Finished AoPS Intro Algebra, what is next?

[lewelma]

My ds(11) will finish AoPS Intro Algebra next month, and I am trying to decide what should be the next book or books in the series. I am not sure that he will like Geometry very much, in fact he has asked to start Intermediate Algebra next.

 

I am wondering if anyone has spread out Geometry over 2 years so that the student can do Counting/Probability and Number Theory at the same time. I was thinking M,T, W Geometry, and Th, F the other books. Is this doable? I can think of 2 possible negatives: 1) If my ds dislikes geometry, it will take him 2 years instead of 1 to get through it, and 2) with so many new concepts, none of them will really sink in because he would spend only 1/2 a week on each.

 

We could also possibly do Counting/Probability and Number theory next year, and then do a 2 year course using Geometry and Intermediate Algebra concurrently.

 

Finally, does the Geometry book do 2 column proofs like I learned in school? Just wondering, because I really disliked them.:tongue_smilie:

 

Suggestions?

 

Ruth in NZ

Edited April 9, 2012 by lewelma

[KAR120C]

Putting Counting & Probability with Number Theory makes a good pair for a year... They complement each other very well, and "flesh out" each other's techniques. DS did them simultaneously as classes, which was really intense, schedule-wise... I don't think I'd recommend that generally, but running both of them in a year-long course would be excellent.

 

If your DS isn't a fan of Geometry, I don't know that I'd do AoPS for that... it covers quite a bit more than is strictly necessary, and you could easily go with something else and not be lacking. We haven't done their Geometry ourselves; we did the relevant chapters of Singapore NEM before moving on to AoPS later... but I have the book. I think at some point we might go through and pick up the parts that he hasn't seen elsewhere, or that he could use more time on.... or we might just keep it as a reference. I don't know what format they use for proofs, although I would tend to think they'd use something more narrative... Everything in AoPS is a proof, really... but even in the classes they don't go with a set structure.

 

Another geometry you might find more entertaining is Zome. It's pricy because you have to buy all the kits, but it does make a really good geometry course. It's been a while now... I don't remember if it covers as much of the "standard" stuff (triangles) as most... but it does require all the critical thinking and spatial reasoning I'd expect from geometry.

[Julie of KY]

From what you say, I'd probably do the Counting and Probability/Number theory with geometry spread over two years.

 

Geometry is my son's favorite of all the books - but he just see it. Most find that geometry is the hardest of the intro books. Aim for about a chapter of geometry per month and then whatever pace for the other books to go along with it.

 

Everything in geometry has to do with proofs, but they don't make you do it in some formal way.

[fractalgal]

My ds(11) will finish AoPS Intro Algebra next month, and I am trying to decide what should be the next book or books in the series.

 

 

Suggestions?

 

Ruth in NZ

 

Have you seen the AoPS 'Recommendations' page?

 

We are planning to do something similar to one of the options you are considering.

 

My daughter wants to dive right into Geometry this fall, but I think I'd rather have her do some C&P along with it. Our plan is to begin AoPS Counting & Probability this summer, then start AoPS Geometry in the fall for 3 days per week, then 2 days per week to finish AoPS C&P and see how that goes. I think it is doable, and I'd rather have her moving forward with Geometry (as she would like) rather than only do C&P. Later I'd like to add in the Number Theory course as well.

 

There is a personal recommendation form at AoPS that you could use, also.

Edited April 9, 2012 by fractalgal

[Kathy in Richmond]

Since your son is eager for more algebra, I'd probably lean toward your second choice so that he could get to it a little earlier. I think that either of your plans would work fine in the long run, though.

 

You will find plenty of proofs in AoPS geometry, but they're not the two-column type that you remember from high school. Rather, you reason through the proofs and write them up in paragraph form, much like mathematicians would do in their everyday work (and not all that different from what he's used to doing in AoPS algebra already).

 

I wouldn't assume yet that your son won't like the geometry course. Like all AoPS courses, it has a strong problem-solving element. It's among the most challenging courses they offer: solving a tough geometry problem requires the student to consider everything he's learned up to that point, synthesizing his knowledge in creative ways. He might really enjoy the challenge!

Edited April 9, 2012 by Kathy in Richmond

[lewelma]

Thanks so much everyone.

 

DH thought of another issue I had not considered.

 

DS in very interested in physics. Should I delay the counting/probability books and number theory until the end of the traditional sequence, so that he can learn the math he needs to succeed in the physics classes he wants to take in high school? Are these books simple enough that it would be silly to loop back around to them after calculus. Or would it be better to just take an intro statistics class after Calc. If we skip the c/p and nt books, he could use the geometry and Algebra 2 books concurrently over 2 years starting in August.

 

Also, ds really likes the discovery approach, so I would like to stick with AoPS. But if he does dislike geometry (which as Kathy said may not come to pass), could he do half of the book and move on? The website calls the Geometry book an "enhanced honors course." Is there a good stopping point to make it a more basic course? He will be taking the Cambridge International Exams, and geometry is not stressed on them.

 

Thanks for all help!

 

Ruth

[onaclairadeluna]

I love the AOPS discrete math books. If it were me I'd do them first. You theoretically could do them after intermediate algebra but they are easier and so much fun. I would not consider statistics a proper substitute. I have more pure math leanings and statistics was like sticking bamboo under my fingernails whereas "real" math is like having Christmas ever time you open a textbook.

 

(apologies to lovers of statistics and applied math in general)

 

Your DS is in the 6th grade? It is a great time to open the doors to awesomely cool math. You have plenty of time to get to Calc and I am pretty sure you have almost enough math to do algebra based physics with the AOPS into to Algebra book.

[regentrude]

DS in very interested in physics. Should I delay the counting/probability books and number theory until the end of the traditional sequence, so that he can learn the math he needs to succeed in the physics classes he wants to take in high school?

 

Your son already has all the math he needs to succeed in an algebra/trig based physics course (the trig needed for that can be learned in one afternoon).

My DD took an algebra based college physics course after finishing Intro to Algebra and did very well.

 

If he is now finishing 6th grade, and you were spending one year on C&P/Number theory, two years on Intermediate Algebra/Geometry, that would put him into precalc in 10th grade and calc 1 in 11th, or the summer before - so he would be able to start calc based physics in 11th grade.

 

My DD has completed AoPS precalc in one semester; we omit ch. 8 and 12, and a few sections. So he could even get a head start on calc then.

I think at your son's age it is way too early to worry about when he will do calculus - you will be able to tweak his courses when it gets closer.

 

One thought: my DS did the first 13 chapters of Intro to Algebra in 6th grade and needed some time to mature for the more abstract concepts; we are taking a semester for C&P to give him this time. It is hard to predict at what rate -even accelerated- kids mature; I would not look further than a year or two at this point.

 

Are these books simple enough that it would be silly to loop back around to them after calculus. Or would it be better to just take an intro statistics class after Calc. If we skip the c/p and nt books, he could use the geometry and Algebra 2 books concurrently over 2 years starting in August.

There is an intermediate C&P book which he could do then instead.

 

Also, ds really likes the discovery approach, so I would like to stick with AoPS. But if he does dislike geometry (which as Kathy said may not come to pass), could he do half of the book and move on? The website calls the Geometry book an "enhanced honors course." Is there a good stopping point to make it a more basic course?

No, I do not think half the book is sufficient. There are important concepts throughout, just each chapter goes into more depth. You would be able to omit certain sections and maybe the chapter about Power of a point.

[lewelma]

It is a great time to open the doors to awesomely cool math.

 

I'm glad to hear that it is so much fun. I have never taken this kind of math

 

You have plenty of time to get to Calc and I am pretty sure you have almost enough math to do algebra based physics with the AOPS into to Algebra book.

 

Yes, he is fine for a first year physics class. My dh was just looking ahead. Perhaps I am misinformed, but I thought that AP Physics or (for us) the A levels from Cambridge required some calculus. I was just extending out into high school, and realized that there might be a squeeze if he needed to finish calc by 11th grade. In NZ, he is actually half way through 7th grade.

 

Thanks,

 

Ruth

[lewelma]

Thanks Regentrude

 

We were posting at the same time.

 

If he is now finishing 6th grade, and you were spending one year on C&P/Number theory, two years on Intermediate Algebra/Geometry, that would put him into precalc in 10th grade and calc 1 in 11th, or the summer before - so he would be able to start calc based physics in 11th grade. My DD has completed AoPS precalc in one semester; we omit ch. 8 and 12, and a few sections. So he could even get a head start on calc then.

 

This is what I needed to know! Thanks!

 

I think at your son's age it is way too early to worry about when he will do calculus - you will be able to tweak his courses when it gets closer.

I am just laying out his exam schedule for high school to make sure that he has university entrance. Obviously, things change, but others have suggested that a road map is useful.

 

One thought: my DS did the first 13 chapters of Intro to Algebra in 6th grade and needed some time to mature for the more abstract concepts; we are taking a semester for C&P to give him this time. It is hard to predict at what rate -even accelerated- kids mature; I would not look further than a year or two at this point.

I will keep this in mind.

 

No, I do not think half the book is sufficient. There are important concepts throughout, just each chapter goes into more depth. You would be able to omit certain sections and maybe the chapter about Power of a point.

Interesting. I think you can tell that *I* dislike geometry. Also, I never found it useful, like calculus and statistics. So I really dislike the idea of spending a year on it! But we can. My dh reminded me that ds is VERY spacial (as in testing as a 25 year old at age 6), so perhaps he will love it.

 

The other problem I have is that the Cambridge International exam syllabus for math is very different than AoPS. So I am trying to add in some time for going over the other material and studying. Dove-tailing the two syllabi is difficult, but I don't want to give up AoPS for what I consider to be an inferior curriculum for talented students.

 

Thanks again,

 

Ruth

Edited April 9, 2012 by lewelma

[Kathy in Richmond]

My dh reminded me that ds is VERY spacial (as in testing as a 25 year old at age 6), so perhaps he will love it.

 

Interesting.:) My daughter is extremely visual spatial (had the highest score in the country on the JHU/CTY Spatial Test Battery without prepping). She absolutely loved, loved AoPS geometry materials. The text wasn't out yet for her geom year, but she studied all the geometry chapters in the two AopS classic problem solving books and took their olympiad level geometry class online. She was one of the few kids on her math team who volunteered for the geometry subtests at competitions. I think your son is going to like this stuff.:D