Mukmuk Posted November 1, 2012 Share Posted November 1, 2012 Excuse me for the ungainly title! It does express my needs however. DS started on AOPS Intro to Algebra and is thoroughly enjoying it. He's asking for more math. I'm thinking of adding a second math book, one that introduces different math ideas. I'm looking for breadth rather than something up the prgression chain, something outside of the usual scope. Looking through the archives and on the internet, i found these: 1. Harold Jacobs' Math- A Human Endeavour 2. The Heart of Mathematics by Ed Burger, which he looked at and liked last year, but it was over his head after a few chapters. 3. Thinking Mathematically by Wolf Blitzer 4. Solve This by James Tanton (unfortunately unavailable at the moment). Except for the second one listed which I own, i dont know about the other books than the reviews on Amazon. Would any of these be suitable? Are these aimed too high or are there other suggestions? For math curriculum, he did Ed Zacarro and the Aims books (very hands on) prior to AOPS. He loved/s Penrose, the Murderous Math books and some rudimentary Physics books. He doesn't like to be taught or to watch math videos, but he loves working through the problems himself. I do explain the beginning bits of each topic, but even when he gets things wrong, he likes a second or a third go before reading the solution or coming to me. Would any of these books be in this style? (I find Ed Zacarro to be similar to AOPS in this regard). Any thoughts would be appreciated! Quote Link to comment Share on other sites More sharing options...
regentrude Posted November 1, 2012 Share Posted November 1, 2012 I do not know any of the titles you mentioned, but the AoPS series has two books that are outside the normal progression: Number Theory and Intro to Counting and Probability. Both are topics that are not normally included in the typical high school curriculum, but very interesting and well worth a detour for a math interested student with time to spare. Quote Link to comment Share on other sites More sharing options...
Mukmuk Posted November 1, 2012 Author Share Posted November 1, 2012 Tks Regentrude. I havent tried them and will take a look. Are these at about the same level as Intro to Algebra, or do they require more basic knowledge? I worry that they may be too tough for him. Quote Link to comment Share on other sites More sharing options...
snowbeltmom Posted November 1, 2012 Share Posted November 1, 2012 Tks Regentrude. I havent tried them and will take a look. Are these at about the same level as Intro to Algebra, or do they require more basic knowledge? I worry that they may be too tough for him. Not Regentrude, but based on my experience with my kids, your son would do well with either C&P or the Number Theory book based on the math that your son has had to-date. Quote Link to comment Share on other sites More sharing options...
regentrude Posted November 1, 2012 Share Posted November 1, 2012 Tks Regentrude. I havent tried them and will take a look. Are these at about the same level as Intro to Algebra, or do they require more basic knowledge? I worry that they may be too tough for him. I have not used Number Theory, but one user on these forums has used Number Theory before Intro to Algebra with good success. My son has used Intro to Counting & Probability when he took a break from Intro to Algebra, and we found C&P significantly easier than the algebra book. You want to have a little basic algebra, but do not have to have a full algebra 1 course to be fine with C&P. Quote Link to comment Share on other sites More sharing options...
Kathy in Richmond Posted November 1, 2012 Share Posted November 1, 2012 Martin Gardner wrote two volumes, Aha Insight and Aha Gotcha, (very inexpensive used copies are available) which are fun and enriching choices for going sideways in math. They're two of my all-time favorites :). My kids devoured them when they were about your son's age. Gardner writes them in a style appealing to kids, with cartoon illustrations, while covering some sophisticated topics from logic, probability, combinatorics, statistics, number theory, & geometry. He offers follow-up resources for several of the topics, which is handy if there's something that catches his fancy & you want to pursue it. I wish that I could show you a page or two! For example, I just opened the Gotcha book randomly, and found a section on "The Inescapable Point" which shows a character mountain climbing. He climbs up the mountain from 7am till 7pm on day one, and hikes back down on day two, again from 7am till 7pm. At the bottom of the mountain, he's greeted by his topology teacher, who informs him that he passed a certain point on the trail on the way down at precisely the same time of day that he passed that same point the previous day on the way up the trail. He goes on to prove why this is true in a simple to understand way. Then he extends the discussion by talking about fixed-point theorems in general (but in a one page discussion that's very appropriate for young kids :D). Then he refers those who want to learn more to an article in Scientific American magazine. The spirit is FUN, the math is an excellent preview of what's ahead, and it's entirely on-your-own for a kid who prefers to teach him/herself. You might be disappointed if you're looking for long problem sets on each topic; you won't find any. But these volumes do develop problem-solving ability like AoPS does; you'll want & need to have paper and pencil on hand while reading them. I also own the Solve This book by Tanton that you mentioned. I like it, too, but find it more difficult to use, especially with younger kids. It's written to provide activities for math circles or clubs, so lots of the activities require a friend or two. Still, it's an interesting and worthwhile addition to my math shelves. Quote Link to comment Share on other sites More sharing options...
Barbara H Posted November 1, 2012 Share Posted November 1, 2012 My suggestion is similar to Kathy's. Martin Gardner books were huge hits here and we actually got a complete CD-ROM collection of his Scientific American columns at one point. There are many inexpensive Dover editions of Martin Gardner puzzle books. Also check out Ian Stewart books: http://www.amazon.com/Math-Hysteria-Fun-Games-Mathematics/dp/0198613369/ref=la_B000APQ9NM_1_13?s=books&ie=UTF8&qid=1351792787&sr=1-13 http://www.amazon.com/Professor-Stewarts-Cabinet-Mathematical-Curiosities/dp/0465013023/ref=pd_bxgy_b_text_y Quote Link to comment Share on other sites More sharing options...
quark Posted November 1, 2012 Share Posted November 1, 2012 Hey Mukmuk :seeya:! Looking through the archives and on the internet, i found these:1. Harold Jacobs' Math- A Human Endeavour 2. The Heart of Mathematics by Ed Burger, which he looked at and liked last year, but it was over his head after a few chapters. 3. Thinking Mathematically by Wolf Blitzer 4. Solve This by James Tanton (unfortunately unavailable at the moment). Except for the second one listed which I own, i dont know about the other books than the reviews on Amazon. Would any of these be suitable? Are these aimed too high or are there other suggestions? For math curriculum, he did Ed Zacarro and the Aims books (very hands on) prior to AOPS. He loved/s Penrose, the Murderous Math books and some rudimentary Physics books. He doesn't like to be taught or to watch math videos, but he loves working through the problems himself. I do explain the beginning bits of each topic, but even when he gets things wrong, he likes a second or a third go before reading the solution or coming to me. Would any of these books be in this style? (I find Ed Zacarro to be similar to AOPS in this regard). Any thoughts would be appreciated! Seconding everything mentioned by pps. Your choices #1 and #2 should work fine. I don't have #3 (or don't remember if I have it lol). I don't have #4 but I did have another book by Tanton and it was challenging. DS attempted that book alongside AoPS NT and found that he could work with AoPS NT more easily. They approach math in similar ways (discovery style) but Tanton's methods, though invigorating, might be too over the head at this age. AoPS CP is also a great choice. In my humble opinion, both NT and CP can be done before AoPS Algebra, with AoPS Algebra or afterwards too. Kathy's suggestions have always been spot on for us. The Aha books are really neat. I've attached some pages here, including the one Kathy mentioned. Hope they are clear. See this post for more ideas. Quote Link to comment Share on other sites More sharing options...
Mukmuk Posted November 1, 2012 Author Share Posted November 1, 2012 Regentrude, Quark, Kathy, Barbara, Snowbeltmom, Gosh!! Thanks so much to all of you!! I don't have the other books. Martin Gardner - the photos look awesome (Tks Quark!!)!! It's exactly DS's idea of chortling good fun. The Inescapable Point, hahaha! And Ian Stewart too!! Looks like I have a lot of shopping to do. Quark, that's an awesome thread!! I will buy the Number Theory and Counting & Probability Books. He loves probability! Its now the happy problem of when to do these rather than what to do! I'm just stunned by DS's love of AOPS. He keeps talking about the beauty of some problems over others (they look the same to me :confused:). But I'm so excited to keep up that happiness and excitement that he has. Thanks once again!! Quote Link to comment Share on other sites More sharing options...
Mukmuk Posted November 2, 2012 Author Share Posted November 2, 2012 I am reading the first few pages of Ian Stewart's book, Math Hysteria, on Amazon, and it is uproarious! How come I never did math like that in school ... Quote Link to comment Share on other sites More sharing options...
Spy Car Posted November 9, 2012 Share Posted November 9, 2012 :lurk5: Quote Link to comment Share on other sites More sharing options...
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