Testing Racket Has Ruined High School

"Banty" <Banty_member.TakeThisOut@newsguy.com> wrote in message
news:g26aaf02d35@drn.newsguy.com...
> In article <rKudnS8r8Kq9N9vVnZ2dnUVZ_hGdnZ2d.TakeThisOut@comcast.com>, Donna Metler
> says...
>>
>>
>>
>>
>>"Banty" <Banty_member.TakeThisOut@newsguy.com> wrote in message
>>news:g25vjr01mv8@drn.newsguy.com...
>>> In article <ov4c44la24k5fur67tm5bkvbo0fdh8h68s.TakeThisOut@4ax.com>, toto says...
>>>>
>>>>On 3 Jun 2008 11:14:09 -0700, Banty <Banty_member.TakeThisOut@newsguy.com> wrote:
>>>>
>>>>>Back to your question - -
>>>>>
>>>>>What are you trying to find out?
>>>>> Make that "x".
>>>>
>>>>As Herman would say, using a single variable often makes things more
>>>>difficult. When you want to teach formulating problems, you can't do
>>>>this by giving specific formulas.
>>>
>>> That is not giving a specific formula! That is teaching using a
>>> variable
>>> as a
>>> part of language - exactly what Herman is talking about. It's saying to
>>> the
>>> student to denote as "x" the concept he is trying to find out. That is
>>> exactly
>>> what a variable is!
>>>
>>>>
>>>>Also, Herman believes that this should be taught to 5 year olds. I
>>>>want *him* to tell me how to do this.
>>>
>>> All he's saying is to introduce concepts of variables to five year olds.
>>> Tell
>>> you what - if the idea of the usual mathematical notation scares you,
>>> how
>>> about
>>> introducing to five year olds that they can call something they like
>>> "oogabooga", and something they don't like "eeekee-ookee". And have
>>> different
>>> oogabooga's and eeekee-ookee's for different situations. Then the next
>>> day
>>> introduce that oogabooga can be "q", and eeekee-ookee can be "r". But
>>> honestly,
>>> I think kindergarteners would have no problem going straight to "q" and
>>> "r",
>>> because they're not all pre-intimidated by mathematical notation. I
>>> think
>>> Herman is right in this regard.
>>
>>Maybe kindergarteners are, but I know my 3 1/2 yr old, while she enjoys
>>playing with mathematical notation and language, and has a good handle on
>>addition and subtraction, both conceptually and numerically (V + U =W,
>>mommy! T + F= E! Dimetrodon + Allosaurus =Spinosaurus!-this is a kid who
>>buys workbooks at the dollar store when she has money to spend, and does
>>them for fun, and who absolutely LOVES symbols, so will ask what they
>>mean)
>>would be very upset at the concept of a variable, because she's so set on
>>things having specific names. If a character in a book doesn't have a
>>name,
>>and she decides today that his name is Pete, I can't call him Paul
>>tomorrow
>>without upsetting her, because names, to her, are inviolate. I don't think
>>she'd accept calling an unknown q, because q has a specific identity-it's
>>a
>>letter of the alphabet. Yet, she's capable of figuring out that if she
>>has
>>three chicken pieces on her plate, and she wants 5, she needs 2 more-which
>>is the same as 3+x=5, solve for X. And, I have to say that my 5 yr old
>>students who will be going into K in the fall generally behave similarly
>>with regard to names-but have less understanding of the concepts of
>>addition
>>and subtraction.
>
> I'm not so sure about variables. What you described in your 3 1/2 year
> old
> sounds very much like the inflexibility that that age has. I think that's
> a bad
> example.
>
> And I also think it has to do with how it's introduced. The oogabooga
> eekee-ookee thing would work I think.
>
> But you know what, I dont want to argue that it has to be specifically
> kindergarteners that are first introduced to it. K used to be (back in
> the bad
> old days) for socialization and some basics in prep for school. Do it
> for 6
> and 7 year olds, or not. But do you know of any studies on this? Id be
> skeptical that this really has been looked at. I agree with Herman that
> these
> are essentially linguistic concepts and I'm skeptical that they can't be
> introduced very early.
>
> Think pronouns. Even a toddler isn't thrown for a loop long that "he"
> could be
> Daddy, or big brother, or puppy.
>
But a pronoun is always a variable. A, though, is A, and young kids who are
just learning to read are learning letters as an absolute with specific
rules that usually work the same way. In many ways, what throws children for
a loop is the variability of letters, which is why vowels are so much harder
for young readers than consonants.

If you always called a variable number an oogabooga, that would probably
work-but if that's your goal, the blank space notation used in most primary
grade math texts will serve equally well until the children get old enough
to grasp the concept that a letter can be more than just a sound in a word.

I've introduced algebraic notation for variables with 3rd graders before,
without problems, so I do believe it can be introduced earlier than most
programs do. But just because it works with 8 yr olds doesn't mean it will
work with 5 yr olds. One of the biggest issues facing early childhood
education is exactly this idea-that if 6 yr olds can learn to read, than 5
yr olds can learn to read, and if 5 year olds can learn to read, then SURELY
all 4 yr olds can learn their alphabet and phonetic sounds, some sight
words, and so on. We're now to the point that many schools expect children
to come into K with skills in reading and math that in the past were taught
in K-and the result is a child who is perfectly normal in development comes
into K already behind.

If a child is still very concrete, they're not ready for the concept of a
variable. And yes, that means most children are ready for the concepts of
putting together items in a set to make a bigger set and removing items from
a set to make a smaller set before they're ready for the concept of a
variable. Because adding and subtracting ARE concrete. Move the unknown,
introduce the idea of incomplete information that's not on the right side of
the equals sign, give an unknown a name like Bletz or Spurg, but I think
that introducing the idea of X and Y to children who are still learning X
and Y as letters of the alphabet is likely to be quite confusing and
unlikely to get the response you want.
 >> Stay informed about: Testing Racket Has Ruined High School 

In article <HoCdnQXX1baPTNvVnZ2dnUVZ_v_inZ2d RemoveThis @comcast.com>, Donna Metler says...
>
>
>"Banty" <Banty_member RemoveThis @newsguy.com> wrote in message
>news:g26aaf02d35@drn.newsguy.com...
>> In article <rKudnS8r8Kq9N9vVnZ2dnUVZ_hGdnZ2d RemoveThis @comcast.com>, Donna Metler
>> says...
>>>
>>>
>>>
>>>
>>>"Banty" <Banty_member RemoveThis @newsguy.com> wrote in message
>>>news:g25vjr01mv8@drn.newsguy.com...
>>>> In article <ov4c44la24k5fur67tm5bkvbo0fdh8h68s RemoveThis @4ax.com>, toto says...
>>>>>
>>>>>On 3 Jun 2008 11:14:09 -0700, Banty <Banty_member RemoveThis @newsguy.com> wrote:
>>>>>
>>>>>>Back to your question - -
>>>>>>
>>>>>>What are you trying to find out?
>>>>>> Make that "x".
>>>>>
>>>>>As Herman would say, using a single variable often makes things more
>>>>>difficult. When you want to teach formulating problems, you can't do
>>>>>this by giving specific formulas.
>>>>
>>>> That is not giving a specific formula! That is teaching using a
>>>> variable
>>>> as a
>>>> part of language - exactly what Herman is talking about. It's saying to
>>>> the
>>>> student to denote as "x" the concept he is trying to find out. That is
>>>> exactly
>>>> what a variable is!
>>>>
>>>>>
>>>>>Also, Herman believes that this should be taught to 5 year olds. I
>>>>>want *him* to tell me how to do this.
>>>>
>>>> All he's saying is to introduce concepts of variables to five year olds.
>>>> Tell
>>>> you what - if the idea of the usual mathematical notation scares you,
>>>> how
>>>> about
>>>> introducing to five year olds that they can call something they like
>>>> "oogabooga", and something they don't like "eeekee-ookee". And have
>>>> different
>>>> oogabooga's and eeekee-ookee's for different situations. Then the next
>>>> day
>>>> introduce that oogabooga can be "q", and eeekee-ookee can be "r". But
>>>> honestly,
>>>> I think kindergarteners would have no problem going straight to "q" and
>>>> "r",
>>>> because they're not all pre-intimidated by mathematical notation. I
>>>> think
>>>> Herman is right in this regard.
>>>
>>>Maybe kindergarteners are, but I know my 3 1/2 yr old, while she enjoys
>>>playing with mathematical notation and language, and has a good handle on
>>>addition and subtraction, both conceptually and numerically (V + U =W,
>>>mommy! T + F= E! Dimetrodon + Allosaurus =Spinosaurus!-this is a kid who
>>>buys workbooks at the dollar store when she has money to spend, and does
>>>them for fun, and who absolutely LOVES symbols, so will ask what they
>>>mean)
>>>would be very upset at the concept of a variable, because she's so set on
>>>things having specific names. If a character in a book doesn't have a
>>>name,
>>>and she decides today that his name is Pete, I can't call him Paul
>>>tomorrow
>>>without upsetting her, because names, to her, are inviolate. I don't think
>>>she'd accept calling an unknown q, because q has a specific identity-it's
>>>a
>>>letter of the alphabet. Yet, she's capable of figuring out that if she
>>>has
>>>three chicken pieces on her plate, and she wants 5, she needs 2 more-which
>>>is the same as 3+x=5, solve for X. And, I have to say that my 5 yr old
>>>students who will be going into K in the fall generally behave similarly
>>>with regard to names-but have less understanding of the concepts of
>>>addition
>>>and subtraction.
>>
>> I'm not so sure about variables. What you described in your 3 1/2 year
>> old
>> sounds very much like the inflexibility that that age has. I think that's
>> a bad
>> example.
>>
>> And I also think it has to do with how it's introduced. The oogabooga
>> eekee-ookee thing would work I think.
>>
>> But you know what, I dont want to argue that it has to be specifically
>> kindergarteners that are first introduced to it. K used to be (back in
>> the bad
>> old days) for socialization and some basics in prep for school. Do it
>> for 6
>> and 7 year olds, or not. But do you know of any studies on this? Id be
>> skeptical that this really has been looked at. I agree with Herman that
>> these
>> are essentially linguistic concepts and I'm skeptical that they can't be
>> introduced very early.
>>
>> Think pronouns. Even a toddler isn't thrown for a loop long that "he"
>> could be
>> Daddy, or big brother, or puppy.
>>
>But a pronoun is always a variable. A, though, is A, and young kids who are
>just learning to read are learning letters as an absolute with specific
>rules that usually work the same way. In many ways, what throws children for
>a loop is the variability of letters, which is why vowels are so much harder
>for young readers than consonants.

Then use Greek letters! Or something like that. You're missing the point or
even avoiding it.

>
>If you always called a variable number an oogabooga, that would probably
>work-but if that's your goal, the blank space notation used in most primary
>grade math texts will serve equally well until the children get old enough
>to grasp the concept that a letter can be more than just a sound in a word.

That does not give the concept of a variable. It only is a question to be
answered, a blank space. Its not even the same concept.

>
>I've introduced algebraic notation for variables with 3rd graders before,
>without problems, so I do believe it can be introduced earlier than most
>programs do. But just because it works with 8 yr olds doesn't mean it will
>work with 5 yr olds. One of the biggest issues facing early childhood
>education is exactly this idea-that if 6 yr olds can learn to read, than 5
>yr olds can learn to read, and if 5 year olds can learn to read, then SURELY
>all 4 yr olds can learn their alphabet and phonetic sounds, some sight
>words, and so on. We're now to the point that many schools expect children
>to come into K with skills in reading and math that in the past were taught
>in K-and the result is a child who is perfectly normal in development comes
>into K already behind.

Again, I'm not saying necessarily by five. But I *do* think the teaching of
math is WAY overburdened with teaching tricks and very specific skills with
limited application, instead of teaching math in terms of what it actually *is*
- a language for concepts. And that is what's NOT done.

>
>If a child is still very concrete, they're not ready for the concept of a
>variable.

I'm not sure I accept that. A variable is actually a rather concrete concept.

>And yes, that means most children are ready for the concepts of
>putting together items in a set to make a bigger set and removing items from
>a set to make a smaller set before they're ready for the concept of a
>variable.

I don't think that necessarily is connected with the concept of a variable Its
just how it's done today.

>Because adding and subtracting ARE concrete. Move the unknown,
>introduce the idea of incomplete information that's not on the right side of
>the equals sign, give an unknown a name like Bletz or Spurg, but I think
>that introducing the idea of X and Y to children who are still learning X
>and Y as letters of the alphabet is likely to be quite confusing and
>unlikely to get the response you want.
>

Oh, get over the LETTER idea! Make different squiggles, or a squiggle and a
bent line. Or something. You're missing the point. Use Princes old symbol now
that he's back to his name.

Arrgh. No wonder we have problems teaching math.

Banty
 >> Stay informed about: Testing Racket Has Ruined High School 

In article <ov4c44la24k5fur67tm5bkvbo0fdh8h68s RemoveThis @4ax.com>,
toto <scarecrow RemoveThis @wicked.witch> wrote:
>On 3 Jun 2008 11:14:09 -0700, Banty <Banty_member RemoveThis @newsguy.com> wrote:

>>Back to your question - -

>>What are you trying to find out?
>> Make that "x".

>As Herman would say, using a single variable often makes things more
>difficult. When you want to teach formulating problems, you can't do
>this by giving specific formulas.

>Also, Herman believes that this should be taught to 5 year olds. I
>want *him* to tell me how to do this.

>Btw, I haven't a clue how to teach poetry. I can't really write a
>poem even now. My kids did sample poetry by copying formulas, but
>neither of them learned to write any creative poems of their own in
>school.

The use of variables is primarily in declarative
sentences, not poetry. I have given examples of
how one can use variables to disambiguate ordinary
English, and using variables as temporary names for
anything, including verbs, adjectives, etc., will
add this useful means of producing expressions.

Don't make it "hard" or "mysterious".
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin RemoveThis @stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
 >> Stay informed about: Testing Racket Has Ruined High School 

On 4 Jun 2008 11:04:14 -0700, Banty <Banty_member DeleteThis @newsguy.com> wrote:

>>If you always called a variable number an oogabooga, that would probably
>>work-but if that's your goal, the blank space notation used in most primary
>>grade math texts will serve equally well until the children get old enough
>>to grasp the concept that a letter can be more than just a sound in a word.
>
>That does not give the concept of a variable. It only is a question to be
>answered, a blank space. Its not even the same concept.

I think the way we use the word variable can be confusing.

An unknown is a constant that can be solved for. A variable is
something that changes, but often it changes in relationship to other
variables in the problem or situation.

Letters are *numbers in disguise* in this formulation. Obviously, you
can use any symbol. You don't have to use a letter. These are called
variables because the particular number they represent can change or
vary.

Perhaps some of this can be done using stories in which events change
or characters change in some way. Perhaps time can be used as time
varies.


--
Dorothy

There is no sound, no cry in all the world
that can be heard unless someone listens ..

The Outer Limits
 >> Stay informed about: Testing Racket Has Ruined High School