What would you do with this math issue?

[joannqn]

While DS11 isn't in high school, he's heading into high school level work so I thought this might be a good place to ask. I don't want to make a decision that ultimately hurts him.

 

DS finished MUS algebra the year before last. He flew through all of the levels of MUS, Alpha through Algebra without any difficulty at all. Not even algebra slowed him down even though he was only 9. I switched him over to AoPS to challenge him, teach him more, and slow him down. I made the mistake of just handing him the book and letting him go at it himself since it was beyond me. Looking at the solutions, I could tell he wasn't getting the point of the problems (and he only got 1/2 way through), so we started over this year.

 

This year, I committed to doing the work with him so that I would have a complete understanding of the math and could help as needed. We have a nice pattern going. On day 1, we sit down and attempt the lesson problems, comparing answers, and reading through the solutions. On day 2, we work all of the practice problems for the lesson. At the end of the chapter, I have him do half of the summary problems. We do the starred problems but not the challenge set that comes after the summary. I figured we'd go back and try the challenge problems at the end of the year.

 

In general, I feel like he gets it. Sometimes we come to a problem he understands and helps me with. Sometimes we come to a problem I understand and help him with. Sometimes we are both stumped, but that doesn't happen too often (except with one section). But when he does the summary problems on his own without me sitting there with him, he bombs half of them.

 

Would you keep working with AoPS considering these results? I don't want him to have poor grades just because he's working a harder curriculum, kwim? Personally, I love AoPS. I'd probably go back to MUS if we quit using AoPS. Now that we've taking 2 years to redo prealgebra, he'd finish Calculus his sophomore year and could probably continue math at the community college through dual enrollment. He hopes to go into an astronomy-based field, so math and physics will be important.

 

So...

 

Continue AoPS through 12th grade at home?

Switch back to MUS, finish Calculus in 10th grade, go to community college for math in 11th and 12th?

 

I'm hesitant about switching to a totally different program because I don't want to start something new and find out that it won't work well. (Singapore and Saxon were disasters for DD and I; I couldn't teach Singapore, and we hate spiral.) I'm familiar with MUS and how it teaches, and it works well for us. I'll also use MUS with DD, if not the younger two, because she hates math but does well with MUS.

[Sebastian (a lady)]

My older two are working through AOPS. They are in the second half now, what would be algebra two.

There were sol me sections where they just needed more time with the concept. Specifically they needed to work more with multiplying polynomials before factoring really clicked. Extra work in an older Dolciani algebra book has been a pretty good bridge for us.

[Luckymama]

Why is he not getting the end-of-chapter problems when he does them on his own? Is he making silly arithmetic or sign mistakes? Or is he not understanding the concepts?

 

Dd does every single review question and one-third to one-half of the challenge problems. She sits at the table with me, does a few on the whiteboard, then I check the problems. We do go through the sections together------she does a "box" problem, I make sure she understands it, repeating until done. Then she does end-of-section problems while sitting next to me. If she gets stuck, I give her a hint similar to the hints at the end of the book.

[regentrude]

Which AoPS are you talking about, prealgebra or Intro to Algebra? Intro to Algebra is a tough book. From what you describe, I really do not see an "issue" - I would consider it entirely normal that a kid is stumped on some problems. Slow and steady. My son started AoPS Intro to Algebra and took the entire 6th grade year for chapters 1 through 12, abandoning chapter 7 to which we returned the following school year because it was too hard for his level of maturity.

 

As for the grades you will give him: you do not have to test him on the hardest problems. You could give him a challenging-by-any-other-standard, but not AoPS-challenging exam.

 

If you both ENJOY the book and he makes progress, keep going and take whatever time he needs. At 11, he is really young. But working slowly through a challenging text will be more beneficial than flying through an easy curriculum.

[snowbeltmom]

JoAnne, are you using AoPS Introduction to Algebra or AoPS Pre-algebra?

 

Are the mistakes your son is making "mechanical mistakes" or mistakes due to a lack of conceptual understanding? If they are mechanical mistakes, you may want to think about supplementing with the Key to Algebra workbooks just to provide more practice for your son.

 

You could also try adding in Alcumus for additional practice. I have my dd spend 30 minutes in Alcumus each day in addition to working the problems in the book. She has a goal of passing all of the topics before we consider the course completed.

[Candid]

Hmmm, I would not be blaming the AoPS as much as wondering if the MUS did not prepare him for this level of work either in teaching some concepts or in setting a level that was too easy for him and having him develop a set of attitudes about how long he should work on math and how carefully, etc.

 

Both of these problems have solutions (go back learn those missed concepts, learn over time that math needs more time and attention, you can't fly through it).

[jennynd]

Given the career path he wants to persuit. I will keep him on AOPS. If it really not working his learning style, I will at least switch out MUS.

[kiana]

As for the grades you will give him: you do not have to test him on the hardest problems. You could give him a challenging-by-any-other-standard, but not AoPS-challenging exam.

 

If you both ENJOY the book and he makes progress, keep going and take whatever time he needs. At 11, he is really young. But working slowly through a challenging text will be more beneficial than flying through an easy curriculum.

 

I agree with both of these points.

 

There is no reason whatsoever that an examination needs to cover the very hardest problems in the curriculum. If he can pass a standard, honors Algebra 1 examination with an A, I would record a grade of 'A' for the class with no qualms whatsoever.

[joannqn]

We're doing prealgebra.

 

He missed 6 out of 14 problems:

1. concept - The problem was a fraction consisting of polynomials in both then numerator and denominator. He attempted to reduce by canceling terms.

 

2. computational - He did a quick division problem off to the side and copied the answer incorrectly in the problem (14 became 24).

 

3. guessing/laziness - This problem was comparing fractions. When he saw the LCM was going to be a crazy high number, he guessed the order from least to greatest rather than doing the work. He forgot that he could compare just two at a time. When I reminded him of that, he ordered them from greatest to least when the question asked him to order them from least to greatest.

 

4. partial answer - The problem asked him to list the fractions that satisfy four criteria. He listed four out of five of them. The one he omitted was 1/1. He needed to remember that whole numbers can be written as fractions too.

 

5. Not writing the problem correctly - He omitted a negative sign in an exponent when copying the problem from the book to the paper.

[regentrude]

Ever single one of these problems could be attributed to a lack in maturity!

We have been through phases with both my (very mathy!) children when they made careless mistakes, forgot signs, this kind of stuff. Around age 12 in both of them.

Time and patience will solve the problem. Correct all mistakes. Use graph paper. Use colors for signs. And again: patience and perseverance. I see none of these problems as a principal issue that would preclude your use of AoPS.

 

 

1. concept - The problem was a fraction consisting of polynomials in both then numerator and denominator. He attempted to reduce by canceling terms.

 

2. computational - He did a quick division problem off to the side and copied the answer incorrectly in the problem (14 became 24).

 

3. guessing/laziness - This problem was comparing fractions. When he saw the LCM was going to be a crazy high number, he guessed the order from least to greatest rather than doing the work. He forgot that he could compare just two at a time. When I reminded him of that, he ordered them from greatest to least when the question asked him to order them from least to greatest.

 

4. partial answer - The problem asked him to list the fractions that satisfy four criteria. He listed four out of five of them. The one he omitted was 1/1. He needed to remember that whole numbers can be written as fractions too.

 

5. Not writing the problem correctly - He omitted a negative sign in an exponent when copying the problem from the book to the paper.

 

[StephanieZ]

IMHO, it sounds like AoPS is a good fit. AoPS is SUPPOSED to be challenging. There should always be some problems that stump the student and teacher. I noticed that some of the challenge set problems (in the online class) for my Geometry student came from AIME tests -- invitational math tests with the best of the best math competitors in high school -- and on which average scores were something like 2 out of 5 correct. LOL, that is when I really took a chill pill about expecting my students to be able to solve every challenge problem!

 

So, anyway, I wouldn't worry about continuing with AoPS, but I would expect to continue to work alongside your student unless he becomes mature enough and you can afford the online classes. My older two work independently on AoPS along with their classmates online, but they have that support system and coaching as well as co-students to work with. They still ask me for help sometimes, and I can often help some with my ds13 because he is in Geometry, so I can coach on basic proof-writing skills (show your thinking) as well as occasionally "see" something in a problem that he doesn't, but for 80% of what he is doing, I couldn't do it to save my life unless I went back to the beginning of the book and worked it all myself, which I don't have time to do for all these levels of AoPS, which is why we budget in the expensive classes.

 

The classes, however, do move at a very rapid pace, so it can be tough for a young learner to put in the time required, and there is no room for an off week, as if you slack off for a week, it is very, very challenging to catch up to that pace. So, even if your student is ready for the interaction and general pace of the class, they also have to have the mental toughness to work double time (so maybe 16 hours instead of 8) for a week if they get sick or moody or whatever for a week and get behind. THAT is tough! For this reason, I will do Algebra with my dd10 (then 11) next year instead of having her take the class. I am comfortable doing it with her, and I have two older AoPS students who can help us if needed, lol.

 

For the higher levels of AoPS (once it gets beyond your easy comfort level), I do think the classes or a VERY motivated parent co-learner are required unless you have a 1/100,000 motivated self-teaching math kid.

 

Also, be aware that the "side topics" are some of the great aspects of AoPS -- these topics that aren't covered in standard math programs. Counting & Probability, Number Theory (two levels of each, the first of which can be done after Alg 1 -- which is just the first half of the Beginning Algebra book), and then there is Alg 3 (between Alg 2 and PreCalc) . . . and many contest prep classes/books, computer programming, etc. So many rabbit trails!

 

So, I'd expect to follow AoPS at your son's pace, expecting it to ebb and flow with his maturity, and expect to follow rabbit trails. I won't encourage my kids do do Calc before junior or senior year unless they have already exhausted the AoPS rabbit trails.

 

The more I see it, and see what it does for my kids, the more committed I am to AoPS and the more I believe it is a true work of beauty and genius. You may have started a bit too soon for your son. I think I let my youngest start too soon, too. She handled PreA just fine, doing well in the classes last year, but we didn't have time to do all the end of chapter stuff as the classes breeze by so fast, so this year, she is reworking PreA by doing JUST the end of chapter stuff (including all the challengers), and we are also doing Patty Paper Geometry. Doing PreA 3-4 days a week and PPG 1-2 days a week.

 

I LOVE Patty Paper Geo. I think it is PERFECT for this point in dd's math career. If you want to slow the move towards AoPS Algebra (as I did this year), you can spend 3-6 months doing PPG full time between PreA & Alg, or mix it in as I have this year, which also works well.

 

ALL my kids enjoyed PPG. I think it ideal as a pre-geometry course, doing it between PreA and Alg, or between Alg and Alg2, or anytime before AoPS Geo.

 

HTH

[Belacqua]

I'll put in another vote for sticking with AoPS. Has your son spent much time on the AoPS forum? The kids there are usually more than willing to help each other with questions (it occasionally devolves into spirited debates about the more elegant way to solve a problem, but I think that just comes with the mathy territory).

 

If your son has a competitive nature, playing FTW at the AoPS site can also be good practice. Losing a game to your rival because you made a silly sign error goes a long way in making you more careful the next time (guess how I know this...:)).

[StephanieZ]

p.s. Looking at the grading from AoPS classes, I can assure you that they do NOT expect anywhere near 90% on challenge sets for an A. I'd say 70%ish is an A, 60%ish a B, 80% or so for an A+. I haven't actually done the math, but that's my estimate from looking at the possible points and their "grades" which is actually not grades, just colors, but the teachers have explained grade equivalents.

 

Just give your son an A and stop testing.

[joannqn]

I hadn't looked at why the problems were wrong until you all asked. He definitely has issues with messiness and carelessness. It just didn't affect his scores with MUS as much because the problems were so simple. With AoPS, the complexity requires more care just to keep things straight. He inherited his dad's atrocious handwriting, which isn't helping.

 

I went through the missed problems with him and had a talk about neatness and being careful. I had him to one of the problems again, taking two rows of graph paper for each line (it had fractions that he was trying to squeeze into one 1/4 inch box) and writing as neatly as he could. He noticed the difference.

 

He just did the even problems for the current chapter. He only got one problem wrong out of 24. Two that he got correct, he hadn't simplified completely, but that was the only problem. One of them, he got the answer by creating a table. I handed it back to him and asked him to find the equation for the problem, reminding him that it would be difficult to do. He was very excited that he successfully figured out the equation. (We found the word problems section the hardest yet.)

 

Also, be aware that the "side topics" are some of the great aspects of AoPS -- these topics that aren't covered in standard math programs. Counting & Probability, Number Theory (two levels of each, the first of which can be done after Alg 1 -- which is just the first half of the Beginning Algebra book), and then there is Alg 3 (between Alg 2 and PreCalc) . . . and many contest prep classes/books, computer programming, etc. So many rabbit trails!

 

Part of the reason I'm not requiring him to work every problem in the summary and challenge sets is that I want to have time to do those rabbit trails. We spend about an hour a day on math. We could do more, but he's already feeling stressed over his schedule. His interests (tkd, Korean, astronomy) cuts into his free time a lot. I'll look into PPG. Thanks.

 

I'll keep working on him about being neat and taking care. It is my plan to work along side him on all levels of AoPS. It's something I want to do for several reasons, and I am enjoying.

[StephanieZ]

Sounds to me like he's doing just great. That "carefulness" factor was huge with my older dc, and was the reason I waited on Algebra for each of them for a while before they were technically "ready" math-wise. Before age 11-12, they just had too many careless errors to handle the lengthy problems in Algebra . . . If you make a careless error 1 out of every 20 "steps", that might mean only missing 1/20 easy elementary problems, but with Algebra problems easily having 20+ steps/arithmetic problems involved, that would be impossible to succeed. In AoPS, even the PreA problems often have many steps, so the carefulness factor comes to play earlier.

 

My youngest child is just, for some reason (maybe having benefited from a mom/teacher who learned the hard way with the older kids to really encourage exactitude, lol), anyway, for some reason, she was/is much more accurate from an early age, so I feel much more confident of her readiness for Algebra and beyond. I think that carefulness is really a maturity factor that has nothing to do with math ability. So, if your son is still having a lot of careless errors, I would guess that delaying Algebra for another year or so (by doing PPG and/or other rabbit trails) would be perfect for him.

 

Sounds to me like he has the math ability, and you might just need to be patient while he matures a bit. I expect he'll do very well.

 

If he's feeling stressed, PPG will definitely be a great rabbit trail to take a break from AoPS, either my mixing it up various days of the week, or taking a 3-5 mo break for PPG. It is very low stress, fun, and exploratory, but they learn heaps.

[Dana]

I find sometimes doing math on completely unlined paper helps students. Maybe see if one problem per page helps.

[Candid]

We're doing prealgebra.

 

He missed 6 out of 14 problems:

1. concept - The problem was a fraction consisting of polynomials in both then numerator and denominator. He attempted to reduce by canceling terms.

 

2. computational - He did a quick division problem off to the side and copied the answer incorrectly in the problem (14 became 24).

 

3. guessing/laziness - This problem was comparing fractions. When he saw the LCM was going to be a crazy high number, he guessed the order from least to greatest rather than doing the work. He forgot that he could compare just two at a time. When I reminded him of that, he ordered them from greatest to least when the question asked him to order them from least to greatest.

 

4. partial answer - The problem asked him to list the fractions that satisfy four criteria. He listed four out of five of them. The one he omitted was 1/1. He needed to remember that whole numbers can be written as fractions too.

 

5. Not writing the problem correctly - He omitted a negative sign in an exponent when copying the problem from the book to the paper.

 

 

I think it is also possible he does not have a strong grounding in fractions. You might consider figuring out what AoPS might help him with them and brush up on them.

[StephanieZ]

In thinking further about this, I think you should reconsider skipping problems in the summary and challenge sets. AoPS is such a challenging curriculum, and I really don't think there is a lot of fluff or excess in there. If you are using just the books (no online class with challenge sets, no Alcumus for online practice problems), then I'd want to do every single problem.

 

There isn't THAT much in there. I don't think AoPS has the fluff and repetition that many curricula do. In general, every AoPS problem teaches something, and later problems often build on earlier ones.

 

I think if the child is ready for AoPS PreA, and it is a good fit for him, he should be able to work through each chapter in about two to three weeks doing every problem, in about 60 min/5 days week. That'd be about a school year for the book. Could it be too much for him right now, or could he need more hands-on-team-work-problem solving?

 

FWIW, IMHO, I would start over, doing ALL the problems both IN and at the end of every chapter. Skipping the challenge sets, etc, isn't a good idea IMHO.

 

Alternatively, you could get him on Alcumus, set it to "follow the PreAlgebra book" and let him use that to get proficiency in the foundational concepts. Alcumus is free, and he might be motivated to be more careful when he is "punished" by the program for wrong answers and "rewarded" for correct answers. My kids all found/find it motivating. It's a pretty amazing, and totally free, resource. You can set up your own parent account, too. Check it out if you haven't already.

 

I think you are shortchanging the curriculum by skipping so much of the best material. The challenge sets are where most of the learning happens.

 

He is young, he is bright, he is probably a great fit for AoPS, but you need to reassess how you are using it. I'd go back to the beginning, and see how that goes. Maybe after a break with PPG.

 

Good luck!

[Mukmuk]

Thanks so much for posting this!!

 

Want to tell you you're not alone. I'm not the least bit mathy and I (after some teaching in the early chapters) handed the AOPS book to ds, without help from me. He's done well, but instead of getting stuck at chapter 7, he got stuck at chap 8. This is the start of graphing. Half of the problem is because he has visual issues although he's a very visual learner (builds a lot of anything around the house, remembers visual patterns easily). He's past the difficulty now, but the replies here have given me a lot of ideas on how to handle the book going forward. For starters, I should actually just work side by side with him.

 

OP, what about the online classes at AOPS? Is your son competitive? If so, he may love the online environment. We just started doing a class, and it's very early days yet, but he loves the energy. This is what I plan to do - help him schedule time for homework and prep. And be a co-learner with him (I did say "we" :D; I view myself as the supporting crew as DS is so young). This is just a trial run of what's ahead anyway for when highschool really starts. Because our kids are young, we can do some experimentation.

[joannqn]

Thought I'd come back with an update. I discussed all this with DS, and he feels a lot better. I also emailed AoPS, and the author wrote back saying that a student getting 80-95% of the review problems at the end of the chapter (where DS is at) and 30-50% of the challenge problems correct, would be getting an A.

 

He's currently working on the all of the summary problems for our current chapter. I'll have him start working the challenge problems as well. He wants to work through his summers to make sure he has time to do all of the books in the curriculum. He also wants to get to calculus as soon as possible because he wants to do physics. When I say "wants," I mean he is telling me that this is the way it is going to be. I like my summers off.

[Julie of KY]

Sounds like you are on track. I'd certainly keep doing AoPS is it's not frustrating to everyone. It might take longer than some other curriculums, but that is because you are LEARNING more. I would also say not to be in a rush to get to calculus. It's best to have a solid understanding of all the algebra fundamentals as this is what so often trips up kids in later years. If you are trying to get to calculus early, you can certainly skip the books like counting and probability and number theory.

 

I also would recommend attempting all the problems at the end of the chapter. You can learn a lot that way.