KSinNS Posted March 15, 2015 Share Posted March 15, 2015 So, my ds 10, on the autism spectrum, is quite good at math. He's finished most pre algebra at a pretty quick pace, and has never been challenged (he made about 3 errors/week and rarely would struggle with a question). However, he has a low tolerance for frustration, and has no process for working through problems he can't immediately see the solution for. Given that we have lots of time, and that I love how AOPS explains things, this seemed like a good time to linger on some math, and work on his problem solving skills. So we started AOPS Prealgebra, and are currently on the challenge problems on the end of chapter 1. Given his personality, I've sat with him, and we've worked through the questions together to avoid frustration (but he's got there with a few hints). So far, it's actually gone well. He had no problems figuring out the teaching problems, and relatively few problems with the practice and review problems. However, he's stuck on all the addition of a sequence (Gauss) problems: 1+2+3+4+5....+99+100 especially the challenge ones. He gets the commutative property stuff, but gets lost in the steps and gives up, or does something weird that he can't explain (I think he added the number of pairs rather than multiplied, so I think he was trying to move into rote memory rather than understand the process). Anyway, my question is, do I keep working with him on this type of problem until he can do it independently, or leave it, and let his brain figure it out in time, when he gets to them in Alcumus? My goal is to get him out of the habit of working in rote memory, and learn to think things through, but I'm pretty sure he really doesn't get this problem type. I recognize that AOPS may not be the best curriculum for him long term, but I'm hoping it will help him to learn to think a bit more freely, so I'm hoping to stick with it for a while. Quote Link to comment Share on other sites More sharing options...
lewelma Posted March 15, 2015 Share Posted March 15, 2015 I can't speak to using AoPS in your situation, but I will say that he might enjoy Mathematics: A Human Endeavour by Jacobs. Lots of deep thinking, but less theoretical and frustrating than AoPS preA. I used it with my younger boy and he loved it. We used the older edition which was cheaper. Ruth in NZ 1 Quote Link to comment Share on other sites More sharing options...
Ravi B Posted March 16, 2015 Share Posted March 16, 2015 However, he's stuck on all the addition of a sequence (Gauss) problems: 1+2+3+4+5....+99+100 especially the challenge ones. Don't know if this will help, but when I look at that problem, I draw (mentally or physically) a line between the 1 and the 100. Those add up to 101. Then I draw a line between 2 and 99; again 101. Keep going. So we're adding a bunch of 101's. How many? Well, we started with 100 numbers, so pairing them up must lead to 50 pairs. Hence we're adding 50 copies of 101. Repeated addition is multiplication, so the answer is 50 * 101. As I recall, all of the other sequence adding problems in the chapter can be solved in a similar way. Good luck to your son. 4 Quote Link to comment Share on other sites More sharing options...
kiana Posted March 16, 2015 Share Posted March 16, 2015 I can't speak to using AoPS in your situation, but I will say that he might enjoy Mathematics: A Human Endeavour by Jacobs. Lots of deep thinking, but less theoretical and frustrating than AoPS preA. I used it with my younger boy and he loved it. We used the older edition which was cheaper. Ruth in NZ Or Jousting Armadillos -- I remember someone (I forgot who) used the first book as a step-up to AOPS. 1 Quote Link to comment Share on other sites More sharing options...
KSinNS Posted March 16, 2015 Author Share Posted March 16, 2015 Thanks, all. Quote Link to comment Share on other sites More sharing options...
ErinE Posted March 16, 2015 Share Posted March 16, 2015 Read the last chapter, Problem Solving Skills. I used many of the techniques with DS (without reading the last chapter first) so when he got to that chapter, he said he already knew the skills. With the example problem you gave, I might start with small numbers. Add up 1 to 4. 1 to 6. 1 to 8. Do I see a relationship between the last number and the sum? Could I find the sum without having to add them all? There are other techniques listed in the last chapter that help as your DS works through the book. 2 Quote Link to comment Share on other sites More sharing options...
KSinNS Posted March 17, 2015 Author Share Posted March 17, 2015 Read the last chapter, Problem Solving Skills. I used many of the techniques with DS (without reading the last chapter first) so when he got to that chapter, he said he already knew the skills. With the example problem you gave, I might start with small numbers. Add up 1 to 4. 1 to 6. 1 to 8. Do I see a relationship between the last number and the sum? Could I find the sum without having to add them all? There are other techniques listed in the last chapter that help as your DS works through the book. Great idea!!! That could really help. Thanks! Quote Link to comment Share on other sites More sharing options...
go_go_gadget Posted March 17, 2015 Share Posted March 17, 2015 Don't know if this will help, but when I look at that problem, I draw (mentally or physically) a line between the 1 and the 100. Those add up to 101. Then I draw a line between 2 and 99; again 101. Keep going. So we're adding a bunch of 101's. How many? Well, we started with 100 numbers, so pairing them up must lead to 50 pairs. Hence we're adding 50 copies of 101. Repeated addition is multiplication, so the answer is 50 * 101. As I recall, all of the other sequence adding problems in the chapter can be solved in a similar way. Good luck to your son. OT totally, but I just showed my ten year-old your post, and when he saw your username, he instantly knew who you must be and said ''OMG it's him! You can talk to him? Can we meet him?'' 2 Quote Link to comment Share on other sites More sharing options...
Arcadia Posted March 17, 2015 Share Posted March 17, 2015 Doing free MOEMS division M sample problems as well as free Canada's Math Kangaroo past year samples as past time helped my kids in being used to having to think. I just load them as PDFs on my tablets so easily portable to dentist or doctors. 1 Quote Link to comment Share on other sites More sharing options...
rzberrymom Posted March 17, 2015 Share Posted March 17, 2015 My 10 year is at almost exactly the same spot in AOPS pre-algebra, and I'm not all that thrilled with it so far. I thought it would be like Beast Academy, where the problems get a little harder each time, and then the authors throw in some spectacular twist that tests the kid's critical thinking skills and shows if the kid *really* understands. Instead, it feels like a lot of memorizing rules. And the questions are either really easy or really difficult, with no build-up and not really much critical thinking required. I'm hoping it gets better as we go along, but so far it feels like a very mainstream math book to me--full of memorization. :( My point is, I feel his pain--I don't think they did a very good job leading up to those challenge problems. I may just be ruined by Beast Academy though. That was just beyond fantastic. 1 Quote Link to comment Share on other sites More sharing options...
wapiti Posted March 17, 2015 Share Posted March 17, 2015 My 10 year is at almost exactly the same spot in AOPS pre-algebra, and I'm not all that thrilled with it so far. I thought it would be like Beast Academy, where the problems get a little harder each time, and then the authors throw in some spectacular twist that tests the kid's critical thinking skills and shows if the kid *really* understands. Instead, it feels like a lot of memorizing rules. And the questions are either really easy or really difficult, with no build-up and not really much critical thinking required. I'm hoping it gets better as we go along, but so far it feels like a very mainstream math book to me--full of memorization. :( My point is, I feel his pain--I don't think they did a very good job leading up to those challenge problems. I may just be ruined by Beast Academy though. That was just beyond fantastic. FWIW, try to hang in there through ch 2, as the style of ch 1 is hardly representative of the whole text. IMO, the book requires *no memorization whatsoever* (the end of ch 1 properties are listed just for review of the concepts that the student should be able to understand, not for memorization). 2 Quote Link to comment Share on other sites More sharing options...
wapiti Posted March 17, 2015 Share Posted March 17, 2015 Anyway, my question is, do I keep working with him on this type of problem until he can do it independently, or leave it, and let his brain figure it out in time, when he gets to them in Alcumus? My goal is to get him out of the habit of working in rote memory, and learn to think things through, but I'm pretty sure he really doesn't get this problem type. FWIW, I like to draw "rainbows" to make the pairs. As long as he understands the concepts underlying the problems, I think it's ok to let the challenge problems marinate awhile and move on. I like to come back to challenge problems later, for review, rather than do them all the first time around. What you are doing sounds good to me :). One of my kids would much prefer a rote approach and getting him to think through things on his own is one of my challenges. It's a gradual process but it does work. 1 Quote Link to comment Share on other sites More sharing options...
KSinNS Posted March 18, 2015 Author Share Posted March 18, 2015 FWIW, I like to draw "rainbows" to make the pairs. As long as he understands the concepts underlying the problems, I think it's ok to let the challenge problems marinate awhile and move on. I like to come back to challenge problems later, for review, rather than do them all the first time around. What you are doing sounds good to me :). One of my kids would much prefer a rote approach and getting him to think through things on his own is one of my challenges. It's a gradual process but it does work. Thanks. This is what I was wondering. I think he'll get it, but this is a new approach for him. He gets the rainbow thing (love the image) but gets confused about what to do next. Thanks so much. Quote Link to comment Share on other sites More sharing options...
ErinE Posted March 18, 2015 Share Posted March 18, 2015 My 10 year is at almost exactly the same spot in AOPS pre-algebra, and I'm not all that thrilled with it so far. I thought it would be like Beast Academy, where the problems get a little harder each time, and then the authors throw in some spectacular twist that tests the kid's critical thinking skills and shows if the kid *really* understands. Instead, it feels like a lot of memorizing rules. And the questions are either really easy or really difficult, with no build-up and not really much critical thinking required. I'm hoping it gets better as we go along, but so far it feels like a very mainstream math book to me--full of memorization. :( My point is, I feel his pain--I don't think they did a very good job leading up to those challenge problems. I may just be ruined by Beast Academy though. That was just beyond fantastic. There is something about the first few chapters that seems unnecessarily difficult. I keep telling myself I need to go back and really review them, but life keeps intervening. Whenever DS would try to memorize the rules, I had him either use problem solving strategies or write it out completely, especially the exponents chapter and anything involving the distributive property. This seemed to help him understand the "rules" without memorization. 1 Quote Link to comment Share on other sites More sharing options...
Arcadia Posted March 18, 2015 Share Posted March 18, 2015 We did the challenge problems as review. I read the book "Competition Math for Middle School" by Jason Batterson recently from the library. If your library has a copy, it's worth taking a look for yourself and maybe your child. http://www.artofproblemsolving.com/store/item/competition-math 1 Quote Link to comment Share on other sites More sharing options...
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