Anonymous
Post 02/02/2015 22:23     Subject: Re:First grader, advanced at math?
Anonymous wrote:
Anonymous wrote:

Anecdotally, I think you can begin to see evidence of a mind that works that way. I do know a kid who discovered a new way to multiply multi-digit numbers in 1st grade (new meaning a way he'd never been taught and that the adults he showed it to had never seen before anyway -- not that its was more efficient, but it worked!); but also a kid who butts in and says, "or you can do it this way!" A kid who can identify many ways to represent a numeral and is talking about negative numbers with understanding; a kid who manipulates objects and shapes in ways that show an inherent sense of geometry, symmetry, balance; or a kid who finds patterns in everything; a toddler who asks questions like "what makes 40?" and then manipulates objects to find hundreds of ways to calculate 40 (and wants to spend time finding new ways to create 40 because it is fascinating to her); or a kid who calculates the Fibonacci sequence without every having heard of it; a kid who asks questions about the beginning and end of numbers and likes to count in patterns; a kid who asks (and answers) "why" questions about math calculations or about shapes and angles; a kid who "gets" that certain math calculating tricks are tricks that work but bear no relation to underlying calculus; a kid who is always calculating something relative to something else (minutes to miles, age to height, cookies to bites to number of teeth), etc. Perhaps a kid who sees poetry in multiplication. With some kids you can tell that they "see" the invisible math world and understand how to manipulate things in that perfect world before they have a vocabulary for it, if you know what I mean (like finding and delighting in the Platonic solids while playing with magna-tiles, but not knowing they are a "thing"). All of that just hints at potential though. The love of figuring it all out needs to be fostered, I think. And you may have to build up resilience to the potential boredom of repetitive school math, so they don't hate "math class" by the time they get to the interesting stuff. Just my thoughts on the subject - lots of math teachers in our family.


Good points. The question is how to foster the love of figuring it out? Sometimes the questions get too tricky to answer -- "Are there always prime numbers two apart?" "Is there a biggest prime number?" etc..... Some you can explain, others not so much....


I think if the child were asking those questions, I'd encourage them to keep thinking about it and try to figure it out. More is learned by trying to figure it out than to be given the answer at age 7. Einstein allegedly puzzled about the questions that lead him to his theory of relatively from age 10 to 33. I would try to foster that -- I'd leave the teaching of the terminology to teachers when the time comes. Fostering the math mind at home to me is more about playing with shapes and building and number games and logic puzzles and problems and music and working at things that are difficult and problems that perhaps no one alive yet knows the answer to. "I don't know, lets try to figure it out" is my go-to answer. Then try to make figuring it out fun, and give up when they are ready to, leaving it until another day. Some day in the future there will be an a-ha moment -- hey, that's like that thing we were trying to figure out that one time, remember? Look there's that pattern again. And so on. On the prime number one, I'd say, gee I don't know, when you count sheep tonight paint each of them with a prime number and then see how far you get before you fall asleep! Frustrations your friend.

What's your take on it?
Anonymous
Post 02/02/2015 19:02     Subject: Re:First grader, advanced at math?
Anonymous wrote:

Anecdotally, I think you can begin to see evidence of a mind that works that way. I do know a kid who discovered a new way to multiply multi-digit numbers in 1st grade (new meaning a way he'd never been taught and that the adults he showed it to had never seen before anyway -- not that its was more efficient, but it worked!); but also a kid who butts in and says, "or you can do it this way!" A kid who can identify many ways to represent a numeral and is talking about negative numbers with understanding; a kid who manipulates objects and shapes in ways that show an inherent sense of geometry, symmetry, balance; or a kid who finds patterns in everything; a toddler who asks questions like "what makes 40?" and then manipulates objects to find hundreds of ways to calculate 40 (and wants to spend time finding new ways to create 40 because it is fascinating to her); or a kid who calculates the Fibonacci sequence without every having heard of it; a kid who asks questions about the beginning and end of numbers and likes to count in patterns; a kid who asks (and answers) "why" questions about math calculations or about shapes and angles; a kid who "gets" that certain math calculating tricks are tricks that work but bear no relation to underlying calculus; a kid who is always calculating something relative to something else (minutes to miles, age to height, cookies to bites to number of teeth), etc. Perhaps a kid who sees poetry in multiplication. With some kids you can tell that they "see" the invisible math world and understand how to manipulate things in that perfect world before they have a vocabulary for it, if you know what I mean (like finding and delighting in the Platonic solids while playing with magna-tiles, but not knowing they are a "thing"). All of that just hints at potential though. The love of figuring it all out needs to be fostered, I think. And you may have to build up resilience to the potential boredom of repetitive school math, so they don't hate "math class" by the time they get to the interesting stuff. Just my thoughts on the subject - lots of math teachers in our family.


Good points. The question is how to foster the love of figuring it out? Sometimes the questions get too tricky to answer -- "Are there always prime numbers two apart?" "Is there a biggest prime number?" etc..... Some you can explain, others not so much....
Anonymous
Post 02/02/2015 18:22     Subject: Re:First grader, advanced at math?
Anonymous wrote:
Anonymous wrote:
Or neither. Some kids can just add fast. But a kid who comes up with a new way to solve complex problems that the teachers have never thought of ... there's a gift there, I think. My math teacher Aunt says some of the most gifted math students she had struggled to past the fast facts tests (not that they didn't know the facts, but they weren't very fast at spitting them back out), but their understanding of math concepts and ability to do complex problem solving was out of this world. Understanding and figuring out proofs without being formally introduced to them, just because "it made sense." That is the gift.


+1. But how do you detect that in a K/1st grader? Or should you even be able?


Anecdotally, I think you can begin to see evidence of a mind that works that way. I do know a kid who discovered a new way to multiply multi-digit numbers in 1st grade (new meaning a way he'd never been taught and that the adults he showed it to had never seen before anyway -- not that its was more efficient, but it worked!); but also a kid who butts in and says, "or you can do it this way!" A kid who can identify many ways to represent a numeral and is talking about negative numbers with understanding; a kid who manipulates objects and shapes in ways that show an inherent sense of geometry, symmetry, balance; or a kid who finds patterns in everything; a toddler who asks questions like "what makes 40?" and then manipulates objects to find hundreds of ways to calculate 40 (and wants to spend time finding new ways to create 40 because it is fascinating to her); or a kid who calculates the Fibonacci sequence without every having heard of it; a kid who asks questions about the beginning and end of numbers and likes to count in patterns; a kid who asks (and answers) "why" questions about math calculations or about shapes and angles; a kid who "gets" that certain math calculating tricks are tricks that work but bear no relation to underlying calculus; a kid who is always calculating something relative to something else (minutes to miles, age to height, cookies to bites to number of teeth), etc. Perhaps a kid who sees poetry in multiplication. With some kids you can tell that they "see" the invisible math world and understand how to manipulate things in that perfect world before they have a vocabulary for it, if you know what I mean (like finding and delighting in the Platonic solids while playing with magna-tiles, but not knowing they are a "thing"). All of that just hints at potential though. The love of figuring it all out needs to be fostered, I think. And you may have to build up resilience to the potential boredom of repetitive school math, so they don't hate "math class" by the time they get to the interesting stuff. Just my thoughts on the subject - lots of math teachers in our family.
Anonymous
Post 02/02/2015 18:09     Subject: Re:First grader, advanced at math?

+1. But how do you detect that in a K/1st grader? Or should you even be able?


that's tough one--I taught a dyslexic kid who could spit out math facts almost instantly in first grade--yet, struggled with letters. I just could not understand.




Anonymous
Post 02/02/2015 17:14     Subject: Re:First grader, advanced at math?
Anonymous wrote:
Or neither. Some kids can just add fast. But a kid who comes up with a new way to solve complex problems that the teachers have never thought of ... there's a gift there, I think. My math teacher Aunt says some of the most gifted math students she had struggled to past the fast facts tests (not that they didn't know the facts, but they weren't very fast at spitting them back out), but their understanding of math concepts and ability to do complex problem solving was out of this world. Understanding and figuring out proofs without being formally introduced to them, just because "it made sense." That is the gift.


+1. But how do you detect that in a K/1st grader? Or should you even be able?
Anonymous
Post 02/02/2015 16:39     Subject: Re:First grader, advanced at math?
Anonymous wrote:
Anonymous wrote:Which would show gifted at math:

Child who know multiplication facts?

Child who could add 3 digit numbers quickly in his head?



The 2nd one. The 1st one is just a good mimic.


Or neither. Some kids can just add fast. But a kid who comes up with a new way to solve complex problems that the teachers have never thought of ... there's a gift there, I think. My math teacher Aunt says some of the most gifted math students she had struggled to past the fast facts tests (not that they didn't know the facts, but they weren't very fast at spitting them back out), but their understanding of math concepts and ability to do complex problem solving was out of this world. Understanding and figuring out proofs without being formally introduced to them, just because "it made sense." That is the gift.
Anonymous
Post 02/02/2015 16:18     Subject: Re:First grader, advanced at math?
OP asked about kids that are "advanced." There's a difference between advanced and gifted but I think the child who could add 3 digit numbers quickly in his/her head without being taught shows aptitude.

My sister was like this. She could instinctively regroup in her head at age 4 without anyone teaching her anything and she did college level math as a freshman in high school, did well at some national math competition, easily got an 800 SAT, and went to Yale. I wouldn't call her gifted in math, though. She was never going to be a math major and has friends who are now math professors and they think on a different plane from her. She's good enough at math to know this but not good enough to keep up with how they think.


Anonymous wrote:
Anonymous wrote:Which would show gifted at math:

Child who know multiplication facts?

Child who could add 3 digit numbers quickly in his head?



Neither of these. Both are indicators of strong memory, not math aptitude.
Anonymous
Post 02/02/2015 15:39     Subject: First grader, advanced at math?
Anonymous wrote:Kindergartener: Can do multiple digit multiplication, addition etc., can prime factorize numbers, can figure out simple squares and square roots, can add and reduce fractions and do simple algebra word problems. But these are rather mechanical and speed of computations is irrelevant. Look for independently understanding concepts, which is true talent.


This was my brother! If this is true - it's an amazing gift and you may want to see a specialist. It's limitless what you can do when you speak math as a language.

Fun!
Anonymous
Post 02/02/2015 15:35     Subject: Re:First grader, advanced at math?
Anonymous wrote:
Anonymous wrote:Which would show gifted at math:

Child who know multiplication facts?

Child who could add 3 digit numbers quickly in his head?



Neither of these. Both are indicators of strong memory, not math aptitude.


I don't see adding multi digits as being good at memory. Being able to spit back out math facts is memorization. Computation is not the same as rote memory.
Anonymous
Post 02/02/2015 15:27     Subject: Re:First grader, advanced at math?
Anonymous wrote:Which would show gifted at math:

Child who know multiplication facts?

Child who could add 3 digit numbers quickly in his head?



Neither of these. Both are indicators of strong memory, not math aptitude.
Anonymous
Post 02/02/2015 15:24     Subject: First grader, advanced at math?
Anonymous wrote:

+1: multiplication, addition, square roots, etc. is simply understanding concept and applying it. That isn't the same as figuring out multistep problems which are more complex. For example, once a kid understands how to do multiplication or addition, then doing it doesn't make him a genius. It simply means he understands a rote concept that has been explained, albeit it is a concept generally reserved for those much older.


No, it is more than doing multi-step problems either, which can also be done by rote -- As long as one can map the words to mathematical symbols, manipulations are easy. I don't mean to trivialize these (my kid does most of these) but being really gifted means figuring out new connections. That said, if any child shows some aptitude, it is important to encourage them to instill a way of thinking about mathematical concepts. Start with a math specialist in the school, if you have any. Mathnasium and other math clubs may be great too.
Anonymous
Post 02/02/2015 13:41     Subject: First grader, advanced at math?
whatever.
Anonymous
Post 02/02/2015 13:40     Subject: First grader, advanced at math?
Anonymous wrote:
Anonymous wrote:
Anonymous wrote:
Anonymous wrote:Kindergartener: Can do multiple digit multiplication, addition etc., can prime factorize numbers, can figure out simple squares and square roots, can add and reduce fractions and do simple algebra word problems. But these are rather mechanical and speed of computations is irrelevant. Look for independently understanding concepts, which is true talent.


If your K kid really can do all those things you listed, there is a lot of understanding going on.


Yes, he can and yes he understands a lot. But that's not the same as a more abstract understanding, like figuring out numbers in different bases (base-2, base-8 etc.), just playing around and asking questions and thinking things through or just relating observations to mathematical patterns.


+1: multiplication, addition, square roots, etc. is simply understanding concept and applying it. That isn't the same as figuring out multistep problems which are more complex. For example, once a kid understands how to do multiplication or addition, then doing it doesn't make him a genius. It simply means he understands a rote concept that has been explained, albeit it is a concept generally reserved for those much older.
Anonymous
Post 02/02/2015 13:38     Subject: First grader, advanced at math?
Anonymous wrote:
Anonymous wrote:
Anonymous wrote:Kindergartener: Can do multiple digit multiplication, addition etc., can prime factorize numbers, can figure out simple squares and square roots, can add and reduce fractions and do simple algebra word problems. But these are rather mechanical and speed of computations is irrelevant. Look for independently understanding concepts, which is true talent.


If your K kid really can do all those things you listed, there is a lot of understanding going on.


Yes, he can and yes he understands a lot. But that's not the same as a more abstract understanding, like figuring out numbers in different bases (base-2, base-8 etc.), just playing around and asking questions and thinking things through or just relating observations to mathematical patterns.
Anonymous
Post 02/02/2015 13:30     Subject: First grader, advanced at math?
Anonymous wrote:
Anonymous wrote:Kindergartener: Can do multiple digit multiplication, addition etc., can prime factorize numbers, can figure out simple squares and square roots, can add and reduce fractions and do simple algebra word problems. But these are rather mechanical and speed of computations is irrelevant. Look for independently understanding concepts, which is true talent.


If your K kid really can do all those things you listed, there is a lot of understanding going on.


Yes, he can and yes he understands a lot. But that's not the same as a more abstract understanding, like figuring out numbers in different bases (base-2, base-8 etc.), just playing around and asking questions and thinking things through or just relating observations to mathematical patterns.