# RE: Math

#### Karen

<<There are 42 boys and 24 girls in a chess club. How many percent more

boys than girls are there?>>

Well, 64% of the kids are boys and 36% of them are girls, so there's 28%

more boys.

Wait: If you're comparing the two populations, then there are 75% more boys

than girls.

Of course, you have to agree on the definition of "boy" and "girl" in our

society...

The question was worded badly. Because 75% is such a nice round number, and

because it's a harder concept, and because that's how I see it used in

print, I'm guessing that's the answer they wanted. I.e., if there had been

48 boys, there would have been 100% more boys than girls.

(But wait: there are only 57% as many girls as boys, so maybe the answer is

43% more boys... :-p)

Mattie

There are three types of lies: lies, damn lies, and statistics.

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boys than girls are there?>>

Well, 64% of the kids are boys and 36% of them are girls, so there's 28%

more boys.

Wait: If you're comparing the two populations, then there are 75% more boys

than girls.

Of course, you have to agree on the definition of "boy" and "girl" in our

society...

The question was worded badly. Because 75% is such a nice round number, and

because it's a harder concept, and because that's how I see it used in

print, I'm guessing that's the answer they wanted. I.e., if there had been

48 boys, there would have been 100% more boys than girls.

(But wait: there are only 57% as many girls as boys, so maybe the answer is

43% more boys... :-p)

Mattie

There are three types of lies: lies, damn lies, and statistics.

_________________________________________________________

Do You Yahoo!?

Get your free @... address at http://mail.yahoo.com

#### [email protected]

I'm feeling stuck here and looking for some help...

I should start by saying that I'm one of those people who really loves math. I read Marvin Gardner for fun, my favorite "job" is teaching math prep for the GRE and GMAT, and when I can't sleep at night I often play with numbers in my head. Perhaps this is the problem, really.

When Rain was little, we had great fun with lots of mathy stuff. We played lots of games, and she had a srorng understanding of lots of mathematical concepts because of that. We used to go to the Lawrence Hall of Science and play their math games for hours... Hex, Nym, Ice Cream combos, all that. At 6 or 7 she found the binary number machine and spent 45 minutes working out how to write all sorts of numbers in Base 2.

She didn't do a lot of arithmetic. She did love to add things in her head, and could add fairly big numbers when she was fairly tiny. When she was 7 or 8 she wanted to learn how I added bigger numbers (with regrouping), and after that she spent 6 months doing this anywhere she went, with trillions and billions and so on.

She never went much beyond this, and now she's 12. Which would be fine, really, except that 6 months ago or so she decided that she wanted to get "caught up" and probably take some classes at the community college, and/or go to school. So, we had some Key to math booklets that we bought a year and a half ago, when she was in a show and all the other kids were doing homework, and she wanted some homework too. I've offered to look for other things, or try other ideas, but she says she likes these. She set up a schedule for herself to "do math" (meaning work in the booklets), and asked if I'd be available to help her during these times.

It's been pretty much a disaster, for 3 months or so. The first issue was when I tried to explain what division meant, when she asked. I drew pictures and circled groups, I got her multiplication chart out and tried to explain how the process was reversed in division, I tried to get objects but she very vocally objected. She objects to pretty much any way I try to explain anything, and she really doesn't like it when I draw things out. "Just tell me!" she says, but when I tell her she says she doesn't understand, and when I ask what part she doesn't understand she says, "Everything!" It was like she thought there was some piece I was keeping from her, some important bit of information, and she was so angry about it.

I did talk with another unschooling mom about it all, at the time, and came to the conclusion that maybe the problem was that she was so comfortable with addition, and more comfortable with multiplication and subtraction (although she doesn't have those "facts" memorized, as I think she does with addition), and when she couldn't mentally conceptualize the division problems like she does with the others, she thought there must be something wrong.

I should mention that she figured out on her own how to do multiplication problems with multi-digit numbers, with her chart for reference for the facts. She doesn't use the standard algorithm, but it works fine.

We got past division, somehow, but she's been working her way through Key to Fractions and it's still fairly miserable. She's finding equivalent fractions, and seems to understand it, but when she asked me to check it over she'd made lots of mistakes. I tried to explain what she was doing wrong and she didn't want to hear it again, she was totally focused on what she should do to get the right answer, and angry because she said I'd explained it wrong. I was explaining how the book did, I thought, but who knows. She won't generally let me say as much as I want, or draw diagrams, which is how I feel most comfortable explaining.

So, she says she hates math. I'm frustrated, she's frustrated. She doesn't want to give up on this "catching up" in math idea. She doesn't want to try a different book or method, so she says. She wants me to be a better resource, but I don't know how. She's also going to visit a school tomorrow - a cool private school, but a school - and she says the math teacher there was really nice (we went to open house). Maybe she needs a different person to help her with math? I wish I knew of someone... wish we were still in the Davis-area, I guess.

Any ideas?

dar

I should start by saying that I'm one of those people who really loves math. I read Marvin Gardner for fun, my favorite "job" is teaching math prep for the GRE and GMAT, and when I can't sleep at night I often play with numbers in my head. Perhaps this is the problem, really.

When Rain was little, we had great fun with lots of mathy stuff. We played lots of games, and she had a srorng understanding of lots of mathematical concepts because of that. We used to go to the Lawrence Hall of Science and play their math games for hours... Hex, Nym, Ice Cream combos, all that. At 6 or 7 she found the binary number machine and spent 45 minutes working out how to write all sorts of numbers in Base 2.

She didn't do a lot of arithmetic. She did love to add things in her head, and could add fairly big numbers when she was fairly tiny. When she was 7 or 8 she wanted to learn how I added bigger numbers (with regrouping), and after that she spent 6 months doing this anywhere she went, with trillions and billions and so on.

She never went much beyond this, and now she's 12. Which would be fine, really, except that 6 months ago or so she decided that she wanted to get "caught up" and probably take some classes at the community college, and/or go to school. So, we had some Key to math booklets that we bought a year and a half ago, when she was in a show and all the other kids were doing homework, and she wanted some homework too. I've offered to look for other things, or try other ideas, but she says she likes these. She set up a schedule for herself to "do math" (meaning work in the booklets), and asked if I'd be available to help her during these times.

It's been pretty much a disaster, for 3 months or so. The first issue was when I tried to explain what division meant, when she asked. I drew pictures and circled groups, I got her multiplication chart out and tried to explain how the process was reversed in division, I tried to get objects but she very vocally objected. She objects to pretty much any way I try to explain anything, and she really doesn't like it when I draw things out. "Just tell me!" she says, but when I tell her she says she doesn't understand, and when I ask what part she doesn't understand she says, "Everything!" It was like she thought there was some piece I was keeping from her, some important bit of information, and she was so angry about it.

I did talk with another unschooling mom about it all, at the time, and came to the conclusion that maybe the problem was that she was so comfortable with addition, and more comfortable with multiplication and subtraction (although she doesn't have those "facts" memorized, as I think she does with addition), and when she couldn't mentally conceptualize the division problems like she does with the others, she thought there must be something wrong.

I should mention that she figured out on her own how to do multiplication problems with multi-digit numbers, with her chart for reference for the facts. She doesn't use the standard algorithm, but it works fine.

We got past division, somehow, but she's been working her way through Key to Fractions and it's still fairly miserable. She's finding equivalent fractions, and seems to understand it, but when she asked me to check it over she'd made lots of mistakes. I tried to explain what she was doing wrong and she didn't want to hear it again, she was totally focused on what she should do to get the right answer, and angry because she said I'd explained it wrong. I was explaining how the book did, I thought, but who knows. She won't generally let me say as much as I want, or draw diagrams, which is how I feel most comfortable explaining.

So, she says she hates math. I'm frustrated, she's frustrated. She doesn't want to give up on this "catching up" in math idea. She doesn't want to try a different book or method, so she says. She wants me to be a better resource, but I don't know how. She's also going to visit a school tomorrow - a cool private school, but a school - and she says the math teacher there was really nice (we went to open house). Maybe she needs a different person to help her with math? I wish I knew of someone... wish we were still in the Davis-area, I guess.

Any ideas?

dar

#### [email protected]

In a message dated 5/2/05 9:44:17 PM, freeform@... writes:

<< he objects to pretty much any way I try to explain anything, and she

really doesn't like it when I draw things out. "Just tell me!" she says, but when I

tell her she says she doesn't understand, and when I ask what part she

doesn't understand she says, "Everything!" It was like she thought there was some

piece I was keeping from her, some important bit of information, and she was so

angry about it. >>

The way I understood division as a kid was to think of a quantity of things

or an amount of money divided by a number of people. Twelve things, six kids;

Twelve things, two kids, etc. Thinking in terms of money always helped me.

I would think of 100 as a dollar, and suddenly I could visualize percentages

and also easy combinations by 25 or 10 or 5. It was like a sensible

map/overlay over what seemed to be to be waste-of-time abstractions (math "problems").

<<She wants me to be a better resource, but I don't know how. >>

<<Maybe she needs a different person to help her with math?>>

Maybe so.

Maybe a video (check interlibrary loan?), Standard Deviants or something?

Maybe she needs a different person or a funny book or brainstorming with you

or others, or poking around the internet, or all of the above.

Maybe she's honestly not ready.

Maybe there are other things going on in her body or mind that are creating

the frustration and the emotional swelling is just coming to head in the math

area, but that's not (maybe) really the problem.

Sandra

<< he objects to pretty much any way I try to explain anything, and she

really doesn't like it when I draw things out. "Just tell me!" she says, but when I

tell her she says she doesn't understand, and when I ask what part she

doesn't understand she says, "Everything!" It was like she thought there was some

piece I was keeping from her, some important bit of information, and she was so

angry about it. >>

The way I understood division as a kid was to think of a quantity of things

or an amount of money divided by a number of people. Twelve things, six kids;

Twelve things, two kids, etc. Thinking in terms of money always helped me.

I would think of 100 as a dollar, and suddenly I could visualize percentages

and also easy combinations by 25 or 10 or 5. It was like a sensible

map/overlay over what seemed to be to be waste-of-time abstractions (math "problems").

<<She wants me to be a better resource, but I don't know how. >>

<<Maybe she needs a different person to help her with math?>>

Maybe so.

Maybe a video (check interlibrary loan?), Standard Deviants or something?

Maybe she needs a different person or a funny book or brainstorming with you

or others, or poking around the internet, or all of the above.

Maybe she's honestly not ready.

Maybe there are other things going on in her body or mind that are creating

the frustration and the emotional swelling is just coming to head in the math

area, but that's not (maybe) really the problem.

Sandra

#### Pam Sorooshian

On May 2, 2005, at 9:05 PM, SandraDodd@... wrote:

that she has to make such an effort to learn it? Didn't want to know it

THAT much?

Probably most things she's learned effortlessly, including arithmetic,

up to now?

The Key to series isn't very good at explaining anything - it doesn't

explain why things work, just how to do them. I bet she's a kid who

doesn't feel comfortable just memorizing how to do something, expects

to really understand? I know you said she doesn't want to get a

different book - but that's probably what she's going to need to do.

I'm sure she understands that different resources are good for

different people - and that these are really more like "practice" books

- she could use them to practice with once she already understood.

-pam

> Maybe she's honestly not ready.Maybe she wants to "know" the stuff, but is surprised and frustrated

that she has to make such an effort to learn it? Didn't want to know it

THAT much?

Probably most things she's learned effortlessly, including arithmetic,

up to now?

The Key to series isn't very good at explaining anything - it doesn't

explain why things work, just how to do them. I bet she's a kid who

doesn't feel comfortable just memorizing how to do something, expects

to really understand? I know you said she doesn't want to get a

different book - but that's probably what she's going to need to do.

I'm sure she understands that different resources are good for

different people - and that these are really more like "practice" books

- she could use them to practice with once she already understood.

-pam

#### [email protected]

That sounds right. I really think her whole problem with division was that it wasn't effortless, so therefore she thought she couldn't be understanding how it worked. You're right, she's never really sat down and made this kind of effort before... she waited, and things came easily. I don't know if this stuff will eventually do that or not, but I've suggested waiting and she's not in favor of the idea (and says I'm not being supportive).

Any ideas for resources? I have Harold Jacobs' first book, which I also love, but I'm beginning to think that the things I love may not be the right things. Our only other dabbling in math curricula was Miquon, while I also loved but Rain wasn't into... but perhaps that was a matter of timing. Of course, I sold it all on ebay.

She liked Key to because it was small, unintimidating, and wordy. Words are her friends.

dar

-- Pam Sorooshian <pamsoroosh@...> wrote:

Any ideas for resources? I have Harold Jacobs' first book, which I also love, but I'm beginning to think that the things I love may not be the right things. Our only other dabbling in math curricula was Miquon, while I also loved but Rain wasn't into... but perhaps that was a matter of timing. Of course, I sold it all on ebay.

She liked Key to because it was small, unintimidating, and wordy. Words are her friends.

dar

-- Pam Sorooshian <pamsoroosh@...> wrote:

On May 2, 2005, at 9:05 PM, SandraDodd@... wrote:

> Maybe she's honestly not ready.

Maybe she wants to "know" the stuff, but is surprised and frustrated

that she has to make such an effort to learn it? Didn't want to know it

THAT much?

Probably most things she's learned effortlessly, including arithmetic,

up to now?

The Key to series isn't very good at explaining anything - it doesn't

explain why things work, just how to do them. I bet she's a kid who

doesn't feel comfortable just memorizing how to do something, expects

to really understand? I know you said she doesn't want to get a

different book - but that's probably what she's going to need to do.

I'm sure she understands that different resources are good for

different people - and that these are really more like "practice" books

- she could use them to practice with once she already understood.

-pam

Yahoo! Groups Links

#### Pam Sorooshian

On May 2, 2005, at 10:10 PM, freeform@... wrote:

'wordy' would be: "Where Do I Put the Decimal Point." It isn't aimed at

kids - aimed at adults who need to review/relearn arithmetic that they

don't remember and feel anxious about. I like the way it is written and

you can find a VERY inexpensive copy, used.

But - how about a computer approach?

<http://www.riverdeep.net/products/mighty_math/calculating_crew.jhtml>

and

<http://www.riverdeep.net/products/mighty_math/number_heroes.jhtml>

Calculating Crew and Number Heroes cover whole number multiplication

and division and fractions, decisions, percentages, and some geometry.

My kids have always enjoyed these games. If Rain has the urge to sort

of keep track of her progress, there is a way to do it - some kind of

scale to make sure you cover everything.

There are two more advanced titles in the same "Mighty Math" series --

Cosmic Geometry and Astro Algebra.

-pam

> Any ideas for resources? I have Harold Jacobs' first book, which IYou said she'd rather have words - the best I can think of that's more

> also love, but I'm beginning to think that the things I love may not

> be the right things. Our only other dabbling in math curricula was

> Miquon, while I also loved but Rain wasn't into... but perhaps that

> was a matter of timing. Of course, I sold it all on ebay.

'wordy' would be: "Where Do I Put the Decimal Point." It isn't aimed at

kids - aimed at adults who need to review/relearn arithmetic that they

don't remember and feel anxious about. I like the way it is written and

you can find a VERY inexpensive copy, used.

But - how about a computer approach?

<http://www.riverdeep.net/products/mighty_math/calculating_crew.jhtml>

and

<http://www.riverdeep.net/products/mighty_math/number_heroes.jhtml>

Calculating Crew and Number Heroes cover whole number multiplication

and division and fractions, decisions, percentages, and some geometry.

My kids have always enjoyed these games. If Rain has the urge to sort

of keep track of her progress, there is a way to do it - some kind of

scale to make sure you cover everything.

There are two more advanced titles in the same "Mighty Math" series --

Cosmic Geometry and Astro Algebra.

-pam

#### Nancy Wooton

On May 2, 2005, at 8:39 PM, freeform@... wrote:

Forgetting"? Well, Frank Smith wrote one for math, which I bought

years ago but just read last month. "The Glass Wall: Why Mathematics

Can Seem Difficult." It's all about how we think and how our

connection to the Real World and the language of speech can interfere

when it comes to understanding math.

Pam can tell you, I'm a card-carrying math-phobe, but I read and

enjoyed and UNDERSTOOD this book, with no one holding a gun to my head

:-)

It might help you help your daughter. She might even enjoy reading it

herself.

Nancy, who can relate degrees centigrade to fahrenheit now. AND --

I've been playing around with it in my head, wondering if I can make

the function work to relate fahrenheit to centigrade...

> She objects to pretty much any way I try to explain anything, and sheYou know that book everyone recommends, "The Book of Learning and

> really doesn't like it when I draw things out. "Just tell me!" she

> says, but when I tell her she says she doesn't understand, and when I

> ask what part she doesn't understand she says, "Everything!" It was

> like she thought there was some piece I was keeping from her, some

> important bit of information, and she was so angry about it.

Forgetting"? Well, Frank Smith wrote one for math, which I bought

years ago but just read last month. "The Glass Wall: Why Mathematics

Can Seem Difficult." It's all about how we think and how our

connection to the Real World and the language of speech can interfere

when it comes to understanding math.

Pam can tell you, I'm a card-carrying math-phobe, but I read and

enjoyed and UNDERSTOOD this book, with no one holding a gun to my head

:-)

It might help you help your daughter. She might even enjoy reading it

herself.

Nancy, who can relate degrees centigrade to fahrenheit now. AND --

I've been playing around with it in my head, wondering if I can make

the function work to relate fahrenheit to centigrade...

#### apfel bluete

Hi-

Here below is a review of Frank Smith's book posted to show another point of view.

Math can be upsetting when we just dont get it. However, it is truly a wonderful thing when that light bulb does go off and our child has that "ah ha" I have got it look. Be patient with your children and dont give up on them. Dont give them watered down versions of anything...dive in. Get her hands around some blocks, geo strips, geo boards, graph paper.

New to the idea of unschooling, but not new to being a mom.

Apfel

The MAA Online book review column

---------------------------------

The Glass Wall:

Why Mathematics Can Seem Difficult

by Frank Smith Reviewed by P. N. Ruane

---------------------------------

The declared intention of this book is to offer insights to those who wish to learn mathematics, or to teach it. It is based upon the premise that there exists something referred to as a 'glass wall', which is said to be an ongoing impediment to mathematical understanding.

On reading the book, one soon realises that by the word mathematics the author really means basic arithmetic, although there is some mention of geometrical ideas. This is compatible with his statement in the introduction that the text is intended to include teachers involved with primary education. However, primary mathematics, in many countries, includes many more themes than arithmetic (algebra, probability, shape and space, problem-solving skills etc). Nonetheless, Frank Smith uses his comments about children's difficulties with basic number work to form various generalisations about the learning of mathematics as a whole.

My chief reservations about this book fall into three categories, as follows:

I still don't know what is meant by a 'glass wall', since the concept is never properly defined. Why not use alternative metaphors such as 'brick wall' or 'dense fog'? Glass walls are transparent and one can gain much understanding of the outside world by gazing through the windows of a train or those of one's own home. To my mind, it isn't clear whether the author believes that this entity arises from inappropriate teaching or whether it is due to the inherent nature of mathematics itself. To what degree is it due to both of these factors?

In the teaching of mathematics, it is soon realised that some concepts and skills are very difficult to teach from the point of view of children's understanding. For example, how can one establish pupils' understanding of the traditional algorithm for doing long division? What physical models can possibly show that 1/3 = 0.3333...? Can the multiplication of negative numbers have a place in a child's mathematical conceptual framework? Can it ever made comprehensible?

In other words, mathematics can sometimes seem difficult because much of it is difficult, but this, for many learners, is part of its appeal, which is something not fully explored in the book.

Much progress, in the world of mathematical education, has been made by basing the teaching of it upon practical work with appropriately chosen apparatus. For example, Dienes base 10 material is an excellent medium for developing of understanding of place value. Geostrips are a wonderful teaching aid for the exploration of 2d polygonal figures etc, etc. However, Frank Smith makes many comments of the following sort:

The world of mathematics doesn't arise from the physical world... except to the extent that it has its roots in the human brain, and it can't be made part of the physical world'

If, by this, he means that a concept is not the same thing as an object representing it, I can see some truth in it. Otherwise, it is not the sort of precept upon which to form an approach to the learning of primary mathematics. But then there is the following contradictory statement of page 13:

The structures of mathematics do not need a human brain or a physical world to support them.

Overall, I find that many of the issues about the learning of mathematics are discussed in a way that tends to obfuscation rather than clarity. I offer two more examples by way of illustration.

In the formation of children's concept of cardinal number, there is a range of practical activities that are based upon the Russell definition, which says that 'a natural number is an equivalence class of finite sets under the relation "is in 1-1 correspondence with".' Therefore, to establish the concept of three, teachers will direct children's attention to a wide variety of class representatives, such as a set of three bananas, a set of three blind mice, the three bears, the three wise men etc. Yet what are readers to make of statements like that on page 35, where it is said that:

Numbers don't derive their meaning from anything in the physical world, but from something in our mind...

And, on page 4: But in fact, holding up three objects to illustrate the meaning of the word three explains nothing at all...

Finally, I refer to the discussion of the topic of fractions, discussed in chapter 10, called 'Numbers between Numbers'. What on earth is one to make of the following three statements, all made within a few pages of one another?

... fractions are numbers and can be treated in exactly the same way as whole numbers. (p. 93)

Ratios aren't numbers- they are relationships between two numbers. (p. 96)

To sum up, a fraction is a ratio or proportion of the numerical distance between one number and the next. (p. 96)

Perhaps this is an example of what the author meant when he included, in the title, the clause 'Why mathematics can sometimes seem difficult'!

---------------------------------

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Tired of spam? Yahoo! Mail has the best spam protection around

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[Non-text portions of this message have been removed]

Here below is a review of Frank Smith's book posted to show another point of view.

Math can be upsetting when we just dont get it. However, it is truly a wonderful thing when that light bulb does go off and our child has that "ah ha" I have got it look. Be patient with your children and dont give up on them. Dont give them watered down versions of anything...dive in. Get her hands around some blocks, geo strips, geo boards, graph paper.

New to the idea of unschooling, but not new to being a mom.

Apfel

The MAA Online book review column

---------------------------------

The Glass Wall:

Why Mathematics Can Seem Difficult

by Frank Smith Reviewed by P. N. Ruane

---------------------------------

The declared intention of this book is to offer insights to those who wish to learn mathematics, or to teach it. It is based upon the premise that there exists something referred to as a 'glass wall', which is said to be an ongoing impediment to mathematical understanding.

On reading the book, one soon realises that by the word mathematics the author really means basic arithmetic, although there is some mention of geometrical ideas. This is compatible with his statement in the introduction that the text is intended to include teachers involved with primary education. However, primary mathematics, in many countries, includes many more themes than arithmetic (algebra, probability, shape and space, problem-solving skills etc). Nonetheless, Frank Smith uses his comments about children's difficulties with basic number work to form various generalisations about the learning of mathematics as a whole.

My chief reservations about this book fall into three categories, as follows:

I still don't know what is meant by a 'glass wall', since the concept is never properly defined. Why not use alternative metaphors such as 'brick wall' or 'dense fog'? Glass walls are transparent and one can gain much understanding of the outside world by gazing through the windows of a train or those of one's own home. To my mind, it isn't clear whether the author believes that this entity arises from inappropriate teaching or whether it is due to the inherent nature of mathematics itself. To what degree is it due to both of these factors?

In the teaching of mathematics, it is soon realised that some concepts and skills are very difficult to teach from the point of view of children's understanding. For example, how can one establish pupils' understanding of the traditional algorithm for doing long division? What physical models can possibly show that 1/3 = 0.3333...? Can the multiplication of negative numbers have a place in a child's mathematical conceptual framework? Can it ever made comprehensible?

In other words, mathematics can sometimes seem difficult because much of it is difficult, but this, for many learners, is part of its appeal, which is something not fully explored in the book.

Much progress, in the world of mathematical education, has been made by basing the teaching of it upon practical work with appropriately chosen apparatus. For example, Dienes base 10 material is an excellent medium for developing of understanding of place value. Geostrips are a wonderful teaching aid for the exploration of 2d polygonal figures etc, etc. However, Frank Smith makes many comments of the following sort:

The world of mathematics doesn't arise from the physical world... except to the extent that it has its roots in the human brain, and it can't be made part of the physical world'

If, by this, he means that a concept is not the same thing as an object representing it, I can see some truth in it. Otherwise, it is not the sort of precept upon which to form an approach to the learning of primary mathematics. But then there is the following contradictory statement of page 13:

The structures of mathematics do not need a human brain or a physical world to support them.

Overall, I find that many of the issues about the learning of mathematics are discussed in a way that tends to obfuscation rather than clarity. I offer two more examples by way of illustration.

In the formation of children's concept of cardinal number, there is a range of practical activities that are based upon the Russell definition, which says that 'a natural number is an equivalence class of finite sets under the relation "is in 1-1 correspondence with".' Therefore, to establish the concept of three, teachers will direct children's attention to a wide variety of class representatives, such as a set of three bananas, a set of three blind mice, the three bears, the three wise men etc. Yet what are readers to make of statements like that on page 35, where it is said that:

Numbers don't derive their meaning from anything in the physical world, but from something in our mind...

And, on page 4: But in fact, holding up three objects to illustrate the meaning of the word three explains nothing at all...

Finally, I refer to the discussion of the topic of fractions, discussed in chapter 10, called 'Numbers between Numbers'. What on earth is one to make of the following three statements, all made within a few pages of one another?

... fractions are numbers and can be treated in exactly the same way as whole numbers. (p. 93)

Ratios aren't numbers- they are relationships between two numbers. (p. 96)

To sum up, a fraction is a ratio or proportion of the numerical distance between one number and the next. (p. 96)

Perhaps this is an example of what the author meant when he included, in the title, the clause 'Why mathematics can sometimes seem difficult'!

---------------------------------

__________________________________________________

Do You Yahoo!?

Tired of spam? Yahoo! Mail has the best spam protection around

http://mail.yahoo.com

[Non-text portions of this message have been removed]

#### [email protected]

In a message dated 5/2/2005 10:44:16 PM Central Standard Time,

freeform@... writes:

She objects to pretty much any way I try to explain anything, and she really

doesn't like it when I draw things out. "Just tell me!" she says, but when I

tell her she says she doesn't understand, and when I ask what part she

doesn't understand she says, "Everything!" It was like she thought there was some

piece I was keeping from her, some important bit of information, and she was

so angry about it.

~~~

That's it! That's exactly how I felt, like they were holding back something

from me. I remember being 10, in 5th grade, and I could NOT "get" long

division. I talked in circles with the teacher and I sat at my desk and stared

the problems and my eyes got all watery. I *wanted* to get it. I thought I

understood what they were saying, but it wasn't coming together. Finally,

after what seemed like weeks of sitting down to do long division in class, I

went to Mr. Crowell, and as he explained, I *got* it. I was so

mad/relieved/frustrated that I burst into tears and almost screamed, "Why didn't you just

tell me that in the first place?!"

*Fat Mr. Crowell, always my favorite teacher, was so kind to me when he saw

the tears, but it was too late by then. Long division had created trauma in

my young life. The frustration had robbed the joy of accomplishment.

I dunno, Dar. I might ask her to take a break. When Will wanted to be able

to ride his bike and just couldn't and got so frustrated about it, we'd have

a talk about brain development. If there are no other better ideas, what

else is there except that it will come with time? When I am working on tough

problem (usually life, not math, related), going about my business and parking

the problem on the back burner allows me to think more clearly about the

thing later. Especially if I'm feeling anxious. I call it 'allowing time to

pass'. The old "sleep on it" thing.

Maybe the pressure Rain is putting on herself to "catch up" is blocking her

ability to think clearly? Maybe the math books need to be removed from

between you for a while?

Karen

*Mr. Crowell looked like Humpty-Dumpty...and egg on legs. He had hair

longer than his shoulders and a beard. He always wore dress pants, a short

sleeved dress shirt and a tie, typical teacher-wear for 1971, and he looked a

little greasy, and was always sweating. I was always afraid that he smelled, but

I never smelled him when he was near me. When we sat in our desks and he

walked near, all you could see was the bottom half of him, from his belt down.

That's how round he was. He was the one who was hired to institute the open

classroom experiment in my school, and I LOVED him. He was teacher of the

year in Illinois once and he wrote to me after we moved away. I have tried to

find him online, but I realize now that his weight probably made for a short

life.

www.badchair.net

[Non-text portions of this message have been removed]

freeform@... writes:

She objects to pretty much any way I try to explain anything, and she really

doesn't like it when I draw things out. "Just tell me!" she says, but when I

tell her she says she doesn't understand, and when I ask what part she

doesn't understand she says, "Everything!" It was like she thought there was some

piece I was keeping from her, some important bit of information, and she was

so angry about it.

~~~

That's it! That's exactly how I felt, like they were holding back something

from me. I remember being 10, in 5th grade, and I could NOT "get" long

division. I talked in circles with the teacher and I sat at my desk and stared

the problems and my eyes got all watery. I *wanted* to get it. I thought I

understood what they were saying, but it wasn't coming together. Finally,

after what seemed like weeks of sitting down to do long division in class, I

went to Mr. Crowell, and as he explained, I *got* it. I was so

mad/relieved/frustrated that I burst into tears and almost screamed, "Why didn't you just

tell me that in the first place?!"

*Fat Mr. Crowell, always my favorite teacher, was so kind to me when he saw

the tears, but it was too late by then. Long division had created trauma in

my young life. The frustration had robbed the joy of accomplishment.

I dunno, Dar. I might ask her to take a break. When Will wanted to be able

to ride his bike and just couldn't and got so frustrated about it, we'd have

a talk about brain development. If there are no other better ideas, what

else is there except that it will come with time? When I am working on tough

problem (usually life, not math, related), going about my business and parking

the problem on the back burner allows me to think more clearly about the

thing later. Especially if I'm feeling anxious. I call it 'allowing time to

pass'. The old "sleep on it" thing.

Maybe the pressure Rain is putting on herself to "catch up" is blocking her

ability to think clearly? Maybe the math books need to be removed from

between you for a while?

Karen

*Mr. Crowell looked like Humpty-Dumpty...and egg on legs. He had hair

longer than his shoulders and a beard. He always wore dress pants, a short

sleeved dress shirt and a tie, typical teacher-wear for 1971, and he looked a

little greasy, and was always sweating. I was always afraid that he smelled, but

I never smelled him when he was near me. When we sat in our desks and he

walked near, all you could see was the bottom half of him, from his belt down.

That's how round he was. He was the one who was hired to institute the open

classroom experiment in my school, and I LOVED him. He was teacher of the

year in Illinois once and he wrote to me after we moved away. I have tried to

find him online, but I realize now that his weight probably made for a short

life.

www.badchair.net

[Non-text portions of this message have been removed]

#### [email protected]

In a message dated 5/2/2005 11:38:10 PM Central Standard Time,

pamsoroosh@... writes:

I know you said she doesn't want to get a

different book - but that's probably what she's going to need to do.

I'm sure she understands that different resources are good for

different people - and that these are really more like "practice" books

- she could use them to practice with once she already understood.

~~~

Here's another example along that line. I've been trying to be healthier

and smaller, and I've lost 13 pounds so far. I've decided I'm going to learn

to be healthier and smaller the same way I learned to play the ukulele. I'm

going to read a lot of books about being healthy (playing ukulele), stay away

from junk science (cheap ukuleles), and use the internet to track my diet and

find recipes (tabs for ukulele). I'm also going to find other people who

are trying to be healthier and smaller (playing ukulele) and learn stuff from

them and play (exercise) with them, and trade recipes (music) and ideas (strum

patterns) with them.

I realized that I'd been going about the dieting/health thing all wrong.

It's not just *one* piece of information I need, it's LOTS of information, from

different sources. Can't know it all, but what I do know I can tailor to my

own needs and lifestyle and way of doing things.

I have 10 giant trees in my yard. No one way of dealing with the limbs and

leaves that fall is going to cut it. So we compost some, bag some, mulch

some with the lawnmower, chip some limbs for mulch, etc.

Same with "catching up" to go to school. One method or technique is not

going to cut it.

Karen

www.badchair.net

[Non-text portions of this message have been removed]

pamsoroosh@... writes:

I know you said she doesn't want to get a

different book - but that's probably what she's going to need to do.

I'm sure she understands that different resources are good for

different people - and that these are really more like "practice" books

- she could use them to practice with once she already understood.

~~~

Here's another example along that line. I've been trying to be healthier

and smaller, and I've lost 13 pounds so far. I've decided I'm going to learn

to be healthier and smaller the same way I learned to play the ukulele. I'm

going to read a lot of books about being healthy (playing ukulele), stay away

from junk science (cheap ukuleles), and use the internet to track my diet and

find recipes (tabs for ukulele). I'm also going to find other people who

are trying to be healthier and smaller (playing ukulele) and learn stuff from

them and play (exercise) with them, and trade recipes (music) and ideas (strum

patterns) with them.

I realized that I'd been going about the dieting/health thing all wrong.

It's not just *one* piece of information I need, it's LOTS of information, from

different sources. Can't know it all, but what I do know I can tailor to my

own needs and lifestyle and way of doing things.

I have 10 giant trees in my yard. No one way of dealing with the limbs and

leaves that fall is going to cut it. So we compost some, bag some, mulch

some with the lawnmower, chip some limbs for mulch, etc.

Same with "catching up" to go to school. One method or technique is not

going to cut it.

Karen

www.badchair.net

[Non-text portions of this message have been removed]

#### [email protected]

In a message dated 5/3/2005 12:12:48 AM Central Standard Time,

freeform@... writes:

while I also loved but Rain wasn't into... but perhaps that was a matter of

timing. Of course, I sold it all on ebay.

~~~

I have all the Miquon books. Would you like me to send you the one you need?

Karen

www.badchair.net

[Non-text portions of this message have been removed]

freeform@... writes:

while I also loved but Rain wasn't into... but perhaps that was a matter of

timing. Of course, I sold it all on ebay.

~~~

I have all the Miquon books. Would you like me to send you the one you need?

Karen

www.badchair.net

[Non-text portions of this message have been removed]

#### Cindy Fox

Funny. My 5 year old is Mr. Math and gets concepts and retains them, but

words are like foreign beings to him.... He just looks at them and makes no

guess, wild guess or repeats memorization, but doesn't even link up word

bunches to the words he is saying...

I'm reading chapter books to him upon his request - we just finished My Side

of the Mountain and he loves me to tell intricate stories that he can follow

and correct if I forget something! :) But the act of reading just is not

there yet. Well, one day I trust it will be.

We are all so different. :)

Cindy Fox

Author of QuickBooks QuickSteps

www.cindyfox.com

Butterfly Consulting LLC

602-692-8923

-----Original Message-----

From: [email protected] [mailto:[email protected]]

On Behalf Of Nancy Wooton

Sent: Monday, May 02, 2005 11:35 PM

To: [email protected]

Subject: Re: [AlwaysLearning] Math

words are like foreign beings to him.... He just looks at them and makes no

guess, wild guess or repeats memorization, but doesn't even link up word

bunches to the words he is saying...

I'm reading chapter books to him upon his request - we just finished My Side

of the Mountain and he loves me to tell intricate stories that he can follow

and correct if I forget something! :) But the act of reading just is not

there yet. Well, one day I trust it will be.

We are all so different. :)

Cindy Fox

Author of QuickBooks QuickSteps

www.cindyfox.com

Butterfly Consulting LLC

602-692-8923

-----Original Message-----

From: [email protected] [mailto:[email protected]]

On Behalf Of Nancy Wooton

Sent: Monday, May 02, 2005 11:35 PM

To: [email protected]

Subject: Re: [AlwaysLearning] Math

On May 2, 2005, at 8:39 PM, freeform@... wrote:

> She objects to pretty much any way I try to explain anything, and she

> really doesn't like it when I draw things out. "Just tell me!" she

> says, but when I tell her she says she doesn't understand, and when I

> ask what part she doesn't understand she says, "Everything!" It was

> like she thought there was some piece I was keeping from her, some

> important bit of information, and she was so angry about it.

You know that book everyone recommends, "The Book of Learning and

Forgetting"? Well, Frank Smith wrote one for math, which I bought years ago

but just read last month. "The Glass Wall: Why Mathematics Can Seem

Difficult." It's all about how we think and how our connection to the Real

World and the language of speech can interfere when it comes to

understanding math.

Pam can tell you, I'm a card-carrying math-phobe, but I read and enjoyed and

UNDERSTOOD this book, with no one holding a gun to my head

:-)

It might help you help your daughter. She might even enjoy reading it

herself.

Nancy, who can relate degrees centigrade to fahrenheit now. AND -- I've

been playing around with it in my head, wondering if I can make the function

work to relate fahrenheit to centigrade...

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#### Nancy Wooton

On May 3, 2005, at 6:03 AM, tuckervill2@... wrote:

mental block, or to choosing between initial ideas for a project, was

to do some distracting activity that required total concentration. He

juggled. Dr. House plays GameBoy <g>

Nancy

> When I am working on toughOne of my art professors taught us that the key to breaking a creative

> problem (usually life, not math, related), going about my business

> and parking

> the problem on the back burner allows me to think more clearly about

> the

> thing later.

mental block, or to choosing between initial ideas for a project, was

to do some distracting activity that required total concentration. He

juggled. Dr. House plays GameBoy <g>

Nancy

#### [email protected]

-=- Dont give them watered down versions of anything...dive in. Get her

hands around some blocks, geo strips, geo boards, graph paper. -=-

-----------------------------------------------

I agree about giving them real things to mess around with.

And I agree that "watered down" (if watered down means schoolish

explanations) is bad.

But "diving in" (depending what is meant <g>) is unnecessary and can be

harmful (if diving means heading straight for math and making sure you get there).

There's a big benefit to parent and child if the word "math" (or any form

thereof) is just not used unless absolutely necessary (like an 18 year old

taking a math class and answering the question, "Where are you going?").

Sandra

[Non-text portions of this message have been removed]

hands around some blocks, geo strips, geo boards, graph paper. -=-

-----------------------------------------------

I agree about giving them real things to mess around with.

And I agree that "watered down" (if watered down means schoolish

explanations) is bad.

But "diving in" (depending what is meant <g>) is unnecessary and can be

harmful (if diving means heading straight for math and making sure you get there).

There's a big benefit to parent and child if the word "math" (or any form

thereof) is just not used unless absolutely necessary (like an 18 year old

taking a math class and answering the question, "Where are you going?").

Sandra

[Non-text portions of this message have been removed]

#### Nancy Wooton

On May 3, 2005, at 3:58 AM, apfel bluete wrote:

discussion of it?

Nancy

> Here below is a review of Frank Smith's book posted to show anotherWhy did you post that review? Would you like a point-by-point

> point of view.

>

> Math can be upsetting when we just dont get it. However, it is truly

> a wonderful thing when that light bulb does go off and our child has

> that "ah ha" I have got it look. Be patient with your children and

> dont give up on them. Dont give them watered down versions of

> anything...dive in. Get her hands around some blocks, geo strips, geo

> boards, graph paper.

>

> New to the idea of unschooling, but not new to being a mom.

>

discussion of it?

Nancy

#### apfel bluete

No. I am just very interested in Math and why so many people fear it. We have tried to raise our daughter to not fear it. I was interested in that book and I thought I would share the review. Is it a popular book? I have not read it so I cant really say much about it. My library does not have it.

Apfel

Nancy Wooton <ikonstitcher@...> wrote:

Apfel

Nancy Wooton <ikonstitcher@...> wrote:

On May 3, 2005, at 3:58 AM, apfel bluete wrote:

> Here below is a review of Frank Smith's book posted to show another

> point of view.

>

> Math can be upsetting when we just dont get it. However, it is truly

> a wonderful thing when that light bulb does go off and our child has

> that "ah ha" I have got it look. Be patient with your children and

> dont give up on them. Dont give them watered down versions of

> anything...dive in. Get her hands around some blocks, geo strips, geo

> boards, graph paper.

>

> New to the idea of unschooling, but not new to being a mom.

>

Why did you post that review? Would you like a point-by-point

discussion of it?

Nancy

---------------------------------

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[Non-text portions of this message have been removed]

#### [email protected]

In a message dated 5/3/2005 12:48:53 PM Mountain Daylight Time,

apfelbluete_0@... writes:

-=-No. I am just very interested in Math and why so many people fear it.

We have tried to raise our daughter to not fear it. I was interested in that

book and I thought I would share the review. -=-

The review was just very VERY school-oriented.

I tried to raise my kids not to know what math was (and it's pretty

impossible to fear something you never heard of). Yet they froclicked in patterns

and numbers, thinking it was just as fun as singing Animaniacs songs or playing

in the mud. It helped everything in all our lives.

Sandra

[Non-text portions of this message have been removed]

apfelbluete_0@... writes:

-=-No. I am just very interested in Math and why so many people fear it.

We have tried to raise our daughter to not fear it. I was interested in that

book and I thought I would share the review. -=-

The review was just very VERY school-oriented.

I tried to raise my kids not to know what math was (and it's pretty

impossible to fear something you never heard of). Yet they froclicked in patterns

and numbers, thinking it was just as fun as singing Animaniacs songs or playing

in the mud. It helped everything in all our lives.

Sandra

[Non-text portions of this message have been removed]

#### apfel bluete

Math is everywhere in art, in nature...it should not be feared. To fear math, is to fear life itself. I think the fear is not so much the fear of math, but the fear of failure. Math is the language that holds the universe together, it is unity.

Apfel

SandraDodd@... wrote:

In a message dated 5/3/2005 12:48:53 PM Mountain Daylight Time,

apfelbluete_0@... writes:

-=-No. I am just very interested in Math and why so many people fear it.

We have tried to raise our daughter to not fear it. I was interested in that

book and I thought I would share the review. -=-

The review was just very VERY school-oriented.

I tried to raise my kids not to know what math was (and it's pretty

impossible to fear something you never heard of). Yet they froclicked in patterns

and numbers, thinking it was just as fun as singing Animaniacs songs or playing

in the mud. It helped everything in all our lives.

Sandra

[Non-text portions of this message have been removed]

---------------------------------

Yahoo! Groups Links

To visit your group on the web, go to:

http://groups.yahoo.com/group/AlwaysLearning/

To unsubscribe from this group, send an email to:

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Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.

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Tired of spam? Yahoo! Mail has the best spam protection around

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[Non-text portions of this message have been removed]

Apfel

SandraDodd@... wrote:

In a message dated 5/3/2005 12:48:53 PM Mountain Daylight Time,

apfelbluete_0@... writes:

-=-No. I am just very interested in Math and why so many people fear it.

We have tried to raise our daughter to not fear it. I was interested in that

book and I thought I would share the review. -=-

The review was just very VERY school-oriented.

I tried to raise my kids not to know what math was (and it's pretty

impossible to fear something you never heard of). Yet they froclicked in patterns

and numbers, thinking it was just as fun as singing Animaniacs songs or playing

in the mud. It helped everything in all our lives.

Sandra

[Non-text portions of this message have been removed]

---------------------------------

Yahoo! Groups Links

To visit your group on the web, go to:

http://groups.yahoo.com/group/AlwaysLearning/

To unsubscribe from this group, send an email to:

[email protected]

Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.

__________________________________________________

Do You Yahoo!?

Tired of spam? Yahoo! Mail has the best spam protection around

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[Non-text portions of this message have been removed]

#### [email protected]

In a message dated 5/3/2005 6:52:04 PM Mountain Daylight Time,

apfelbluete_0@... writes:

Math is everywhere in art, in nature...it should not be feared. To fear

math, is to fear life itself. I think the fear is not so much the fear of math,

but the fear of failure. Math is the language that holds the universe

together, it is unity.

Right.

But you missed my point.

And you're somewhat overstating yours, I think.

Sandra

[Non-text portions of this message have been removed]

apfelbluete_0@... writes:

Math is everywhere in art, in nature...it should not be feared. To fear

math, is to fear life itself. I think the fear is not so much the fear of math,

but the fear of failure. Math is the language that holds the universe

together, it is unity.

Right.

But you missed my point.

And you're somewhat overstating yours, I think.

Sandra

[Non-text portions of this message have been removed]

#### Nancy Wooton

On May 3, 2005, at 5:09 PM, apfel bluete wrote:

Math in California in 1966 was THE subject, the way reading is now.

The commies had beaten us to space and America had to catch up. Math

was not beautiful, or poetic -- it was science, and the future, and the

atomic bomb. Math and fear were taught together.

I grew up in Orange County, in an area where the dads worked in

aerospace; nearly everyone I knew was an engineer or the child of one.

My dad worked on the Minuteman Missile, and I learned geography from

studying the polar routes the bombs would take. Science, engineering,

The Space Race was what mattered. Failure at math was failure at the

future. The math geniuses were the golden children; art, music,

literature? a waste of time, although music was supposed to make you

better at math. (It didn't work for me. I failed at piano from the

second lesson, when my teacher wrote the word COUNT! across my

notebook; the association of math with music ruined it.)

I'm healing, though. I had to decide to do that for myself. To be

told math is life, it's beautiful, etc., is nonsense to someone who was

abused by its instruction. What I have to do is enjoy the mathy stuff,

like pattern blocks and Set, without thinking about it as math. To me,

Math exists within the covers of public school textbooks, not out here

where I live. I can keep safe from it if I never open the books.

Nancy

> Math is everywhere in art, in nature...it should not be feared. ToYou didn't have Mrs. Gaunt for third grade, then.

> fear math, is to fear life itself. I think the fear is not so much

> the fear of math, but the fear of failure. Math is the language that

> holds the universe together, it is unity.

> Apfel

>

Math in California in 1966 was THE subject, the way reading is now.

The commies had beaten us to space and America had to catch up. Math

was not beautiful, or poetic -- it was science, and the future, and the

atomic bomb. Math and fear were taught together.

I grew up in Orange County, in an area where the dads worked in

aerospace; nearly everyone I knew was an engineer or the child of one.

My dad worked on the Minuteman Missile, and I learned geography from

studying the polar routes the bombs would take. Science, engineering,

The Space Race was what mattered. Failure at math was failure at the

future. The math geniuses were the golden children; art, music,

literature? a waste of time, although music was supposed to make you

better at math. (It didn't work for me. I failed at piano from the

second lesson, when my teacher wrote the word COUNT! across my

notebook; the association of math with music ruined it.)

I'm healing, though. I had to decide to do that for myself. To be

told math is life, it's beautiful, etc., is nonsense to someone who was

abused by its instruction. What I have to do is enjoy the mathy stuff,

like pattern blocks and Set, without thinking about it as math. To me,

Math exists within the covers of public school textbooks, not out here

where I live. I can keep safe from it if I never open the books.

Nancy

#### ecsamhill

**It's been pretty much a disaster, for 3 months or so. The first

issue was when I

tried to explain what division meant, when she asked. I drew pictures and

circled groups, I got her multiplication chart out and tried to

explain how the

process was reversed in division, I tried to get objects but she very

vocally

objected. She objects to pretty much any way I try to explain

anything, and she

really doesn't like it when I draw things out. "Just tell me!" she

says, but

when I tell her she says she doesn't understand, and when I ask what

part she

doesn't understand she says, "Everything!" It was like she thought

there was

some piece I was keeping from her, some important bit of information,

and she

was so angry about it.**

My theory is that we all vary wildly in how we represent math ideas

inside our brain, so that there is variation in how we picture it or

what words we use to describe it. This means one person's sense is

another person's nonsense. This can be frustrating. (But if you've

had lots of success in tutoring other kids in math, it must feel

strange to you.)

I don't see how you can make your style much different. I understand

the urge sometimes to fling a book across the room, but I don't like

seeing that urge applied to human beings.

Giving her time to calm down between attempts is all that I can think

of. (That and resource suggestions, if she becomes willing to try new

ones.)

Betsy

PS Sometimes, when clarifying, we reset ourselves back to the

beginning and repeat the basic principals, looking for the point where

confusion sets in. Maybe this repetition of simple facts is a

flashpoint of exasperation for a preteen who is being driven by the

urge to grow up *now*?

PPS How can she engage physically in what she is doing? Would

walking while talking about math help any? It would leave the

chalkboard behind!

issue was when I

tried to explain what division meant, when she asked. I drew pictures and

circled groups, I got her multiplication chart out and tried to

explain how the

process was reversed in division, I tried to get objects but she very

vocally

objected. She objects to pretty much any way I try to explain

anything, and she

really doesn't like it when I draw things out. "Just tell me!" she

says, but

when I tell her she says she doesn't understand, and when I ask what

part she

doesn't understand she says, "Everything!" It was like she thought

there was

some piece I was keeping from her, some important bit of information,

and she

was so angry about it.**

My theory is that we all vary wildly in how we represent math ideas

inside our brain, so that there is variation in how we picture it or

what words we use to describe it. This means one person's sense is

another person's nonsense. This can be frustrating. (But if you've

had lots of success in tutoring other kids in math, it must feel

strange to you.)

I don't see how you can make your style much different. I understand

the urge sometimes to fling a book across the room, but I don't like

seeing that urge applied to human beings.

Giving her time to calm down between attempts is all that I can think

of. (That and resource suggestions, if she becomes willing to try new

ones.)

Betsy

PS Sometimes, when clarifying, we reset ourselves back to the

beginning and repeat the basic principals, looking for the point where

confusion sets in. Maybe this repetition of simple facts is a

flashpoint of exasperation for a preteen who is being driven by the

urge to grow up *now*?

PPS How can she engage physically in what she is doing? Would

walking while talking about math help any? It would leave the

chalkboard behind!

#### mwinders

> Any ideas?I have lots...

>

> dar

I'm new to the list, a math lover as well. I don't have any children

as old as your daughter, so I hope that my suggestions are appropriate

for her.

Do you know why she likes the "key to" workbooks? Why did she choose

those over anything else?

There are a number of story-books that are math oriented that she may

enjoy reading outside of her involvement with the key to workbooks.

The Number Devil

The Murderous Maths books

The Man Who Counted

MathSmart Jr.

There is also a series called "Hello Math Reader" which will most

likely be way below your dd's reading abilities....HOWEVER, the level

four books would have some interesting math for her to read.

I would also suggest that reading some history of math could help. It

could help put things into perspective for her without focusing on

problem solving abilities. It's been great for us to talk about how

mathematical concepts came about.

Mathematicians are People Too has a number of short biographies

String, Straightedge and Shadow

Archimedes and the Door of Science

Along Came Galileo

There is also a cool math show on pbs that my kids like called

Cyberchase - they do a great job of explaining concepts like

fractions, decimals, percents, as well as some simpler concepts, but

it is always fun. Cyberchase also has ventured into novels....

Maybe it would help for her to go to a website for a topic with which

she is having trouble? Pick a topic of interest and step through the

explanation? It would take the burden of explanation off of you at

the least.

http://www.free-ed.net/free-ed/Math/PreAlg01/default.asp

(there are others if this one doesn't suit you)

I have never found a math syllabus that I thought was worth anything

until recently....

http://ceure.buffalostate.edu/~csmp/

It takes a bunch of downloading and sorting, but this is a free

program, it's innovative, and my children have deemed it FUN. It's

for K-6, but I think it would be enjoyable to an older child (if you

can convince her out of those boring key to workbooks). The follow up

program for older children isn't free, but it's available at

http://imacs.org/imacsweb/default.aspx

Do you have any younger children? If so, you could read some basic

picture books that cover math concepts...I could give you some ideas

for those if you like.

Mara (a mathaholic)

#### Dawn Falbe

Haven't posted for a while, but continue to read as much of what is written.

Zak was doing Calculus (SP?) at 7... We decided to put him in school (long story) and he went back to 4th Grade Math. Reason? He told me "I'm in 4th Grade so I only have to do up to 4th Grade math and they are trying to get me to do Math their way, rather than the way I know how to do it".... What a disaster.

Namaste

Dawn

____________________________________________________________________________________

Looking for earth-friendly autos?

Browse Top Cars by "Green Rating" at Yahoo! Autos' Green Center.

http://autos.yahoo.com/green_center/

[Non-text portions of this message have been removed]

Zak was doing Calculus (SP?) at 7... We decided to put him in school (long story) and he went back to 4th Grade Math. Reason? He told me "I'm in 4th Grade so I only have to do up to 4th Grade math and they are trying to get me to do Math their way, rather than the way I know how to do it".... What a disaster.

Namaste

Dawn

____________________________________________________________________________________

Looking for earth-friendly autos?

Browse Top Cars by "Green Rating" at Yahoo! Autos' Green Center.

http://autos.yahoo.com/green_center/

[Non-text portions of this message have been removed]

#### in4mkaren

This is just something I'm excited to share. In my experience with the unschoolers in my city, many of them unschool everything but math.

In the 1930's L. P. Benezet, a Superintendent in Massachussets, experimented with dropping math from the curriculum of his public schools until 6th grade. His results might be encouraging for anyone who is struggling with what to do about math with their unschool kids. (I was trained as a teacher and love academic educational philosophy type stuff, even though and in some ways even more now that I unschool my children.)

Here's a tidbit: "In other words these [6th graders], by avoiding the early drill on combinations, tables, and that sort of thing, had been able, in one year, to attain the level of accomplishment which the traditionally taught children had reached after three and one-half years of arithmetical drill."

Here is the link to describe how he got started in his experiment: http://www.inference.phy.cam.ac.uk/sanjoy/benezet/1.html

When he expanded the dropping of math from the curriculum to other classrooms, here is the compromise he worked up with the hesitant principals. Essentially it's a starter list for teaching math "incidentally" without formal instruction! http://www.inference.phy.cam.ac.uk/sanjoy/benezet/2.html

Peter Gray also wrote about this experiment if you want a less academic summary: http://www.psychologytoday.com/blog/freedom-learn/201003/when-less-is-more-the-case-teaching-less-math-in-schools

I greatly appreciate reassurances to relax and the personal testimonies of unschoolers who have gone before, but I also like it when a good study backs it up!

Karen W.

In the 1930's L. P. Benezet, a Superintendent in Massachussets, experimented with dropping math from the curriculum of his public schools until 6th grade. His results might be encouraging for anyone who is struggling with what to do about math with their unschool kids. (I was trained as a teacher and love academic educational philosophy type stuff, even though and in some ways even more now that I unschool my children.)

Here's a tidbit: "In other words these [6th graders], by avoiding the early drill on combinations, tables, and that sort of thing, had been able, in one year, to attain the level of accomplishment which the traditionally taught children had reached after three and one-half years of arithmetical drill."

Here is the link to describe how he got started in his experiment: http://www.inference.phy.cam.ac.uk/sanjoy/benezet/1.html

When he expanded the dropping of math from the curriculum to other classrooms, here is the compromise he worked up with the hesitant principals. Essentially it's a starter list for teaching math "incidentally" without formal instruction! http://www.inference.phy.cam.ac.uk/sanjoy/benezet/2.html

Peter Gray also wrote about this experiment if you want a less academic summary: http://www.psychologytoday.com/blog/freedom-learn/201003/when-less-is-more-the-case-teaching-less-math-in-schools

I greatly appreciate reassurances to relax and the personal testimonies of unschoolers who have gone before, but I also like it when a good study backs it up!

Karen W.