AoPs as electives... Number Theory and Counting/Probability?

[mirabillis]

I have a question... we are working on rounding out our standard 5 credit year (English, Math, Science, History, Language) with 1 full credit elective, or 2 .5 credit electives.

 

I'm thinking of trying Edhesive's Intro to Computer Science - semester long (so 0.5 credit) ahead of next year's foray into AP Comp Sci (not sure where yet)

 

So that leaves me with 5.5 credits. I'd like to have a solid 6. Math is my ds's favorite subject. He's currently taking WHA Algebra II. He's used Richard Ruscyk's videos during MathCounts grades 6-8, so is familiar with the AoPs style. I'm thinking he might like taking through the AoPS online school some shorter courses, like Number Theory and/or Counting/Probability.

 

How many high school credits would NT or Counting/Prob take?

 

Anyone with any experience with these? Would he start with Intro level, since he's only taking Algebra II (not AoPs, but rather Dolciani)?

 

Thanks!

[mom2bee]

Yes, start with the Intro books unless your sons studied the topic elsewhere already at depth. I don't know about the credits and such.

 

I would suggest starting with Counting and Probability because I remember some people saying Intro to NT was the weakest AoPS book of the series.

 

 

[quark]

My son combined Intro C&P and Intro NT and miscellaneous other number theory-based self study for a total of one credit. I listed this under math and not electives. HTH!

[regentrude]

I would give half a credit for each of the books. They are each a good amount for a semester.

 

Like quark, I am listing this under math. I list all academic electives under the subject areas to which they belong, not as a "misc electives".

Edited October 2, 2016 by regentrude

[JoJosMom]

I considered each to be a one semester course (in my state 1 credit, under the Cambridge system 1/2 credit.)  My DD has taken both online and found Counting and Probability to be the harder, by far.  In case you are interested in the online option, the University of California does consider the classes to meet their A-G requirements, each for Advanced Mathematics.  HTH.

[mirabillis]

I would list it under Math. It would just mean he has (1) credit for Algebra II and then (.5) credit for NT and (.5) credit for C/P.  So total of 1.5 - 2 credits for Math for 9th grade. Does that work? Or should I look for something else to round out electives? Anyone have ideas for a good 1/2 credit elective?

 

 

[lewelma]

Just thought I should mention that the intermediate number theory class is WAY harder than the intermediate counting class.  This is the opposite of the intro classes. 

 

Ruth in NZ

[JoJosMom]

Just thought I should mention that the intermediate number theory class is WAY harder than the intermediate counting class.  This is the opposite of the intro classes. 

 

Ruth in NZ

 

Well.  That's something to look forward to.  Assuming we survive Geometry around here. :blink:

 

[lewelma]

Haha.  Quark's son and my son were in the same intermediate number theory class together, and it was pretty hard core!

[quark]

Haha.  Quark's son and my son were in the same intermediate number theory class together, and it was pretty hard core!

 

:laugh: I remember thinking that we had failed him big time. The problems were seriously a case of :zombiechase: :zombiechase: :zombiechase: :zombiechase:

 

But wow, when he finished, it felt like he had made one huge cognitive leap.

[mirabillis]

But if we're only currently in Algebra II - we should be looking at Intro level ones, yes?

 

Is this a good idea as an extra elective - will it help with his math future? I thought he might enjoy it as he's a mathy kid - it just depends how 'hard' it is. Or should we stick with easier 'electives'?

[quark]

I'm sorry for that Intermediate level side track. Shouldn't have gone there. The Intro levels should definitely be good electives for mathy kids. My only possibly useful data point in this case is that I listed these as math courses and not as electives but you could list them as electives if you like. It is your transcript! :001_smile:

[mirabillis]

Well I'd list them as math courses, in the math section, but alongside his core math, Algebra II.

 

I say 'elective' b/c he has his cores (english, math, science, history, language) but needs another full or half credit 'elective'

I figure he's mathy, why not an AoPs online course? Good idea?

[quark]

Yes good idea imho. Hope he likes them!

[mirabillis]

Since he's in Alg II now - would Intro NT & C/P be too easy for him? I see many show it's concurrent along with Pre-A/Algebra. He's already finished Geometry. Would the Intermediate level be better suited to him at this stage?

 

And we are planning to try the AoPs school, rather than teaching it to him on his own

[mirabillis]

I considered each to be a one semester course (in my state 1 credit, under the Cambridge system 1/2 credit.)  My DD has taken both online and found Counting and Probability to be the harder, by far.  In case you are interested in the online option, the University of California does consider the classes to meet their A-G requirements, each for Advanced Mathematics.  HTH.

 

And yes I am looking at the online option. He's at the age (14) where outsourced and accountable to other than me is better! And yes, I've seen they are A-G approved.

 

Just need to figure out if INTRO level is good for him - not too light?

[JoJosMom]

Since he's in Alg II now - would Intro NT & C/P be too easy for him? I see many show it's concurrent along with Pre-A/Algebra. He's already finished Geometry. Would the Intermediate level be better suited to him at this stage?

 

And we are planning to try the AoPs school, rather than teaching it to him on his own

 

Tiptoeing back into this with much trepidation.  I think you need to know that the children of many of the prolific AoPS posters are EXTRAORDINARY math students - as in "brilliant" or "genius."  Another wrinkle is that many of those parents are very talented in mathematics in their own right and can teach/support their students. I say this not to denigrate anyone, but because I think it is important that you know the context.  If your student fits that profile, please disregard this; he may well be ready for the Intermediate classes. 

 

My perspective is as the non-mathy parent of a very bright, math-loving student.  She loves AoPS and has done well with the classes, but they're really, really hard and they go very, very fast.  Personally, I cannot imagine jumping right into an intermediate class. Also, AoPS does not recommend the Intermediate Counting/Prob and Number Theory classes until after their Intermediate Algebra; their Intermediate Algebra is much more involved than the typical Algebra II class.

 

All that said, I think either one would be a fantastic elective that your student will enjoy and benefit from.  But it (likely) won't be a cakewalk.

[mirabillis]

yes i know these kids are beyond brilliant - i've spoken with some of these moms before. :-)) you are quite right, i should stick with INTRO level.  :laugh:

[lewelma]

Tiptoeing back into this with much trepidation.  

 

Heehee. Subtle.  :001_smile:

 

My ds has done the books for Algebra, Geometry, Intro Number Theory, and Intro Combinatorics.  And taken the classes for Intermediate algebra, counting, precalculus, number theory.  And taken the olympiad geometry class and WOOT.  (yes, we have funded the organization). Here is my take on the order of difficulty

 

Intro Number Theory = 1/2 half of Algebra

2nd half of algebra = Intro Geometry = Intro Combinatorics

Intermediate Counting = Intermediate Algebra = PreCalc

Intermediate Number Theory = Olympiad Geometry

WOOT

 

I actually did the intro number theory and combinatorics books with my ds, and we found intro combinatorics deceptively easy.  When told which technique to use it was obvious to the point of stupidity, but the moment the problems were mixed up it was shockingly hard to sort out which technique to use in which situation.  DS was 13 at the time.  Intro Number Theory was super easy until the last 1/4 of the book when we got into Mods. 

 

Intermediate Number Theory was the first AoPS class ds took, he was 13, and he cried every day for the first 2 weeks.  At first I thought this was just that the classes were too difficult, as he had always used the books in the past.  But I soon learned that there were others that thought that the class should be renamed Olympiad Number Theory.  There was just way too big a jump between the intro book and the intermediate class.  DS persevered, but I would not recommend the class until the end of the intermediate series when you have much more problem solving experience. 

 

DS loved the Intermediate Counting class.  He took it concurrently with Intermediate Algebra, but before PreCalc. 

 

Hope that helps,

 

Ruth in NZ

Edited October 4, 2016 by lewelma

[Arcadia]

Since he's in Alg II now - would Intro NT & C/P be too easy for him? I see many show it's concurrent along with Pre-A/Algebra. He's already finished Geometry. Would the Intermediate level be better suited to him at this stage?

 

It depends on your child's current workload. We didn't do the online class for those, my kids did the books over summer.  My kids did the intro to Number Theory book after they had plenty of fun with cryptography books, so there was some prior knowledge. My oldest did the intermediate C&P book after lots of fun probability/game theory (lady luck/casino kind) books and he was doing at his own pace so he could spend zero hours one day and four hours the next.

 

There is no textbook for Intermediate Number Theory so you basically can't skim through the book before signing up for the class. For Intro to NT, Intro to C&P, Intermediate C&P there are textbooks so you can Link+ and take a look at them. Palo Alto library has the intro and intermediate C&P books and solution manuals and you should be able to Link+ those.

[mirabillis]

I hate to rehash an old topic... but I was browsing again as I'm back to AoPs planning.

 

A few weeks went by. We signed up for Intro to NT online, my ds was really excited about it, then he logged in first class and well, hated it. It was entirely too remedial from the get-go, and that combined with the text-only, non-audio style, he couldn't get a handle on it. That and we had just opted into to AP Comp Sci so didn't really 'need' the extra 1/2 credit so I told him not to beat a dead horse and we could just cancel.

 

Fast forward, he still wants a math elective. And we've got his first AMC 10 upcoming and like to get some AoPs style math in.

 

Unfortunately, AoPs AMC 10 Problem Series is waitlisted, so that leaves us with Intro to C&P, which some here have said is more challenging, harder than NT?

 

1. So... is Intro to C&P less remedial, more challenging and fun from the get-go than Intro NT?

2. How do we get used to the text-only style? Make us like it!

3. And/or do we just get the Intro to NT & C&P books, and get an extra full credit working through them on our own? Do I need to be a math aficionado to help him with these? And how did those who did it at home (non-AoPs school) do it for credit - quizzes, tests?

 

Thanks!!

[regentrude]

 

I hate to rehash an old topic... but I was browsing again as I'm back to AoPs planning.

 

A few weeks went by. We signed up for Intro to NT online, my ds was really excited about it, then he logged in first class and well, hated it. It was entirely too remedial from the get-go, and that combined with the text-only, non-audio style, he couldn't get a handle on it. That and we had just opted into to AP Comp Sci so didn't really 'need' the extra 1/2 credit so I told him not to beat a dead horse and we could just cancel.

 

Fast forward, he still wants a math elective. And we've got his first AMC 10 upcoming and like to get some AoPs style math in.

 

Unfortunately, AoPs AMC 10 Problem Series is waitlisted, so that leaves us with Intro to C&P, which some here have said is more challenging, harder than NT?

 

1. So... is Intro to C&P less remedial, more challenging and fun from the get-go than Intro NT?

2. How do we get used to the text-only style? Make us like it!

3. And/or do we just get the Intro to NT & C&P books, and get an extra full credit working through them on our own? Do I need to be a math aficionado to help him with these? And how did those who did it at home (non-AoPs school) do it for credit - quizzes, tests?

 

The Intro to NT is very easy. As explained in the description, it just requires some basic algebra. So I would not have expected a challenging course.

You can work through the books yourself. They are written to the student and designed to be used without a teacher. Get the solution manual. We did C&P in 8th grade to take a break from algebra. It is interesting, but should not be challenging to a high schooler with good math background.

I have used AoPS textbooks (no class) for all high school math. I based grades on an end of semester final exam which I wrote, based on problems from the text. There are solution manuals available that I highly recommend.

 

Edited October 27, 2016 by regentrude

[daijobu]

 

I hate to rehash an old topic... but I was browsing again as I'm back to AoPs planning.

 

A few weeks went by. We signed up for Intro to NT online, my ds was really excited about it, then he logged in first class and well, hated it. It was entirely too remedial from the get-go, and that combined with the text-only, non-audio style, he couldn't get a handle on it. That and we had just opted into to AP Comp Sci so didn't really 'need' the extra 1/2 credit so I told him not to beat a dead horse and we could just cancel.

 

Fast forward, he still wants a math elective. And we've got his first AMC 10 upcoming and like to get some AoPs style math in.

 

Unfortunately, AoPs AMC 10 Problem Series is waitlisted, so that leaves us with Intro to C&P, which some here have said is more challenging, harder than NT?

 

1. So... is Intro to C&P less remedial, more challenging and fun from the get-go than Intro NT?

2. How do we get used to the text-only style? Make us like it!

3. And/or do we just get the Intro to NT & C&P books, and get an extra full credit working through them on our own? Do I need to be a math aficionado to help him with these? And how did those who did it at home (non-AoPs school) do it for credit - quizzes, tests?

 

Thanks!!

 

 

"Remedial" is a relative term, relative to your student.  If he's already studied basic counting and probability, then it will be remedial for him.  Take a look at the TOC for the textbook.  There might also be a "Do I need this?" exam for him.  

 

If he doesn't like the text-only style, then he doesn't like it.  We love it because it "mutes" distractions from other students.  But there's no need to force him into it.  

 

A few of options for you:

 

(1) Return to the Intro NT textbook, specifically the 2nd half which covers modular arithmetic.  Does he have a solid understanding of mods?  They come up a fair bit on the AMCs.

(2) Take a look at the Intermediate C&P book.  There's lots of difficult problems in that book.  (We're going through it now, and it's a doozy.)

(3)  Just do old AMC10s.  They are available for free on the AoPS website, along with detailed solutions.  That's a really good prep, IMO.  

(4)  Take a look at volumes 1 and 2, which should also be good quick prep for the AMCs.  

 

HTH!  

[mirabillis]

 

If he doesn't like the text-only style, then he doesn't like it.  We love it because it "mutes" distractions from other students.  But there's no need to force him into it.  

 

 

Well, he didn't give it much of a chance. It was hard with the type of material that begins Intro to NT - so I feel with something he enjoys more, he could get used to it. He's just used to outsourced audio or visual content. I was just hoping those that liked it could tell me all the pros of it! I could persuade him (not force!) LOL

 

Thanks for the tips. Anyone else want to weigh in?

[Julie of KY]

We've done most all the books on our own rather than the online classes.

 

Consider doing Number Theory on your own - the first 5 or so chapters are very easy so he might just look over the review or challenge problems for those chapters and move on. The modular artithmetic at the end of the book is likely to be new and very important. The books are very well written and so are the solution guides.

 

Counting and Probability - I think this book is much more fun, though there are fans of the NT book as well. If you want to do this on your own, then there are also videos online available for this book.

 

For either book, you can do Alcumus which is free online.

 

If you do any of these on your own, then you can certainly give credit for them on your transcript.

 

 

[quark]

I'm not much good commenting on content as my son handles math relatively independently. Some quick thoughts on methods (probably repeated):

1. My son's experience has been that AoPS classes tend to start out easy and then get very hard as they progress and then ease out again. But he hasn't done many of the classes for me to provide reliable info.
2. The solutions manuals are a good investment.
3. Some kids I know read the transcripts after the class instead of taking the class live. It doesn't seem to have affected their understanding or performance. My son preferred attending and participating because he enjoys the interaction.
4. The Volume 1 and 2 books are very good (according to my son). My son doesn't do anything from cover to cover though, preferring to choose topics and work on them randomly so I am not a good judge of how much time a book will take or how many credits to award for these.

[mirabillis]

 

 

1. The Volume 1 and 2 books are very good (according to my son). My son doesn't do anything from cover to cover though, preferring to choose topics and work on them randomly so I am not a good judge of how much time a book will take or how many credits to award for these.

 

 

Very interesting. Two of you have mentioned Volume 1 & 2 books. I'd never seen those. I see them now... Do those have solutions manuals as well? My ds is also very independent mathematically, so if there are solutions to problems, he can figure out any he can't get on his own. 

 

And would going through Volume 1 & 2 count as a 1/2 credit in math perhaps? Or only if we do more of their de rigeur books like Intro to NT or Intro to C&P?

 

*ETA - never mind on the solutions manual. Answered my own question, I see it does have solutions guides.

Edited October 27, 2016 by mirabillis

[quark]

And would going through Volume 1 & 2 count as a 1/2 credit in math perhaps? Or only if we do more of their de rigeur books like Intro to NT or Intro to C&P?

 

My kid goes through math like water. He has lots of math credits and I only listed his NT/CP/Vol1-2/ a few other number theory sources as 1 credit in total to show he took that bunny trail and went wide as well as deep before hitting calculus. In fact, I just realized I was so harried during writing his course descriptions that I did not even list the other sources (yikes!).

 

[mirabillis]

I got the idea really from Kathy in Richmond (yay kathy!) and seeing her dd's transcript and it had many more than your standard math courses. since this is my son's forte, i figured those would make good 'academic' electives. plus they can help with amc and i think they will help with a stronger transcript. i thought they looked good on there... ;)

 

speaking of math - are there other math 'electives' we can add to the mix to round out a strong transcript? he's only in algebra II now (9th grade) and breezing along. i have to wait on pre-calculus until after algebra II right? I can't do them concurrently, correct? if i had known how fast we could have gone through math, and seen what some of your brilliant mathy kids were doing, i would have gone much faster. how knew? i thought we were on a quick clip, until all your brilliant kids were taking calculus by 9th grade! yikes!  

[snowbeltmom]

 

I hate to rehash an old topic... but I was browsing again as I'm back to AoPs planning.

 

A few weeks went by. We signed up for Intro to NT online, my ds was really excited about it, then he logged in first class and well, hated it. It was entirely too remedial from the get-go, and that combined with the text-only, non-audio style, he couldn't get a handle on it. That and we had just opted into to AP Comp Sci so didn't really 'need' the extra 1/2 credit so I told him not to beat a dead horse and we could just cancel.

 

Fast forward, he still wants a math elective. And we've got his first AMC 10 upcoming and like to get some AoPs style math in.

 

Unfortunately, AoPs AMC 10 Problem Series is waitlisted, so that leaves us with Intro to C&P, which some here have said is more challenging, harder than NT?

 

1. So... is Intro to C&P less remedial, more challenging and fun from the get-go than Intro NT?

2. How do we get used to the text-only style? Make us like it!

3. And/or do we just get the Intro to NT & C&P books, and get an extra full credit working through them on our own? Do I need to be a math aficionado to help him with these? And how did those who did it at home (non-AoPs school) do it for credit - quizzes, tests?

 

Thanks!!

 

All three of my kids have taken many online classes with AoPS, including Introduction to Number Theory.  There is no way that any of them could have skipped the Intro Level NT class and jumped right in to the Intermediate Level.  

 

AoPS has a diagnostic section on its website to help a student determine whether he would benefit from taking a certain class.  You could look over the diagnostic test for Intro to Number Theory to help you determine whether your child would learn any new material in the class.

 

My kids found the Intro to Number Theory class less challenging than the Intro Counting and Probability class, but they still learned a lot from the Intro to Number Theory class.

 

To answer your third question: You definitely can work through the books on your own.  You could work to mastery, and "mastery" could be determined with Alcumus - once your child has mastered the Number Theory and C&P topics in Alcumus, I would award him an A in both classes.

 

Good luck!

 

 

 

 

[mirabillis]

thanks! i think we'll do Intro to NT on our own. And think about whether to try Intro to C&P next week online - or whether to do it also on our own. I think that sounds like sound advice.

 

Any other tips on how to better make the aops interface work and liked?? :) :) :)

[snowbeltmom]

thanks! i think we'll do Intro to NT on our own. And think about whether to try Intro to C&P next week online - or whether to do it also on our own. I think that sounds like sound advice.

 

Any other tips on how to better make the aops interface work and liked?? :) :) :)

 

Have your son work through the problems in the textbook that pertain to the week's topic before he attends the class lecture for that week.  The online discussion moves quickly and it is easy to get "lost" if you don't have any prior knowledge of the topic.

 

[daijobu]

 

Any other tips on how to better make the aops interface work and liked?? :) :) :)

 

 

Your son may already be aware, but just in case.  Does he know that during class he can type in specific questions and get a response from a TA within a minute or so?  This is very handy, as sometimes questions posted to the discussion board can take much longer to generate a response (depending on the teacher and class).  

 

Communicating with TAs may help with making the class worthwhile.  HTH.

[mirabillis]

thank you snowbeltmom & daijobu.

 

we've gone ahead and signed up for Intro to C&P so will go for it. he'll work that week first. and no, daijobu - he did not know that. in fact, that's what he felt disheartened is when he would respond or 'chat' he wouldn't see it at all. so maybe that will help him. instant gratification and all. LOL! :D