AoPS w/o challenge problems?

[smgwynn]

Has anyone used AoPS for the discovery method approach but skipped the more challenging of the challenge problems? I am convinced that my ds would thrive with the method, however, I can't see taking hours out of a day to try solving one difficult problem. My thought was to present them, give him a chance to solve for a certain period of time and then helping him through it using the solutions manual. Either that or just skipping some of them altogether. Anyone else doing this? Will it ruin the whole approach if i spare him the most difficult problems?

[wapiti]

Are you talking about the Prealgebra book or something else? IMO, there would not be a huge problem with skipping the more challenging of the challenge problems in terms of learning the math, though of course the more challenge problems skipped, the less experience in facing hard problems, which is another matter. For the sake of clear communication, I assume you are talking about the challenge section at the end of each chapter (and not the lesson problems in the gray boxes, which should not be skipped; when my dd was stuck with those, I'd just ask her some leading questions until she figured it out).

 

It does seem to me that sometimes the starred problem or two at the end of the exercises do lean toward discovering yet another lesson. I had dd at least attempt those. As for the end-of-chapter challenge problems, I assigned some in the beginning, but eventually we decided to skip them temporarily. When she got to the end of the book, I assigned some of the challenge problems from each chapter as part of her review. Interestingly, they were less scary and easier for her to do by the time she had gotten through the rest of the book. (Maybe she's less freaked out by hard problems? I hope so :)) FWIW, in the Prealgebra book, although dd did not do all the challenge problems, she did all the regular ones, and we did not encounter any situation where it took hours to solve one problem. She'd ask for help before it came to that - that's where the judgment can get a little delicate - how do you ask leading questions without giving it away.

 

As for the discovery method generally, see this thread. I see the discovery method of learning the math and facing hard problems are two separate, though sometimes related, aspects of AoPS. It seems to me that the more difficult problems your student attempts independently, the better he may learn the math, but only you know where the line is, where too much struggle either backfires in terms of confidence or becomes inefficient in learning the math. Of course, confidence increases by completing challenging tasks, a bit of a vicious cycle.

Edited July 5, 2012 by wapiti

[Matryoshka]

I do think at least some of the challenge problems are necessary, but perhaps not all.

 

My dd is taking the online Prealgebra class, and they do not use the problems in the book at all. They use Alcumus instead of the end-of-section problems, and then assign 6-10 challenge problems per week (online, not from the book).

 

I'm not signing dd up for the Algebra I class, as I think the pace will be too fast for her. She loves doing the problems online, so I think I'm going to hybridize the book/online approach. I'll have her do the Alcumus problems for each section rather than the end-of-section problems in the book, and then I'll divide up the end-of-chapter challenge problems from the book so she also has some of those to do each week (rather than waiting to do them in a chunk at the end of the chapter). I'm hoping that will work.

[melmichigan]

My dd is taking the online Prealgebra class, and they do not use the problems in the book at all. They use Alcumus instead of the end-of-section problems, and then assign 6-10 challenge problems per week (online, not from the book).

 

 

It was explained in my DD's class that you completed the end-of-section problems before attempting the ones in alcumus, and alcumus before the class challenge problems for the week, etc. There was a list of the order in which you should be trying to complete the book and online work. The recommendation was that you were completing the problems in the book, although you didn't have to solve every single problem. I just wanted others reading this to know that the class is using the problems in the book, they just aren't a component you are using. The idea was/is to find what components of the list you find most useful. :)

 

I like the idea of review so I saved a few of the end-of-chapter problems for summer review, especially from the geometry sections.

Edited July 5, 2012 by melmichigan

[Matryoshka]

It was explained in my DD's class that you completed the end-of-section problems before attempting the ones in alcumus, and alcumus before the class challenge problems for the week, etc. There was a list of the order in which you should be trying to complete the book and online work. The recommendation was that you were completing the problems in the book, although you didn't have to solve every single problem. I just wanted others reading this to know that the class is using the problems in the book, they just aren't a component you are using. The idea was/is to find what components of the list you find most useful. :)

 

 

Where did you get this information? In a handout, on the website, from the teacher during class? I just looked at all her class info - the PDF file with all the overview information, all the homework assignments, and the transcript from the first class, and it's not mentioned anywhere that you're supposed to do the end-of-section questions.

 

It says there are Reading Assignments in the text (which I do understand to mean working through all the problems in the lesson before reading the solutions), Alcumus and Challenge problems. I can't even find anywhere it recommends doing Alcumus before the Challenge problems (although that makes perfect sense to me, and it's how I've suggested she do it, but dd is very resistant to the idea and insists on splitting them up evenly during the week - I'd love to point her to a place where they suggest that order, as perhaps that would reduce some frustration on her part, and mine).

 

It does say to do the Reading Assignments before class (which she does, and work the lesson problems) - but I don't see any reference to the end-of-section questions. It does say "... it is very important that you work through the problems that are solved in each section of the textbook." - but those are the lesson problems (the ones that are solved), not the end-of-section problems.

Edited July 5, 2012 by matroyshka

[smgwynn]

Are you talking about the Prealgebra book or something else? IMO, there would not be a huge problem with skipping the more challenging of the challenge problems in terms of learning the math, though of course the more challenge problems skipped, the less experience in facing hard problems, which is another matter. For the sake of clear communication, I assume you are talking about the challenge section at the end of each chapter (and not the lesson problems in the gray boxes, which should not be skipped; when my dd was stuck with those, I'd just ask her some leading questions until she figured it out).

 

I'm talking about the pre-algebra book. I haven't actually gotten my hands on the book yet, I just keep hearing about these challenge problems. I assume they're the challenge section at the end. I have played around on alcamus a bit. Would you say those problems are comparable to the lesson problems? I would have him do the alcamus problems as well for additional practice.

[wapiti]

Where did you get this information? In a handout, on the website, from the teacher during class? I just looked at all her class info - the PDF file with all the overview information, all the homework assignments, and the transcript from the first class, and it's not mentioned anywhere that you're supposed to do the end-of-section questions.

 

FWIW, I don't remember seeing this either (though dd started the class later, so she was well ahead in the book and had already done the regular end-of-section questions; plus, I wasn't paying attention). Dd does her class homework and Alcumus assignments all out of order, I'm sure (and always at or beyond the last minute - wonder where she gets that from :tongue_smilie:)

 

I'm talking about the pre-algebra book. I haven't actually gotten my hands on the book yet, I just keep hearing about these challenge problems. I assume they're the challenge section at the end. I have played around on alcamus a bit. Would you say those problems are comparable to the lesson problems? I would have him do the alcamus problems as well for additional practice.

 

I'm not sure which posts you have been reading. I remember reading threads/posts about the Intro to Algebra book discussing some particularly difficult problems even in the lesson problem section, but I don't remember reading many posts about struggling for hours on end with the challenge problems in the Prealgebra book (not that one couldn't spend that kind of time if they wanted to on occasion, but that's not how we've used the Prealgebra book in our house).

 

Also, to be clear: there are (1) lesson problems (the shaded problems at the beginning of each lesson that need to be worked through to learn the lesson), (2) exercises at the end of each lesson (practice problems, which may or may not include a few starred ones at the end to indicate greater challenge), (3) end-of-chapter review problems, and (4) end-of-chapter challenge problems. The on-line class also has its own weekly homework in addition to the book and Alcumus - sometimes those might be called "challenge problems."

 

Hopefully others will share their opinions, but for the most part, the Alcumus problems that dd does seem to me to be "regular" problems, easier than the book end-of-chapter challenge problems, though note that the level of challenge in Alcumus can be adjusted somewhere in the settings. In addition, each Alcumus problem gives a "level number." (I don't know much about how Alcumus determines levels, except that I played around on my own account too much because I keep getting prealgebra problems with high-numbered levels. So I don't get around to playing on Alcumus much these days :tongue_smilie:)

[boscopup]

I'm talking about the pre-algebra book. I haven't actually gotten my hands on the book yet, I just keep hearing about these challenge problems. I assume they're the challenge section at the end. I have played around on alcamus a bit. Would you say those problems are comparable to the lesson problems? I would have him do the alcamus problems as well for additional practice.

 

The hour-long problems aren't in the prealgebra book, I don't think. Granted, I'm only in chapter 4 myself, but so far, there hasn't been anything that would take an hour. And when I try this out with DS1, I will help him out if he can't figure it out in a reasonable (for him) amount of time. That will be WAY less than an hour. :lol:

[Violet Crown]

We skip the more difficult of the challenge problems with Middle Girl. ("We" not because I'm feeling royal, but because I use two AoPS books with her, and dh uses two others.) We check off problems as we go, and occasionally go back and try one of the challenge problems that had been too difficult for her earlier. Meanwhile, we use Alcumus for additional problems in each area, as well as the tons of old math competition materials we have on hand. And dh will if needed just make up problems for her to work on weak areas.

 

Among all these, we find we have plenty of problems for Middle Girl to work on; it's not necessary to force her through advanced competition-style problems that she's just not ready for.

[redsquirrel]

I want to thank you all for sharing your experiences with the pre-a program.

 

I will be starting this in the autumn with ds1 and am feeling nervous. I am not that concerned about the content, but the procedure or process. I only ever used SM with ds1 and am feeling on very shaky ground. I don't know what facilitating AoPS pre-A looks like and that always makes cranky.

[melmichigan]

Where did you get this information? In a handout, on the website, from the teacher during class? I just looked at all her class info - the PDF file with all the overview information, all the homework assignments, and the transcript from the first class, and it's not mentioned anywhere that you're supposed to do the end-of-section questions.

 

It says there are Reading Assignments in the text (which I do understand to mean working through all the problems in the lesson before reading the solutions), Alcumus and Challenge problems. I can't even find anywhere it recommends doing Alcumus before the Challenge problems (although that makes perfect sense to me, and it's how I've suggested she do it, but dd is very resistant to the idea and insists on splitting them up evenly during the week - I'd love to point her to a place where they suggest that order, as perhaps that would reduce some frustration on her part, and mine).

 

It does say to do the Reading Assignments before class (which she does, and work the lesson problems) - but I don't see any reference to the end-of-section questions. It does say "... it is very important that you work through the problems that are solved in each section of the textbook." - but those are the lesson problems (the ones that are solved), not the end-of-section problems.

 

I PM'd you.

[daijobu]

I think the advantage of the AOPS books is that they offer challenging problems (taken from MOEMS, MathCounts, and AMC), that you won't find in other textbooks. If you plan to skip these problems, then you really should consider another textbook, IMO, as this the "value add" of this curriculum. Also, as previous poster mentioned, there are otherwise not a lot of other practice problems to solve.

 

OTOH, it seems demoralizing to let a student struggle for hours on a problem. I encourage dd to give it her best effort, then we attempt to solve it together at the white board. I do this without looking at the answer key, so she can see my false starts, educated guesses, attempts to simplify the problem, etc.

 

I think sometimes students need to overcome a kind of "writer's block" for math. They need to have the confidence and faith to put *something* down on paper, even if they aren't sure if it's the path to the solution. It might not be. Or it might give them a lightbulb moment to the real solution.

 

HTH!