Switching to AoPS after algebra?

[4KookieKids]

I'm just hashing some thoughts out, and am looking for hive wisdom. What are your thoughts on doing something "simpler" than AoPS for preA and Algebra, but then jumping into AoPS for their fun stuff like number theory and combinatorics? I have a kiddo who I think would thrive on the problem solving aspect if it was part of some of these other courses, but I'm not so sure he would if it was in Algebra. I value the problem solving focus of AoPS. And I don't want to "rush" Algebra, because I do think solid Algebra skills are valuable (I teach math at the collegiate level.... I really do understand the value of solid algebra skills.... lol.), but I'd rather spend the bulk of our time in content that is a little... more... exciting...

[Pegs]

AOPS' Intro to Number Theory is a perfectly good standalone text. :)

 

I haven't used Counting and Probability, so can't comment on that one in particular.

[seaben]

I've used 3 out of the 4 of those books. I liked them all but PreAlg was actually my favorite due to the brilliance of the problem set arrangements. However, format wise they all are very similar. So I'm curious what you mean by more exciting?

Its just a textbook and there certainly is a low barrier to just trying them out to see if any of them, Number Theory or Counting and Probability included are a good fit.  But I would assume if you dislike one then you're going to have a similar experience with the rest of them.  Another option is to use them as enrichment resources around another curriculum, picking and choosing problems and sections as desired.

 

 

[4KookieKids]

I've used 3 out of the 4 of those books. I liked them all but PreAlg was actually my favorite due to the brilliance of the problem set arrangements. However, format wise they all are very similar. So I'm curious what you mean by more exciting?

Its just a textbook and there certainly is a low barrier to just trying them out to see if any of them, Number Theory or Counting and Probability included are a good fit. But I would assume if you dislike one then you're going to have a similar experience with the rest of them. Another option is to use them as enrichment resources around another curriculum, picking and choosing problems and sections as desired.

I just meant more exciting content. I find Number theory, counting, probability, graph Theory and the like to be infinitely more interesting than algebra, trigonometry, and the calculus. And while he’s young, it appears that at least one of my kids feels the same way. So my thought was just that if we’re going to spend a long time on one or more of the AoPS books, it would just be more fun to learn those problem-solving skills in a context that wasn’t algebra.

[Crimson Wife]

My DS is using Elements of Mathematics and just started the 1st algebra course. I am planning on having him do the AoPS Intro to Algebra book after the EoM algebra sequence because he is still youngish and while I think EoM is a solid program, I think my DS would benefit from working through the AoPS problems.

 

 

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[SoCal_Bear]

You could use the Jousting Armadillos series. My son is using JA and seems to enjoy it. It's a lot less dense yet still discovery method. Maybe consider Jacob's Mathematics: A Human Endeavor? We are also enjoying using Glenn Ellison's Hard Math books as well.

[wendyroo]

I just meant more exciting content. I find Number theory, counting, probability, graph Theory and the like to be infinitely more interesting than algebra, trigonometry, and the calculus. And while he’s young, it appears that at least one of my kids feels the same way. So my thought was just that if we’re going to spend a long time on one or more of the AoPS books, it would just be more fun to learn those problem-solving skills in a context that wasn’t algebra.

 

There are many words that I would use to describe AOPS pre-algebra, but boring is not one of them.  

 

It is challenging and frustrating and demanding.  It is dense and overwhelming and interminable.

It is delicious and satisfying and engrossing.  It is thrilling and elegant and breathtaking.

 

It is not a run-of-the-mill, tedious, simplistic, boring pre-algebra.

 

My son was so, so done with easy, pointless, boring math.  He finds AOPS so much harder and so much more fun.

 

Wendy

[4KookieKids]

There are many words that I would use to describe AOPS pre-algebra, but boring is not one of them.  

 

It is challenging and frustrating and demanding.  It is dense and overwhelming and interminable.

It is delicious and satisfying and engrossing.  It is thrilling and elegant and breathtaking.

 

It is not a run-of-the-mill, tedious, simplistic, boring pre-algebra.

 

My son was so, so done with easy, pointless, boring math.  He finds AOPS so much harder and so much more fun.

 

Wendy

 

Ha ha. Maybe this is really my issue - my experience with pre-algebra, then algebra, then trig, precalc, calc I, II, and III was just so boring... It's hard for me to imagine algebra that's not, I guess! Maybe I just need to get my hands on it and actually read through it carefully. Thanks for these thoughts.

[Gil]

I don't want to just "bash" AOPS, but because I wish someone would've warned me, I will be the voice of dissent.

 

We really disliked Introduction to NT. Like...really disliked it by the end.

 

I asked about NT and no one said anything so we went and did Introduction to Number Theory as our first AoPS book.

It was sooooo slow, repetivitve and made everything so much more long and drawn out than it needed to be. It didn't take long before the pacing was frustrating. By the end, even I felt that it drug on and on and on and even in the end? With hindsight? We feel that the book was not all that good.

 

That book kind of soured The Boys on the AoPS series because it was both the first AOPS math book we did and the first math book that they "hated" and decided was "just really, really dumb".

 

And they did a lot of math even in early elementary years. By the time they started NT they were pretty used to the idea of occasionally "slogging" through math, but man did they wind up hating that book by the end.

 

I would not start AoPS books with Intro to NT because it seems to be a divisive book. Some people report loving it, but others absolutely do not.

[quark]

I'm just hashing some thoughts out, and am looking for hive wisdom. What are your thoughts on doing something "simpler" than AoPS for preA and Algebra, but then jumping into AoPS for their fun stuff like number theory and combinatorics? I have a kiddo who I think would thrive on the problem solving aspect if it was part of some of these other courses, but I'm not so sure he would if it was in Algebra. I value the problem solving focus of AoPS. And I don't want to "rush" Algebra, because I do think solid Algebra skills are valuable (I teach math at the collegiate level.... I really do understand the value of solid algebra skills.... lol.), but I'd rather spend the bulk of our time in content that is a little... more... exciting...

 

Here's kiddo's path:

2nd-3rd grade-ish: Intro to C&P

3rd grade: Algebra 1 with Dolciani + Intro to NT

4th: AoPS Intro to Alg (half) + Jurgensen geometry

5th: Dolciani Alg 2/Trig + abstract algebra (tutor's own curriculum)

6th onwards: Abstract algebra concentration followed by calculus and other things.

 

But throughout, from kindy onwards, kiddo used a lot of books in my siggy for leisure reading and learned a good amount of number theory without using AoPS. In fact, kiddo preferred the non AoPS number theory resources. So yeah I'm sure you can do what you are saying and create lots of excitement for math without starting Algebra very rigidly or formally.

 

[daijobu]

I just meant more exciting content. I find Number theory, counting, probability, graph Theory and the like to be infinitely more interesting than algebra, trigonometry, and the calculus. 

 

I agree with the PP that the Intro NT book is not the best in the lot.  However, the second half of the book that covers mods is quite good.  I'd just skip the first half.  

 

Graph theory is covered in the Intermediate C&P book, while the basics of C&P are covered in the intro book.  Here's the Intermediate TOC.

[4KookieKids]

I agree with the PP that the Intro NT book is not the best in the lot.  However, the second half of the book that covers mods is quite good.  I'd just skip the first half.  

 

Graph theory is covered in the Intermediate C&P book, while the basics of C&P are covered in the intro book.  Here's the Intermediate TOC.

 

Hmmm. I appreciate the voices of dissent, since it gives me things to think about that I hadn't considered. Perhaps we'd just be better of using AoPS for algebra, since folks say it's better than I was expecting, and using one of my college texts for Number theory and other stuff, since I have a few that I thought were excellent. I'll have to keep thinking about this. Thank you all so much!

[kiana]

I agree that I'd try to make algebra exciting instead of treating it like "eat your boiled spinach and then you can have your fun stuff". There are so many interesting things that are totally within the scope of the standard curriculum but are omitted because the focus is on dragging everyone through the basic level. 

[4KookieKids]

I agree that I'd try to make algebra exciting instead of treating it like "eat your boiled spinach and then you can have your fun stuff". There are so many interesting things that are totally within the scope of the standard curriculum but are omitted because the focus is on dragging everyone through the basic level. 

 

I agree to an extent, and would like it if ALL their math were fun and interesting. At the same time, I think it's ok that some people like different things more, just like people have different tastes in music and food. In grad school, I knew folks who loved the analytical side of things, even if Fourier series were enough to make me run in the opposite direction. And I knew folks who dreaded graph theory and would have hated every minute of looking at the group structures of graph isomorphisms, which I absolutely loved! 

 

I'd like to give my kids ample exposure to all sorts of topics so that they can go whichever direction they like in math, but I also think it's ok to acknowledge that not every topic in math is riveting to everyone (even if they *like* math) and it's not always because you just don't have a good book or good presentation.

[wendyroo]

I agree to an extent, and would like it if ALL their math were fun and interesting. At the same time, I think it's ok that some people like different things more, just like people have different tastes in music and food. In grad school, I knew folks who loved the analytical side of things, even if Fourier series were enough to make me run in the opposite direction. And I knew folks who dreaded graph theory and would have hated every minute of looking at the group structures of graph isomorphisms, which I absolutely loved! 

 

I'd like to give my kids ample exposure to all sorts of topics so that they can go whichever direction they like in math, but I also think it's ok to acknowledge that not every topic in math is riveting to everyone (even if they *like* math) and it's not always because you just don't have a good book or good presentation.

 

I agree with the bolded, however, I think algebra is much broader than a "topic", or at least it can be if you take the time to go deep and wide.  Algebra has so many diverse facets, that surely a math-lover will find many aspects interesting, even if some specific topics don't float their boat.

 

Wendy

[kiana]

I agree to an extent, and would like it if ALL their math were fun and interesting. At the same time, I think it's ok that some people like different things more, just like people have different tastes in music and food. In grad school, I knew folks who loved the analytical side of things, even if Fourier series were enough to make me run in the opposite direction. And I knew folks who dreaded graph theory and would have hated every minute of looking at the group structures of graph isomorphisms, which I absolutely loved! 

 

I'd like to give my kids ample exposure to all sorts of topics so that they can go whichever direction they like in math, but I also think it's ok to acknowledge that not every topic in math is riveting to everyone (even if they *like* math) and it's not always because you just don't have a good book or good presentation.

 

Yes ... but I wouldn't assume that it was going to be boring/tedious without at least *trying* to make it interesting :)

 

I'm also basing my comments on your statement about your own experiences in algebra through calculus. I had the same experience as you did in calculus, and also in linear and diffeq, FWIW. It was easy, but rather uninteresting and tedious. Then I took discrete and discovered how much fun there was and changed my major that semester. 

 

But going back through, and teaching these topics (algebra/precalculus/calculus), and researching alternative ways of doing and explaining, and looking at the fun theoretical problems in my calc textbook (it's not AOPS but Thomas is a pretty decent book, much better than what I used), well, there's a lot more to it than I thought there was, and a lot more that can be done at a relatively elementary level, and I very much wish I'd seen all of my math that way. 

 

There are also a lot of very interesting links to other math topics within elementary algebra that kids can totally work with but we omit because ... well, that would lead into a rant, but ... anyway, we don't do them. 

 

That being said -- if the pre-algebra/algebra books just aren't for them -- I would totally switch away. I would just try it first. 

[4KookieKids]

Yes ... but I wouldn't assume that it was going to be boring/tedious without at least *trying* to make it interesting :)

 

I'm also basing my comments on your statement about your own experiences in algebra through calculus. I had the same experience as you did in calculus, and also in linear and diffeq, FWIW. It was easy, but rather uninteresting and tedious. Then I took discrete and discovered how much fun there was and changed my major that semester. 

 

But going back through, and teaching these topics (algebra/precalculus/calculus), and researching alternative ways of doing and explaining, and looking at the fun theoretical problems in my calc textbook (it's not AOPS but Thomas is a pretty decent book, much better than what I used), well, there's a lot more to it than I thought there was, and a lot more that can be done at a relatively elementary level, and I very much wish I'd seen all of my math that way. 

 

There are also a lot of very interesting links to other math topics within elementary algebra that kids can totally work with but we omit because ... well, that would lead into a rant, but ... anyway, we don't do them. 

 

That being said -- if the pre-algebra/algebra books just aren't for them -- I would totally switch away. I would just try it first. 

 

I agree with this! I did find much more interesting content once I was actually teaching it. And who knows? DS really loved learning about fractions and *why* you do stuff with them (common denominators for addition/subtraction, but not when multiplying, for example, or why dividing by a fraction is really multiplying by its inverse), so maybe we're already doing a better job at making that stuff interesting than I remember it being! lol. :)  I guess I really love teaching all sorts of math, and I love trying to make even the "boring" stuff interesting, but I'm uncertain as to which texts will do that for kiddos, since mosts of the texts where I was actually paying attention to the quality of the text was at a higher level than my kids will be seeing in the near future - I just wasn't attentive enough or invested enough to be able to judge a "good" text before grad school, unfortunately. I wonder if anyone local would have some of these resources that have been mentioned so I could take a good long look at them (The AoPS, but also the jousting armadillos, and such).... Hmmm...