help with math plan for 8yo ... Ruth & Kathy, would be grateful for your thoughts ...

[serendipitous journey]

I think we are at a crossroads with A. and I would love some perspective and help plotting out a general trajectory/set of intermediate goals. 

 

A. is 8yo (he turned 8 at the end of August, so a young 3rd grader).  He does not love math -- he does not profess to enjoy any of his school subjects -- but he's been doing math since he was about 3 years old, because at that age he did not do unstructured play very well and he both loved doing his math and was much more happy & well when he did math regularly (at that age, and while I was working, 2x/week).  Since he has seemed to need regular formal math for his mental well-being we are in the position of having a radically accelerated 8yo who "doesn't like" math.  He does like thinking about math concepts and numbers, and reading about math sometimes, but not doing problems. 

 

A. began formal piano lessons this fall and, watching him with his excellent teacher (who thinks his piano aptitude is quite unusual) I realized that he was displaying signs of boredom with AoPS PreA.  It is not that the computations were trivial to him, but the concepts were not new -- or not new for very long.  So it felt tedious.  Some of this is because he'd covered similar topics in SM7, but not all I think ... at any rate, I am trying him in AoPS Algebra and that is clearly the right conceptual level. 

 

We are moving through Algebra at a glacial pace which is fine: but I am not sure what my goals should be.  At the moment we are doing problems on the chalkboard, interspersed throughout our day to keep his motivation high, and sometimes taking a stretch to go over something.  We are in chapter 2 with factoring and he is struggling with doing more complex factors (like (2x-1) as opposed to (x)) so we are taking our time.  I do a lot of prompting to help him think.  He cannot do these problems on paper because he is not good enough at/careful enough with writing things down neatly. 

 

He occasionally gets excited about the math!  which is what we want. 

 

Should I be teaching him to work on paper, and more independently?  How?  Would it be a good idea to move him through the PreA material, perhaps pulling a few problems each day, since I am sure there are techniques &c there that would be helpful?  Given his developmental level how do we get the most out of AoPS (which is by far the most successful program I have for getting him interested)?

 

 

 

 

[wapiti]

Not Ruth or Kathy, but here are some random thoughts:  independence can be affected by age as well as how far he is being stretched, particularly for a less-than-willing student.  Also, some kids seem to need a little time for more difficult topics to sink in, so you may find that after an attempt at the topic, followed by some time away, the return to the topic goes much smoother the second time around.

 

However, the second chapter being tough for him (it depends on what you mean, exactly) may indicate that you may want to hold off on the much tougher stuff that is to come in Intro to Alg or use a simpler presentation like Jacobs Algebra for now and then follow it up with AoPS Intro to Algebra later on.

 

How far did you get in the prealgebra?  My kids found the second half (geometry and the C&P chapter) to be more fun.  If you can work around whatever it was that he found tedious, I would switch to, or alternate with, AoPS Prealgebra or Jacobs Algebra, depending on what topics you want to cover.  Jacobs Algebra has simpler practice problems than AoPS Intro to Algebra for situations where that would be helpful, such as the factoring.  Alternatively, you could take some time to wallow in fun stuff like MOEMS-type problems or geometry or whatever else for a bit and save the rest of Intro to Algebra for a while.

 

Eta, about the writing stuff down, that is why my ds10 struggled with Intro to Alg ch 5 (simultaneous equations) - he has dysgraphia issues and was trying to do it all in his head and naturally made lots of mistakes even though he thoroughly understood the concepts.  Following the Prealgebra text, the first four chapters of Intro to Algebra were relatively easy for him.  Partway through ch 5, we backed up to Jacobs, did the chapter in Jacobs and then returned to AoPS.  (and around that same time, we discovered that his convergence is not so hot, so he is wearing the reading glasses he was prescribed two years ago; seems to help.)  Ch 6 and 7 weren't as terrible as I feared - he has always been very intuitive with ratios and such - but he hated the few problems that involved writing the dreaded simultaneous equations.  Now in ch 8, he's on easy street because he covered some of it in Jacobs awhile ago.  I'm not looking forward to ch 9 though...

 

[quark]

Not Ruth and Kathy. :D Agreeing with wapiti. I am responding for two reasons:

 

"It is not that the computations were trivial to him, but the concepts were not new -- or not new for very long.  So it felt tedious."

This sounds very familiar to me. At points like these we stopped curriculum for a while and went the alternative route of logic puzzles and doing stuff outdoors or in the kitchen with math experiments (based on the Man Who Counted by Malba Tahan). You could easily use that second level of Family Math or perhaps Kitchen Table Math (? not sure, I haven't see this but sounds like it's similar to Family Math) in its place if you don't have that Tahan book.

 

ETA: more suggestions if Family Math and KT Math are too easy.

NRich goes through many levels

Go on a problem solving spree with AMC problems - the earlier problems are accessible to bright 8yos

Virtual math club problems (with video solutions)

Math Forum problems and puzzles

 

"Should I be teaching him to work on paper, and more independently?  How?"

You could try. This was the age that we started working more frequently on paper. I used the Dolciani algebra book (because that was his tutor's preferred book, I didn't know AoPS well at that time). The book is very straightforward. We read the example sections together and discussed them. Then we chose a few problems assigned by his tutor (or I reassigned problems if I thought that would be beneficial), then I sat next to him with my own graph paper notebook and we did the work side by side step by step. There were lots of false starts and mistakes and signs not lining up correctly and crazy handwriting etc but we persevered. We did this about 4x a week, and about 30-40 mins each time. We had another practice math strand running at a different time of the day for about 15-20 minutes. About 3 months later I started seeing a big leap in executive function ability. We did about 3 or 4 problems a day at most increasing to 5-7 problems a day till he could do more. Remember that I was using Dolciani which is less wordy than AoPS with fewer challenge problems. I don't feel as if DS was any less prepared for geometry and algebra 2 though. He can work on AoPS problems in his free time without huge difficulty.

 

For a child who doesn't enjoy math I might just keep sessions shorter (you might be doing that already). And I like the chalkboard method too (we used a whiteboard) and interspersing throughout the day. I might wait another year before asking him to show each step of his work.

 

Instead I would introduce more games e.g. Manga High, Math Moves U, Lure of the Labyrinth as well as math on YouTube with Numberphile and Vi Hart. It really helps to get him to like the stuff. :) Please excuse my generalizing...just from what I see with my guy and his friends, most boys seem to need a slightly different approach. One that allows some wiggles, with less focus on exactness in writing and steps just for a little while till the maturity comes in.

 

I think picking a few problems from AoPS is a good idea. You can always revisit problems later. Or you can assign a problem of the week for him to think about. Write it somewhere on a whiteboard in a high traffic area of your home and make it like a "mystery"/ "adventure" special thing in a way that you know would appeal to him to want to know more.

 

I don't completely understand the link between piano and math...are you saying that he does well with piano because of the teacher? In that case, have you considered finding a math mentor? Sometimes kids do more for mentors than they do for moms. Sad fact of life.

[serendipitous journey]

Okay, this is helping me clarify & think: thank you! 

 

We will definitely schedule an optometrist visit soon, that seems a no-brainer and something we ought to do anyhow. 

 

I am not really sure how much trouble he's having with the factoring; he seems to get it by the end of the assigned exercises but he can not explain it to me very well which is my concern.  So we're sort of sitting here for a bit at least.  Trying Jacobs or Dollciani for a first presentation might be what I should do, though I hate to spend any more money on curricula right now; we have MUS algebra and so perhaps that would be a thing to try: the MUS presentation and problems, then the AoPS. 

 

We didn't get very far in PreA, so skipping the "boring" bits and moving ahead sounds excellent advice.  Ruth seemed to think that working through the PreA Challenge problems was really excellent experience for her child, and part of my conundrum is whether I should be having A. do those; or do them after we do the rest of PreA; or if skipping them is best. 

 

The number games & the AMC suggestions seem very apt -- I will investigate those, and follow the links you gave, Quark! 

 

Since he does not have a motor impairment or struggle with dysgraphia I am thinking perhaps we would do best to move very slowly through either Algebra, or the rest of PreAlgebra, and hammer in those equation-writing skills as we go. 

 

The piano link is somewhat vague ... he started weekly lessons this fall and his teacher noticed that he was getting bored (so we moved to twice-weekly lessons -- thank you to my in-laws who are making this possible!).  That is when I realized that I was seeing boredom-related behavior during our PreAlgebra time.  His piano teacher (who is excellent, and very interested in music pedagogy as well as performance) mentioned that she was scootching him along through material until he hits a ceiling where he is being really challenged.  I think this is very analogous to what I am seeing in his math.  I think that, just like he may be ready to move beyond music pieces even though he isn't playing them perfectly, he may be ready to move into AoPS Algebra -- this factoring thing may be his natural learning-spot at the moment.  It feels right to me, it feels like he is well-placed in terms of ability and challenge.  But I can see that what is hindering his progress is some experience, and some mechanical stuff like the writing which is only going to become more of a problem as we move along. 

 

So what ought I focus on scaffolding, and where should I focus on building skills and aptitudes?  He is far enough along that there is no point skimming his arithmetic/computation skills to get him to meatier concepts: he won't be able to really process the meatier concepts without a very solid underpinning.  I'd like to stay in AoPS materials, or perhaps MEP, both because I own them and because he responds pretty well to them; and I'd like to build up his problem-solving abilities because I suspect that in a month, give or take a week or two, he'll just have clicked into the factoring thing and be ready to zoom on. 

 

Also, given his interest in engineering-type things and in astronomy,  I think his interest in math might take off more when we hit calculus and some post-calculus topics.  So while I am not in a hurry to get there, I do want to move us onto a track that will give an excellent background and lead-up to that point.  Yet another reason I'd be so so happy to find a way to keep moving gently forward through AoPS (plus extra things as needed) no matter how slow the pace.  It is possible that (in several years) non-linear dynamical systems would be a real hit, or advanced statistics, or at least calculus-based physics ...

[wapiti]

Also, given his interest in engineering-type things and in astronomy,  I think his interest in math might take off more when we hit calculus and some post-calculus topics.  So while I am not in a hurry to get there, I do want to move us onto a track that will give an excellent background and lead-up to that point.  Yet another reason I'd be so so happy to find a way to keep moving gently forward through AoPS (plus extra things as needed) no matter how slow the pace.  It is possible that (in several years) non-linear dynamical systems would be a real hit, or advanced statistics, or at least calculus-based physics ...

 

Don't forget the whole world of discrete math that he hasn't been exposed to yet.  As RR might say, there is so much more to math than just calculus.  Even now, you could have him try the C&P chapter in the Prealgebra book for a little taste, and the Intro to C&P and NT books can be done long before he hits calculus (after he's finished with algebra?).  Exploring such additional angles is well worth the time, IMO, for the fun math as well as the problem-solving experience.

[quark]

The piano link is somewhat vague ... he started weekly lessons this fall and his teacher noticed that he was getting bored (so we moved to twice-weekly lessons -- thank you to my in-laws who are making this possible!).  That is when I realized that I was seeing boredom-related behavior during our PreAlgebra time.  His piano teacher (who is excellent, and very interested in music pedagogy as well as performance) mentioned that she was scootching him along through material until he hits a ceiling where he is being really challenged.  I think this is very analogous to what I am seeing in his math.  I think that, just like he may be ready to move beyond music pieces even though he isn't playing them perfectly, he may be ready to move into AoPS Algebra -- this factoring thing may be his natural learning-spot at the moment.  It feels right to me, it feels like he is well-placed in terms of ability and challenge.  But I can see that what is hindering his progress is some experience, and some mechanical stuff like the writing which is only going to become more of a problem as we move along. 

 

So what ought I focus on scaffolding, and where should I focus on building skills and aptitudes?  He is far enough along that there is no point skimming his arithmetic/computation skills to get him to meatier concepts: he won't be able to really process the meatier concepts without a very solid underpinning.  I'd like to stay in AoPS materials, or perhaps MEP, both because I own them and because he responds pretty well to them; and I'd like to build up his problem-solving abilities because I suspect that in a month, give or take a week or two, he'll just have clicked into the factoring thing and be ready to zoom on. 

 

Also, given his interest in engineering-type things and in astronomy,  I think his interest in math might take off more when we hit calculus and some post-calculus topics.  So while I am not in a hurry to get there, I do want to move us onto a track that will give an excellent background and lead-up to that point.  Yet another reason I'd be so so happy to find a way to keep moving gently forward through AoPS (plus extra things as needed) no matter how slow the pace.  It is possible that (in several years) non-linear dynamical systems would be a real hit, or advanced statistics, or at least calculus-based physics ...

 

Some thoughts...

 

We have a very similar piano teacher. And I think the reality with these kids is that they just learn differently...not at all like how we expect them to. What works at one time might not at another and vice versa. You sound like you are really doing well with this by the way, I wanted to give you that reassurance. It takes a good amount of exhausting mental acrobatics to wrap your head around non-sequential learners!

 

"It feels right to me" I bolded this because sometimes what works for me too is to follow this intuition. Remember that you have time and usually it's not so much the gut instinct that is wrong but how we choose to follow it. There's no one single way and just remain flexible and try different things. I am always at a loss when someone asks me for step by step tips on how we accelerated through math. We just did. We took lots of leaps in material and in faith. It just felt right. Sometimes there was no scaffolding at all. There was just a "okay looks like you already know this huh? Let's try this instead". Lots of messy leaping around. But somehow, it worked because by leaping around, I was keeping interest strong and the interest took care of a number of things.

 

That's why I suggested trying to increase his interest because it really smooths the way. We did come back to strengthen some areas of weakness or we just left those areas, trusting that he will eventually come across them again when hitting higher math. For example, we went into algebra without waiting for ratios and proportions to be strong. On hindsight, I am really glad I did that but at that time I was perplexed and worried. His mentor even skipped the whole ratio chapter (with all those wonderful word problems, I was terrified about that for a while truth be told) in the Dolciani algebra book because this lovely man seems to know my kiddo very well, I don't know how. But when kiddo encountered it in geometry it all fell into place wonderfully for him. He was mentally ready. He did not need an entire week or month on ratios once he was ready.

 

I have also learned to not be afraid to retrace steps. I have been known to throw arithmetic and prealg problems at DS despite him working on alg2 now. There's nothing wrong in that. They are young too so they have time to go back and relearn, solidify, practice, etc. I do understand it's scary sometimes.

 

Does it work for A if you split approaches into different "subjects"? I sometimes treated the accelerated math as "math", the writing steps/ scaffolding as "life skills", the logic puzzles as "fun freetime stuff", the problem solving as another form of "life skills" and made time for each in our schedule (now you know why we don't get much history and writing done lol). While DS is very much a whole to parts kid, I still needed to introduce some parts to whole approaches to help him. I left the higher level math in whole to parts mode to keep his love of math strong. Then I introduced the other stuff where possible but always giving priority to the higher level math first.

 

I wanted to suggest MEP but didn't because at one point if I remember correctly, you mentioned that it was not working out for you guys. I loved MEP and often wish we could re-use it someday lol.

 

That last para...just wanted to share what my son's mentor mentioned to me a few months ago. He deals with lots of gifted kids, both math loving and not math loving but all at least a year or 2 math accelerated. And he's very experienced in what he does. He told me that calculus in itself will not be a problem for most of these kids. DS's mentor suggested building the capacity (ETA: and stamina) for math thinking first. He doesn't believe in spending a lot of time shoring up computation skills but he does believe in teaching the kids to think and giving them lots of non linear concepts to work their heads around first. This includes teaching the kids some discrete math or abstract concepts along with the more traditional concepts and not being afraid to throw hard problems at them and let those problems stew for months on end. He is a godsend.

 

In addition, having your DS explain his thought processes, teaching some of the math back to you if possible, and continuing the use of problem solving materials will be some of the best prep you can give him imho.

 

ETA: sorry to repeat what wapiti so eloquently said. I didn't see her reply when I was writing my novella. :)

[serendipitous journey]

Don't forget the whole world of discrete math that he hasn't been exposed to yet.  As RR might say, there is so much more to math than just calculus.  Even now, you could have him try the C&P chapter in the Prealgebra book for a little taste, and the Intro to C&P and NT books can be done long before he hits calculus (after he's finished with algebra?).  Exploring such additional angles is well worth the time, IMO, for the fun math as well as the problem-solving experience.

 

I agree!  I plan to do the C&P and NT books with him, and his interest rises over the next few years I would love to work with him in the Art and Craft of Problem Solving book.  We are really in no hurry to hit calculus -- I don't expect to get to it before late middle school at the earliest. 

 

I realize that part of my General Confusion is that, for the first time, DH and are not quite in agreement about how best to proceed with A.'s math education.  DH suggests that I keep doing what I've been doing, which is moving into interesting concepts and keeping A. challenged while providing generous help with scribing, prompting various strategies, &c -- because A. is only 8 years old.  OTOH I think that we can't really get much further without tackling some of these issues of math "mechanics". 

[serendipitous journey]

...

 

 

 

Does it work for A if you split approaches into different "subjects"? I sometimes treated the accelerated math as "math", the writing steps/ scaffolding as "life skills", the logic puzzles as "fun freetime stuff", the problem solving as another form of "life skills" and made time for each in our schedule (now you know why we don't get much history and writing done lol). While DS is very much a whole to parts kid, I still needed to introduce some parts to whole approaches to help him. I left the higher level math in whole to parts mode to keep his love of math strong. Then I introduced the other stuff where possible but always giving priority to the higher level math first.

 

I wanted to suggest MEP but didn't because at one point if I remember correctly, you mentioned that it was not working out for you guys. I loved MEP and often wish we could re-use it someday lol.

 

...

 

 

Thank you for your kind words and this perspective!  I think that moving the writing steps/scaffolding onto their own topic as "life skills" & cetera might really work for both A. and myself.  Perhaps we can focus on that with the PreA chapters that look good for him, and work with the conceptual stuff as our "math" ... this is something that makes sense to me. 

 

You are right that MEP is hard for me to use!  I don't know why.  But if it helped us in these early years I think it would be worth it ... DH disagrees; he points out that I've never been able to use MEP with A. for very long, for whatever reason, and hopes I get over my obsession with it ;).  I don't think I'm obsessed: just persistent, yes? 

 

and I am looking at the math games you recommended, I think this might go over very well, just need to make preschooler-free time for it ...

 

[wapiti]

I agree!  I plan to do the C&P and NT books with him, and his interest rises over the next few years I would love to work with him in the Art and Craft of Problem Solving book.  We are really in no hurry to hit calculus -- I don't expect to get to it before late middle school at the earliest. 

 

I realize that part of my General Confusion is that, for the first time, DH and are not quite in agreement about how best to proceed with A.'s math education.  DH suggests that I keep doing what I've been doing, which is moving into interesting concepts and keeping A. challenged while providing generous help with scribing, prompting various strategies, &c -- because A. is only 8 years old.  OTOH I think that we can't really get much further without tackling some of these issues of math "mechanics". 

 

I think if you keep yourselves steeped in fun stuff, there will be plenty to do for quite awhile.

 

Other random fun stuff:  IIRC, you might look into mathwonk's on-line notes for Euclidean geometry - I vaguely recall that he posted a link at some point.

 

Might your student become interested in programming at some point?  Ds sometimes expresses annoyance with being so much further ahead in math than his classmates, but it turned out to be useful last summer when he knew enough algebra to begin learning Java in a programming summer camp (not that I know whether he actually needed that knowledge, lol; I was just going off what the instructor had said).  Anyway, Scratch would be the place to start.

[acurtis75]

I'm kind distracted because dd is working on beast academy out loud next to me and the baby is banging math blocks on her walker so I'm probably going to re-read this thread later but I wanted to share a few quick thoughts. If they don't make sense I'll blame it on the ridiculous amount of noise here right now :).

 

dd8 is way ahead in math and it has never been her favorite subject. We have finally hit a point where she is enjoying it more and I think a combination of lots of time off lately (due to family situations) and finding the right challenge level has really helped.

 

I chose to do MUS pre-algebra while working on the beast academy books before we started aops pre-algebra because it is easy and fun for her. We only do one worksheet and the test and if it weren't for breaks would probably have finished the whole book in about a month. The beast academy is a change of pace. Only one or two problems per section present a challenge but she enjoys it.

 

You might consider doing a quick review of the mus algebra since you already have it to break up the monotony of the longer problems and have him write for himself on that since it is probably easier and more straight forward than the writing required for aops. Keep scribing for him on the more challenging stuff so he can focus on "thinking" about the problems instead of having to focus on writing and being able to decipher what he wrote.

 

Also, what about alcumus. DD is just starting to play with the site and he could get in some independent practice without having to write. DD thinks it is cool to get to do stuff on the computer and that may or may not be the same for your son.

 

We started piano this past January and have had a similar experience. Our piano teacher is a homeschooled teen who is very talented but not extremely experienced so he was a bit confused about what to do when dd started lessons. I think they have a nice pace working now. He has moved her ahead way faster than originally planned and she seems happy.

[lewelma]

What an awesome thread!  And fascinating!  These kids are all so different and yet the same.  I'm agreeing with everything I have read and can't even think of anything I disagree with.

 

Just a few details on my ds's experience.

He did not use AoPS PreA because it was not out then

He started Intro Algebra the week he turned 9, and worked through it independently

He took 9 months to finish the first 5 chapters of Intro Algebra, so I know about glacial!

Then entire book took him 3 school years to finish (but we took a 2 month trial of Jacobs early on)

He did every single challenger in the Intro Algebra book

 

I think you need to think about goals for the next few years and then lay out a plan to reach them.  Something like:

1) Begin to enjoy math (He will get much further in math if he likes it because he will be willing to fight for the hard problems)

2) Work without scaffolding

3) Deal with the mechanics.

 

Goal 1) Given his age, I would work this year on goal #1: getting him to like math.  Basically, do anything he likes.  Rotate programs, rotate topics, only do conceptual problems, only do word problems, play games, focus on investigations, work together, use a chalkboard, talk to mathematicians, read some biographies/living books, whatever.  He needs to build some passion.

 

Starting at age 9 (or whenever you deem it appropriate) work on goals 2 and 3.

 

Goal 2) working without scaffolding. 

 

a) Begin to clearly differentiate which problems will be 'do together' vs 'do independently.'

 

b )Reading and learning from the text: Sit down with the book and together each of you read it silently, then have him explain it to you (whether it is directions, or concepts, whatever we are talking reading comprehension of a math book).  Then you take a turn and describe *how* you interpret the instructions, explanations, etc and *how* you know they say what they say.  Do this for as long as it takes (as in 6 months).  Some kids need training with a coach, rather than to be thrown in the deep end to muddle through on their own. 

 

c) As for scaffolding problems, once again, silent reading side by side, and then ask him how *he* would scaffold it.  Then give him your take.  Keep a little list of the things you should look for that help you to identify what you should do. 

 

Goal 3) Mechanics.  I definitely have had to do this at ever increasing levels of difficulty/maturity

 

a) Teach him to take pride in his notebook.  We use gridded notebooks with a line down the middle so 2 columns.  I just went and got his first notebook (age 9) and his most recent notebook (age 13) and he is still doing *exactly* what I taught him to do 4 years ago.  Red pen for the date and a line under it.  Always skip lines. Put a box around your answer. Write the problem number outside the margin. Write in red pen when you start a new chapter.

 

b ) Showing work.  You have to teach him *exactly* what you have to show.  A lot of smart kids just skip to the answer, so you need to show him what can be skipped and what has to be written down.  Obviously, this is subjective, but don't tell him that yet.  Give him a reward if he needs it to encourage him until it is automatic.  I tried to teach my kid to line up the equal signs as he manipulated an equation, and this was a very very bad idea for a perfectionist kid, so we dropped it.  When we hit geometry, I had to teach him again what he needed to write down.  Very very specifically what he had to write down. First I taught him the 2 column proof so he really internalized that every assertion needed a reason, and then after 6 months I taught him how to write it in paragraph form using the style from the AoPS solution manual. This past year, we studied the form of non-geometric proofs using free materials on the AoPS site. And then we studied *how* to write up your argumentation using the Art and Craft of Problem solving. We actually kept a list, and quizzed each other on phrases that you could use, connector words, intro and conclusion styles, etc. We will be doing even more this upcoming year because on timed exams you need to get to the point with your proofs, so we will be examining previous exam solutions to figure out what can be assumed and what has to be explained.

 

So starting at age 9, we worked on the mechanics a little bit every year.  (and I will add that we definitely had some arguments along the way!)

 

 

 

[lewelma]

Oh some thoughts on using an algebra program *before* AoPS intro algebra.  There have definitely been different opinions on this on the board.  I believe it was 8filltheheart that used something else first and later regretted it because the 'discovery' approach of AoPS was ruined.  But then there are younger kids like dmmetler's that used something first and it worked wonderfully.

 

For my kid the discovery aspect is key.  Part of it is his personality - that he does not want to be taught.  But also I think it has shaped how he view what exactly mathematics is all about.  Basically, he never knows how to do a problem until he tries this and tries that.  He simply does not have the expectation that math is about copying or extending an approach; but rather it is about always working in the dark.  He has no fear of 'being confused' or 'not understanding' like I see with the kids that I tutor. Instead, he expects it and loves the process of working through his confusion and coming out the other side.  

[Dmmetler]

Chapters 1 and 2 are BY FAR the most tedious and frustrating in AOPS pre-algebra, IMO, and also are the ones with the most review. Chapter 3 was fun, and almost all novel applications, Chapter 4,5 and 6 are less new conceptually, but the applications have been new enough to be fun. I'd suggest at least picking and choosing though AOPS pre-algebra and playing with the challengers, since you have the book anyway.

[lewelma]

Chapters 1 and 2 are BY FAR the most tedious and frustrating in AOPS pre-algebra, IMO, and also are the ones with the most review. Chapter 3 was fun, and almost all novel applications, Chapter 4,5 and 6 are less new conceptually, but the applications have been new enough to be fun.

 

Sounds like I might have hopped ship too soon with my younger.  We were almost through chapter 2, and I just thought there is no way I am doing this for a year.  We switched to MEP secondary, but perhaps I should revisit PreA.

[serendipitous journey]

Chapters 1 and 2 are BY FAR the most tedious and frustrating in AOPS pre-algebra, IMO, and also are the ones with the most review. Chapter 3 was fun, and almost all novel applications, Chapter 4,5 and 6 are less new conceptually, but the applications have been new enough to be fun. I'd suggest at least picking and choosing though AOPS pre-algebra and playing with the challengers, since you have the book anyway.

hmmm ... it was Chapter 3 that bored him (after the divisibility bit -- that was fun).  I'll look at the others again for sure ...

 

acurtis and Ruth, I am mulling over your posts and will write on them tomorrow. 

 

one thought/question, Ruth (your plan has given me joy and hope -- that is just the sort of goal-driven outline I can sink my teeth into!).  I am stymied on the developing passion/interest/joy front.  The child really doesn't like anything for long (that is assigned).  Even if I let him pick from an array of options interest would quickly wane.  I think my best hope may be to come up with a plan for engendering interest and then carry it out regardless of apparent interest on the theory that it'll eventually light a spark ...

[serendipitous journey]

Ruth -- RE the two-column notebook -- how do you use the two columns?  Are these full-sheet notebooks or composition sized?  I am trying to imagine the details, this sounds like a very very useful approach. 

 

ETA: I think you are right RE teaching A. via the discovery method -- he does get excited to learn new things.  Thank you for mentioning that aspect and the possible pitfalls of teaching algebra with another book first. 

[lewelma]

I will try to get a photo up tomorrow, but have to go to bed.  He uses a "Warwick 1E5 with margins Quad Book".  I googled it but could not find an image of inside.

[acurtis75]

 

Goal 1) Given his age, I would work this year on goal #1: getting him to like math.  Basically, do anything he likes.  Rotate programs, rotate topics, only do conceptual problems, only do word problems, play games, focus on investigations, work together, use a chalkboard, talk to mathematicians, read some biographies/living books, whatever.  He needs to build some passion.

 

 

 

I think this might be the best advice I've seen. I wish someone had given me that advice about 2 years ago when math was such a struggle for both of us because dd hated it so much.

 

I wouldn't have articulated it as a goal at the time but essentially that is what I was trying to do when we started all the supplementation and the rapid acceleration of mus and I believe we have achieved that goal. She loves beast academy and has been enjoying mus pre-agebra and doing the occasional problem on alcumus for fun. We're a long way from the 2 hour, tear filled dramatic battles over math we went through during mus delta. 

 

btw, on the other point about not doing a program first you are right...lots of different opinions on that. I decided to do mus pre-algebra instead of algebra hoping that it won't ruin all the discovery aspect of AOPs pre-algebra since the consensus here seemed to be that AOPs pre-algebra = algebra elsewhere. I was hoping it would give her a little background so the challenge level is more appropriate on the AOPs. I won't know for a few months whether that was the right decision. Based on watching her do a few problems on alcumus she probably could have gone straight in to AOPs and saved me the $ on the mus book but she's enjoying it. 

[boscopup]

For working on things like writing stuff down, have you tried doing two separate strands of math? We now have "math practice" and "prealgebra" - two separate math sessions. Now I'm not having to work on writing stuff down (we worked on that during elementary math), but you could have a "writing stuff down" strand and an "algebra" or "prealgebra" strand. :) Our "math practice" strand is CLE Math 500 level. It's easy peasy. Just keeping his arithmetic skills fresh, so things don't fall out of his head. He actually likes doing it, and one lesson only takes 15 minutes (I told him early on that if it's easy, it won't take long). For our "prealgebra" strand, we are using Dolciani and AoPS. Talk about moving at glacial speed through AoPS. :lol: We are 3 sections into Chapter 3, and we started AoPS mid-June. :lol: We're actually moving faster now than we did before. That first chapter was B-O-R-I-N-G, and the second chapter showed me that while he understood the concepts of exponents, he hadn't had enough practice time to be comfortable applying them. That's when I pulled out Dolciani and had him do all the odd problems (written and independent) for some exponent sections. Then we went back over to AoPS, and he enjoyed the exercises and challenge questions a lot more, since he was able to focus on the problem solving bit. We're in Chapter 3 now, and he loves the divisibility and prime number stuff. In fact, I really didn't need to do Dolciani first for these sections. He's doing the exercises independently now. I don't intend for him to use this book independently quite yet, but by time we get to the Intro to Algebra book, I do want him to be working it independently (and just using me for discussion as needed). He does AoPS at the white board, and the other, easier, math all gets done on paper (CLE is a workbook, but it does stress having them show their work and such, even for easy problems). So we work on all aspects of math, but in separate sessions - drilling the basics, understanding everything conceptually (AoPS makes sure of that!), being able to work from a textbook, etc.

 

Speaking of working from a textbook, I have a sheet of lined paper hanging on the wall of the school room that says "FRONT" across it, so when he pulls out the paper, he can look up there and compare to see which side the holes go. :lol: I have had to explicitly teach how to use paper/notebooks - writing near the red line, putting one line of math on each line of paper, lining up the equal signs, circling/boxing your answer, etc. It's a tedious process.

 

Don't know if any of that is helpful to you, as your kid is different from mine, and I don't think I have a PG kid or anything, so he isn't so wildly different like the PG kids on this board are... mine is fairly straightforward... just hates  to physically write stuff. I did find that now that he's 9, he's more willing to do easy/boring/repetitious things compared to when he was 6 or 7. I'm not sure if that's because I've eased him into doing such things (I did want him to learn that not everything in life is going to be new and exciting... as an engineer, I had to do a LOT of tedious work before I got to do the fun new stuff), or if it's because he's older and more mature now. Maybe a little of both. Who knows? And again, he has a laid back personality, so it's not like he shuts down or throws fits or anything like that (that would be DS2 :lol:, but he's doing well with a mixture of drill and "fun stuff" also - CLE Math 200 and Beast Academy 3A).

[acurtis75]

 

 

Speaking of working from a textbook, I have a sheet of lined paper hanging on the wall of the school room that says "FRONT" across it, so when he pulls out the paper, he can look up there and compare to see which side the holes go. :lol: I have had to explicitly teach how to use paper/notebooks - writing near the red line, putting one line of math on each line of paper, lining up the equal signs, circling/boxing your answer, etc. It's a tedious process.

 

 

This made me smile. We are still working on these very things for all subjects not just math. 

[quark]

Speaking of working from a textbook, I have a sheet of lined paper hanging on the wall of the school room that says "FRONT" across it, so when he pulls out the paper, he can look up there and compare to see which side the holes go. :lol: I have had to explicitly teach how to use paper/notebooks - writing near the red line, putting one line of math on each line of paper, lining up the equal signs, circling/boxing your answer, etc. It's a tedious process.

 

We're finally past the front page, watch for the red margin stage. My son's bulletin board above his study desk, however, still has this card pinned on it. I'm hoping that he won't need me to mail him something like this when he's in college. Or maybe he will.

 

[acurtis75]

We're finally past the front page, watch for the red margin stage. My son's bulletin board above his study desk, however, still has this card pinned on it. I'm hoping that he won't need me to mail him something like this when he's in college. Or maybe he will.

 

 

  I looked at that list and decided it is a bit too challenging for dd right now but now I have a goal for when we get past the red margin stage. This board is so helpful :lol:

[serendipitous journey]

quark, that card is terrific! 

 

I do agree with Ruth & acurtis & everyone, really, that upping passion is key.  You will have to believe me that it does not matter what I do in our math time, it will never be popular (not this year at least!).  So I think the best strategy for upping passion is coming up with some sort of plan and implementing it and ignoring the groans.  For instance I think if I restart our Calculus Without Tears (I know the name is horrid) and reading Penrose the the Mathematical Cat chapters regularly it would be a start. 

 

I'd love ideas on working with his interests.  Here's where we are at the moment:

* when he grows up he wants to design a probe to go to the under-ice, liquid part of Eurpoa and report back. 

* his most pressing scientific question is what, EXACTLY, is fire.  DH and I have given the level of response generally satisfactory but he's not happy with it so more needs to be done. 

* his current mathy hobby is trying to draw or somehow design a 4-D cube (he's been watching Flatland lately). 

 

For him, I don't think a different algebra program first will suit because he gets so bored with stuff he knows, even if the original presentation wasn't AoPS-quality or depth. 

 

boscopup, 2 tracks is ideal.  At the moment we're doing skills via Singapore Sprints, some Calculadder, &c.  The Sprints are rich enough to keep him used to computing with fractions, decimals, percents, &c which he'd otherwise forget.  We were doing Pizzazz Prealgebra but he became disenchanted.  I think we should do more than Sprints but not sure what ... we may pull out Galore Park's SYRWTLM for this. 

 

Ruth, thanks for the title of your books, I can find something similar but I am curious/confused about the "middle line".  Do you make use of this?  if so, what for?  Do you have any thoughts for upping passion?  I do think if I gently move him through AoPS eventually he'll get interested, but would love to generate energy around math!  And thank you so very much for writing out that draft of a plan.  I will use that going forward. 

 

Ruth,

[lewelma]

unfortunately I have used up all my space, so can't post a picture, and to make space I have to delete the science fair photos.  :tongue_smilie:

 

I'll try to put the photos up on my g+ account and pm you the link tonight. 

 

Here is a feel for the book:

 

 

_________________________________________________

 I  3＋4 ï¼ 7       I       x+y=          i      xxxxxxx     I        xxxxxx    I                        

Ｉ                       I                         i                          I                        I

Ｉ  6 ＋4 ï¼ 1ï¼  I      xxxxx          i     xxxxxxx     I        xxxxxx    I

Ｉ                       I                          i                         I                        I

Ｉ 8＊2ï¼16        I    xxxxxx          i     xxxxxxx     I        xxxxxx    I

Ｉ                       I                          i                         I                        I

Ｉ   xxxxx           I                         i     xxxxxxx     I        xxxxxx    I

Ｉ                       I                          i                         I                        I

Ｉ  xxxxxx          I                         i     xxxxxxx     I        xxxxxx    I

Ｉ__________________________________________________

 

I is the column divider

i is the middle of the notebook.

so 2 columns per page, and 4 columns if you open the book all the way up.

 

He just finishes the first column and if not done with a problem, he just carries it over to the next column.  If it is a particularly long problem, he simply draws a line across the page to box off the space that can't be used in the second column, but that is pretty rare.

 

[wapiti]

Even if I let him pick from an array of options interest would quickly wane.  I think my best hope may be to come up with a plan for engendering interest and then carry it out regardless of apparent interest on the theory that it'll eventually light a spark ...

 

This reminded me of something... more than once, when ds was dragging his feet (more like dragging his head - he'd lay it down on the table), I thought, "oh, maybe this is too hard or too much all at once" so I'd downshift to Jacobs.  While I like Jacobs very much and it was easier to just tell him to do it because it's more straightforward, he'd still do the same thing - head down on the table.  I thought, what's the difference.  So, we always end up back at AoPS after a few sections.  Truly, I think that's what he prefers, especially now that he's finally getting the exercises done while he's at school so that he can get more computer time when he gets home in the afternoon.

 

I don't know what to say about the spark (still looking for it here) but I was rather amused when I found him googling logarithms after something about them had turned up in his programming stuff.

[acurtis75]

After reading your follow-up notes and seeing that the idea of making math enjoyable is a priority maybe dedicating a day or two a week to "fun math" might work. Do problems on alcumus instead of paper (dd and I have on occasion worked on alcumus sitting next to each other and turned it in to a game), read books, find some math games that you can play together.

 

After doing a similar problem on alcumus or beast academy or somewhere (can't remember what prompted it) dd, dh and I spent an hour creating number pattern puzzles for each other. I counted that as math for the day. DD also enjoys making math problems for dh or I. The rule is that she must know the answer before she presents it to us and she does her best to stump us. 

 

Another day recently I had her do calculations for doubling and tripling recipes we were working on and counted that as math for the day.

 

Ipad math games are another way we've practiced math computation.

 

These might not be examples your son would enjoy but looking for opportunities to substitute some real life math or a game at times seems to be helping.

 

I keep reminding myself that dd is far enough ahead that I don't need to worry about time off or detours to have some fun right now. For us, we are doing a lot of outside science classes this year and it means less seat work but I think in the long run the attitude improvement and excitement about learning will be a great benefit for us.

 

 

 

 

[wapiti]

btw, on the other point about not doing a program first you are right...lots of different opinions on that. I decided to do mus pre-algebra instead of algebra hoping that it won't ruin all the discovery aspect of AOPs pre-algebra since the consensus here seemed to be that AOPs pre-algebra = algebra elsewhere.

 

FWIW, I would not say that AoPS Prealgebra = algebra elsewhere.  The topics in AoPS Prealgebra are genuinely pre-algebra topics; it's just that those topics are covered at a greater depth and challenge level than elsewhere.  That doesn't make it algebra.

 

My vague understanding of MUS is that the prealgebra includes a bunch of topics that are typically covered earlier elsewhere, so it sounds like a good idea to do that first.

[serendipitous journey]

unfortunately I have used up all my space, so can't post a picture, and to make space I have to delete the science fair photos.  :tongue_smilie:

 

Ruth, thank you for that explanation and impromptu diagram!  No photos needed!!  This makes perfect sense, and is a logical and efficient use of space -- I will try this approach.  Thank you so much!

[Kathy G]

Great thread!  I agree with growing the passion.  Have you used Life of Fred?  Sometimes we intersperse that to liven things up.  Also agree that prealgebra AOPS is not the same as othe algebra courses and that I would not use another algebra course first- it would ruin the discovery method of AOPS. 

[MamaSprout]

 

Goal 1) Given his age, I would work this year on goal #1: getting him to like math.  Basically, do anything he likes.  Rotate programs, rotate topics, only do conceptual problems, only do word problems, play games, focus on investigations, work together, use a chalkboard, talk to mathematicians, read some biographies/living books, whatever.  He needs to build some passion.

 

 

We just did/ are doing this with Dd8, who sounds similar to your Ds. We actually ended doing a combo of jumping back for independent daily work at a really brisk pace, solidifying showing work, etc, in Singapore and Beast, and moving forward with concepts.

 

Instead of into Algebra (or even PreA) curricula, which she wants to do, we are working on a buffet of problem solving and Algebra enrichments, videos and puzzles. I don't even have the AoPS books in the house. I want her to be able to do those independently of me. (She loves RR, so I'd have to hide the books)

 

She's loving this approach, in part because she can do it fast and independently. Then we work together on the harder stuff, sometimes with other kids.

 

We also are piano people. Similarly, her piano teacher sees her boredom. We approach it differently, though. He gives her a month's worth of work and sees us every two weeks (he's an hour away). I play piano so I can steer in between. He also gives her a combo of at level lesson work (about 25%) and the rest is above-level (like you would prepare for a recital, but all the time).

 

Just our .02- Good Luck with whatever course of action you choose.

[serendipitous journey]

Great thread!  I agree with growing the passion.  Have you used Life of Fred?  Sometimes we intersperse that to liven things up.  Also agree that prealgebra AOPS is not the same as othe algebra courses and that I would not use another algebra course first- it would ruin the discovery method of AOPS. 

 

I'd sort of forgotten about Life of Fred -- we ran out of steam at the end of decimals, but I think the later books may liven things up.  Plus, this is an enrichment strategy that is straightforward to implement and doesn't require the child to express enthusiasm! 

 

We just did/ are doing this with Dd8, who sounds similar to your Ds. We actually ended doing a combo of jumping back for independent daily work at a really brisk pace, solidifying showing work, etc, in Singapore and Beast, and moving forward with concepts.

 

Instead of into Algebra (or even PreA) curricula, which she wants to do, we are working on a buffet of problem solving and Algebra enrichments, videos and puzzles. I don't even have the AoPS books in the house. I want her to be able to do those independently of me. (She loves RR, so I'd have to hide the books)

 

She's loving this approach, in part because she can do it fast and independently. Then we work together on the harder stuff, sometimes with other kids.

 

We also are piano people. Similarly, her piano teacher sees her boredom. We approach it differently, though. He gives her a month's worth of work and sees us every two weeks (he's an hour away). I play piano so I can steer in between. He also gives her a combo of at level lesson work (about 25%) and the rest is above-level (like you would prepare for a recital, but all the time).

 

Just our .02- Good Luck with whatever course of action you choose.

Your piano strategy give me hope that piano for N. won't be so expensive -- at the moment I am learning along with A. so I can't really steer him other than to do what his teacher's taught, but for the second one I'll have a better background. 

 

Your approach sounds like my own ideal!  Unfortunately A. would wilt under this -- the solidifying would not be any fun at all for him, just drudgery and annoying arithmetic.  His main motivation for learning to show his work and be neat is that it will make more interesting problems possible & fun for him (thank goodness he believes me about these things!).  And he would never in a million years grab a math book and start going through it on his own ... well, never in the next two or three years at least.  For him I really think the fun in math will come when he sees what it can "buy" him in his science. 

[Dmmetler]

A prime example of AOPS-DD did the first section of chapter 6 on decimals. The problems were all ones she could easily solve using techniques she had-really, nothing not covered in SM by about 5B. But the explanations actually proved WHY it worked to do those manipulations, at a level which she wouldn't have had the skills yet to understand when she first was learning how to manipulate decimals. What seemed like a repetition of something that she'd learned long before PA turned into "Oh! That makes sense"-and she dived into the exercises to find the interesting applications-the problems that couldn't easily be solved procedurally, but could be solved by the deeper understanding.

 

FWIW, I'm guessing that almost no child is going to fully "discover" AOPS PA, whether they did a book labeled PA previously or not, because most of the topics simply aren't going to be new. It's the WHY and the applications-the math contest problems and starred problems, and especially the challengers that elevate it to a totally new experience. And I think the proof and application component of AOPS is, by itself, a reason to take a year and work through the book, even though, conceptually, DD is beyond it. She was ready for a "middle school" year to solidify and extend.

 

I'd imagine that AOPS algebra really could be more "Discovery" for most students simply because algebra introduces more topics that haven't been covered in 1st-5th or 1st-6th grade math.

[MamaSprout]

I'd sort of forgotten about Life of Fred -- we ran out of steam at the end of decimals, but I think the later books may liven things up. Plus, this is an enrichment strategy that is straightforward to implement and doesn't require the child to express enthusiasm!

 

Your piano strategy give me hope that piano for N. won't be so expensive -- at the moment I am learning along with A. so I can't really steer him other than to do what his teacher's taught, but for the second one I'll have a better background.

 

Your approach sounds like my own ideal! Unfortunately A. would wilt under this -- the solidifying would not be any fun at all for him, just drudgery and annoying arithmetic. His main motivation for learning to show his work and be neat is that it will make more interesting problems possible & fun for him (thank goodness he believes me about these things!). And he would never in a million years grab a math book and start going through it on his own ... well, never in the next two or three years at least. For him I really think the fun in math will come when he sees what it can "buy" him in his science.

Initially, this was against dd's wishes (and not in line with her test results) but I insist she has a good foundation. Small errors = more practice needed at our house. Her older sibs were less radically accelerated, but my experience with them has shown me that it is more important than often stressed on this list. This is not directed at the OP, but at many people read these threads think they are behind if DC isn't doing AoPS by 9. Maybe for a motivated PG kiddo, but that accounts for a fraction of a percent of the population. There are many rich materials out there to explore before AoPS... Enjoy them!

[acurtis75]

A prime example of AOPS-DD did the first section of chapter 6 on decimals. The problems were all ones she could easily solve using techniques she had-really, nothing not covered in SM by about 5B. But the explanations actually proved WHY it worked to do those manipulations, at a level which she wouldn't have had the skills yet to understand when she first was learning how to manipulate decimals. What seemed like a repetition of something that she'd learned long before PA turned into "Oh! That makes sense"-and she dived into the exercises to find the interesting applications-the problems that couldn't easily be solved procedurally, but could be solved by the deeper understanding.

 

FWIW, I'm guessing that almost no child is going to fully "discover" AOPS PA, whether they did a book labeled PA previously or not, because most of the topics simply aren't going to be new. It's the WHY and the applications-the math contest problems and starred problems, and especially the challengers that elevate it to a totally new experience. And I think the proof and application component of AOPS is, by itself, a reason to take a year and work through the book, even though, conceptually, DD is beyond it. She was ready for a "middle school" year to solidify and extend.

 

I'd imagine that AOPS algebra really could be more "Discovery" for most students simply because algebra introduces more topics that haven't been covered in 1st-5th or 1st-6th grade math.

Good thoughts again. After reading this thread the last few days I pulled out the PA book last night to start working through myself before dd gets to it. Beast Academy covers some of what I'm seeing in AOPs PA so far...so even using the recommended AOPs track will allow for introduction of some topics before the PA book. 

 

After working through the first chapter I see dd is going to love it...partially because she is a very verbal child and won't mind the long explanations and mostly because she loves knowing "why" things work.

[acurtis75]

Initially, this was against dd's wishes (and not in line with her test results) but I insist she has a good foundation. Small errors = more practice needed at our house. Her older sibs were less radically accelerated, but my experience with them has shown me that it is more important than often stressed on this list. This is not directed at the OP, but at many people read these threads think they are behind if DC isn't doing AoPS by 9. Maybe for a motivated PG kiddo, but that accounts for a fraction of a percent of the population. There are many rich materials out there to explore before AoPS... Enjoy them!

 

Valid points and this is why we're taking time to do BA & Life of Fred which I forgot about until someone else mentioned it. DD does LOF by herself. I am attempting to meet her need for challenge while making sure we aren't moving so fast that she isn't solid on concepts she will need later.

[acurtis75]

 And he would never in a million years grab a math book and start going through it on his own ... well, never in the next two or three years at least.  For him I really think the fun in math will come when he sees what it can "buy" him in his science. 

 

Keep in mind that at this age change happens fast. I would have said this exact thing 2 or 3 months ago. I would never have imagined dd enjoying math as much as she is right now. 2 or 3 years is a long time. DD has changed a lot in her maturity and enthusiasm for subjects in the last few months.

[serendipitous journey]

I agree that the point of the AoPS PreA isn't new concepts, but is deepening understanding/developing an intuition for WHY things work. 

 

He might light up about math soon -- acurtis, that is hopeful news!  However, I think my 2-ish years timeframe is more likely.  That is what I am seeing in his general interests and development; it sort of lags by a couple of years or so.  So this year is really laid-back academically because it is the first year he's been able to enjoy large chunks of unstructured play without cracking up (or melting down) -- his 3 yo brother is already at that point.  A. didn't start enjoying read-alouds until first or second grade (in Kindergarten I bribed him with chocolate to get him to listen to stories) ... and so on.  So I truly think it will be a bit before the passion hits, esp. since he has zero expressed passion for any schoolish activity (with the sometimes exception of favorite read-alouds). 

 

I think we'll be trying to continue with the algebra (which really has the level of challenge and resistance I associate with A. being in a learning sweet spot).  But if he is too frustrated without the reward of breakthrough moments we'll move over the PreA for a bit, probably doing PreA for our main program and tackling the algebra for a short time each day.  Drills & Sprints to keep fluency, and I'll be using Ruth's ideas for notebook practice this term and move onto her plan for lessening the scaffolding during the next year. 

 

And look for ways to build passion ...

 

whoo-hoo, a Plan!  :grouphug:  everybody. 

 

 

[raptor_dad]

FWIW, I'm guessing that almost no child is going to fully "discover" AOPS PA, whether they did a book labeled PA previously or not, because most of the topics simply aren't going to be new. It's the WHY and the applications-the math contest problems and starred problems, and especially the challengers that elevate it to a totally new experience. And I think the proof and application component of AOPS is, by itself, a reason to take a year and work through the book, even though, conceptually, DD is beyond it. She was ready for a "middle school" year to solidify and extend.

 

I'm looking ahead for DS7 and this captures much of my impression on AoPS PA, which is the only AoPS book I currently own or have seen. The books seems to be trying to do several things at the same time. They are trying to teach logic and proofs and teach math skills via contest problems. The last two starred problems in the sometimes reviled first chapter illustrate this. One is a great contest problem in applied math. The other is a great problem in extending your understanding of the field axioms. I don't see any reason to assume a kid who is good at one will necessarily be good at the other. By the end of the book, hopefully you will have remedied which ever deficit was present.

 

I think this issue is exacerbated by Singapore which is relatively light on logic. I hope either MEP or problem solving rabbit trails will help with this. I am currently looking at the Allen and Pearson's "Modern Algebra: A Logical Approach" books and they make this link explicit. Charon/Myrtle referred to them as Saxon for proof writing with the +/- that implies. They wouldn't work for my 2e accelerated kid but they do point out a deficiency in the standard curriculum. It will be interesting to see what AoPS  does with the logic portions of Beast Academy 4B and beyond.

 

AoPS prealgebra looks good, but part of its benefit is allowing the time and scaffolding for the much vaunted "mathematical maturity" to develop.

[Pen]

Is he advanced enough to be at the special math camp Kathy and Mathwonk are involved in (forgot its name)?   Maybe that would help with enjoyment?

[serendipitous journey]

Is he advanced enough to be at the special math camp Kathy and Mathwonk are involved in (forgot its name)?   Maybe that would help with enjoyment?

 

We haven't funds for it this year.  I'm not sure if he would qualify this summer anyhow ... I haven't pursued the preparatory testing b/c it isn't financially feasible.  But I do think he'd love it. 

[Pen]

Maybe it would be something to work towards anyway.   Maybe they have scholarships even.

 

 

Also, my ds is mildly advanced, but not nearly as much so as yours in math, so take this for what its worth.  He wanted to go into AoPS intro alg. bec. a friend is doing Algebra and he did not want to be only in pre-Algebra (even though AoPS is a harder program than the friend has, I could not sell the more "baby" sounding "pre").   We did some Jousting w/ Armadillos over summer--it has a lot of writing where you would probably have to scribe for your son to use it--but it is another thing to consider as a bridge between math that was not especially Discovery oriented and AoPS Algebra level.   JA is Discovery oriented but a little softer, gentler, more user friendly to the younger student, I think than AoPS.  My ds also liked balance benders and balance math teaches algebra which I think were helpful as fun transitional materials into more logic.  The fact that AoPS is actually a challenge is a hurdle for him emotionally, so having that separate from also his first experience with Discovery style math and more logic in math was a help, I think.  Though we are still finding AoPS algebra a challenge (and the word Intro still makes it sound like it should be easier than what his friend has!).

[serendipitous journey]

Pen, thanks for the encouragement and ideas.  The Jousting Armadillos series looks excellent!  and I'd not seen it before; it may be a great way to up enthusiasm.  And I do think I ought to lay the groundwork for Epsilon Camp in case the way opens for it.