T, who just turned 10, is currently reading Ender's Game for the first time and absolutely loving it. It's clearly the right book at the right time for him
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For the mathematically inclined, pre-algebra isn't really that hard. If he's solid on his division and his fractions, there's no reason to stop him from knowing more, especially if it's in "Life of Fred" where Fred always has a reason to use what he's doing.
We've been enjoying reading a Life of Fred as a family one chapter a night this summer. It's filling in some holes with respect to set theory. I don't know how it is at the more advanced level though.
Taking him to a math lecture seems like a fine idea to me as long as he's been told in advance about all the rules of social etiquette, such as not talking over the speaker, waiting until they ask for questions, raising your hand before speaking, and not shouting out the answer unless the speaker gestures for everyone to do so. If you're lucky and he can talk to the speaker after the lecture, you may eventually even find someone local who wants to take him under his/her wing and meet with him from time to time to discuss math competitions and paths for further study.
I saw that the Homeschool Buyer's Club has ALEKS on discount right now. I don't know if that's right for your family. I've never used it myself.
We did ALEKS for a while several years ago. It did an excellent job of letting the kids (just D and T at the time) speed through a bunch of stuff they were more than ready for, but once things started getting challenging, it didn't do nearly a good enough job of teaching - if I'm going to use a computer learning program, I'd like it to actually do the teaching - and allowed the kids to get in over their heads by allowing them to prove "mastery" of topics they really hadn't mastered yet and never really reviewing anything. I think it would probably work really well as a summer review of the previous year's material, , but I wasn't impressed with it as a stand-alone.
R is doing quite well. She's 4 now, 4.5 actually, and and doing well. So far, she's far more balanced in her development than either of the boys; she seems age-appropriate emotionally, is starting to do basic addition and subtraction with small numbers, and is learning basic pre-reading skills - all age-appropriate or perhaps a little ahead, but nothing obviously exceptional. She'll surprise us periodically with some really high-level abstractions and observations, but mostly she's just having fun being 4, which is a welcome bit of easiness, parenting-wise.
I feel like I should eventually ask a bunch of you slightly-ahead parents for educational insights. We have no plans for homeschooling (I don't know that we could manage that even if we were tempted, with all of the collegeschooling that we spend our days doing), but it might be nice to hear about any fun at-home supplements in case certain topics catch P's interest down the road. (Right now, at age three, we're mostly just enjoying the chance to encourage her to explore and think about things. We've paid relatively little attention to milestones beyond the basic "yeah, she's clearly doing fine" level. I really don't know what's typical, on any axis.)
For us the challenge with Peter is keeping him balanced and living up to his potential. I'm sure you've read the summaries of the studies that say, "Don't tell kids their 'smart' because then they'll try to do easy things well to please you and show you how smart they are. Tell kids they 'worked hard' at something in order to encourage a growth mindset so that they'll work hard at other things in the future."
While I can see that telling kids their smart all the time could be detrimental, I'm not sure I buy the results of the study (unfortunately there's been so much news about the actual study that I can't seem to find the study itself anymore. When I read it, I recall that it was a study of two 'randomly' assigned groups of middle school students given an easy test followed by the option to try a harder test. One group was told "you did well. You are smart at that." and the other was told, "You did well. You worked hard at that." The "worked hard" group was much more likely to choose to take the second test, and the effects persisted at a followup study more than 6 months later.) I don't think that study would be repeatable -- A one-sentence statement by a researcher makes a difference in outcomes for students after 6 month's time? Really? Are you sure some of the kids weren't absent and you just averaged in zeros for their scores?
Peter has had for his whole life their "fixed" mindset, the "gives up easily" mindset, the "I want something to sooth me and numb me" mindset, the "this is too hard" mindset. This is not something he's had because I've told him he's smart and he doesn't want to fail, it's something that has persisted since before he could roll over from front to back. Reading was harder than math for him. It's not that he couldn't learn it, in large part it's that he didn't want to. After some very expensive, intensive, training, he learned to read and now it's not a problem at all.
It's my job as a parent to find ways to force him to do things that are good for him that he doesn't want to do. I try to provide him with educational opportunities and nudges, and I walk the fine line between allowing him to be a couch potato and forcing him to do too much.
Amber is a different beast entirely. She's somewhere in the middle between growth and fixed mindsets. She hates to fail, and will beat herself up over doing something wrong, but that's internal. If she wants to do something, she will persist and she'll get it done, with help or not. I am a fan of the Montessori education because it gives her the chance to get ahead when she wants to.
Although Peter was initially ahead of her in the minecraft modding class, she's caught up to him and passed him because she's more persistent.
I think the overall lesson I've learned is that each kid is a little different. You get the most success with teaching them things when it is something a little bit hard, but not too challenging. When they're stuck in a rut and something is too easy, it's up to you to notice and pull them out and give them the appropriately leveled encounter. Sometimes there are boring parts, like memorizing math facts, but giving them a helping hand with the motivational side of the hard parts helps them make more progress and thank you for it later.
Just a quick aside: I can't comment on the specific research you're talking about for "fixed vs. growth midset" stuff. But I've had the impression that "surprisingly large impact from a single, simple early action" is seen fairly often.
In Physics Education Research, just for instance, there are studies with pretty good looking error bars showing that if you run a one-time "writing practice" activity during the first week of an intro class where students spend 10 minutes talking about some situation where they felt competent (I don't recall the exact wording of the prompt, but it had nothing to do with physics), there is a marked improvement in the male/female achievement gap throughout the semester (including both overall course grade and the final exam in particular). The theory seems to be that by writing about their strengths, they subconsciously feel more comfortable in that classroom context early on (reducing stereotype threat), and the resulting increase in confidence leads to a virtuous cycle for the rest of the class.
I don't know how similar that is to the studies you're talking about, and I certainly expect that some of what you're describing comes down to innate personality differences just as you've observed. But the idea that short, small interventions like this can have significant lasting effects isn't a matter of just one or two badly run studies. (I can make no claims about whether the entire field consists of badly run studies, but I'm never comfortable making that sort of accusation in areas where I'm not an expert.)
Part of my skepticism in their study is that I've known about it for most of my children's lives, and tried to put the information to good use, but I have not noticed any effect on my kids' behaviors. They're both of the fixed, "I can't, it's too hard, I won't try" mindset no matter what I say and how I encourage them.
D has been of this mindset forever too; it's very frustrating. I posted to FB recently (and really ought to post about it here, too) about an incident in which D ran into a problem in her prealgebra physics book (a Fred book) that she just could not do. It involved parallel resistors and finding the effective resistance across the combination, so the unknown was in the denominator. We walked her through the solution a couple times, and while she could smile-and-nod her way through it, she couldn't do it, explain it, or apply it; clearly, there was something she wasn't grasping about the algebraic manipulations involved.
After Chris and I both tried explaining every step to her and both failed, we decided that backing off was called for. We gave her no math assignment aside from playing with the DragonBox app (algebraic manipulations in the form of a game, so comfortable non-threatening environment), and we sat on our parental hands for two weeks.
It was probably the second hardest thing I've ever done, parenting-wise, with the first being deciding to put T on attention meds. The common thread there: I wasn't actually completely confident that I was doing the right thing, and there was every chance I was screwing up in something that Mattered.
But it paid off. She came back to it after two weeks away, followed my explanation (including explaining what the next step should be when asked), worked through it herself from fresh the next day with only a couple prompts to keep her from making an algebra mistake, and got the answer correct. She then worked out the follow-up problems on her own, came to a second problem of the same type with different numbers, and worked through that second problem on her own without help.
When I pointed out to her what she'd just done, her grin could have rivaled some stars in brightness.
And then she turned to T, who surpassed her in math progress about a year ago, and said, "Look out, T! I'm going to be doing two chapters of math a day now! I'm going to be catching up with you!" We're still in parental discussions on how much we ought to encourage/discourage competition between siblings as a motivating factor for academic progress, but the boost to her confidence level and willingness to tackle new things in math has been tremendous and persists a week later, and I'm hopeful that it will establish new patterns for her.
Carryover to other academic disciplines, however, has not happened, so far as I can tell. I still don't know how to engineer such a situation, either. I think mostly what I can say is, I feel your pain, I sympathize with your struggle, there is definitely reason for hope that small crises appropriately addressed can make a long-term difference, but this fixed mindset is still ridiculously difficult to counter and I'm sorry you're having to struggle with it too. It sucks.
I'm with beth_leonard....different kids can be so different, and it's as much about temperament as ability. So our experiences may or may not be relevant. (I wholly endorse your parenthesis, though. :)
Aside from the DragonBox app that was discussed on FB, I think the most important thing to know is that we live in an age of unprecedented access to fun at-home supplements. Thanks to the combination of homeschooling, "helicopter parenting," and the Internet, just about anything you want can be found. Want a children's book that discusses prime factorizations? There is one, and you have friends who know about it; also, there are blog posts with lists of children's books that discuss math topics. Want a science experiment kit delivered to your home monthly? There are services for that, as well as books that enable you to build your own at a fraction of the cost. Want fun workbooks and/or computer games that will seemingly magically teach your kid to read? They exist, though their magic will be (or at least appear) stronger with kids who would've had an easy time of it anyway. Want a kid-friendly electronics kit? They exist. Want to help your child live in medieval Spain for a week? Resources exist to help with that. A list of all the resources I'm familiar with that you might possibly want at some point would be overwhelming, both to me to produce and to you to read. Far more important than any list we could give you guys is simply the knowledge that fun stuff exists, and you will be able to find it when you want it.
On the other hand, the farther you are from the beaten path, the more work you will have to put into synthesizing available materials to get what you want. I'm on a couple FB lists for parents/educators of gifted kids, and the parents who post questions along the lines of, "My 5yo who can add and subtract single-digit numbers and is just starting to learn to read is obsessed with nuclear physics. I'd like a semester-long curriculum that he can work through on his own that will feed his interest in this. I have no time to put anything together and no money to buy anything new. Can you help me?" bug me no end. Encouraging a child's interests does take resources, in time or money or both, and moreso when they aren't reading independently yet. (In fairness, most parents do know this. It's mostly in August and September that the ones who don't seem to come out of the woodwork.)
We've been enjoying reading a Life of Fred as a family one chapter a night this summer. It's filling in some holes with respect to set theory. I don't know how it is at the more advanced level though.
Taking him to a math lecture seems like a fine idea to me as long as he's been told in advance about all the rules of social etiquette, such as not talking over the speaker, waiting until they ask for questions, raising your hand before speaking, and not shouting out the answer unless the speaker gestures for everyone to do so. If you're lucky and he can talk to the speaker after the lecture, you may eventually even find someone local who wants to take him under his/her wing and meet with him from time to time to discuss math competitions and paths for further study.
I saw that the Homeschool Buyer's Club has ALEKS on discount right now. I don't know if that's right for your family. I've never used it myself.
How is R doing? She must be 4 by now? 5?
--Beth
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R is doing quite well. She's 4 now, 4.5 actually, and and doing well. So far, she's far more balanced in her development than either of the boys; she seems age-appropriate emotionally, is starting to do basic addition and subtraction with small numbers, and is learning basic pre-reading skills - all age-appropriate or perhaps a little ahead, but nothing obviously exceptional. She'll surprise us periodically with some really high-level abstractions and observations, but mostly she's just having fun being 4, which is a welcome bit of easiness, parenting-wise.
Newt
Reply
Reply
While I can see that telling kids their smart all the time could be detrimental, I'm not sure I buy the results of the study (unfortunately there's been so much news about the actual study that I can't seem to find the study itself anymore. When I read it, I recall that it was a study of two 'randomly' assigned groups of middle school students given an easy test followed by the option to try a harder test. One group was told "you did well. You are smart at that." and the other was told, "You did well. You worked hard at that." The "worked hard" group was much more likely to choose to take the second test, and the effects persisted at a followup study more than 6 months later.) I don't think that study would be repeatable -- A one-sentence statement by a researcher makes a difference in outcomes for students after 6 month's time? Really? Are you sure some of the kids weren't absent and you just averaged in zeros for their scores?
Peter has had for his whole life their "fixed" mindset, the "gives up easily" mindset, the "I want something to sooth me and numb me" mindset, the "this is too hard" mindset. This is not something he's had because I've told him he's smart and he doesn't want to fail, it's something that has persisted since before he could roll over from front to back. Reading was harder than math for him. It's not that he couldn't learn it, in large part it's that he didn't want to. After some very expensive, intensive, training, he learned to read and now it's not a problem at all.
It's my job as a parent to find ways to force him to do things that are good for him that he doesn't want to do. I try to provide him with educational opportunities and nudges, and I walk the fine line between allowing him to be a couch potato and forcing him to do too much.
Amber is a different beast entirely. She's somewhere in the middle between growth and fixed mindsets. She hates to fail, and will beat herself up over doing something wrong, but that's internal. If she wants to do something, she will persist and she'll get it done, with help or not. I am a fan of the Montessori education because it gives her the chance to get ahead when she wants to.
Although Peter was initially ahead of her in the minecraft modding class, she's caught up to him and passed him because she's more persistent.
I think the overall lesson I've learned is that each kid is a little different. You get the most success with teaching them things when it is something a little bit hard, but not too challenging. When they're stuck in a rut and something is too easy, it's up to you to notice and pull them out and give them the appropriately leveled encounter. Sometimes there are boring parts, like memorizing math facts, but giving them a helping hand with the motivational side of the hard parts helps them make more progress and thank you for it later.
--Beth
Reply
In Physics Education Research, just for instance, there are studies with pretty good looking error bars showing that if you run a one-time "writing practice" activity during the first week of an intro class where students spend 10 minutes talking about some situation where they felt competent (I don't recall the exact wording of the prompt, but it had nothing to do with physics), there is a marked improvement in the male/female achievement gap throughout the semester (including both overall course grade and the final exam in particular). The theory seems to be that by writing about their strengths, they subconsciously feel more comfortable in that classroom context early on (reducing stereotype threat), and the resulting increase in confidence leads to a virtuous cycle for the rest of the class.
I don't know how similar that is to the studies you're talking about, and I certainly expect that some of what you're describing comes down to innate personality differences just as you've observed. But the idea that short, small interventions like this can have significant lasting effects isn't a matter of just one or two badly run studies. (I can make no claims about whether the entire field consists of badly run studies, but I'm never comfortable making that sort of accusation in areas where I'm not an expert.)
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--Beth
Reply
After Chris and I both tried explaining every step to her and both failed, we decided that backing off was called for. We gave her no math assignment aside from playing with the DragonBox app (algebraic manipulations in the form of a game, so comfortable non-threatening environment), and we sat on our parental hands for two weeks.
It was probably the second hardest thing I've ever done, parenting-wise, with the first being deciding to put T on attention meds. The common thread there: I wasn't actually completely confident that I was doing the right thing, and there was every chance I was screwing up in something that Mattered.
But it paid off. She came back to it after two weeks away, followed my explanation (including explaining what the next step should be when asked), worked through it herself from fresh the next day with only a couple prompts to keep her from making an algebra mistake, and got the answer correct. She then worked out the follow-up problems on her own, came to a second problem of the same type with different numbers, and worked through that second problem on her own without help.
When I pointed out to her what she'd just done, her grin could have rivaled some stars in brightness.
And then she turned to T, who surpassed her in math progress about a year ago, and said, "Look out, T! I'm going to be doing two chapters of math a day now! I'm going to be catching up with you!" We're still in parental discussions on how much we ought to encourage/discourage competition between siblings as a motivating factor for academic progress, but the boost to her confidence level and willingness to tackle new things in math has been tremendous and persists a week later, and I'm hopeful that it will establish new patterns for her.
Carryover to other academic disciplines, however, has not happened, so far as I can tell. I still don't know how to engineer such a situation, either. I think mostly what I can say is, I feel your pain, I sympathize with your struggle, there is definitely reason for hope that small crises appropriately addressed can make a long-term difference, but this fixed mindset is still ridiculously difficult to counter and I'm sorry you're having to struggle with it too. It sucks.
Newt
Reply
Reply
On the other hand, the farther you are from the beaten path, the more work you will have to put into synthesizing available materials to get what you want. I'm on a couple FB lists for parents/educators of gifted kids, and the parents who post questions along the lines of, "My 5yo who can add and subtract single-digit numbers and is just starting to learn to read is obsessed with nuclear physics. I'd like a semester-long curriculum that he can work through on his own that will feed his interest in this. I have no time to put anything together and no money to buy anything new. Can you help me?" bug me no end. Encouraging a child's interests does take resources, in time or money or both, and moreso when they aren't reading independently yet. (In fairness, most parents do know this. It's mostly in August and September that the ones who don't seem to come out of the woodwork.)
Newt
Reply
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