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Joined: Jan 2008
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Cathy  thanks for your example! i printed it out for when we get to fractions. This so makes sense to me. I am one of those people who was told that boys were good at math, and girls weren't, and i suppose i believed it. I always got good math grades, but only took the courses that were required. I was thrilled when my college accepted logic courses for math requirements! I do not even have the foggiest idea what calculus is. But, I do know how to ask for help when needed, and DH is very good at math. So DS4 will be OK.




Joined: May 2007
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Calculus sounds a lot more daunting that it is. Basically, it is a way of cutting curved things into little pieces that have practically straight sides so that we can add them up just like regular old geometric shapes. It's a clever concept which was developed as way to calculate phenomena encountered in physics. It has its own notationyou may have seen integral signs which look like elongated esses. They are for adding things up. The esses stand for "sums". It's actually a very visually based kind of math.
ETA: I wish more people would take logic!
Last edited by Cathy A; 04/23/08 12:53 PM.




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Great thoughts, Cathy!
Can I ask you some questions about Descartes' Cove game, or has this been discussed in a different post already?




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Great thoughts, Cathy!
Can I ask you some questions about Descartes' Cove game, or has this been discussed in a different post already? Sure. We haven't played all of it yet. DS is working on the easiest level (Measurement) which is about unit conversions, decimals and metric system. There is other stuff thrown in, though like formulas for volumes and areas of different shapes. I checked out the Algebra level and there were some reasonable tricky problems on there. Good for stretching your brain!




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I did learn my math facts in grade school but it wasn't exactly by rote. It was more that I repeatedly thought about them until the answers were clear. For example, 7+8=15 because 8+8=16 and 7 is one less than 8. This process builds upon itselfi.e. at some point I had to become convinced that 8+8=16 before I could use that to conclude that 7+8=15. After a while, I felt that I could skip the reasoning part and just go straight to the answer. Exactly! This is exactly what Dr. F was saying! If you get it, then the doing is easy and you learn math facts just from daily use. If you don't get it, then you're forced to rely on rote memorization for the doing, and that's painful for a GT kid. Better to start with the concepts and let the knowledge of the math facts come naturally from there. My point (I think I have one ) is that verbal reasoning can be used to understand math as a language for representing real problems. This is SO important for kids to understand. The way math is taught in school you would think that the math and verbal domains were completely seperate. I think that GT kids have the ability to intuit this connection. Mathy kids don't need to have things translated for them this way. Exposing kids like this to math is like immersing them in a foreign language. They will soak it up. Exposing them to calculus at a young age is like letting them read books with big words in them. They may not understand them right away but that's ok. EXACTLY! This is something Dr. F said, too, almost verbatim! That's why he believes ALL GT kids are naturals at math, even if they're highly verbal. Because language and math are not separate entities. Our brains don't divide math and language that way. Oh, Cathy, you're explaining this SOOOOOOO much better than I did! Thanks! This kind of enrichment is beneficial to kids at all levelswithout it, math just seems like an arithmetic wasteland to them and they lose interest. Again, right on the money. Dr. F said we should, in effect, aim high with these kids. If they don't get it all at age 6, so what? They've got years more to pick up what they missed on the first exposure! But showing them what's out there, what math REALLY isand it ain't workbooks!captivates them, shows them that math is beautiful. We don't teach kids to read by diagramming sentences, so why would we try to teach math by starting with arithmetic. Teach them to love it first, then the nutsandbolts will come. You rock, Cathy! You made that a whole lot clearer than I did!
Kriston




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OHG: I see what you're saying. Thanks for the clarification. I think you're absolutely right that anything can get old if done to death. Good point. It's not like math facts have the corner on that market! LOL! And I'm definitely not suggesting this style of math for a general classroom. I have no idea how that would play, and frankly, I don't really have to know. Dr. F is doing it with GT kids in a GT school, so there's that, I guess. But for my part, all I'm worried about is my own progeny! I thought it might work for some of the afterschoolers out there, perhaps in some modified form. ...Or not. You know meI'm not highly evangelical about anything I'm doing! At least it's made for an interesting conversation!
Kriston




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Granted, I can kind of be a laissezfaire parent, but I don't really understand the concern here. Kriston, or anyone, if your son is gifted, to the point of being accepted into DYS, is ahead of age/grade mates already in math, doesn't want or like to do math right now, and you are homeschooling so there is no need to be concerned about standardized testing or acceptance into academic programs, then.. why do math at all? Isn't the major benefit of homeschooling the ability to follow your child's lead? Well, because I don't think that it's *math* he dislikes; I think it's *my approach to math* that he has disliked. He's fascinated by engineering principles and has always had a mind for patterns and mazes that astounds me. Dropping math altogether doesn't seem like it solves anything, and may in fact mean we'd be missing some opportunities. An entirely new approach, however, may be just the thing to light his fire again, a fire that he's always had until he hit school age and workbookseither the public school's workbooks or mine. I can always back off if it looks like that's what's needed. I can appreciate some deschooling time as much as any homeschooler. But before I just give up and hope that he comes to math on his own, I'd rather try to SOLVE the problem, a problem that I feel is mine, not his. Does that make sense? He's also a lot less far ahead in math than he is in his other subjects. He's reading at the 7th+ grade level, but he's only doing 3rd grade math. I have no trouble with asynchronous development, but I think this has less to do with his abilities and more to do with my teaching. I feel like I'm letting him down, and this offers a different way to give him what he needs. It seems worth a try. And BTW, geometry, which I've approached in a far more conceptual and far less arithmeticky manner than our previous math work led us to, has been pretty successful. He's having fun with it. Geometry is one of my data points suggesting going for higherlevel, conceptual math rather than arithmetic is going to work better with him.
Kriston




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Ooh! DOK! I wish we had such a club for HSers my son's age!
It may be time to start creating the things I want instead of just wishing they were around...
Kriston




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Thanks for the simple definition, Cathy! I actually liked geometry maybe I'll like calculus too.
I suppose now's a good time to also confess that for years as a child I thought engineers drove trains. (Not entirely my fault  my grandpa was a train engineer).




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Dr. F gave some examples of just this sort of intuitiondeadening, cym. People who figure 100/8 by doing long division in their heads, for example. That's not the "natural" way to do it; it's learned. And sometimes that learning can kill the intuition. Do you mean that whoever can figure out 100/8 in their head or just whoever does it the same way like long division on the paper? It's about the method. Long division is one way to get the answer, but if you basically write the problem out in long division form in your head, then you're not using intuition because long division is a method taught to you, not one you would just come to on your own. Yes, pretty much everyone can figure out 100/8 in their heads, I hope! The problem itself has nothing to do with intuition; it's just a way to check how you think about math.
Kriston




