it. Moving forward, we wonder should we still make her do all the problems in Intro. Algebra? We feel it would still take a long time. We wonder what's the approach you take to finish AoPS curriculum? We notice that some people also use Alcumus at the same time. But, same question here, how can one solve so many problems (or problems that take some deep thinking) but still be able to accelerate?

[El...]

We do every problem. They build on each other, and the texts are so fantastic, in our opinion, that why would you skip anything? 😁

I offer help on the challenge problems, when needed. I try to give just a little bump or suggestion of a new direction, rather than just showing the kid the answer or method. 

Is there a good reason to limit how long each book takes? Are you trying to get done before a deadline? We do math for about an hour every day. Sometimes I've asked the kids to complete a certain section, but other times I've set a timer so their whole day wasn't filled with math. 

[El...]

Oh, I should add that Intro to Algebra went much faster than PreAlgebra for my first kid, especially the first half of the book. Second kid's pace remains to be seen! 

[EmilyGF]

DS17 did AoPS prealgebra that way, but then moved onto reading the chapter and then doing just the challenge problems at the end of the chapter. Then he started taking the classes, which require, at the intermediate level, about 10 questions per chapter. He's been highly successful that way, but not all my kids would have been.

Emily

[purpleowl]

We never did alcumus. I did require every problem in the book for prealgebra and intro to algebra, and I think for intro to number theory as well. Geometry, though - there's too much. We started skipping problems there. Intro to C&P is what my oldest is doing now, and she does most of the problems. But we've set a precedent of skipping some at this point, and also her schedule is particularly busy right now, so I do let her skip some there as well. She will finish that and start intermediate algebra in a couple of months, and her schedule will also relax a bit around that time; I'm not sure what we'll do with that. I have to wait and see how she does with the actual problems. Intermediate alg book is HUGE though. 😳 

I do think it can be kid-dependent, though. My youngest works at a much slower pace than his sisters, so even though they never skipped problems in Beast Academy, he does often. I have him do enough for me to gauge understanding. So when he gets to prealg/alg, assuming I use the AOPS texts, I can't guarantee that I'll approach it the same way as I did with the girls.

[daijobu]

We did every problem in the textbook, and yes it takes longer, especially if your student is studying independently, but IMO it's time well spent.  (We did not do alcumus.)  Algebra is so foundational, you'll be glad you spent the extra time here.  

If however, you are in a rush, then you can skip the Challenge Problems.  The problem sets are fairly short, but each individual problem is time-intensive, so when you start cutting out problems you are losing a lot of the value.

Know, too, that a typical Algebra I class is about half of the AoPS Intro to Algebra textbook.  

It sounds like your student is off to a great start!  

[mathnerd]

We did every problem. And most of the alcumus until he reached the "Intermediate" AOPS books. The problemsets are designed to provoke deep thinking and to increase problem solving stamina. My child took what seemed like forever to complete the entire series of AOPS books because of this approach. But, has developed a very strong problem solving ability as a result. He is doing post-calculus work now and his instructor feedback is that he is not intimidated when faced with a problem that he has never seen before, approaches it head-on, tackles it using a multitude of approaches and sometimes submits more than one valid solution to the problem which even the instructor did not think about. This level of deep thinking is what the AOPS problem sets in the books build.

So, if your goal is to develop solid problem solving skills, doing all problems in the AOPS books is one way to go. If the goal is to accelerate or reach AP Calculus in a short time frame, I have seen many skipping the AOPS Challenge problems and alcumus and finishing one book in one semester. Some move to other texts to increase the speed or if their kids lose interest in AOPS.

[EmilyGF]

With the online classes, the students do nowhere near all the problems. It really is about 10 challenge problems per week. For the introduction level classes, they do Alcumus, but they don't with intermediate and advanced. 

Taking the online classes saved AoPS for DS17 because it no longer dragged. 

If your kid is complaining about too many boring problems, believe the kid and speed it up. But if you are just worried about time, that isn't a good reason to reduce the number of problems.

[mckittre]

My kid has always preferred to skip most of the regular problems in favor of the challenge problems. He'd much rather through struggle through one hard problem than do 10 easy ones, and always has. As a result he's probably done many fewer total math problems in his life than most kids his age, but with lots of deep thinking. He's working through precalculus now, and that approach seems to be working well for him.

[kirstenhill]

We've only used the Pre-Algebra and Intro to Algebra books because so far my older two boys started public school classes for math at the Geometry level after finishing those books:

Kid #1 (DS currently 15) did every problem in both books

Kid #2 (DS currently 13) had a bit stronger preparation before starting pre-Algebra, and I allowed him to only do the review/challenge sections of several chapters of pre-Algebra that he felt he already had a strong grasp of.  Then he did every problem in the other chapters.  In the Intro to Algebra book he did not do all the challenge problems.  We had a bit of a time schedule to keep because we anticipated him doing public school geometry class as a part time student in 8th grade.  So we allotted a certain amount of time to the challenge problems (maybe, 2 days per chapter), and then he moved on after completing what he could complete of the challenge problems in that time. He also has very slow processing speed, which makes some of these problems take even longer than they might otherwise.

Kid #3, DS10, is doing pre-Algebra right now, as a 5th grader (we started last spring so we are over half way through).  He also has some learning challenges (dyslexia, dysgraphia), and just isn't as mature for dealing with the challenge problems...so we have definitely skipped some of them.  I'm finding he is less apt to have the patience to persevere though the challenge problems that require making some definite conceptual leaps or require parsing a lot of complicated info in the problem.  I read the text and problems to him, but on the more complex problems there is occasionally a comprehension gap for him.  Because I am really trying hard not to rush, we may circle back around and come back to the challenge problems again later after we have finished more of the text.

Edited October 20, 2022 by kirstenhill