AOPS math question

[Embassy]

I started my almost 11 year old on AOPS Pre-Algebra earlier this year, but only part-time.  He is doing things like Life of Fred, Murderous Maths books, Zometools Geometry, and watching Vi Hart and Numberphile videos for the other half of his math time.  AOPS hasn't really been challenging for him so far (unless you count part of chapter 2).  AOPS is really suited to his visual-spatial learning style.  He doesn't particularly like the book, but he would prefer math to be a video game.  I think it is growing on him though.  

 

I had previously accelerated him through Singapore because he is a whole to parts learner who needs to focus on the concepts without being held up by learning things by rote.  He was making tons of mistakes on easier problems, but we plowed ahead and I gave him harder problems and he learned easier concepts that way.   Even when doing AOPS he might ask me questions like "does 7 go into 28?" but he typically doesn't require help figuring out the problems aside from questions like that.  

 

I'm not sure the best approach to take with him right now.  I had thought that AOPS Pre-Algebra would be more challenging for him and I do want him to face challenge.  He also seems to find math more engaging when it is more difficult.  Testing revealed that this kid is PG.  

 

Do you think we should spend more time on AOPS or continue on our meandering stream approach that we have been doing this year?  Or something else?  I'm also wondering if it would be a good option to put him in AOPS Intro to Algebra instead.  His older brother is starting that in a month or two and they had previously concocted a plan that would have them doing the book together (this involved my older son not doing math for awhile so that didn't work :p ).  I think they might do well and enjoy the topic more if they worked together, but I have no idea if it is too much of a jump.

 

Thoughts?

 

[Julie of KY]

I would tend to recommend staying with AoPS. If it's easy, just move faster. I do think you can skip the prealgebra book and jump to the algebra book if you desire. Also note that starting with chapter 10 (I think) in the prealgebra book, it moves on to topics in geometry and counting and probability.

 

My concern about starting both brothers together in the algebra book would be that the younger might find it much easier than the older. It might work well in your family, but I know it wouldn't work well in other families.

 

I'd also think about starting some of the other AoPS books like number theory and counting and probability. This might provide a challenge in a different direction.

 

 

[Mike in SA]

I would tend to recommend staying with AoPS. If it's easy, just move faster. I do think you can skip the prealgebra book and jump to the algebra book if you desire. Also note that starting with chapter 10 (I think) in the prealgebra book, it moves on to topics in geometry and counting and probability.

 

My concern about starting both brothers together in the algebra book would be that the younger might find it much easier than the older. It might work well in your family, but I know it wouldn't work well in other families.

 

I'd also think about starting some of the other AoPS books like number theory and counting and probability. This might provide a challenge in a different direction.

 

Counting can be quite difficult, and number theory is good about teaching different ways of looking at arithmetic. 

 

If the AoPS book is easy (even the challenge problems), then zip along a little more quickly.  It won't take too long to find the right point for your child.  PreAlgebra may be way, way below his level.  For DS12, we tried holding off as long as we could, but it really made things worse in the end.  When we took the reigns off, he blew through Prealgebra, algebra, geometry, and algebra 2 in about a year and a half.  He has enjoyed the other AoPS material.

 

If you run out of AoPS material, there is plenty else to be done that won't do any harm...

 

[Embassy]

Thanks for the input.  How does someone go through AOPS at a quicker pace?  

[Julie of KY]

Thanks for the input.  How does someone go through AOPS at a quicker pace?  

 

I think a "typical" pace for an average student would be one section per day in the textbook and then 3-5 days on the reveiw problems.

 

To go faster, you can cover multiple sections on one day and move through the review sections faster. Alternatively, what we did was cover one section per day per book but out of multiple books so that we were going through one book at an average pace, but covering multiple books at the same time. Often we'd do the new sections in one book while working on the review problems from a different book and then flip-flop which book we are learning new sections in.

 

Don't be afraid to change it up to make it work for you.

[Embassy]

Thanks for all the suggestions.  Now that I stop to think about it, I will probably just have my son go a little faster through AOPS Pre-Algebra.  Putting my boys together may not be the best fit because I forgot that my younger son was going to have time to do the counting and number theory books.  

[Embassy]

I think a "typical" pace for an average student would be one section per day in the textbook and then 3-5 days on the reveiw problems.

 

To go faster, you can cover multiple sections on one day and move through the review sections faster. Alternatively, what we did was cover one section per day per book but out of multiple books so that we were going through one book at an average pace, but covering multiple books at the same time. Often we'd do the new sections in one book while working on the review problems from a different book and then flip-flop which book we are learning new sections in.

 

Don't be afraid to change it up to make it work for you.

 

A typical pace is to cover the exercises and problems for one section in a day?  I've done more like the exercises one day and the problems another day.  We use the videos too.

[wapiti]

In the Prealgebra text, the lessons differ in length, especially in the first half of the book.  In the second half, IMO it is doable to get through the lesson problems and exercises in the same day for a child of that age.

 

I would avoid using the videos prior to doing the lesson problems.  In your situation, I'd probably just drop them unless he especially enjoys them.

 

In the review sections, you could assign more challenge problems and fewer regular review problems.

 

We think chapters 2 and 5 are the more difficult ones in the book, though my kids' strengths tend to be more visual-spatial than sequential (and so overall the second half was more fun for them).

[Mike in SA]

DS8 does 1-2 sections per day, or sometimes one over two days, depending on the topic.  DS12 tends to do a chapter every 1-2 days, then spend an average of 2 days on the review and challenge problems.  We have slowed him a bit by giving him a parallel thread of math coursework -- which actually turns into a pace of 3-4 courses per year.  He's a fairly extreme case, though.

 

We don't use the videos, but sometimes do use Alcumus for review (especially for DS8, who needs the extra iteration).

 

Don't worry about the pace if he is mastering the material.  If he needs review, give him some interspersed with his regular material.  It is not unreasonable to ask for mastery before moving forward, nor is it unreasonable to go slower if that is what he is comfortable with.

[Embassy]

We hit AOPS again today.  We just made it through the exercises in an hour.  He understood the concepts, but he doesn't have his multiplication facts mastered so it really slows him down.  Learning multiplication facts was something we focused on mastering last school year and by the end of the year he had most of them down.  He hasn't retained them well though.  He usually figures them out in his head each time.  Hmmm...not sure what to do about that.  He did use a multiplication chart for a couple years and used it extensively, but didn't retain the facts.

 

He does enjoy the videos and learns well through that method.  I usually have him watch them after the exercises and before the problems.  

[lewelma]

We hit AOPS again today.  We just made it through the exercises in an hour.  He understood the concepts, but he doesn't have his multiplication facts mastered so it really slows him down.  Learning multiplication facts was something we focused on mastering last school year and by the end of the year he had most of them down.  He hasn't retained them well though.  He usually figures them out in his head each time.  Hmmm...not sure what to do about that.  He did use a multiplication chart for a couple years and used it extensively, but didn't retain the facts.

 

He does enjoy the videos and learns well through that method.  I usually have him watch them after the exercises and before the problems.  

 

My ds really struggled to learn the math facts.  He was still doing the subtraction facts while concurrently using AoPS Intro Algebra.  So we made a plan.... 3x per day 7 days per week.  It seems extreme, but he knew it had to be done and they were just not sticking in any other way.  3 months later the job was done, and he was moving fast enough in math at that time that he was reviewing them daily.  I found the situation incredibly odd because my ds has an awesome memory.  But there was something about memorizing math facts that went counter to his math intuition, and was a huge hurdle to overcome.

 

Also, this boy moved from Singapore 5b to AoPS Intro Algebra with some struggle, but it was doable.  At age 12, he completed Intro Number theory and Intro Counting in 3 months each, by reading the text and then just doing the review and challengers.  In the classes he has taken, they do one chapter per week, and homework includes about 8 short answer and 2 proofs. I've said it before, but if they are *hard* problems, and you don't get hints and struggle through them, then these 10 problems are enough for mastery of the chapter.  If your student needs a more scaffolded approach, then he also probably needs more problems for mastery.

 

If you don't want younger and older working on the same books, younger could do intro number theory and intro counting prior to intro algebra. 

 

Ruth in NZ

[StephanieZ]

We hit AOPS again today.  We just made it through the exercises in an hour.  He understood the concepts, but he doesn't have his multiplication facts mastered so it really slows him down.  Learning multiplication facts was something we focused on mastering last school year and by the end of the year he had most of them down.  He hasn't retained them well though.  He usually figures them out in his head each time.  Hmmm...not sure what to do about that.  He did use a multiplication chart for a couple years and used it extensively, but didn't retain the facts.

 

He does enjoy the videos and learns well through that method.  I usually have him watch them after the exercises and before the problems.  

 

1) You really must get him to truly master his facts ASAP. Anything less will frustrate him for eternity. Devote 5 min per day to fact practice until he truly has them all mastered. Honestly. Do this. It is late, but late is better than never.

 

2) The videos are purely optional. If the material is easy for your son, you can skip the videos. But, since he is enjoying them, I'd likely keep them so long as he's enjoying them. Note that videos are only available for the first few AoPS books, so he won't always be able to use them to learn the material . . . and will need to rely on the "AOPS way" of struggling through the problem solving . . . My kids did use the videos sometimes, but not routinely. They use the videos just when they are struggling. If things are going easily, they tend to zip right along with just the book. I don't push them to routinely use the videos since that'd be a time waste and also would build a reliance on that method of hand-feeding-the-methods that is not really the foundation of AoPS. I love having the videos available when needed, but I wouldn't encourage anyone to watch every video every week unless they really struggled without them. 

 

3) IME, the PreA book is *vastly* easier than subsequent books. Having already done the PreA book (at around age 9-10) made Intro to A quite manageable for my then-11 year old (during the first half of Alg. . . now just 12 and wrapping up the book) It prepared her very well for the Algebra book. She's my youngest and the only to find AoPS so early, but so far, I've been very impressed with the preparation the PreA book provided. SO, I'd not skip it, but I would accelerate it. 

[Dmmetler]

The single thing that helped my DD realize that she needed to get her math facts cold was competing in competitons (world Maths games, American math challenge, N2K) which were speed driven. She needed to have those other people out there that were much faster than she was to challenge her to learn them and overlearn them.

 

We're on chapter 6 of Intro algebra after PA, and I agree with Stephanie-PA is a good prep for Intro algebra and the thinking required. The book basically throws you in the deep end from the first problem. We never used the videos for PA, and only a couple of things were challenging for DD, but she's had to struggle more with Intro A. Since you have PA, I'd accelerate through it when easy, but do go through it.

[bibiche]

We used Reflex Math to have DS memorize his math facts.  It's a video game format and he really got them down with it.  We did this concurrently with AoPS pre-algebra.

[Embassy]

1) You really must get him to truly master his facts ASAP. Anything less will frustrate him for eternity. Devote 5 min per day to fact practice until he truly has them all mastered. Honestly. Do this. It is late, but late is better than never.

 

Last school year i slowed down his math progression greatly to focus on math facts after a couple years of work on them.  He learned them and was pretty quick with his facts by the end of the school year and now he is no longer fast with his multiplication facts.   :huh:   I've added in some review, maybe that will help.  

[Embassy]

The single thing that helped my DD realize that she needed to get her math facts cold was competing in competitons (world Maths games, American math challenge, N2K) which were speed driven. She needed to have those other people out there that were much faster than she was to challenge her to learn them and overlearn them.

 

We're on chapter 6 of Intro algebra after PA, and I agree with Stephanie-PA is a good prep for Intro algebra and the thinking required. The book basically throws you in the deep end from the first problem. We never used the videos for PA, and only a couple of things were challenging for DD, but she's had to struggle more with Intro A. Since you have PA, I'd accelerate through it when easy, but do go through it.

 

I took a look at the Intro to Algebra book and decided that it wouldn't be good to skip over pre-algebra.  This week I started to cut out some problems when my son showed that he fully understood the concepts.  I don't think my son would be into the competition angle - meaning that he would be just peachy if he didn't win, lol.

[Embassy]

We used Reflex Math to have DS memorize his math facts.  It's a video game format and he really got them down with it.  We did this concurrently with AoPS pre-algebra.

 

Thanks for the tip.  I might do the trial and see how it goes.  He hasn't been too successful with anything other than an interactive (person to person) approach to learning his facts so far, but I think he would like to play this one.

[StephanieZ]

Last school year i slowed down his math progression greatly to focus on math facts after a couple years of work on them.  He learned them and was pretty quick with his facts by the end of the school year and now he is no longer fast with his multiplication facts.   :huh:   I've added in some review, maybe that will help.  

 

It's not about slowing him down in "real math". It's about setting aside 5 minutes every school day as a separate line item to study facts. Do it with games, flash cards, wrap its, worksheeets, whatever . . . and keep doing it every day until they are all mastered. When they are mastered, they will stay mastered because he has to use that knowledge daily when doing real math. (Assuming you don't allow calculator math for routine calculations which you SHOULD NOT allow.)

 

Trust me. I've been through this rodeo with three math-gifted kids. Each subsequent kid had an easier and happier time with math since I learned from my "tester pancake" kid when to teach what . . . Mastering facts is easy, so long as you give it a few minutes daily and try a variety of resources to see what fits best. 

 

Favorite resources: Triangle flash cards (best), wrap-its (nice for variety), Peggy Kaye games books (super fun, but more mom-time required), and a wide range of printed worksheets such as Calculadders. Just do it. If you have more kids coming up, you'll see how big a difference it makes for them if you make sure they master facts early. (I learned to time it so that they mastered a set of facts just before hitting that section in Singapore Math . . . So, they practiced 4x tables the couple weeks before hitting the 4x sections of Singapore, etc. Works beautifully and dramatically reduces frustration.

 

ps. IMHO, I would have told you to make sure facts were learned when they were learning the corresponding skills . ..  So around 3rd grade math is when I insist on fact mastery. I am conceptual math person, not a drill-and-kill person . . . but math facts are sort of like reading skills or letter recognition . . . a foundation for all that follows . . . must be learned. If you don't like drill, do the Peggy Kaye games . . . but do it one way or another.

[Embassy]

It's not about slowing him down in "real math". It's about setting aside 5 minutes every school day as a separate line item to study facts. Do it with games, flash cards, wrap its, worksheeets, whatever . . . and keep doing it every day until they are all mastered. When they are mastered, they will stay mastered because he has to use that knowledge daily when doing real math. (Assuming you don't allow calculator math for routine calculations which you SHOULD NOT allow.)

 

Trust me. I've been through this rodeo with three math-gifted kids. Each subsequent kid had an easier and happier time with math since I learned from my "tester pancake" kid when to teach what . . . Mastering facts is easy, so long as you give it a few minutes daily and try a variety of resources to see what fits best. 

 

Favorite resources: Triangle flash cards (best), wrap-its (nice for variety), Peggy Kaye games books (super fun, but more mom-time required), and a wide range of printed worksheets such as Calculadders. Just do it. If you have more kids coming up, you'll see how big a difference it makes for them if you make sure they master facts early. (I learned to time it so that they mastered a set of facts just before hitting that section in Singapore Math . . . So, they practiced 4x tables the couple weeks before hitting the 4x sections of Singapore, etc. Works beautifully and dramatically reduces frustration.

 

ps. IMHO, I would have told you to make sure facts were learned when they were learning the corresponding skills . ..  So around 3rd grade math is when I insist on fact mastery. I am conceptual math person, not a drill-and-kill person . . . but math facts are sort of like reading skills or letter recognition . . . a foundation for all that follows . . . must be learned. If you don't like drill, do the Peggy Kaye games . . . but do it one way or another.

I appreciate your suggestions.  My oldest child (sequential learner) learned them quite easily without any drill.  I have done more than the 5 minutes a day for this kid (very visual-spatial whole-to-parts learner) and have done multiple years learning multiplication facts.  Last year we did drill, games, and wrap-its for a good part of our math time. It isn't easy for him. He just doesn't learn in a sequential manner.  He is rather backwards - easy is hard and hard is easy.  When he went on Khan Academy he started doing calculus problems and was getting many right.  He learned things like multiple digit subtraction when I gave him a huge number, but did not do well with 2-3 digit number subtraction.  When he was doing multiplication in Singapore, he was mastering addition and subtraction facts.  I actually gave up on him mastering those and he eventually got there through day to day math.  Maybe I should do the same here.  

[StephanieZ]

I appreciate your suggestions.  My oldest child (sequential learner) learned them quite easily without any drill.  I have done more than the 5 minutes a day for this kid (very visual-spatial whole-to-parts learner) and have done multiple years learning multiplication facts.  Last year we did drill, games, and wrap-its for a good part of our math time. It isn't easy for him. He just doesn't learn in a sequential manner.  He is rather backwards - easy is hard and hard is easy.  When he went on Khan Academy he started doing calculus problems and was getting many right.  He learned things like multiple digit subtraction when I gave him a huge number, but did not do well with 2-3 digit number subtraction.  When he was doing multiplication in Singapore, he was mastering addition and subtraction facts.  I actually gave up on him mastering those and he eventually got there through day to day math.  Maybe I should do the same here.  

 

Sounds like you have a unique learner on your hands. I haven't faced that, so I can't judge. :) I'd just keep 5 min a day every day until it's mastered, then. I also used to do "car math" with various drills, skip counting, etc . . . for a few minutes many drives . . . Can be fun. :)