Art of Problem Solving too hard?

[Jenn in Mo]

My 13 yo son did great with Singapore. After 6b, we did an old Dolciani for a little while to keep him working while I tried to figure out what to do next. I opted for the AoPS Algebra instead of NEM. We're only two weeks in and he's already overwhelmed. He did REALLY well with Singapore. He understands the concept of algebra fine. But AoPS is throwing negative and fractional exponents in right off the bat and doing hardly any review before upping the difficulty. He thrives on challenge, but this is too much! Where do we go from here??:confused:

[Matryoshka]

AoPS, from their pre-test, expects a student to have already had a lot of exposure to pre-Algebra (exponents, negative numbers, radicals, equations with multiple variables and the distributive property - all of those are in the pretest) before starting. I'd actually say more than just exposure, lots of practice and use with those topics. Since Singapore, strong as it is, doesn't include any of those topics in its Primary Math program, I think some kind of intermediary course is necessary. This may not be true with a less rigorous Algebra program.

 

My dd also just finished up 6b. My plan for her this year is to do Singapore's Discovering Mathematics 1a/b (similar to NEM), where those topics are introduced and used, and then head into Algebra. NEM, rigorous as it is, doesn't expect kids to have already studied those topics, as it's following the Singapore sequence.

 

We made our first foray into AoPS this summer with their Number Theory book, which actually expects less Algebra knowledge than their Algebra course. Odd, but there it is. My dd's enjoyed that course so much that I just bought the AoPS Algebra books - but I still plan on going through DM1 first - may just be a bit faster than I'd thought - but maybe not - have to see how it goes when we start it.

[Miss Marple]

AoPS, from their pre-test, expects a student to have already had a lot of exposure to pre-Algebra (exponents, negative numbers, radicals, equations with multiple variables and the distributive property - all of those are in the pretest) before starting. I'd actually say more than just exposure, lots of practice and use with those topics. Since Singapore, strong as it is, doesn't include any of those topics in its Primary Math program, I think some kind of intermediary course is necessary. This may not be true with a less rigorous Algebra program.

.

 

I agree with this. My ds#4 used LOF beginning algebra in 7th after finishing PM6. He started LOF Advanced algebra but hit a wall. So we backed off and started AoPS Geometry and AoPS Intro. Algebra. While the first few chapters of the algebra were easy, he has found that subsequent chapters are much more challenging than LOF.

 

We're doing NEM 2 this year (started school yesterday) and we'll add in AoPS Alg. 1 throughout the year in order to finish the book. I'm not sure what we'll do after that...probably a combination of NEM 3 and AoPS Algebra 2 (or whatever they call it).

[naturalmom]

matroyshka -

 

I've got this book, and ds is very very interested in it. Is it possible to do before algebra? Would you recommend right after Singapore 6B (or EPGY 6, since we're on a detour right now)? Or would it be good to pre-algebra first, either through EPGY, or else going through NEM1? It definitely appeals to him more than algebra right now!

 

Or - is it possible to do some of it without algebra, and hold off on other chapters till after algebra?

[Nissi]

Ds. worked on Number Theory after finishing up Foerster's Algebra I and found it challenging.

[regentrude]

The skills tested in the pretest are really necessary. Was he able to do all those things without difficulty?

Chapter 1 is partly review, but also introduces new concepts. How much time did your son spend on Chapter 1? Does he work all the problems? Do the initial problems by himself first before looking at the solution?

Just to give perspective, my DD spent 20 hours working on the first chapter (DS a little less).

 

Chapter 1 brought on a lot of material. It was our impression that chapter 2 they went a bit slower. So where exactly is your son having trouble?

AoPS is a wonderful book - but it might not be the best fit for every student.

[Matryoshka]

I've got this book, and ds is very very interested in it. Is it possible to do before algebra? Would you recommend right after Singapore 6B

 

We went right into Number Theory after 6b. It was her "fun summer math". We'll complete through chapter 9 before school starts up again in a couple of weeks. She has not done an Algebra course; we probably won't get to a full Algebra course for another year.

 

We have done everything except chapter 7 (specifically deals with Algebra - but that chapter is very short and only has one topic), and I haven't had her do the challenging problems at the end of the chapter. I figured tackling this book before Algebra was challenge enough. :tongue_smilie: She has done all of the sections with "stars" which designate them more challenging.

 

The plan is to finish the book next summer, or I told her she could do some more as a reward if she finishes her "regular" math early. :lol: She loves this book. I'll have her go back and do the end-of-chapter challenge questions at some point too.

 

The book does not include any advanced algebra - it does deal quite a bit with factoring, prime numbers, and exponents - which happen to be the first topics in DM, so that should be a breeze after this! There's lots on divisibility rules, and now we're doing math with different bases, which is what she's most excited about, and why she wanted to get to chapters 8-9 before the end of the summer. Most of the chapters build on each other, so it wasn't really possible to skip ahead. Skipping the one topic in chapter 7 doesnt' seem to be a problem, though - it doesn't really carry on to anything else.

 

I've had to explain the distributive property to her, and how to factor something out, ie 16x + 4 = 4(4x + 1), but the examples of this they use stay pretty basic. It's actually been a great introduction to these topics.

 

I'd have a look at the pre-test for the book and see what you think. It's a much more straightforward test than the pre-test for the Algebra book.

[naturalmom]

I glanced through the pre-tests for Number Theory, Counting & Probability, and Algebra - Number Theory definitely looks the easiest! Plus, it's more up his alley, if that makes any sense.

 

We have the book already (found it used), but I haven't had time to evaluate the level. He'll be glad to tackle it before algebra, I think!

[Jenn in Mo]

The skills tested in the pretest are really necessary. Was he able to do all those things without difficulty?

Chapter 1 is partly review, but also introduces new concepts. How much time did your son spend on Chapter 1? Does he work all the problems? Do the initial problems by himself first before looking at the solution?

Just to give perspective, my DD spent 20 hours working on the first chapter (DS a little less).

 

Chapter 1 brought on a lot of material. It was our impression that chapter 2 they went a bit slower. So where exactly is your son having trouble?

AoPS is a wonderful book - but it might not be the best fit for every student.

 

He was able to dot he pretest, but I wouldn't say without difficulty. The Dolciani walked gave vocabulary to the algebra Sing. 6b had him doing. I think he went into it with enough prep for a regular algebra text, but this is much meatier than any other algebra text I've looked at. I'm glad, truly, but not sure he's ready yet. He has spent about an hour a day for two weeks on chapter one and still has a few hours to go before finishing it....and we're using the solutions manual for nearly all of these. He definitely tries them on his own first...will spend half an hour on one problem (really WANTING to get it himself) before looking at the solution.

 

Cube root, exponents, prime factorization...no problem. But the cube root of -1371 to the -3/4 power is....daunting. I think the part that has him skittish is that sometimes, he should go ahead and cube the # 1st. Other times, he should break it down into easier factors 1st. Sometimes he should factor down the exponents, sometimes not. It's not that the rules change, but sometimes one option makes the parts of the problem easier to manage....but having so many options is confusing him. I know that at this point, he wants a formula to follow, simply because he's exhausted from this. We chose this text to avoid 'formula math' and I guess I got my wish. :D

 

I peeked ahead with him and Ch. 2 looks like a breeze, so maybe we'll try and stick with it. If it stays too hard, we might need to take a break and come back after a basic algebra text.