children and math

[Athena]

In the cutting Edge math theory thread, I provide a link to a very exciting DVD about Origami and its relation with math, science and art. The DVD is titled "Independent Lens: Between the Folds" and is great for getting high school students excited about math.

 

Then this morning on the National Public Radio station, I heard about a book for children, done by a college professor. http://www.richardev...m/monsters.html

 

Surely everyone has heard Pythagoras put down for treating numbers like beings with personalities, but that is exactly what the college professor has done. His number characters are monsters with individual personalities that children can identify with and love. The idea behind this is, we are more interested and remember better when we humanize objects and numbers. The ancients humanized things like rock formations and told stories about them, so people would remember the land marks, that had some kind of survival purpose, like where to find water. We like to name our cars and computers and talk about their personalities. It is fun and does help us remember. Richard Schwartz has taped into this for introducing children to math, and now that a modern mathemetician has done this, I question how seriously Pythororas took his ugly numbers? Perhaps he too was only speaking of numbers in a more interest way and did not expect people to take him literally? Richard said this is what people who engage in math do, so they can better relate to the meaning behind the numbers and symbols.

 

Whatever, I just wanted to created a space for discussing what parents and grandparents might do to encourage children to enjoy math. Do you have any memories of something that got you interested in math, or an idea for encouraging a child to get excited about math?

 

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Edited January 22, 2011 by Athena

[dragonstar57]

1 truck and another truck =2 trucks is not very exciting even for little kids

[Athena]

Oh you read the book? Surely you have more to say than that, because it is about more than that.

 

Perhaps you know at what age a child can grasp mathematical concepts? How many 3 year olds have worked with and what was the most successful for getting a young child to understand the concepts?

Edited January 23, 2011 by Athena

[khaled]

Oh you read the book? Surely you have more to say than that, because it is about more than that.

 

Perhaps you know at what age a child can grasp mathematical concepts? How many 3 year olds have worked with and what was the most successful for getting a young child to understand the concepts?

 

I haven't read any book but what i think is that teaching a child math concepts need to

transform the concepts into games, I suggest the following:

 

- Count Specific Cars in the other side of the street (group game in car)

- Addition and Subtraction using logos at home

- play monopoly, learn how to count money, and raise odds on bets

- Ask your child about the change before getting the change in a shop

- Multiplication using group theory (ex: if you have 5 dollars, and so 5 boys, how many dollars we have seen ?)

- Multiplication by letting the child look at a matrix of glass windows of a building

...

[the tree]

I've never been too keen on patronising children of any age, for the most part they are far too smart to fall for it and "making it into a game" just gives the impression that they are supposed to enjoy it but not really expected to ("if you eat these sprouts then you'll get your desert" immediately makes the descision for the child that sprouts are disgusting and desert is the best thing ever, so you haven't done them a favour even if it happens to work once or twice).

 

I think probably nearly everyone here has read Lockhart's Lament and I've got to say that I sympathise with his lack of patience when it comes to cutesiness - the exception in this case is that Schwartz is trying to teach an actual concept rather than how to numb your mind with routine calculations - the difference being that rather than trying to make maths interesting with contrived games and stories, Schwartz here is actually trying to show that it already is interesting.

 

It's incredibly hard to show that something is interesting when the interesting parts are far from what you're actuallly teaching ("hey, look at the Mandlebrot Set, if you work hard for the next 15 years or so then you might have some idea of what the hell you're looking at") so the challenge is to find something that is both interesting and concieveable to teach to a young child. That's why I think elements of discrete maths should be introduced a lot earlier, there is nothing for instance particuarly difficult about the travelling salesman problem but it is a damn sight more interesting than factoring quadratics, even though the latter is still important it can be taught along with it's wider implications relating to classical mechanics or as a direct follow on from factoring integers to see how they are essentially two faces of the same coin.

 

If you try to sell maths and arithmetic in one bundle then obviously maths is going to come across as incredibly dull, if anything arithmetic should be taught seperately as it is "useful" but it shouldn't be allowed to ruin maths.

Edited January 25, 2011 by the tree

[Athena]

I've never been too keen on patronising children of any age, for the most part they are far too smart to fall for it and "making it into a game" just gives the impression that they are supposed to enjoy it but not really expected to ("if you eat these sprouts then you'll get your desert" immediately makes the descision for the child that sprouts are disgusting and desert is the best thing ever, so you haven't done them a favour even if it happens to work once or twice). I think probably nearly everyone here has read Lockhart's Lament and I've got to say that I sympathise with his lack of patience when it comes to cutesiness - the exception in this case is that Schwartz is trying to teach an actual concept rather than how to numb your mind with routine calculations - the difference being that rather than trying to make maths interesting with contrived games and stories, Schwartz here is actually trying to show that it already is interesting. It's incredibly hard to show that something is interesting when the interesting parts are far from what you're actuallly teaching ("hey, look at the Mandlebrot Set, if you work hard for the next 15 years or so then you might have some idea of what the hell you're looking at") so the challenge is to find something that is both interesting and concieveable to teach to a young child. That's why I think elements of discrete maths should be introduced a lot earlier, there is nothing for instance particuarly difficult about the travelling salesman problem but it is a damn sight more interesting than factoring quadratics, even though the latter is still important it can be taught along with it's wider implications relating to classical mechanics or as a direct follow on from factoring integers to see how they are essentially two faces of the same coin. If you try to sell maths and arithmetic in one bundle then obviously maths is going to come across as incredibly dull, if anything arithmetic should be taught seperately as it is "useful" but it shouldn't be allowed to ruin maths.

 

http://www.suite101.com/content/pythagoras-and-the-history-of-universe-a189473

 

Pythagoras saw numbers as representing more than quantity, and as I understood Schwartz's public radio interview, he also presents numbers as something than stands for more then quantity. There is an element of quality.

 

 

I tried to obtain "You Can Count on Monsters" from a local book store and was told it is sold out. I will have to wait for a second printing before I can find out if there is any relationship between the qualities of Pythagoras's numbers and and Schwartz's numbers.

 

 

In the mean time, does anyone know the child's cognitive developmental stages regarding math? I believe it would be harmful to expect more of a child than is possible. For sure a 3 year old isn't ready for addition flash cards or algebra. But I did find much more age appropriate learning material at a local book store than expected. Either this is an unusual book store, or times have changed a lot! Still rather than depend on the labeling of learning material, I would like a better understanding of a child's cognitive development stages.

 

 

I know Socrates lead a young man through a complex math problem by asking a series of questions. He believed we were born knowing everything and only had to remember what we already knew. I sure the boy would have been over 8 years of when the brain is more developed.

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Edited January 29, 2011 by Athena

[Gozonji]

http://www.suite101....niverse-a189473 Pythagoras saw numbers as representing more than quantity, and as I understood Schwartz's public radio interview, he also presents numbers as something that stands for my then quantity. There is an element of quality.

 

Yes, well, that's a load of religious crap that has nothing to do with mathematics. Or the universe.

[Athena]

Here is the information I was looking for about the stages of math skills development in children. Anyone interested in working with children and developing their math skills might check this site.

 

http://www.ixl.com/1c

 

 

I found that site while checking out Ramanujan. Ramanujan saw each number as a personal friend with its own characteristics. What Schwartz has done is put this kind of imagining in a book for children.

 

In reply to the comment about religious crap, the Greek understanding of the monad, dyad, triad, etc., it is the foundation of our sciences, and we can thank men such as Pythagoras for this.

Edited January 29, 2011 by Athena

[Schrödinger's hat]

One sorely underestimated way of encouraging kids is letting them see you using it.

Go build something that requires you to use Pythagoras.

Play card games that involve maths. Start easy, blackjack, variants of memory where instead of making pairs you make a sum. As they get a little bit older try playing Mao (I'm not sure how well this would work with children as creating rules can be a bit subtle, maybe if they worked in teams with an adult).

Use mathematical language in the house where you can. Use words from set theory or statistics when explaining things (this will also aid communication between adults, as nerdy as it is ).

In response to talk of making a game of things, and of being too condescending. If you are genuinely interested in something and think it's neat then it shouldn't come off as condescending. Give them puzzles such as monty hall (playing cards with candy as a prize works great) or i have two coins, one of which is heads..... Don't explain the maths straight away, let them figure out the right strategy on their own, then explain the general concept, or refer to the previous puzzle..

Hell, design a boat. Rather than looking up some plans do a bit of reading, calculate some moments, tensions, strength of mast, for yourself.

Kids naturally want to do whatever the adults are doing, even if they don't understand it initially. If you use a white board to do your calculations in front of them, they'll want to join in. Let them play just drawing random squiggles for a while, then maybe let them help with the arithmetic.

[khaled]

There is a very powerful method, but it's not used, and none would agree to ...

 

It's a method where we can make 3-year-old children learn complex mathematics,

 

By using media such as TV channel, and by deploying both Graph theory & Fuzzy Media theory,

 

This method works because of a simple reason, because this method communicate

with the child's brain, not with the child him-self ...

 

and the brain works the same at all times (not talking about understand level), and young

humans have better perceiving of things ...

Edited January 31, 2011 by khaled

[the tree]

@Athena: I don't know why you quoted my whole post there since you didn't address a single point mentioned in it. The problem with trying to measure cognitive development in something that more or less has to be taught is extreme experimental bias, every child is going to find algebra and geometry easier than number theory and graph theory because every child has been taught the former and not the latter from an early age - we can't decide that they are incapable of comprehending something we've never tried teaching them.

 

@Gozonji: Everyone knows that Pythagoras was batshit crazy, but that doesn't mean that there aren't any potential applications of what he spouted, if you're smart enough to find them.

 

@Schrödinger's hat: That is a fantastic idea, you should see what I mean, if something is fun you shouldn't have to "make it fun" and there really is no need to contrive a game out of something as inherently satisfying as building something.

 

@khaled: Are you going to keep this method secret from us or what? And I'm going to throw a Citation Needed on that entire post, as it goes.

[Athena]

One sorely underestimated way of encouraging kids is letting them see you using it.

Go build something that requires you to use Pythagoras.

Play card games that involve maths. Start easy, blackjack, variants of memory where instead of making pairs you make a sum. As they get a little bit older try playing Mao (I'm not sure how well this would work with children as creating rules can be a bit subtle, maybe if they worked in teams with an adult).

Use mathematical language in the house where you can. Use words from set theory or statistics when explaining things (this will also aid communication between adults, as nerdy as it is ).

In response to talk of making a game of things, and of being too condescending. If you are genuinely interested in something and think it's neat then it shouldn't come off as condescending. Give them puzzles such as monty hall (playing cards with candy as a prize works great) or i have two coins, one of which is heads..... Don't explain the maths straight away, let them figure out the right strategy on their own, then explain the general concept, or refer to the previous puzzle..

Hell, design a boat. Rather than looking up some plans do a bit of reading, calculate some moments, tensions, strength of mast, for yourself.

Kids naturally want to do whatever the adults are doing, even if they don't understand it initially. If you use a white board to do your calculations in front of them, they'll want to join in. Let them play just drawing random squiggles for a while, then maybe let them help with the arithmetic.

 

Yes, the more I have been reading about math and thinking about how children learn, the more certain I am, the children who appear to do very well in math, are probably the children who have parents that communicate in mathematically helpful way, just as a matter of every day life. I am now totally convinced that parents should not expect public schools to provide their children a good understanding in math. Teachers will teach children to parrot, but few elementary school teachers, have the skill to teach children how to really understanding of math. Unfortunately, few parents can help a child with math, beyond adding and subtracting whole numbers and maybe multiplication. This is so sad. The parents can not help the children, and the public schools are not really doing the job, leaving only a very few students who can successfully go on to higher math skills. The really successful students are going to be the ones who have parents who are accustom to using math concepts daily, and aren't even aware of why math seems to come to them so naturally.

 

There is a very powerful method, but it's not used, and none would agree to ...

 

It's a method where we can make 3-year-old children learn complex mathematics,

 

By using media such as TV channel, and by deploying both Graph theory & Fuzzy Media theory,

 

This method works because of a simple reason, because this method communicate

with the child's brain, not with the child him-self ...

 

and the brain works the same at all times (not talking about understand level), and young

humans have better perceiving of things ...

 

I really want a better explanation of what you have said. If you don't provide a fuller explanation, I will google for information. The math book I am reading now, makes it very clear graphing information is essential to comprehension. Without some kind of visual, children learn to parrot, but are not actually learning the concepts. Please, explain what you mean by Graph theory and Fussy Media theory.

 

- we can't decide that they are incapable of comprehending something we've never tried teaching them.

 

 

Last week I would not have recognized the value in what you said. Thanks to the math book I am reading now, I see great value in what you said. But now, back to preparing a 3 year old to have the better comprehension. A 3 years old is not ready for the popular math games, because they are still having trouble conceptualizing the sequence of numbers, and relating a number to number of objects on a page. The math DVD I got for the 3 year old is no longer my idea of what is helpful. It can teach him to parrot the numbers, but not to understand math.

[khaled]

@The Tree:

@Athena:

 

I started a new thread for that, but it's gonna take a while to follow, it's a long research that might

give you a headache, and you might get lost, because it's all about logic, neural systems, and

fuzzy structures ...

 

http://www.scienceforums.net/topic/54510-fuzzy-neural-structures/

 

The aim is to understand many things including how the brain builds its own language, how

the brain builds its fuzzy definition of things in reality, and the understanding mythology inside

the inner-mind, which will help us to know how to translate any context into that

structure, that will be accepted and integrated the way it should inside the brain of

any human ...

 

best wishes,

Edited February 2, 2011 by khaled

[Athena]

@The Tree:

@Athena:

 

I started a new thread for that, but it's gonna take a while to follow, it's a long research that might

give you a headache, and you might get lost, because it's all about logic, neural systems, and

fuzzy structures ...

 

http://www.sciencefo...ral-structures/

 

The aim is to understand many things including how the brain builds its own language, how

the brain builds its fuzzy definition of things in reality, and the understanding mythology inside

the inner-mind, which will help us to know how to translate any context into that

structure, that will be accepted and integrated the way it should inside the brain of

any human ...

 

best wishes,

 

Yes, that is what I want to know! I need to know both how the brain develops and what to do to help the young in my family comprehend math. By the way, grandparents are important, because their personal agenda of our early years is in the past, and we have the time to learn this stuff that working and over stressed parents do not have. This also is not what getting an elementary teaching degree is about. When my grandmother began teaching, 18 year old's with a little preparation for teaching, began teachers and often taught several grades in one class room. There is no way they could do the teaching that a better informed person, and I don't think the college education for teachers has improved much. They learn what to teach the children, and may be teaching math, although they barely understand algebra, because their knowledge of math is dependent on math and parroting, not a functional understanding of math, so they can not adequately teach the children. Making "the tree's" statement quite profound. How many parents are knowledgeable on how to prepare a child for thinking? At home the child is not prepared to think. The teacher knows too little about how the brain works, what psychological/emotional issues do a child's ability to learn, and how to best prepare the brain for thinking. What is human potential if we have a better understanding of how to prepare a child for thinking?

[lemur]

I've never been too keen on patronising children of any age, for the most part they are far too smart to fall for it and "making it into a game" just gives the impression that they are supposed to enjoy it but not really expected to ("if you eat these sprouts then you'll get your desert" immediately makes the descision for the child that sprouts are disgusting and desert is the best thing ever, so you haven't done them a favour even if it happens to work once or twice).

 

I used to think this way before I had a child. Children develop their own tastes as they get older, even if you feed them everything as a baby. I love sprouts and rarely eat dessert but that doesn't stop my child from rejecting anything because it is green and/or slimy. Also, they are smart, yes, but it's more that they are clever and they use it to avert long-term investment in discipline whose immediate experience isn't pleasant. This is because they are not experienced and thus lack wisdom and foresight. When you try to explain this to them in their intelligence, they cleverly avert the explanation or pretend like they understand to appease you.

 

Regarding math learning, I think the most successful approach is to get them to count change to see if they have enough money for something they want to buy. Another method that seems to inspire interest is to have a glass container filled with something colorful or otherwise visually interesting, like marbles, yoyos, tops, etc. Then talk about how you wonder how many there are in the container and they are also curious enough to make a guess and then count them. As you're counting, you can group the things into multiples. For division, try bargaining with them about how many peas or bites or some other unit they have to eat to be finished. You can make up an estimate of bites left in a plate, e.g. 10 or 8, and then tell them if they eat 1/2 of what's left they're done. Then ask them how many bites would be 1/2 of 8. Then, if you teach them that a third is less that half, they will bargain with you about how little they can eat. Make sure you teach them 2/3 and 3/4, though, or else you will always get bargained down somewhere below half.