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Anyone else have a concept-oriented kiddo in math?

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I've posted about this, but I'm now curious if this is common or not! My 6.5 year old daughter is very good at math, but gets easily bored by rote calculations and is also not particularly interested in puzzles like the ones in Beast Academy (although she's good at them when she occasionally feels like doing them.) 

However, she's extremely enthusiastic about new ideas. She asked to learn about negative numbers and loved figuring them out, she loved binary and has become very proficient at it, and she's currently really enjoying combinatorics. There's something that really appeals to her about mastering the patterns that come with a new concept or idea. 

Anyone else have any experience with this? I have a hunch that people wouldn't think of her as a mathy kid if she were in a standard classroom, because she doesn't like calculations or puzzles. But she's so extremely motivated by ideas that I do think of her as mathy. 

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My kid has always preferred learning new math concepts to “doing math”. She learns concepts quickly, and can easily extrapolate. But it’s like she feels that doing actual calculations just slows her brain down. It’s always been a balancing act of having her do enough calculations that I know she’s got it down, and letting her explore the concepts as much as she wants. But this is also a kid who reads math books and watches math videos/lectures for fun, so I don’t know that I’d call her altogether normal. 😉

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8 minutes ago, Jackie said:

My kid has always preferred learning new math concepts to “doing math”. She learns concepts quickly, and can easily extrapolate. But it’s like she feels that doing actual calculations just slows her brain down. It’s always been a balancing act of having her do enough calculations that I know she’s got it down, and letting her explore the concepts as much as she wants. But this is also a kid who reads math books and watches math videos/lectures for fun, so I don’t know that I’d call her altogether normal. 😉

 

Yeah, we've had to switch to doing largely verbal drills for math facts, because otherwise there's mutiny! Luckily, my kiddo has a good memory so that's been working for us. How old is your daughter? 

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28 minutes ago, Arcadia said:

Worth a read

 

 

Lovely thread, thank you! A good reminder to buy some Martin Gardiner books (I loved them as a kid), and of course, there are tons of newer ideas on there I'm going to have to ponder :-). 

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20 minutes ago, square_25 said:

 A good reminder to buy some Martin Gardiner books (I loved them as a kid), and of course, there are tons of newer ideas on there I'm going to have to ponder :-). 

 

Martin Gardner festivals 

https://www.celebrationofmind.org/

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square_25, my older ds is on the extreme end of concept driven. I'm a science person, not a math person, so when he was little, we just played shop. I had no grand visions or pedagogical opinions, I just taught him about money, made up funny word problems, estimated stuff, played multiplication war, etc.  Then, at the age of 6, having never been introduced to the concepts, he invented algebra, reasonably complex algebra. I had no idea that these thoughts were in his head, none. We had been playing shop. That is when I started reading up on how to teach him.  But interestingly, he was extremely computation adverse.  He *refused* drill, completely refused to do it.  He seemed to only be able to practice his numeracy skills through complex 10 step word problems.  It was at the age of 8 that he decided that all teaching was cheating, in fact, that all textbook explanations were cheating.  I'm actually not sure how he learned fractions - he must have had insight and just confirmed his method by checking his answers in the back of the book, because he *refused* to be taught how to do it by me or by any written explanation. At the time he was working his way through the word problems in singapore math intensive practice.  Over time, I came to believe that his mathematical skill was so high, that drill of any sort was the equivalent of proof-reading a phone book.  You might have good intentions, but there is just no way you can actually *do* something so boring. However, this boy then took 3 years to get through AoPS intro algebra, and this slow speed just about gave me a heart attack. But he had to do it on his own. And he had to do it at his own pace. And he had to *derive* every. single. concept independently.  But you know what, he was on the NZ IMO team at 15, and now is taking grad level math classes at MIT as a freshman. So his very strange path was apparently just right for him.

My point is that you are mathy and your child is mathy. Perhaps there is just NO drill in her future. I remember my son memorizing his subtraction facts while concurrently working through AoPS algebra independently.  Conceptually, he was far far far ahead, but when it came to *computation* he was very average.  I've often wondered what would have happened to him if he had been forced to do math in school. My guess is that it would have drained the passion right out of him.  I'm so grateful to be able to have offered him another path.

Ruth in NZ

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8 hours ago, lewelma said:

square_25, my older ds is on the extreme end of concept driven. I'm a science person, not a math person, so when he was little, we just played shop. I had no grand visions or pedagogical opinions, I just taught him about money, made up funny word problems, estimated stuff, played multiplication war, etc.  Then, at the age of 6, having never been introduced to the concepts, he invented algebra, reasonably complex algebra. I had no idea that these thoughts were in his head, none. We had been playing shop. That is when I started reading up on how to teach him.  But interestingly, he was extremely computation adverse.  He *refused* drill, completely refused to do it.  He seemed to only be able to practice his numeracy skills through complex 10 step word problems.  It was at the age of 8 that he decided that all teaching was cheating, in fact, that all textbook explanations were cheating.  I'm actually not sure how he learned fractions - he must have had insight and just confirmed his method by checking his answers in the back of the book, because he *refused* to be taught how to do it by me or by any written explanation. At the time he was working his way through the word problems in singapore math intensive practice.  Over time, I came to believe that his mathematical skill was so high, that drill of any sort was the equivalent of proof-reading a phone book.  You might have good intentions, but there is just no way you can actually *do* something so boring. However, this boy then took 3 years to get through AoPS intro algebra, and this slow speed just about gave me a heart attack. But he had to do it on his own. And he had to do it at his own pace. And he had to *derive* every. single. concept independently.  But you know what, he was on the NZ IMO team at 15, and now is taking grad level math classes at MIT as a freshman. So his very strange path was apparently just right for him.

My point is that you are mathy and your child is mathy. Perhaps there is just NO drill in her future. I remember my son memorizing his subtraction facts while concurrently working through AoPS algebra independently.  Conceptually, he was far far far ahead, but when it came to *computation* he was very average.  I've often wondered what would have happened to him if he had been forced to do math in school. My guess is that it would have drained the passion right out of him.  I'm so grateful to be able to have offered him another path.

Ruth in NZ

 

Your kiddo sounds mathier than my daughter, to be fair! I assume he liked math puzzles more than her, anyway: at least, that's what I expect from people who do contests and go to the IMO. But yeah... she'd much rather learn her facts in the process of solving a system of equations or figuring out a number in binary than she'd drill them. That bit sounds familiar! 

Do you not receive PMs for some reason, by the way? I was going to message you about MIT... we know it well, since my husband's from Boston and is also a mathematician. Wasn't sure if you wanted any recommendations or anything like that :-). 

 

 

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Sure, but I have to say you are assuming the standard classroom is computation based and offers challenge via puzzles.  Ours are not, the K-3 teachers here had much to offer.

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28 minutes ago, HeighHo said:

Sure, but I have to say you are assuming the standard classroom is computation based and offers challenge via puzzles.  Ours are not, the K-3 teachers here had much to offer.

 

I'm sure there are as many classroom experiences as there are classrooms. I can only speak to what I've experienced myself (my daughter went to kindergarten) and via children of friends. I'm sure there are better experiences out there. 

What activities did your children enjoy in their classrooms from K to 3? I'm always interested in resources. 

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20 minutes ago, square_25 said:

 

I'm sure there are as many classroom experiences as there are classrooms. I can only speak to what I've experienced myself (my daughter went to kindergarten) and via children of friends. I'm sure there are better experiences out there. 

What activities did your children enjoy in their classrooms from K to 3? I'm always interested in resources. 

 

The discussion of  concepts, the ability to experiment, the games (NIM, etc) and figuring out the strategies and discussing same with like minds, the weights and balance beams (they are getting the algebriac concepts done practically), exploring the concept of  measuring quantities of time, temperature, length, figuring out other bases, optimization schemes, mapping, on and on.  They aren't doing 'units' via resources, they are answering questions posed by themselves or by their teacher, things they want to figure out, patterns they have noticed and want to discuss. 

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2 minutes ago, HeighHo said:

 

The discussion of  concepts, the ability to experiment, the games (NIM, etc) and figuring out the strategies and discussing same with like minds, the weights and balance beams (they are getting the algebriac concepts done practically), exploring the concept of  measuring quantities of time, temperature, length, figuring out other bases, optimization schemes, mapping, on and on.  They aren't doing 'units' via resources, they are answering questions posed by themselves or by their teacher, things they want to figure out, patterns they have noticed and want to discuss. 

 

That sounds awesome! Sounds like you have great schools near you. That reminds me that we should play something like Nim with my daughter, that's a fun one. And game theory in general, hm. Maybe we'll should try that after we do geometry (which is on our list after combinatorics.) 

Thanks for the suggestions! 

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2 minutes ago, square_25 said:

 

That sounds awesome! Sounds like you have great schools near you. That reminds me that we should play something like Nim with my daughter, that's a fun one. And game theory in general, hm. Maybe we'll should try that after we do geometry (which is on our list after combinatorics.) 

Thanks for the suggestions! 

 

All of this stuff is available on the internet  using search terms such as 'math club resources'. 

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17 hours ago, square_25 said:

 

Yeah, we've had to switch to doing largely verbal drills for math facts, because otherwise there's mutiny! Luckily, my kiddo has a good memory so that's been working for us. How old is your daughter? 

She’s about to turn 9.

We never did math fact drill. She wanted nothing to do with it. She calculates as she needs to, with tricks like x4 is doubling twice, and I put up a multiplication chart for her to reference until she pretty much had them down. She just finished Algebra A and I didn’t let her use a calculator, so it doesn’t seem to have slowed her down much. She really runs with the concepts, though. 

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17 minutes ago, Jackie said:

She’s about to turn 9.

We never did math fact drill. She wanted nothing to do with it. She calculates as she needs to, with tricks like x4 is doubling twice, and I put up a multiplication chart for her to reference until she pretty much had them down. She just finished Algebra A and I didn’t let her use a calculator, so it doesn’t seem to have slowed her down much. She really runs with the concepts, though. 

 

Yeah, I'm sure if the verbal fact drill hadn't worked, we'd have given it up entirely. I'd much rather my daughter knows the whole bag of multiplication "tricks" (which are really thorough understanding of how multiplication works) than have her tediously memorize the multiplication table :-). Luckily, she seems to have gotten it down naturally with practice and a bit of drill as we walk around. We only drilled after she had figured out about 4 ways to figure each one out, and that worked well for us. 

What concepts has your daughter enjoyed the most so far? :-) 

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2 hours ago, square_25 said:

 

Yeah, I'm sure if the verbal fact drill hadn't worked, we'd have given it up entirely. I'd much rather my daughter knows the whole bag of multiplication "tricks" (which are really thorough understanding of how multiplication works) than have her tediously memorize the multiplication table :-). Luckily, she seems to have gotten it down naturally with practice and a bit of drill as we walk around. We only drilled after she had figured out about 4 ways to figure each one out, and that worked well for us. 

What concepts has your daughter enjoyed the most so far? 🙂

 

Imaginary numbers and sizes of infinity are two that she’s really loved. Different base systems fascinate her. She’s taking a break from formal math for a bit now, but I suspect she’ll want to try the AOPS Number Theory book next.

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22 hours ago, Jackie said:

 

Imaginary numbers and sizes of infinity are two that she’s really loved. Different base systems fascinate her. She’s taking a break from formal math for a bit now, but I suspect she’ll want to try the AOPS Number Theory book next.

 

Cool! AoPS Number Theory will go through different bases, and precalc does complex numbers... possibly one other class does complex numbers before that, too, I don't quite remember. 

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