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Talk to me about AoPS Pre-Algebra


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12 yo dd is using AoPS Pre-Algebra this year after completing Singapore Math 1-6.  I expected the beginning of the year to go slow since we have switched math programs and dd is a little math-phobic.  

 

I cannot decide if this is going well, horribly, or somewhere in between so I need help establishing my expectations.  I have some questions from those who have been there that will help.

 

1.  How many of the end-of-chapter review problems do you expect your child to complete on their own successfully before you feel they have mastered the material?

 

2.  How many of the end-of-chapter challenge problems do you expect your child to complete on their own successfully before you feel they have mastered the material?

 

We are still on the first chapter after three full weeks.  I don't feel we can move on because dd seems to need too much help figuring how to approach the problems.  She did all of the review questions on her own.  She got a handful incorrect because of sloppy math and copying numbers down incorrectly.  This is something we have been working on for years and I know will take more time so I am not very concerned about that.  But there were also three that she just did not set up correctly.....mixing up math rules and/or not getting the "trick" they were expecting her to see.  Honestly, I did not see where they were going with one of those three and I am very mathy.  

 

The challenge problems are frustrating.  Dd is only able to even start 50% of them without help.  

 

What should I be expecting here?  I feel like we will be in chapter one forever if I expect any sort of mastery of the challenge problems.  If that is what we are aiming for, I am going to have to seek out another program.  Even though I feel it is a great approach I fear my dd is feeling like a failure.

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I don't even recall using the challenge problems from ch 1 (I typically would only assign a few in any event, as that seemed to be the best for my particular students).  Developing problem solving skills is a process that can take time.  If you feel good about her understanding of the math concepts presented in the chapter, aside from problem solving, I'd move on.  You can go back to the challenge problems in chapter 1 at a later time and I'll bet her skills will have improved.  Chapter 1 always seemed a little weird, though aside from the basic math concepts, part of the purpose is to get outside the box of ordinary arithmetic and look at the big picture, to use what we know about numbers to find a better approach.  Chapter 2 puts that on steroids.  The rubber will meet the road soon enough.  Ch 2 is hard but one of my favorites.

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I would move ahead to chapter 2 by that point. Consider chapter one her introduction to AoPS methods. :)

 

I don't expect my kids to have complete mastery of every single problem in AoPS. That's not the authors intention, and much of the teaching is in the problems themselves. I do expect mine to do every single exercise, and all or nearly all of the challenge problems. If we can't figure it out we'll use the tips and I'll suggest the first steps the solutions manual shows to help unstick them. Even if they couldn't figure it out themselves they/we will learn from the problem.

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Also, gently, you might keep another math curriculum tucked in your back pocket if she truly is math phobic. (Dolciani?) My AoPS kids like math and problem solving abs they are in a math competition team. Even these kids are brain fried by the end of some lessons. We work until they're spent and close the book; the next day we pick it up wherever we left off.

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I made my kid do all the problems himself. I didn't have a magic number for 'mastery' since we discussed every problem (even ones he got right). For reference, he probably got 80% of all problems correct on the first go. He spends on average 6 weeks per chapter, but is on the young and didtractable side.

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My son was 12 when he finished AoPS Pre-Algebra. For the first few chapters, we did buddy math. We'd work through the examples together and he'd work through the section problems independently BUT I was always right there with him. He did all the end of chapter problems independently, but he would tell me when he was stuck. I would ask him guiding questions to get the answer. For the challenge sections, I made myself available in order to head off severe frustration. He did all the problems, bu the first few chapters were very slow.

 

 

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I expect my daughter to complete all the review problems successfully. She has been completing 80-90% of them correctly on the first go. If there are any that are wrong, then I will send her back to try to find the error on her own. I would say that 99% of the time it is a computational error, and she will immediately find it on her own. There have been only 1 or 2 times where she couldn't find the error or had actually approached the problem incorrectly. In those cases, I have given her a hint to nudge her toward a better way of approaching the problem. We talk through all the review problems to be sure that she understands the underlying concept and/or to point out better approaches than what she may have used.

 

I only have her do selected Challenge problems. Normally, I just tell her to choose 3 that look interesting to her. I wouldn't call my dd "math-phobic", but she is most definitely not a math-lover like many of the kids using AOPS seem to be. I think it would just kill her interest in math if I required all of the Challenge problems. The funny thing is that when I let her choose just 3, she tends to choose 3 of the harder problems. She sometimes needs a hint getting started on them, but that sense of control that comes from choosing her own problems has seemed to be a real positive motivator in working through the hard problems. As it is, she is doing very well in AOPS, her confidence has grown exponentially, and she is finally feeling excited about the idea of math.

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1. All of the review on their own. If they get a couple wrong, they correct them. If they get a lot wrong, we need to go back either then, or later, and review the chapter and figure out where understanding is off.

 

2. Some of the challenge. Always try first on their own. For pre-algebra, he did most of them. We left off some of the starred ones toward the end of the book. When we got to algebra, we did fewer of the challenge problems, but added some back in over the summer as review, after completing the first 13 chapters.

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I would sit and do the starred and challenge problems together. Your daughter can still learn a lot by working through them with you (or with the solution manual, if writing it out herself).

 

I will let a few sloppy mistakes slide, but not many - usually I just make them go back and correct it.

 

I don't like conceptual mistakes as it often means they need a little more practice to firm up their understanding.

 

I have students that can do most of the challenge problems and others that I don't even assign any to do on their own - it really depends on the student.

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Thanks all.  It sounds like people take varying approaches.  I know AoPS is not always a great fit for kids that struggle with math.  I would not say dd "struggles" as much as she gets frustrated very easily when a problem does not come easily to her.  So, I am not ready to throw in the towel yet although I certainly will if things do not improve.  She always has a hard time ramping up math in the fall so it is a bit too early to really know what is going on.  It is good to know that not everyone does every challenge problem.  We ran into the same thing with Singapore.  The Challenging word problems were very hit or miss and she never was at a point where she could do them all.

 

I'm trying to be very careful here because I know far too many people who got a plug-and-chug math education and really suffered long term for it.  We really have no idea what dd might want to do later on but she is attracted to the sciences so I feel like a solid math background, no matter how long it takes, is important.  The AoPS approach appeals to dd because it answers a lot of her "why" questions.  I also know that I did not come into my own math brain until high school.  One day it just all clicked and I really understood and enjoyed it after barely surviving Algebra in the 8th grade.  So my original plan was to take this as slowly as necessary and not worry if it even takes two years to do pre-algebra but to not gloss over things that are getting lost.

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I also think that another reasonable approach would be to do any challenge problems she thinks she can do, and after each chapter, return to any omitted from previous chapters to see if they now look approachable. If there are more than a few left when she finishes the book, go back and start on the chapter challengers, in order, as review. 

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I also think that another reasonable approach would be to do any challenge problems she thinks she can do, and after each chapter, return to any omitted from previous chapters to see if they now look approachable. If there are more than a few left when she finishes the book, go back and start on the chapter challengers, in order, as review. 

 

That's a great idea!

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The challenge problems are frustrating.  Dd is only able to even start 50% of them without help.  

 

DS9 did the challenge problems as review after he finish the whole book.  So we skip the challenge sections until the whole book was done.  DS9 is doing that for the intro to algebra and the intro to geometry books as well.  DS10 is just how he is.

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My 12 yr old ds is still on chapter 1. It's a completely new form of presentation. We're working on it together when we can and he's working independently when I'm not available. He's enjoying it, abiet slowly, so I'm just going to let him go at his pace for a while and see what happens. We're interspersing it with baseball math. After baseball we're going to mix it up with CM business math. For us having a relevant alternative is great for days when the "harder" math is too much.

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  I would not say dd "struggles" as much as she gets frustrated very easily when a problem does not come easily to her.  So, I am not ready to throw in the towel yet although I certainly will if things do not improve.  

 

I'm trying to be very careful here because I know far too many people who got a plug-and-chug math education and really suffered long term for it.  We really have no idea what dd might want to do later on but she is attracted to the sciences so I feel like a solid math background, no matter how long it takes, is important.  

 

You hit it on the head here.  I believe it is an important skill to try to solve problems where the solution isn't obvious.  It's a scary thing to try solving a problem when you don't even know if your approach will even lead you to the solution.  But if you give up here, then you are saying good bye to lots and lots of difficult problems that will come up in college math, college physics, college chemistry, etc.  

 

I believe students need to get accustomed to solving hard problems, learning to be brave enough to try something, anything, that may or may not lead to a solution.  

 

I model this behavior a lot.  "Uh...I have not idea how to solve this, but let's try this and hope for the best..."  

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Can I add 2 more points on this topic:

 

1.  I'm a big fan of the AMC solutions generated by James Tanton.  He begins every solution with this:

 

STEP 1: Read the question, have an
emotional reaction to it, take a deep
breath, and then reread the question.

 

 

Every difficult problem begins with an emotional reaction.  "I have no idea what this means, and I have no idea how to solve it."  I love how he acknowledges this reaction and normalizes it.  We all feel this way when encountering hard problems.  

 

2.  I don't often use sports metaphors, but I do play tennis.  One thing I notice with tennis newbies is they will often judge a ball to be beyond their reach and won't bother to attempt to run after it.  At some point I decided I was going to go after every ball, even if it was out of my reach.  To my surprise, I often did get those out of reach balls.  Also, running after out of reach balls improved my speed, so I was able to get more of them, too.  It is embarrassing to chase after a ball only to have it slip by, but worth the effort.

 

I think this applies to math problems as well.  Even if the problem is too hard, try it anyway.  If you fail, you are no worse off than before, and probably better off even if you don't solve it, because you will have a deeper understanding of the problem and solution.  Always go for it!  

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You hit it on the head here.  I believe it is an important skill to try to solve problems where the solution isn't obvious.  It's a scary thing to try solving a problem when you don't even know if your approach will even lead you to the solution.  But if you give up here, then you are saying good bye to lots and lots of difficult problems that will come up in college math, college physics, college chemistry, etc.  

 

I believe students need to get accustomed to solving hard problems, learning to be brave enough to try something, anything, that may or may not lead to a solution.  

 

I model this behavior a lot.  "Uh...I have not idea how to solve this, but let's try this and hope for the best..."  

 

Yes!  I also model the "Hmmmm....  I'm not sure but let's try _______ and see what happens."  This amuses my dd to no end since I teach math to college students.  She thinks I should know it all and just loves when I have to play around with a problem to figure out where to go.  Unfortunately, this does not seem to be rubbing off on her.  Yet.

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Can I add 2 more points on this topic:

 

1.  I'm a big fan of the AMC solutions generated by James Tanton.  He begins every solution with this:

 

STEP 1: Read the question, have an

emotional reaction to it, take a deep

breath, and then reread the question.

 

 

Every difficult problem begins with an emotional reaction.  "I have no idea what this means, and I have no idea how to solve it."  I love how he acknowledges this reaction and normalizes it.  We all feel this way when encountering hard problems.  

 

 

I love this!

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12 yo dd is using AoPS Pre-Algebra this year after completing Singapore Math 1-6.  I expected the beginning of the year to go slow since we have switched math programs and dd is a little math-phobic.  

 

I cannot decide if this is going well, horribly, or somewhere in between so I need help establishing my expectations.  I have some questions from those who have been there that will help.

 

1.  How many of the end-of-chapter review problems do you expect your child to complete on their own successfully before you feel they have mastered the material?

 

2.  How many of the end-of-chapter challenge problems do you expect your child to complete on their own successfully before you feel they have mastered the material?

 

 

What should I be expecting here?  I feel like we will be in chapter one forever if I expect any sort of mastery of the challenge problems.  If that is what we are aiming for, I am going to have to seek out another program.  Even though I feel it is a great approach I fear my dd is feeling like a failure.

 

As I'm sure you've discovered, there's a huge range.

 

I've had 2 kids do it, both had very different experiences.

 

DS HATED HATED HATED the 'discovery' approach.  After a couple of false starts and eventually re-starting the book from the beginning, we ended up with an effective process for him.

 

I'd teach by working the problems at the beginning of the section and talking him through what I was doing - it was conversational, so he was involved, but I was doing/teaching, he was listening/watching.  We'd then read through the instructional section which reinforced what I'd just shown him.  That took 1 day / section.  Then, he'd spend the next day working the problems - we'd check answers and go through any he missed or did 'the hard way'.  Then an extra day for review, then he'd work the chapter review problems over 2 days.  If he missed more than just a few (or, the errors were more than just dumb mistakes) we'd spend allocate an extra day to work through the troublesome problems.

 

So, for him, a chapter took 2 days / section + 3 (sometimes 4) days.  He didn't do the challenge problems.  For nearly all chapters, he got 80% or more of the chapter review problems correct.

 

DD loves the discovery process, but also wanted to finish really quickly (prepping for the AMC8).  She did a section / day (sometimes two), and the chapter review problems on a separate day.  She focuses better if she's talking to an audience, so SHE would work through the problems at the beginning of a section, thinking out loud and explaining to me what she was doing.  If she got stuck I occasionally provided a hint, but mostly she got the path they were taking her down.  She read through their explanations, then did the section exercises, then alcumus.

 

She went, end to end, through the book in 16 weeks.

 

She skipped the challenge problems the first time through, then went back and did them once she'd finished the book - which, honestly, I think worked out really well.  It provided some good review and left some time for the concepts to sink in before trying the really hard problems.  Some of the challenge problems ARE really challenging.  I wouldn't require a student to know how to solve them all, unassisted, before moving on to the next chapter.

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  • 1 month later...

DD 11 is taking pre-algebra AoPS through WTMA.  It is her first online class and first time using this curriculum.  We had used Modern Curriculum Press for grades 1 - 5 and Montessori math concepts/materials.  

 

She and I both struggled in the beginning of the semester.  I had to put in a lot of support and structure for her.  She was ready to quit by the end of week 2.  I think she even told me, "Jane already quit; can I quit too?"  I told her no and we plugged along.  

 

The biggest shock for us was how long it takes to grasp a different way to thinking and the amount of time it took to keep up with paced class.  We have been so used to stopping and sitting on a subject/concept if it was difficult or needed more time to explore.  We weren't able to do that with this class.  On average, we spent 2 hours a day on math 7 days a week.  Other subjects took a backseat for a while.  

 

Chapter 2 was a bear.  We could have stayed there for a good 6 weeks and had a lot more practice. 

 

Fast forward to week 9/10.  It is so much better.  DD has actually become more confident with math.  She is doing a wonderful job with the "proof problems" in the class.  Proof problems mean you solve the problem and then explain what you did, kind of justifying your answer.  These were so difficult for her.  I had to prod her the whole way through a problem.  She is also participating more in class - raising her hand, explaining how to do problems, and participating in the breakout rooms with other students.  While she isn't mastering every problem, she is getting more comfortable with trying them on her own.  We are not doing the challenge problems at this point.

 

As much of a struggle it was at the beginning, I am very pleased that we did not drop the class and try to do it on our own.  The instructor has been great with giving feedback, answering my questions, and meeting with DD during office hours to go over a problem that has proved difficult.

 

It is still too early to say what we will do next year.  A few weeks ago, I was planning on reteaching the book next year to give her a deeper understanding, do the challenge problems, et cetera.  However, now I am leaning toward working on the trouble areas over the summer with her and then enrolling her in Algebra AoPS with WTMA again with the same teacher.

 

 

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She and I both struggled in the beginning of the semester.  I had to put in a lot of support and structure for her.  She was ready to quit by the end of week 2.  I think she even told me, "Jane already quit; can I quit too?"  I told her no and we plugged along.  

 

Fast forward to week 9/10.  It is so much better.  DD has actually become more confident with math.  

 

As much of a struggle it was at the beginning, I am very pleased that we did not drop the class and try to do it on our own.  The instructor has been great with giving feedback, answering my questions, and meeting with DD during office hours to go over a problem that has proved difficult.

 

 

That's awesome.  It's always a tough call on whether to continue or drop a class and I'm glad you stuck it out AND it worked out.  

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I thought I'd come back to update.

 

We are still at it and it is going much better.  I still think dd is significantly "behind" where I would like to see her at this point in the year but the frustration level has decreased overall.  She is halfway though Chapter 4 and she did survive Chapter 2.  She still LIKES the program so we are sticking with it for now and I am seeing a good deal of growth in her ability to handle the discovery approach.  It still may take two years but that is time well-spent if it sets the stage for deeper understanding of math.  We have a little bit of a break in some of her other subjects for the month of December and into January.  I am considering embarking on a math "intensive" during that time to catch up a little and allow some time to explore without worrying about the clock.

 

In case anyone is interested, we implemented the following changes:

 

1.  I work all problems at the same time on a white board so I am mentally prepared to help when/if trouble starts.  This also helps me to learn the AoPS approach anyway.

 

2.  I pick 5-8 challenge problems that I feel are a good spread of the content.  The amount was just too overwhelming for my not-so-speedy student.

 

3.  We now take a break from math when the tears start.  I have usually encouraged dd to plow forward as I feel dealing with frustration is important.  But I started adding up the lost time and decided to take a new approach.  We now switch subjects for a bit and come back to math.  On most occasions, dd comes back refreshed and feeling ready to tackle.

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I will also add that dd finds the online videos go too fast.  Every time I have pulled one out to see if a different person talking through a problem will help has just caused more frustration due to the speed.  Dd is pokey about everything so this should not surprise me.

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My ds's progress was sooo inconsistent throughout PreA.  I wish I had mapped which chapters took forever and which ones zipped by.  By the time he got to 11 or 12 he was zipping through.  It depended on health (allergies) as much as difficulty level. I interact very little with him  -- he loves the video. His twin sister who is doing BA 4A I work through every problem with her! She loves it, finds it challenging, but I just don't see her tackling these problems without me there to help her through.  I do at least try to wean my support off after doing a few problems with her, but I generally can't even leave the table!

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3.  We now take a break from math when the tears start.  I have usually encouraged dd to plow forward as I feel dealing with frustration is important.  But I started adding up the lost time and decided to take a new approach.  We now switch subjects for a bit and come back to math.  On most occasions, dd comes back refreshed and feeling ready to tackle.

 

I had to do this a lot in graduate school. I just couldn't handle plowing forward. I'd go to the gym or something and take my frustration out on the weights, and usually after a workout I could handle some more math.

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I had to do this a lot in graduate school. I just couldn't handle plowing forward. I'd go to the gym or something and take my frustration out on the weights, and usually after a workout I could handle some more math.

 

It is a fine line with a 12 yo girl to know when the tears are from true frustration or an attempt to get out of math.  Dd is not a try-to-get-out-of-something person so I'm not sure why I pushed the "power through" mentality.  Hindsight is 20/20, I guess.    

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