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My oldest, who just turned 11, is finishing up Algebra. 

He had completed AOPS Pre-Algebra, and then the first 9 chapters of AOPS Algebra with little problem.  He got to chapter 10 (Quadratic Equations) and he really, really struggled.  We took some time off for him to level up to blue on the first 9 algebra chapters in Alcumus, to ensure he was rock solid on foundational concepts.  Started back at the beginning of chapter 10 - disaster.  We took some more time off and studied quadratic equations on Khan Academy and Math Mammoth.  Started back at the beginning of chapter 10 - disaster.

At that point I officially abandoned AOPS and instead got Chuckles the Rocket Dog (the third book in the Arbor Center series after Jousting Armadillos and Crocodiles and Coconuts), which is entirely focused on polynomials and quadratics.  DS has thrived with Chuckles and is back to enjoying and feeling confident about math.  I especially love how Chuckles explicitly includes and requires taking math notes - I think this is really helping DS because he has ASD and ADHD, and executive function is his nemesis.

DS is about to start the last chapter in Chuckles and I am starting to plan where to head next.  If you had asked me a couple months ago, I would have unhesitatingly said that after the first 13 chapters of AOPS Algebra, that DS would work through AOPS intro to Counting & Probability and then probably Number Theory, before finishing the rest of AOPS Algebra and moving on to AOPS Geometry.  I am very conscious of "The Calculus Trap" and want DS to explore math broadly and deeply rather than racing through the standard, narrow math sequence.

At this point, I haven't ruled out further AOPS books, but I am looking for other options to consider.  Preferably text books - online and video formats do not work as well for DS, and both DH and I are engineers who can help DS with upper level math...well, at least through Differential Equations and Linear Algebra, after that he will be beyond us.

What would you do next with a very mathy, 2e kiddo?  DS is officially finishing up 5th grade now, so he has 7 more years of math courses to fill.

Thanks,
Wendy

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Given your child's age (you aren't in any rush), look at SM Dimensions Math as a bridge. I find Singapore program is also very challenging and might be just a good enough bridge to wait on a little more math muscle and maturity before returning to aops if you so choose.  The TOC will guide you where you want to jump in and how/if you want to contract or pick and chose. Then see in another 6 month to a year if you want to come back. 

There is a lot of math out there to do! Don't worry 🙂 Mine was done with the Intro to Algebra book in 5th grade and we still have so much aops to cover with their extras. And we are going back to Algebra books this summer just for extra practice because it has been so long. 

And also trying to do Into to C&P might not be a bad idea while Algebra is on hold. It's not a particularly difficult book at all. 

 

Edited by Roadrunner
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9 minutes ago, Roadrunner said:

Given your child's age (you aren't in any rush), look at SM Dimensions Math as a bridge. I find Singapore program is also very challenging and might be just a good enough bridge to wait on a little more math muscle and maturity before returning to aops if you so choose.  The TOC will guide you where you want to jump in and how/if you want to contract or pick and chose. Then see in another 6 month to a year if you want to come back. 

There is a lot of math out there to do! Don't worry 🙂 Mine was done with the Intro to Algebra book in 5th grade and we still have so much aops to cover with their extras. And we are going back to Algebra books this summer just for extra practice because it has been so long. 

And also trying to do Into to C&P might not be a bad idea while Algebra is on hold. It's not a particularly difficult book at all. 

 

I'm not worried about running out of math.  I am starting to contemplate what resources I will use to go broad and deep if AOPS doesn't turn out to ever be the right fit. 

AOPS makes it easy - the whole sequence of books specifically designed to teach deep, conceptual math to young, advanced learners.  But, if AOPS doesn't work for DS for whatever reason, then I will have to figure out a different, more ad hoc path.

The resources have to be out there - there must be some other well-written, challenging, accessible upper-level math textbooks - but finding them, when often Amazon doesn't even offer a Look Inside for that type of book, feels like finding a needle in a haystack.

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It sounds like he might do well with Derek Owens, if you wanted to farm it out. It's still pretty challenging and the math notes are a part of it. But  I think what you really want is to keep him on a slow and steady but really deep path. I don't know that DO would really let you do that.

But you could use Jacob's... that's what the Arbor series is based on. It's definitely a lot easier than AoPS. But it's not easy, if that makes sense. It really jibes with certain kids, I think. There is a sort of deeper thinking challenge problem for each set, which is nice. These are not anywhere near as hard as the really hard AoPS problems... they're more about applying knowledge or extending it with some creative thinking.

I second Roadrunner's suggestions as well.

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I still think SM math series is the closest alternative to AoPS if one is looking for a challenge. We didn’t like Arbor math. It didn’t seem to bring to the table what we needed and ended up being a waste of time. For a kid who has gone through AoPS prealgebra and the first 10 chapter of algebra, it might not feel like anything other than a filler. But I guess all kids are different. My choice if any of my children were to opt out of AoPS would be SM. I would be hunting down those books like crazy. 
 

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Singapore Dimensions only goes through 8th grade, right?  I went and looked at that, and up through the 8th grade book there would be nothing new or challenging for DS.

At this point, DS is pretty much done with algebra.  As he has worked through the last Arbor math book, I have been having him also finish up algebra chapters 10-13 on Alcumus, so I am sure that he has got it and is ready to move on.

I looked at Jacob's.  I saw Algebra and Geometry...are there others?  DS certainly could jump right into Geometry, but I guess what I am looking for are books other than AOPS that would let him stop and smell the roses a bit.  What would be another good Number Theory or Probability book?

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Well, I have a sort of peculiar idea...what about some cool problem-solving? My mathiest kid loved this book:

https://store.doverpublications.com/0486409171.html

(If that link doesn't work--it's Bonnie Averbach and Orin Chein, Problem Solving through Recreational Mathematics, published by Dover.) There is a lot of advanced math in it--I think it would likely keep him busy, progressing, and having fun, too.

Anyway, that might be too odd, but I thought it was worth mentioning--hope it helps!

Edited by Emerald Stoker
tried to fix link
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Elements of Mathematics Foundations. https://www.elementsofmathematics.com/

The first course if free for 30 days right now. My kiddo who doesn't love AoPS, really likes these. She uses them as a supplement because she came to them during Algebra 2, but your son could do the whole series and then move on to calc if he likes it.

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We also hit some walls at various points in AOPS pre-A and A and took some breaks.  My kiddo has found doing Life of Fred to be fun and helpful - we did LOF Algebra during AOPS geometry to keep ideas fresh, and he said that it was really helpful to see the same ideas a different way.  Even now as we finish middle school and have done geometry and are working through advanced algebra, we still do LOF once/week or take LOF breaks when things get hectic - it keeps kiddo from feeling bogged down, I think.  He also found number theory and probability to be much easier than algebra, although I won't rule out the idea that he matured a lot in between.  I think his favorite was number theory.  

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Since you're looking for a textbook and you don't mind doing the teaching, I might recommend Brown's classic Algebra I, Geometry, and Algebra II & Trigonometry sequence from Houghton Mifflin. You can find used versions of the textbooks and teacher's editions on Amazon. We turned to these when we hit the wall with AoPS and we've been really happy with them. 

Algebra 1: https://www.amazon.com/gp/offer-listing/0395977223/ref=dp_olp_used?ie=UTF8&condition=used

Geometry: https://www.amazon.com/gp/offer-listing/0395977274/ref=dp_olp_used?ie=UTF8&condition=used

Algebra 2 & Trigonometry (basically covers Algebra 2 + Precalculus):  https://www.amazon.com/gp/offer-listing/0395771188/ref=dp_olp_used?ie=UTF8&condition=used

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4 hours ago, square_25 said:

 

There aren't good alternatives in the same vein, frankly, which bums me out, because the AoPS books aren't always nearly as educationally sound as they may be. But they are also the most mathematically rigorous things on the market. 

Update - I think I found something!

First I decided to look through Great Courses to see if there were any math courses we could use to bide our time.  I found The Power of Mathematical Visualization by James Tanton and I fell in love.  It is amazing, and the course guide includes detailed lecture notes and problems (and fully worked solutions) to go with each lecture.  DH and I have been devouring the lectures the last two nights - they are fascinating.

So then I went looking for any textbooks written by Tanton and I found his Middle School Mathematics series on Edfinity.  They are not "full" courses, but rather deep, conceptual introductions to a variety of topics along with challenging problem sets (auto-graded with performance analysis).  His course are:  8 Tips to Conquer Any Problem; Counting and Probability; Numbers and the Number System; Structure, Patterns and Logic; and Relations and Equations.  You can buy 6 months of access to each course for $5.

He also has a geometry course on Great Courses, a two volume Geometry text, several comprehensive videos series on YouTube, and a series of high school math texts that look very interesting called Thinking Mathematics! (but I can't currently find them for sale anywhere 😕).

I think once DS finishes Algebra 1 (with Chuckles the Rocket Dog and Alcumus) then he is going to take a break by going through The Power of Mathematical Visualization.  He is going to LOVE it.  Then I think I will have him go through the Edfinity courses.  At that point we might decide to try AOPS intro to Counting & Probability (and perhaps Number Theory), or if DS is really connecting to Tanton then we might go right into his Geometry course.

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I got the Tanton geometry books on Lulu years ago--maybe look there, if you haven't already? Those were fun books, as I recall. (I have math book addiction....it's the one thing I really, really, really didn't want to mess up when I first started homeschooling!)

 

Oops, edit--I see that it's the Thinking Mathematics that you can't currently find--sorry! His site links to Lulu for those books, too, though: http://www.jamestanton.com/?page_id=20

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11 minutes ago, Emerald Stoker said:

Oops, edit--I see that it's the Thinking Mathematics that you can't currently find--sorry! His site links to Lulu for those books, too, though: http://www.jamestanton.com/?page_id=20

His site links to lulu, but it just takes you to a 404 error.  His Thinking Mathematics books don't appear to be on lulu anymore.  I sent him a message to see if they are available anywhere.

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A really interesting deep and broad Christian math with a unique sequence is James Nickel's series, The Dance of Number. You really need both, there is some interesting and hard math in the first book.  I can't remember if you are a Christian or not.  If not, others may enjoy it.

1. https://www.amazon.com/gp/product/099910540X/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1

2. https://www.amazon.com/gp/product/0999105477/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1

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7 hours ago, wendyroo said:

Update - I think I found something!

 

So then I went looking for any textbooks written by Tanton and I found his Middle School Mathematics series on Edfinity.  They are not "full" courses, but rather deep, conceptual introductions to a variety of topics along with challenging problem sets (auto-graded with performance analysis).  His course are:  8 Tips to Conquer Any Problem; Counting and Probability; Numbers and the Number System; Structure, Patterns and Logic; and Relations and Equations.  You can buy 6 months of access to each course for $5.

Thanks for posting these. I had seen these once log ago and could not find them again.

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9 hours ago, wendyroo said:

Update - I think I found something!

First I decided to look through Great Courses to see if there were any math courses we could use to bide our time.  I found The Power of Mathematical Visualization by James Tanton and I fell in love.  It is amazing, and the course guide includes detailed lecture notes and problems (and fully worked solutions) to go with each lecture.  DH and I have been devouring the lectures the last two nights - they are fascinating.

So then I went looking for any textbooks written by Tanton and I found his Middle School Mathematics series on Edfinity.  They are not "full" courses, but rather deep, conceptual introductions to a variety of topics along with challenging problem sets (auto-graded with performance analysis).  His course are:  8 Tips to Conquer Any Problem; Counting and Probability; Numbers and the Number System; Structure, Patterns and Logic; and Relations and Equations.  You can buy 6 months of access to each course for $5.

He also has a geometry course on Great Courses, a two volume Geometry text, several comprehensive videos series on YouTube, and a series of high school math texts that look very interesting called Thinking Mathematics! (but I can't currently find them for sale anywhere 😕).

I think once DS finishes Algebra 1 (with Chuckles the Rocket Dog and Alcumus) then he is going to take a break by going through The Power of Mathematical Visualization.  He is going to LOVE it.  Then I think I will have him go through the Edfinity courses.  At that point we might decide to try AOPS intro to Counting & Probability (and perhaps Number Theory), or if DS is really connecting to Tanton then we might go right into his Geometry course.

Thanks for sharing the link.  I think my 10 yr old will have fun with the elementary/middle school ones.  I think I'll buy access and on rainy days this summer let her spend time with them. 

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