AOPS Algebra Pace

[MrSmith]

Some background: It took my son 18 months to finish AOPS Pre-Algebra.  During that time, he completed every section exercise and every review and challenging problem.  He worked very hard throughout the book, and I would say he has come away with a very thorough understanding of the material.

 

We started Intro to Algebra 2 months ago.  In that time he has completed 4 chapters (45 minutes a day, 5x a week; lecture replacing exercises as needed).  He has completed all section and review exercises, and also completed a sampling of challenging questions.  My concerns are: pace, understanding, and retention.

 

1. Pace - Is he going too fast?  When he was younger, he went through a couple of years of SM in 9 months, so there is precedent.  But still - a chapter every two weeks just seems...really fast for Algebra, especially considering the 5 weeks per chapter average from the Pre-A book.  Right now, I only give him 3 or 4 challenging problems.  I think even if I were to assign all the challenge questions, that may only extend each chapter by a week.  Looking at some of those questions, I am hesitant to assign them all just for the sake of taking more time (plus I want to save them for review later).

 

2. Understanding - Is it possible to go so fast and still truly understand the material at a 'conceptual' level?  Again, there is precedent from prior use of SM.  In addition, looking through these 4 chapters, I'm finding very little in the way of 'concept' that hasn't already been explained by the Pre-A book.  The one salient area I see is that when working a problem he often does not use his latest tools.  I think that this will come with exposure and practice.  How might I assess conceptual understanding beyond the review questions?

 

Through the four completed chapters he has maintained about 85% accuracy on review exercises (of those 15% I would say 90% are silly errors (signs) and 10% conceptual errors).  Based on this I would say that has at least shown procedural proficiency of the topics.

 

3. Retention - Will he remember all this stuff in a year?  I think we are OK here.  The AOPS questions seem great at mixing concepts together to keep them fresh (but someday he will run out of book...).  But...there is Alcumus and the left over challenge questions.  I think I will also torture him with the Algebra A/B online classes at some point.  What else could I potentially include to help retention?

[Roadrunner]

The first four chapters of Intro to Algebra are review and deceptively easy. The material gets harder and harder as you progress, so don't worry, he will slow down. 😂

It took my son 8 months to get through preAlgebra text while Intro to Algebra (we are wrapping it up now) is solid 11 months.

 

We decided to do the second half of Alcumus algebra (half of it he had to complete for an online class) once a week next year while he is working my on geometry, so he won't be away from algebra for the entire year.

Edited May 8, 2016 by Roadrunner

[regentrude]

As pp wrote: the first chapters are review; he has seen this material in prealgebra. So, his pace may not remain as fast.

 

It is not possible to work the AoPS problems without conceptual understanding. They are designed so that they cannot be solved by somebody who is just memorizing algorithms.

 

He will retain the most important concepts because they are applied over and over again. He may forget some details or special topics, but that is OK; if he has learned to think, he will be able to rederive anything once he needs it.

[Mike in SA]

AOPS Prealgebra is probably the hardest of the series.  Algebra is much easier afterwards.  It WILL be faster.

[Roadrunner]

AOPS Prealgebra is probably the hardest of the series. Algebra is much easier afterwards. It WILL be faster.

See, I disagree with this. I think topics covered in algebra are much more difficult and you go from MOEMS problems in challenging sections to often AMC 10 and the likes. I look back at preA book and it seems so easy to us in comparison.

[Dmmetler]

I think PA tends to feel hard because it's just plain different. That may change as kids who have done BA 2-5 come into AOPS. By Intro Algebra, the content is harder, but the format is familiar. Although DD found Intro Geometry to be quite brain stretching.

[wapiti]

I also think there may be a bit of sequential vs spatial - some people feel more natural with one or the other, with algebra leaning more sequential, geometry more spatial, and the topics in the prealgebra text being a combination (therefore hard for everyone? LOL).  Personally, I prefer the prealgebra and geometry texts though I think that's just because algebra topics are less interesting to me.  I think they're all equally hard, though a challenging geometry problem is much more fun for me than a challenging algebra one.

 

To the OP, first 4 chapters of the algebra text are definitely review for a student who completed the prealgebra text so thoroughly!

[madteaparty]

I can't comment on pace as Aops is not the right program for us and yet that's what we keep using. Anyway, we are taking the class and it is about a chapter a week.

 

I don't think aops algebra is enough for my particular child and at some point in time we will need to circle back with more review. This could be my non mathy kid, who is 12 and there's some tween brain leak I'm told. But this has always been the case with us, we need spiral.

Having taken less than a semester to go through the first half of the book, we are taking the entire next school year to do the second half, with WTMA. I understand the teacher there adds Singapore problems, which is the correct approach for us and another reason we are taking the class.

[Mike in SA]

See, I disagree with this. I think topics covered in algebra are much more difficult and you go from MOEMS problems in challenging sections to often AMC 10 and the likes. I look back at preA book and it seems so easy to us in comparison.

 

Interesting.  DS didn't see it that way.  :)  He found the challengers in Pre-A much tougher, but did them all.  After those, the Intro to Algebra has been very straightforward, right to the end (he is on the last chapter now).

 

Can't speak to geometry - DS did Kiselev, which is a little bit harder than AoPS, but also discovery-style.  He found the AoPS samples to be easy after (and Jurgensen a tad silly in its simplicity).

 

The thought of sequential vs spatial is an interesting one, because that is how most see it.  We don't - DS learned some abstract algebra long before pre-A, so for us, algebra is just as spatial as geometry is.  As well it should be...

[Roadrunner]

Maybe it's the age? Things seem harder at a younger age. DS thought toughest chapter in preA was chapter 5, which is basically just the intro to linear equations. Intro to Algebra book takes that chapter to another dimension. I won't mention the optimization problems 😱. We also thought chapter 21 on geometric sequences was immensely interesting, but tough. PreA just has a taste of what's coming. Sample a little geo, taste a little algebra or number theory. It's an appetizer platter. 😆

[SparklyUnicorn]

I thought pre A was more difficult than the first algebra book.  So this doesn't sound crazy to me at all.

 

 

[daijobu]

 

3. Retention - Will he remember all this stuff in a year? ...  What else could I potentially include to help retention?

 

If you are concerned about retention, you can throw your student an old MathCounts or AMC8 every once in a while to keep his skills sharp.  The MC exams come in different difficulties (school--> chapter--> state--> national) so you can match to his problem solving skills.  If he's already doing AoPS, you can probably skip to chapter level exams.  Check the exams to see that he is retaining the algebra concepts and review as needed.  (Again if he's doing AoPS successfully, he should have no probems.)

 

The above exams will also introduce him to some concepts in geometry, number theory, and counting which will pave the way for future AoPS texts.  Good luck!  

[Julie of KY]

2 weeks per chapter is fine if he's getting it. A student who has had AoPS Prealgebra should be able to move faster than one who hasn't since it is simply taking the next step on concepts already introduced.

 

If he's doing well in later chapters of the AoPS book, then I would say that he's retained most of it as you cannot progress without retaining most of the material. Some pieces of the material only show up here and there so they might be more easily forgotten, but the base algebra has to be understood to keep moving through the book.

 

Slow down as needed if it gets hard.