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We are using a Prentice-Hall Algebra 2 (Bellman, et al) with our 12 year old, which is going fine, and I think it will go fine throughout the year.  While we were using Jacobs Geometry, my DS read P-H Algebra 1 and did some problems as an algebra 1 review, so the P-H Algebra 2 approach was familiar.  We like that both P-H algebra books show a lot of applications of the algebra being learned.  I also like that it includes some data analysis and very basic statistics along the way, since that’s so important in real life and the science we’re planning next year.  I also didn’t find a compelling alternative.  But now I’m wondering what we’ll use next. 

Some possibilities are:

  1. Larsen Pre-calculus (haven’t actually seen it);
  2. Foerster Pre-calculus
  3. AoPS Introduction to Counting and Probability as a short “detour,†although we could do pre-calc simultaneously Counting and Probability.  I actually have this book.
  4. Statistics.  Has anyone here used the text “Practice of Statistics for AP, 4th ed†by Starnes, et al.?  Anything else?  We would like to learn more statistics to help with science next year.
  5. Very slowly start a calculus book and reviewing algebra 2 and filling in any gaps along the way.  But we’re in no rush to do calculus.
  6. Go to AoPS’s 2nd algebra book, Intermediate Algebra. I’m a little hesitant here since we tried AoPS Intro to Algebra and it wasn’t enjoyed by DS after a while.  He feels he should “know†how to do the problems he sees and the AoPS approach stresses him out no matter how much I try to explain the approach and he reads their introductory materials.  We tried the Intro to Algebra a while ago, when he was 9 ½ and had a very solid background in pre-algebra, so it’s been awhile and a lot of maturing has occurred.  But my DS very much likes to see how what he’s learning can be used and AoPS doesn’t seem to have a lot of that.  Yes, he’ll play around with some advanced math concepts and logic, but it’s not as much fun for him when it’s assigned. 
  7. Something else??

I've learned the hard way that just because the prerequisites are met and pre-tests are easy, sometimes the age and interests of the student makes a big difference too.  Thanks for any and all insights!

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I think the approach by the AoPS books takes some maturity as well as math knowledge. As he is a little older, he might be able to take their approach better.

 

I think there is a lot of math out their beyond the traditional path of precalc and calculus after algebra 2.

 

AoPS Counting and Probability - I like the idea of this - it's different than what he's been doing and a fun book. It might also be a more gentle introduction to the AoPS style if you think you might like to use these books later.

 

AoPS Int. Algebra - a great book to do to continue to develop the algebra skills.

 

I have the Statistics book and like the looks of it - haven't actually done it yet.

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Brad, what are your goals for your student?  Finishing Algebra 2 at 12 gives you lots of time to do lots of other classes!  Do you have a plan for highschool?  Do you have a CC or University available for post-Calculus classes? If I were you, I would lay out a plan to make sure that I am not stuck by the time my kid is 16. 

 

AoPS will slow most children down! 

 

Ruth in NZ

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My kids both used The Practice of Statistics text, one self-studying at home with me & the other with PA Homeschoolers AP online class. The only math prerequisite is algebra 2 through logarithms and exponentials (briefly used). If he's thinking about taking the AP exam, then he'd also need the ability to make concise & clear written arguments. It's a good book IMO, and chock full of interesting applications.

 

I'd also recommend a year of AoPS C&P and Number Theory for your son. For precalc, if he's more interested in applications, then Foerster's precalc text might be appropriate. On the other hand, the AoPS books (Int Alg & Precalc) can't be beat IMO and, as Julie said, he might appreciate their approach more as he gets older.

 

Take a look at EPGY's math offerings for lots of classes beyond calculus.

 

Other thoughts:

algebra based physics

mathematical logic

computer programming

robotics

AoPS vol 1 & 2 original problem solving series (i used vol 2 along with Gelfand's Trigonometry as a spine for my kids' "precalc" year)

Alcumus programmed learning (online at AoPS)

 

Is he a social learner? He might want to investigate MathCounts at his age, or see whether there's a nearby Math Circle.

 

Look at cogito.org for lots of good ideas on extending learning beyond the standard coursework.

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Wow, you three are all great! This is much appreciated on what I think is my first time starting a post.

 

Julie: I think the maturity issue for DS with AoPS might have been an issue and it's worth trying again. Thanks for the tip on AoPS Intermediate Algebra and the confirmation on trying AoPS Intro to Counting and Probability.

 

Ruth: I don't really have any definite goals after single-variable calculus. It's really up to him at that point, but maybe linear algebra since that's what I did and loved Gilbert Strang's book (he even has his lectures online at the free MIT website). I could tutor DS in most standard courses for a few years after calculus, especially since he's been reading math books on his own for years as I work weekdays, when he prefers to do his schoolwork, and there are several universities local here (incl. U. of North Carolina, Duke, and NC State) so I'm not worried about running out of things to do. But DS may ask for my recommendations, so I'll need to work that out sometime.

 

Kathy: Thanks for the feedback on Practice of Statistics which really helps as well as the other courses. I may try the AoPS Intro to Counting and Probability and if AoPS works for that try some of the others, such as Intermediate Algebra and Precalculus. If it still doesn't mesh, perhaps Foerster's precalc if it's good with applications. DS isn't much of a social learner with math. He loves book groups and a couple of (informal) logic/critical thinking courses, etc., but he's resisted taking a math class as being “inefficient†compared to reading and didn't really enjoy two years of MathCounts. I've been planning to get to a Math Circle for the last 9 months, but they've always been in conflict with sports games or a family event, and sports come waaay ahead of math for DS. But your plug for a Math Circle is encouraging me to keep trying. Finally, we're definitely planning on an algebra-based physics course next year, although I don't think the math component of that particular course goes beyond algebra 1.  We'll still do math as a separate subject.

 

I am very appreciative of all of your terrific suggestions!

 

Brad in NC

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Brad,

 

My ds was about that age when we we learned about AoPS from Kathy. He had completed Foerster's algs 1&2 and Houghton Mifflin's geo text that Chalkdust was using. He was also doing a math circle with Kathy's dd.

 

His first AoPs course was counting and prob online. He really enjoyed it and it did trigger a love for AoPs. He went from that book into the Intermediate alg text Without any problems. He did both of those courses online. In 9th grade he was taking a heavy load and didn't want that pace, so he actually did the pre-cal text with Kathy. At the same time she worked through Foerster's precal with our oldest dd which our oldest ds used.

 

I have written several posts about my thoughts on the different texts. Our oldest ds is a chemE and he worked through Foersters. He is an applied type of person......he was always building, tinkering projects and is now working as a process chemE. Our youngest ds that went through the upper AoPs texts (he took their cal course online in 10th) is definitely more of a theorizer. His love switched from math to physics and he now plans on double majoring in both in undergrad, but his goal is definitely something in the particle physics area.

 

Anyway, that is a roundabout way of saying that the 2 different books suit their 2 different approaches and goals. Where I am not so sure, and have thought about this a lot, is did the one lead to the other or vice versa. Did one pursue applied and the other theoretical based on how they studied and learned math or would that have been the case if you had switched texts between them. I have often wondered what our oldest ds would have done if he had had the opportunity to use AoPS and be around a family like Kathy's or our youngest ds if he had been stuck with Foersters.

 

I am unsure about both. Our youngest ds has always seen mathematical patterns and taught himself many mathematical concepts that way. Our oldest didn't "see" those things or if he did, he didn't tell me. But he did "see" how things worked and went together to function.

 

But, I can say w/o doubt that younger ds's grasp of math now far exceeds his oldest brother(who is no math slouch by any means) and I do think it is all bc of AoPS (and the awesome math coaching of Kathy and her dd ;) )

 

Anyway, those are my unscientific thoughts as someone who is not a math person at all and stops understanding things my kids talk about in science and math sound alg 2. (If you have evere seen the tv show Eureka, I feel like Sheriff Carter around a couple of my kids. ;) and they would love living there. :) )

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Having completed so much math at such a young age I think you have a great opportunity to go deep into some subjects before going for Calculus or Statistics. I would suggest you have a look at "The Calculus Trap"

by Richard Rusczyk. I second the suggestions here to do some AOPS books.My personal favorite is AOPS Introduction to Geometry. I see that you have done Jacobs Geometry but you can easily get 1 more year of math using the AOPS book.
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I would recommend going for the AOPS C+P book, and if he enjoys that he might like the number theory book as well. C+P would also be a great lead-in to statistics, and if statistics goes well with your planned science for next year that seems like a great idea. FWIW, Discrete Math (which includes an intro to C+P and NT usually) was the course which made me change my major to mathematics.

 

I would recommend against 5 -- there's no reason to jump there instead of doing precalculus first. If he were in a school setting, it might be necessary to keep him challenged, but where you are he can go through rapidly and skip anything he already knows.

 

Larson is a solid text but I would prefer Foerster for a young mathy kid interested in applications, if you decide not to go with statistics.

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Anyway, that is a roundabout way of saying that the 2 different books suit their 2 different approaches and goals. Where I am not so sure, and have thought about this a lot, is did the one lead to the other or vice versa. Did one pursue applied and the other theoretical based on how they studied and learned math or would that have been the case if you had switched texts between them. I have often wondered what our oldest ds would have done if he had had the opportunity to use AoPS and be around a family like Kathy's or our youngest ds if he had been stuck with Foersters.

 

8, this is fascinating.

 

I think that my older ds's mind has been molded into the AoPs image, and he is now definitely a theoretician who wants a career in math.  But who would he have been with something like Foersters?  In contrast, my younger is much more practical so AoPS is a hard sell.  I am simply not sure if it is worth the effort to get him into that style of thinking.

 

I do think that there is both nature and nurture involved with my kids.

 

Ruth in NZ

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8, this is fascinating.

 

I think that my older ds's mind has been molded into the AoPs image, and he is now definitely a theoretician who wants a career in math.  But who would he have been with something like Foersters?  In contrast, my younger is much more practical so AoPS is a hard sell.  I am simply not sure if it is worth the effort to get him into that style of thinking.

 

I do think that there is both nature and nurture involved with my kids.

 

Ruth in NZ

 

I do think there is a nature vs. nurture component.   I know for my younger dd, AoPS is beyond a hard sell.   She is strong math student, but AoPS is most definitely not worth the effort for her.   Really, she doesn't have the time anyway b/c she is spending so much time studying multiple foreign langs....her love.

 

With my sons.....again, they are very different from each other.   My oldest has always worked with his hands.   From the time he was 2 or 3, he was always trying to take things apart or put things together.  (We got him a train when he was 2 and he had absolutely not interest in it on the tracks.   He watched it and ran and got a screw driver b/c he wanted to take it apart.   That fascination never ended....even now!   He is attempting to make bio-diesel at home as well as has his own home brewery (hey, he is a chemE after all....he figures he should make use of it at home.)

 

Our 17 yr, otoh, has always been a deep thinker.   He would make patterns, sit and stare at things, and create designs (he loved creating unique designs with Legos when he was little and would spend hrs doing so).   He has stacks of notebooks full of thought experiments that he has written down.

 

So, would how much does math curriculum influence choice? I really don't know.   But, I do think about it b/c our oldest ds was incredibly gifted in math as well and I wonder which he would have preferred.   Would he have liked AoPS style?   Would it have pulled him into more of a research area vs. process?     I know that being part of the math circle and being around Kathy had a huge influence on how our youngest ds thinks and approaches math and theory in general.   (can't say enough about the blessing she has been on his life.  :) )     He is on such a different level than dh and I that being around people that are "up there" (we most definitely are not.....we are definitely more the Sheriff Carter's of the world) has opened doors that he would otherwise have never experienced.

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I do think there is a nature vs. nurture component.   I know for my younger dd, AoPS is beyond a hard sell.   She is strong math student, but AoPS is most definitely not worth the effort for her.   Really, she doesn't have the time anyway b/c she is spending so much time studying multiple foreign langs....her love.

 

Well, I am getting OT here, but this is my trouble with my youngest.  He is good at math, but much more of a humanities type.  AoPS takes time, and thus by definition will take him away from other subjects that he loves.  He is good at math, he can do AoPS, but the question is, should he?

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Well, I am getting OT here, but this is my trouble with my youngest.  He is good at math, but much more of a humanities type.  AoPS takes time, and thus by definition will take him away from other subjects that he loves.  He is good at math, he can do AoPS, but the question is, should he?

 

The set of AoPS books provide a great, very advanced, no nonsense math course. While most people concentrate on the "advanced" part, the "course" part should not be forgotten. I think that many students of slightly above average intelligence that have an interest to learn and have supporting families would profit greatly from a course based on the AoPS books. A good curricula could be : Pre-A in 7th grade, Introduction to Algebra + Introduction to Geometry in grades 8 to 10 (both subjects in parallel), Pre-Calc in 11 grade and Calculus in 12 grade. Of course one would need willing and able teachers. I after-schooled the son of a friend of mine in the second part of his 2nd year and first part of 3rd year of high school using AoPS  Introduction to Algebra and Introduction to Geometry. He was a slightly above average student who did not love but also did not hate math. Every week we spent 2 hours together and he also spent about 2 hours alone working on the problems. In just a few weeks he went from getting 70-80 in his regular math tests to getting 100 in each one, even after we stopped tutoring. His SAT math score went from an estimated 500 to a real 720. I am convinced that this score helped him get accepted in the best public university in the state (his reading and writing SAT scores were in the low 500). He pursued a Biology degree in college where he again did very well in math related subjects.Today he is well on his way to becoming a doctor.

 

So yes, I am strongly convinced that if your son (or anybody else) can do AoPS math, he should do AoPS math. If he or you think that it is taking too much time, why not take less time? Your son is in 4th grade after all. If the goal is to learn just a little bit of math, you can do that using the AoPS books too and you can be sure that what you learned was beautiful and correct and not boring.

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Avilma,  Thanks so much for your thoughts.  And I do think that this discussion is headed back towards Brad's original question.  If a student can, should he?  Clearly Brad's ds could do AoPS as could mine, but I am not convinced that AoPS is the right choice for all talented students. There are many paths to success.

 

Also, we are in NZ where math is integrated and does not include the same material as the AoPS curriculum.  So using AoPS means that my kids will have to study a different syllabus before taking their annual exams in highschool.  My oldest won't care, but my youngest might if he would rather be learning Latin and Psychology and Economics.  My current thought is that Cambridge textbooks might be a better choice than AoPS textbooks.

 

Ruth in NZ

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The set of AoPS books provide a great, very advanced, no nonsense math course. While most people concentrate on the "advanced" part, the "course" part should not be forgotten. I think that many students of slightly above average intelligence that have an interest to learn and have supporting families would profit greatly from a course based on the AoPS books. A good curricula could be : Pre-A in 7th grade, Introduction to Algebra + Introduction to Geometry in grades 8 to 10 (both subjects in parallel), Pre-Calc in 11 grade and Calculus in 12 grade. Of course one would need willing and able teachers. I after-schooled the son of a friend of mine in the second part of his 2nd year and first part of 3rd year of high school using AoPS  Introduction to Algebra and Introduction to Geometry. He was a slightly above average student who did not love but also did not hate math. Every week we spent 2 hours together and he also spent about 2 hours alone working on the problems. In just a few weeks he went from getting 70-80 in his regular math tests to getting 100 in each one, even after we stopped tutoring. His SAT math score went from an estimated 500 to a real 720. I am convinced that this score helped him get accepted in the best public university in the state (his reading and writing SAT scores were in the low 500). He pursued a Biology degree in college where he again did very well in math related subjects.Today he is well on his way to becoming a doctor.

 

So yes, I am strongly convinced that if your son (or anybody else) can do AoPS math, he should do AoPS math. If he or you think that it is taking too much time, why not take less time? Your son is in 4th grade after all. If the goal is to learn just a little bit of math, you can do that using the AoPS books too and you can be sure that what you learned was beautiful and correct and not boring.

 

While I think the AoPS texts are fabulous, I do disagree that they are necessary for the majority of students, even strong students.   I consider our dd a strong math student.  She just doesn't love math like they do.  She gave AoPS a fair try (she completed their alg 1 course online) and she really detests the approach and would much rather be taught explicitly.  

 

AoPS teaches deep thinking/critical reasoning/developing proofs.   Other programs like Foerster's teach the process and make sure students know how to apply what they have learned.   While the 2 are not directly equivalent, not everyone needs to delve into mathematical concepts the way that AoPS approaches the material.    She will (and does) happily work 3+ hrs daily on foreign languages.   But her math.....she prefers to be done in around an hr.

 

Considering her math skills are excellent via Foerster's, I do not believe she is being short-changed at all by not using AoPS.   

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Well, I am getting OT here, but this is my trouble with my youngest.  He is good at math, but much more of a humanities type.  AoPS takes time, and thus by definition will take him away from other subjects that he loves.  He is good at math, he can do AoPS, but the question is, should he?

OP, please forgive the digression ... perhaps one of these resources will apply to your DS? 

 

Ruth, I am a humanities-mathy person myself, and I do wish I'd had something like AoPS around when I was younger (though I mightn't have appreciated it).  I think that the clarity of presentation and the combination of simplicity + rigor in the concepts & definitions is very appealing, AND makes it possible for a person to be competent enough to enjoy popular treatments of maths.  Which is to say that it might be a good foundation from which to launch a humanities-centered maths program. 

 

Anyhow, there is one very appealing resource that is also very problematic -- it is quite idiosyncratic, and the history is not always properly fact-checked --  Hogben's Mathematics for the Million.  Hogben was opinionated & occasionally wrong, but his book is entertaining, erudite, and made many mathematical ideas tractable and interesting for me.  He links maths to topics interesting, germane, and humanities-friendly.  I've linked the original b/c when I had both I preferred it (forget why) but I think the new one is worth reading too.  I worked through most of the book before being derailed by Life.  And it's not written for children (Hogben has another book that is, but there's no actual math in it).  I'm thinking of using it as a springboard for math thinking in middle school. 

 

just thought I'd mention it -- it's a favorite book, but so weird I almost never recommend it!

 

ETA: I think one factor in considering AoPS for a child is the precision of the language and concepts presented.  It reminds me of the MCT grammar materials in that the presentation is both precise and intuitive (that is, builds up a good "feel" for the subject).  So perhaps one axis to consider with AoPS for the non-uber-mathy is whether or not the child enjoys making clear distinctions, organizing things, being very precise, &c;

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My oldest found the AoPS Number Theory book a lot of fun!  It was a lot easier than Intro to Alg for him and he really enjoyed it.  (So much so that he would try to explain modular congruence to anyone who would listen, usually 9 and 10 year olds who looked at him blankly).  We did it between the first and second half of Intro to Alg.  (We're still in the second half so I have no experience with recommending other things).  We have the C & P book on hand for when we need another detour.

 

My son also started AoPS Intro to Alg at 9.  He did do well with it, but it took me sitting with him for the first few months since his maturity wasn't quite there.  He was willing to work through, but he needed me by his side.  By the end of the year, he wanted me to instruct him as little as possible.  Number Theory was a different story for the start.  He started that much later the same year, so a couple months before he turned 10.  He absolutely loved Intro to Number Theory and it was much easier than even the first half of Intro to Alg.

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...
  1. Go to AoPS’s 2nd algebra book, Intermediate Algebra. I’m a little hesitant here since we tried AoPS Intro to Algebra and it wasn’t enjoyed by DS after a while.  He feels he should “know†how to do the problems he sees and the AoPS approach stresses him out no matter how much I try to explain the approach and he reads their introductory materials.  We tried the Intro to Algebra a while ago, when he was 9 ½ and had a very solid background in pre-algebra, so it’s been awhile and a lot of maturing has occurred.  But my DS very much likes to see how what he’s learning can be used and AoPS doesn’t seem to have a lot of that.  Yes, he’ll play around with some advanced math concepts and logic, but it’s not as much fun for him when it’s assigned. 

...

 

Brad, have you considering emailing Richard at AoPS?  It seems to me that you could just teach the AoPS in the more traditional manner, as opposed to the "discovery" approach.  Many on this board object to this approach but the AoPS materials themselves suggest it if the student isn't thriving with the materials as presented. 

 

Also, if the child likes to see the use of the maths and can read at a high level, it is possible he'd be interested in the Hogben book I linked above.  Hogben is wordy, though; the revised edition might be more tightly written and accessible.  The whole point of this book is that maths is a social and a practical enterprise. 

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Also, we are in NZ where math is integrated and does not include the same material as the AoPS curriculum.  So using AoPS means that my kids will have to study a different syllabus before taking their annual exams in highschool.  My oldest won't care, but my youngest might if he would rather be learning Latin and Psychology and Economics.  My current thought is that Cambridge textbooks might be a better choice than AoPS textbooks.

 

Ruth in NZ

 

We're in England, so we have the same issue. At the moment I'm using AoPS Algebra to dip into alongside English textbooks (from Elmwood Press) I wish we could use more AoPS books, but buying them all to use as we work towards IGCSEs just isn't an affordable option. Perhaps we'll use one of them as a detour between IGCSE & A level.

 

Ruth, when you talk about Cambridge exams, which level is that?

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We're in England, so we have the same issue. At the moment I'm using AoPS Algebra to dip into alongside English textbooks (from Elmwood Press) I wish we could use more AoPS books, but buying them all to use as we work towards IGCSEs just isn't an affordable option. Perhaps we'll use one of them as a detour between IGCSE & A level.

 

Ruth, when you talk about Cambridge exams, which level is that?

I would suggest that the problem-solving I and II texts would be ideal for someone wanting to add challenge to a different curriculum.

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We're in England, so we have the same issue. At the moment I'm using AoPS Algebra to dip into alongside English textbooks (from Elmwood Press) I wish we could use more AoPS books, but buying them all to use as we work towards IGCSEs just isn't an affordable option. Perhaps we'll use one of them as a detour between IGCSE & A level.

 

Ruth, when you talk about Cambridge exams, which level is that?

 

For my older, he is just going to do the A levels when he finishes the AoPS calculus book. 

 

I will start my younger with IGCSE.  I have been trying to find a Checkpoint textbook for him now so that the IGCSE is not a big jump up in a few topics (thanks for the link!).  I am planning for him to use AoPS without challengers until he has the maturity and speed for the IGCSE exam.  And I will use a Checkpoint textbook to shore up any areas that AoPS is not covering.  We are also using LoF because he has a lot of trouble with the language of math and Fred makes that aspect fun and quite variable.  It will also help to stall him so he does not hit the IGCSE exam until his is at least 14.  I plan to make the Cambridge textbooks his core curriculum starting at the IGCSE level.

 

My plan is to get my younger through the A levels.  My plan for my older is to get him to the IMO. :001_smile:

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  • 3 months later...

Thanks again to everyone for the great suggestions!  I've looked into the suggestions and am sharing what we're doing in case it helps others.

 

  1. We're continuing the Prentice-Hall (Bellman,Bragg, et al, 2004) Algebra 2 text, cover to cover, going slowly so as to do a lot of the applied problems. DS still prefers to see the applications.
  2. We purchased and slowly started, in parallel, Starnes, et al, 4th ed, The Practice of Statistics, which looks to be an excellent book.  DS seems to like it and sees the value of it, although we haven't gotten far yet.
  3. We are reviewing a bit of the end of Jacobs Geometry, a little of Euclid's Elements, and dabbling with some non-math logic, in the hope that the logic is applied in other settings.
  4. We are also doing a little bit of review with KhanAcademy.org.  There's a good bit of review in algebra 2, since previous math is actually used, but Khan Academy is still useful and DS seems to like it. 
  5. We will probably use Foerster's precalculus, although I'm not sure yet.  DS already understands limits intuitively and some other precalculus topics, and I'm considering going through calculus in an applied and conceptual sense and then again in a more theorem-proof approach instead of precalculus then calculus.  I may use Foerster's calculus for that first pass if we do it that way. [Later note: our algebra 2 book has two chapters on trigonometry, but doesn't seem to cover everything needed before calculus (the unit circle much or polar coordinates, so we'd need to cover a few topics somewhere before calculus).  From a sample chapter from Foerster Precalculus (3rd ed.), it looks like it has some applications, although mostly physical science and engineering.] 
  6. A terrific AP Physics B (not C) class may be offered locally next year and we might do that and go lighter on the math next year.  That use of algebra 2 and trigonometry might be something that's very appealing to DS.  He hasn't found an academic passion yet, but physics is one of his favorites.  It might be nice to wait a year for the physics, for maturity, but if it's offered, we'll probably sign up for it -- it could be years later when it's available next, or never. [Later note: looks like AP Physics B will be offered 2015-16.]
  7. We may still try AoPS Intro to Counting and Probability (we have the books) and perhaps one of the algebra books to see if it works better now that DS is older.  But I'm not going to push it. [Later note: after looking at the AoPS Intermediate Algebra book, I don't think DS would like it at all.]

I'm a fan of integrating math concepts over the year, such as algebra and geometry and statistics.  When we did geometry, we reviewed algebra with a different text and did a little data analysis.  When the algebra 1 text was done, we started algebra 2 before geometry was done.  It really helped keep the algebra fresh.  Thanks again to everyone, and please let me know if you have any suggestions!

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If he hasn't done trigonometry with a circular function approach (not sure how much you've covered in geometry), I would strongly, strongly recommend this before calculus. Topics such as trigonometric substitution are challenging for any student and far more so for someone who is attempting to learn the trigonometry at the same time.

 

If you have Foerster's Precalc already, you could just do the trig chapters.

If you would like a more challenging text, Gelfand's Trigonometry may be a good fit for you.

If you just want a fast run-through, you could consider Life of Fred's Trigonometry text.

If you really want to go ahead and start calculus, you could consider supplementing with something like Mueller and Brent's just-in-time Algebra and Trigonometry for Calculus.

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Thanks, kiana, these are some real nice ideas.  There are two basic chapters on trig in the algebra 2 book we're using, but there are still gaps, including the circular function approach.  I don't have the Foerster Precalc book at this time, but we went through the Foerster (3rd ed) chapter 6 sample chapter quickly last night and DS seemed to pick up the material pretty easily, partially from some previous exposure.  The book seems good to me, but not a "must have," and I'm having a hard time justifying a big expense (book + solutions manual) when I've got some other trig books lying around. If I had Foerster Precalculus lying around, esp. the 3rd edition, I'd probably use it.  Not sure yet.

 

I looked over an online sample of the Gelfand Trigonometry book, and I kind of like it.  It's clear and explains why trig answers questions algebra and geometry don't.  I'm sure DS would prefer more applications, but I might get it and have him read it.  I looked over a paper copy of Life of Fred Trigonometry and didn't think it would be a good fit for us -- it doesn't cover much more than our algebra 2 book or what we've otherwise covered, yet it looks like it would take a lot of time. Mueller and Brent's Just-in-time Algebra and Trigonometry for Calculus looks intriguing, and there are lots of used copies at Amazon; I picked one up real cheap.  Thanks again!

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