abbeyej Posted March 14, 2012 Share Posted March 14, 2012 Ds is currently in 8th grade. He's a very strong math student and is finishing up honors algebra 2 right now. In looking to the next four years, I can see great value in *not* rushing into precalculus and AP calculus in 9th and 10th grades. I have no doubt that he would handle the work just fine -- but then what? Yes, he could take statistics or head to a university to take linear algebra, but... I'm thinking that taking 9th grade to do a year of discrete math with AoPS might actually be more valuable to his ultimate depth of understanding. But there are so many books! Do we go for number theory or counting and probability or one of the original (contest-prep) type books? And will a typical book last us a semester or a school year? (And how on earth would I list it on his transcript?!) Any thoughts? Quote Link to comment Share on other sites More sharing options...

MBM Posted March 14, 2012 Share Posted March 14, 2012 (edited) Intro to Number Theory and Intro to Counting and Probability could be done in a semester each. I think for a student who is strong in math, having done those two would be more meaningful to a university than doing something like Volumes I and II. You could also do a mathematical logics course through eIMACS -- super easy to use, challenging enough, good for an auto-didact. My son will be starting the second course this month. Each course is spread out over about nine months, but kids can move at their own pace. http://www.eimacs.com/parent_aml_overview.htm You could also use the Suppes, Hill logic book that Myrtle was using with her kids. The problem with that, IIRC, is that there were no solutions at the time, but I believe they might be available now. Not sure. Here's a link to the logic books Myrtle mentioned: http://myrtlehocklemeier.blogspot.com/ Edited March 14, 2012 by MBM added a link Quote Link to comment Share on other sites More sharing options...

KAR120C Posted March 14, 2012 Share Posted March 14, 2012 If I were doing it now, I think we'd take the whole year for both (going through them simultaneously and at a fairly leisurely pace), and do just the books and not the classes - just because the classes are so breakneck. Option B, which also has a lot to recommend it, would be the Problem Solving books.... DS did C&P and Number Theory last year, and is working through the first Problem Solving book this year, planning to do the second next year. I listed C&P and Number Theory as "Discrete Math 1" and I think I'm going to list Problem Solving as "Algebra 2" (if only because we never really did an Algebra 2 year...) -- it could also be listed as Math Problem Solving. Of course if you haven't done Statistics, I would highly recommend that, just because everyone potentially going into a STEM field should know enough statistics to read scientific papers... AP Stats can be done right after Algebra 2 provided logarithms were covered in the Algebra class... (or you could do a bit about logarithms on the side if they weren't...) For a strong math student, and it certainly sounds like that's what you have, you could likely get through AP Stats and one of the AoPS options in a year. Stats isn't a ton of work, and it could be done in a semester. I prefer it as a year just so you have time to work it into other courses (science in particular) and really get into a project or two. Quote Link to comment Share on other sites More sharing options...

HodgesSchool Posted March 14, 2012 Share Posted March 14, 2012 We loved the AoPS Number Theory and Counting and Prob books. There is an intermediate book for both subjects as well, which I think we may work through soon. I'm interested in the idea of my son taking Statistics before Calculus. Have any of you had experience with kids doing that? It would work really well for us. My husband thinks Calc is pretty straightforward where Stats is something that requires analytical/creative thinking which a more mature thinker might find easier. Any thoughts? Quote Link to comment Share on other sites More sharing options...

8filltheheart Posted March 14, 2012 Share Posted March 14, 2012 If you aren't set on what he will use for the pre-cal/cal, how about their alg 3 book? (intermediate alg) If he wants to use the AoPS pre-cal book, it will lay the foundation. (fwiw, ds took C&P simultaneously w/the end of Foerster's alg 2 and took their alg 3 as his first traditional sequence AoPS book) Quote Link to comment Share on other sites More sharing options...

MBM Posted March 14, 2012 Share Posted March 14, 2012 We loved the AoPS Number Theory and Counting and Prob books. There is an intermediate book for both subjects as well, which I think we may work through soon. I'm interested in the idea of my son taking Statistics before Calculus. Have any of you had experience with kids doing that? It would work really well for us. My husband thinks Calc is pretty straightforward where Stats is something that requires analytical/creative thinking which a more mature thinker might find easier. Any thoughts? I don't believe AoPS has an Intermediate Number Theory book yet. My son is taking the online version of it now. They need to get cracking on that. ;) Yep, you can do AP Stats before calc. If you do a search, you should be able to find the recommended text for stats. You can also take it through PA Homeschool (is that what it's called), which one of the posters here (Blue Hen, I believe?) has taught. It's definitely do-able. Well, I hope so because my son is going to be doing it himself next year so that he can sit for the AP next spring! Quote Link to comment Share on other sites More sharing options...

regentrude Posted March 14, 2012 Share Posted March 14, 2012 If you aren't set on what he will use for the pre-cal/cal, how about their alg 3 book? (intermediate alg) If he wants to use the AoPS pre-cal book, it will lay the foundation. (fwiw, ds took C&P simultaneously w/the end of Foerster's alg 2 and took their alg 3 as his first traditional sequence AoPS book) I was going to suggest the same thing. What kind of algebra 2 did he study? If it is a traditional algebra 2 program, chances are that he has covered only the equivalent of the second half of AoPS Introduction to Algebra text. In order to successfully complete the prealgebra book, he needs to have studied the topics covered in their Intermediate Algebra, because they already do things that are commonly put into a prealgebra course. Quote Link to comment Share on other sites More sharing options...

Kathy in Richmond Posted March 14, 2012 Share Posted March 14, 2012 Abbey, you've received lots of great options already.:) Yes, the the AoPS introductory books on number theory and counting and probability would combine to make a very nice discrete math year for your son at his age. Is he at all interested in computer science? These classes lay the mathematical foundation for university level study in that field (see Richard R's article). The AoPS solution manuals are excellent and make it very possible to study these subjects on your own at home. One further suggestion if you opt for this course would be to consider the online version of one of these classes for next spring. They usually start up at this time of the year and run through early summer. He'd then have some outside evaluation for his year in addition to the chance to be part of a terrific community of similarly-able and interested learners. If you're wondering about the break-neck speed, I think that the number theory class would especially work well online. My daughter found it fun in the eighth grade and not too breathless. And your son could always get started on the text on his own before the class starts up. We used the two AoPS problem solving volumes much like Erica described. I never had a real algebra 2 text (AoPS texts weren't on the market yet) that I liked for my daughter, so we used Vol 1 as the spine for her algebra 2 year. We supplemented with MathCounts, AMCs, and a little Dolciani for challenging word problems. Then we used Vol 2 as a spine for her precalculus year (similar reasons). 8Fill also gave you some good advice. The AoPS intermediate algebra book has a lot more to it (scope and depth) than other intermdiate algebra texts. That volume and AoPS precalculus are literally stuffed with good things to learn! What's interesting to me is that in the old days of AoPS, their precalculus year consisted of a semester of Intermediate Algebra online, followed by a semester of Trig and Complex Numbers online. Now they've expanded their old trig and complex course into a year-long 'precalculus' text by adding a lot of linear algebra. The advanced algebra (or college algebra) portion of the course is still in the Intermediate Algebra text, though. So in order to get full coverage, you'd still want to do the college algebra topics in that text. Your son is at a very good stage for that level now. AP stats is another good idea, and could be added to either of the above ideas if your son desired. It's an easy AP for a math-oriented kid who's interested in the topic. My daughter loved the online version from PA Homeschoolers; she took it in addition to her regular math sequence. Lots of fun, too! It required about an hour per day of her time. Quote Link to comment Share on other sites More sharing options...

abbeyej Posted March 14, 2012 Author Share Posted March 14, 2012 ...What kind of algebra 2 did he study?... He used Dolciani for Algebra 1, then started taking local classes with Derek Owens, so Jacobs for geometry and Derek's own course for alg 2, though it draws heavily on the 2001 McDougal-Littell. Quote Link to comment Share on other sites More sharing options...

abbeyej Posted March 14, 2012 Author Share Posted March 14, 2012 If you aren't set on what he will use for the pre-cal/cal, how about their alg 3 book? (intermediate alg) If he wants to use the AoPS pre-cal book, it will lay the foundation. (fwiw, ds took C&P simultaneously w/the end of Foerster's alg 2 and took their alg 3 as his first traditional sequence AoPS book) I'm fairly certain we'll go back to Derek Owens for pre-Calculus. Quote Link to comment Share on other sites More sharing options...

HodgesSchool Posted March 14, 2012 Share Posted March 14, 2012 I don't believe AoPS has an Intermediate Number Theory book yet. My son is taking the online version of it now. They need to get cracking on that. ;) Yep, you can do AP Stats before calc. If you do a search, you should be able to find the recommended text for stats. You can also take it through PA Homeschool (is that what it's called), which one of the posters here (Blue Hen, I believe?) has taught. It's definitely do-able. Well, I hope so because my son is going to be doing it himself next year so that he can sit for the AP next spring! Thanks for the note about Stats. I see great things on the list about her class! And you are absolutely right about the Int NT book. If we get to it before they have a book, I suppose my son might take the class. Has your son enjoyed it? Quote Link to comment Share on other sites More sharing options...

MBM Posted March 15, 2012 Share Posted March 15, 2012 Thanks for the note about Stats. I see great things on the list about her class! And you are absolutely right about the Int NT book. If we get to it before they have a book, I suppose my son might take the class. Has your son enjoyed it? I'm not 100% sure. My son finds everything and I just pay for it. Maybe they do have something! I am just the writer of checks around here. :D As for the class, this Friday is the second one and so far, my son likes it a lot. Austin Shapiro is teaching. What's nice is that students can just read the transcript and ask questions on the forum if they can't make the class (they can also download transcripts to look over later on). Very handy. It also seems that classes that don't have a book move at a slightly slower pace. That's the impression I get from my son. Quote Link to comment Share on other sites More sharing options...

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