entering kindergarten early

Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:

..............


Is this a non sequitur? Surely you're not arguing
that knowing any mathematics means knowing all mathematics.

This is NOT a non sequitur. It is questionable whether
knowing how to calculate, even well, is of much value in
learning mathematics. It is NOT mathematics.

Let's go over this again. You said enrichment is
useless because it just means exposing them to things that
they'll have to unlearn later on. I said that in the
case of math, enrichment can mean encountering areas of
math that they won't be exposed to at all, particularly
if they don't choose to go into math or science. And
then you asked if they'll know any math. How, precisely,
is that relevant to the conversation unless you're suggesting
somehow that they all must learn all areas of mathematics
(which is, after all, quite a lot of territory)?

I never indicated that they need to learn all areas of
mathematics; a few basic ones are important.

Then if you're so sure that they can complete all
the areas you believe to be necessary in elementary school,
surely you would agree, ipso facto, that enrichment activities
in the *other* areas (whichever you define those to be) could
be added as enrichment activities.
Clearly we disagree on what should be taught and
how, but the argument that enrichment is necessarily bogus
because it must mean you're introducing concepts that will
only have to be unlearned later falls under its own weight
almost regardless of what you think ought to be taught.

Best wishes,
Ericka

Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Donna Metler wrote:
"Herman Rubin" wrote in message
...

...............

The type of pattern-looking taught in schools

And what sort of pattern matching might that be?
I don't recall encountering a particular syllabus describing
the limits to what might be taught/encouraged/expected/supported
in terms of pattern matching in schools.

is valid only
if the model is simple, the errors in the data are small,
but not too small, and the errors in the models which will
come to mind are smaller. When these are not all present,
that type of pattern search is likely to lead down blind
alleys; data cannot generate theories, but only choose
between them.

Ah, so deductive logic rules and there is no role
for inductive thinking? How unfortunate, particularly for
one who sets himself out as an authority on what gifted kids
can or should do. (And of course data doesn't generate *or*
choose between theories. *People* generate and evaluate
theories.)

What do you mean by inductive thinking?

The usual definition--moving from the specific to
the general.

One form of inductive
thinking is that in mathematics; it is very important. The
other form is subsumed in the general problem of reasoning
from data; this is properly formalized in statistical decision
theory, in which I was one of the pioneers. I say was, because
it is more than half a century ago. Even 19th century statistics
shows the problems.

That is not the only, or even always the best,
way to engage in inductive thinking processes. There are
many ways to do it, ranging from the highly structured to
the relatively unstructured. Depending on the circumstance,
they each have a role to play.

Every good researcher does "inductive" thinking. I tell my
students that research consists in seeing the obvious. There
are times when I do this by looking at special cases, but
mostly by thinking, and I regret that I do not know how to
teach this.

Because you're so focused on such a narrow view
of education. You can't just open their little heads up
and stuff things in--even when they're gifted.

As for knowing what gifted children can do, I myself am gifted,
as is my son, and I know others and have had communication with
them, and also with some of their parents. As to what they
should do, I do not see how anyone who is not gifted is in a
position to proscribe their progress.

You do, of course, realize that you've been carrying
on a conversation with quite a few gifted folks and/or parents of
gifted children who disagree with your assertions? And that's
before looking into what the research into gifted education has
to say about it.

Best wishes,
Ericka

Herman Rubin wrote:
[snip]
The same holds for physics, chemistry, astronomy, biology,
economics, etc. One needs mathematics to formulate the
relevant theories, which while approximate, are what we
need to get understanding. Making a leaf collection or
a bug collection does not help in understanding biology.


I rather suspect that at least some of the pioneers
in the biological sciences would suggest that collecting
specimens was rather important in furthering their understanding
of the field.


This was necessary to get a historical start. Studying
the history of a science does not help in understanding
the science.
[snip]

I would absolutely disagree with this.

Obviously, you don't expect the children to follow the same
thought processes (imagine having to unlearn Aristolian physics!),
but understanding why they thought *that* then, can help people
understand why we think *this* now.

--
Penny Gaines
UK mum to three

In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:

..............


Is this a non sequitur? Surely you're not arguing
that knowing any mathematics means knowing all mathematics.

This is NOT a non sequitur. It is questionable whether
knowing how to calculate, even well, is of much value in
learning mathematics. It is NOT mathematics.

Let's go over this again. You said enrichment is
useless because it just means exposing them to things that
they'll have to unlearn later on. I said that in the
case of math, enrichment can mean encountering areas of
math that they won't be exposed to at all, particularly
if they don't choose to go into math or science. And
then you asked if they'll know any math. How, precisely,
is that relevant to the conversation unless you're suggesting
somehow that they all must learn all areas of mathematics
(which is, after all, quite a lot of territory)?

I never indicated that they need to learn all areas of
mathematics; a few basic ones are important.

Then if you're so sure that they can complete all
the areas you believe to be necessary in elementary school,
surely you would agree, ipso facto, that enrichment activities
in the *other* areas (whichever you define those to be) could
be added as enrichment activities.

No. In every field, education should be done at the
level of the individual. And it should not waste time
by delivering the message that key material is being
presented when it is the exact opposite.

This is not just in mathematics, but in science, and
even in history. I do not see how one can understand
American history without knowing a good bit of ancient
history, especially considering that this had much to
do with the science and culture of the Europeans who
came over, and of those who founded the country.

Clearly we disagree on what should be taught and
how, but the argument that enrichment is necessarily bogus
because it must mean you're introducing concepts that will
only have to be unlearned later falls under its own weight
almost regardless of what you think ought to be taught.

I suggest you learn the basic concepts yourself before
making this statement. Concepts are not words; the
definition of a group does not convey the concept, and
it helps to have the definition down before looking at
special cases.
--
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
Phone: (765)494-6054 FAX: (765)494-0558

In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Donna Metler wrote:
"Herman Rubin" wrote in message
...

...............

The type of pattern-looking taught in schools

And what sort of pattern matching might that be?
I don't recall encountering a particular syllabus describing
the limits to what might be taught/encouraged/expected/supported
in terms of pattern matching in schools.

is valid only
if the model is simple, the errors in the data are small,
but not too small, and the errors in the models which will
come to mind are smaller. When these are not all present,
that type of pattern search is likely to lead down blind
alleys; data cannot generate theories, but only choose
between them.

Ah, so deductive logic rules and there is no role
for inductive thinking? How unfortunate, particularly for
one who sets himself out as an authority on what gifted kids
can or should do. (And of course data doesn't generate *or*
choose between theories. *People* generate and evaluate
theories.)

What do you mean by inductive thinking?

The usual definition--moving from the specific to
the general.

One form of inductive
thinking is that in mathematics; it is very important. The
other form is subsumed in the general problem of reasoning
from data; this is properly formalized in statistical decision
theory, in which I was one of the pioneers. I say was, because
it is more than half a century ago. Even 19th century statistics
shows the problems.

That is not the only, or even always the best,
way to engage in inductive thinking processes. There are
many ways to do it, ranging from the highly structured to
the relatively unstructured. Depending on the circumstance,
they each have a role to play.

Every good researcher does "inductive" thinking. I tell my
students that research consists in seeing the obvious. There
are times when I do this by looking at special cases, but
mostly by thinking, and I regret that I do not know how to
teach this.

Because you're so focused on such a narrow view
of education. You can't just open their little heads up
and stuff things in--even when they're gifted.

Nobody knows how to teach thinking. What we can do
is to point out problems, and point out methods which
have worked in the past. We can point out how the
concepts have led to "tricks" which work.

I do not want to "stuff things in". I want them to
understand the structure, even when precise concepts
are not available.

As for knowing what gifted children can do, I myself am gifted,
as is my son, and I know others and have had communication with
them, and also with some of their parents. As to what they
should do, I do not see how anyone who is not gifted is in a
position to proscribe their progress.

You do, of course, realize that you've been carrying
on a conversation with quite a few gifted folks and/or parents of
gifted children who disagree with your assertions? And that's
before looking into what the research into gifted education has
to say about it.

There are a few gifted people posting, and I do not see
any strong opposition from them. As for parents of
gifted, they appear to detect giftedness fairly well,
but do not know what to do with it; teachers are not as
good at recognizing giftedness, confusing it with doing
well on the standard stuff.

There has been imprecise research on giftedness, usually
done by people who are not in education, or who are
considered to reject the "truth" in education. The
studies by mainstream educationists uses their incorrect
understanding of statistics.

In giving advice to gifted children, it is at least necessary
to understand the subjects, and to have some idea of what
they can do. Those who do not understand their subjects
are not even in a good position to teach anything; alas,
the current educationist curriculum almost makes in impossible
for teachers to get the understanding which can be taught
to children.
--
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
Phone: (765)494-6054 FAX: (765)494-0558

Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:

..............


Is this a non sequitur? Surely you're not arguing
that knowing any mathematics means knowing all mathematics.

This is NOT a non sequitur. It is questionable whether
knowing how to calculate, even well, is of much value in
learning mathematics. It is NOT mathematics.

Let's go over this again. You said enrichment is
useless because it just means exposing them to things that
they'll have to unlearn later on. I said that in the
case of math, enrichment can mean encountering areas of
math that they won't be exposed to at all, particularly
if they don't choose to go into math or science. And
then you asked if they'll know any math. How, precisely,
is that relevant to the conversation unless you're suggesting
somehow that they all must learn all areas of mathematics
(which is, after all, quite a lot of territory)?

I never indicated that they need to learn all areas of
mathematics; a few basic ones are important.

Then if you're so sure that they can complete all
the areas you believe to be necessary in elementary school,
surely you would agree, ipso facto, that enrichment activities
in the *other* areas (whichever you define those to be) could
be added as enrichment activities.

No. In every field, education should be done at the
level of the individual. And it should not waste time
by delivering the message that key material is being
presented when it is the exact opposite.

I really can't tell if you just don't understand
what I'm saying, the thread has become too fragmented to
follow the discussion, or you're being deliberately antagonistic,
so I'm not sure how to respond to this.

This is not just in mathematics, but in science, and
even in history. I do not see how one can understand
American history without knowing a good bit of ancient
history, especially considering that this had much to
do with the science and culture of the Europeans who
came over, and of those who founded the country.

I'm also not sure of the relevance of this.
Are you saying it's important to learn history? I'd
definitely agree with that. Are you trying to imply
that students don't learn history? I'd have to disagree
with that. My kids aren't even out of elementary school
yet and have had ancient history at least two years.
I'm also not quite sure how this statement squares
with your assertion that "Studying the history of a science
does not help in understanding the science."

Clearly we disagree on what should be taught and
how, but the argument that enrichment is necessarily bogus
because it must mean you're introducing concepts that will
only have to be unlearned later falls under its own weight
almost regardless of what you think ought to be taught.

I suggest you learn the basic concepts yourself before
making this statement. Concepts are not words; the
definition of a group does not convey the concept, and
it helps to have the definition down before looking at
special cases.

You have yet to provide an argument (besides your
assertion) for why acceleration is the only effective strategy
and enrichment is not useful. The only situation in which
that would hold is a situation in which the entire curriculum
in an area is a single strand with a linear progression. While
math is more that way that other areas, even in math there are
branches that can be introduced as enrichment that otherwise
aren't covered at all in primary or secondary education and
could easily be taught to children who master the basics quickly
enough to have time left over.

Best wishes,
Ericka

Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:


Every good researcher does "inductive" thinking. I tell my
students that research consists in seeing the obvious. There
are times when I do this by looking at special cases, but
mostly by thinking, and I regret that I do not know how to
teach this.

Because you're so focused on such a narrow view
of education. You can't just open their little heads up
and stuff things in--even when they're gifted.

Nobody knows how to teach thinking. What we can do
is to point out problems, and point out methods which
have worked in the past. We can point out how the
concepts have led to "tricks" which work.

I do not want to "stuff things in". I want them to
understand the structure, even when precise concepts
are not available.

But you just said you didn't know how to teach
this sort of thing. You teach it by providing opportunities
for experiences that encourage the children to explore
and think and understand and perhaps by asking some questions
or providing a little guidance where needed. This is not
in alignment with the hurry-hurry, get-through-the-concepts-
as-soon-as-possible-so-they-can-get-on-to-something-more-meaningful
approach. The process they go through to learn things is
as important as the concepts they learn, because it's the
process that will fuel a lifetime of independent learning.
Even gifted kids who can accumulate concepts faster benefit
from more opportunities to really think about things and
push the limits of their understanding, even if it's in
an enrichment area rather than the core curriculum, even
if it's collecting leaves, even if doesn't get them out of
school years earlier.

As for knowing what gifted children can do, I myself am gifted,
as is my son, and I know others and have had communication with
them, and also with some of their parents. As to what they
should do, I do not see how anyone who is not gifted is in a
position to proscribe their progress.

You do, of course, realize that you've been carrying
on a conversation with quite a few gifted folks and/or parents of
gifted children who disagree with your assertions? And that's
before looking into what the research into gifted education has
to say about it.

There are a few gifted people posting, and I do not see
any strong opposition from them.

How would you characterize my responses?

As for parents of
gifted, they appear to detect giftedness fairly well,

Actually, it is not uncommon for gifted
parents have difficulties detecting giftedness
in their children. Their children's behavior often seems
normal to them because that's what they're used to.

In giving advice to gifted children, it is at least necessary
to understand the subjects, and to have some idea of what
they can do. Those who do not understand their subjects
are not even in a good position to teach anything; alas,
the current educationist curriculum almost makes in impossible
for teachers to get the understanding which can be taught
to children.

Again, what is this "educationist curriculum" you
keep talking about?

Best wishes,
Ericka

In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:
In article ,
Ericka Kammerer wrote:
Herman Rubin wrote:


Every good researcher does "inductive" thinking. I tell my
students that research consists in seeing the obvious. There
are times when I do this by looking at special cases, but
mostly by thinking, and I regret that I do not know how to
teach this.

Because you're so focused on such a narrow view
of education. You can't just open their little heads up
and stuff things in--even when they're gifted.

Nobody knows how to teach thinking. What we can do
is to point out problems, and point out methods which
have worked in the past. We can point out how the
concepts have led to "tricks" which work.

I do not want to "stuff things in". I want them to
understand the structure, even when precise concepts
are not available.

But you just said you didn't know how to teach
this sort of thing.

Nor does anyone else.

You teach it by providing opportunities
for experiences that encourage the children to explore
and think and understand and perhaps by asking some questions
or providing a little guidance where needed.

One needs the basics. I doubt that much, if any, of the
exploring I did before I saw that algebra book did anything
at all for me, other than point out that I was bright. I
did not know what "gifted" was until I was doing research.
And I had NO guidance of any kind after my aunt taught me
to read at age three, and my father taught me to add and
multiply shortly thereafter. I did have an intuitive
understanding of linguistic structure then, but nothing
about mathematics.

This is not
in alignment with the hurry-hurry, get-through-the-concepts-
as-soon-as-possible-so-they-can-get-on-to-something-more-meaningful
approach.

This approach is taken only take for the mentally weak, who
cannot keep up. Reading needs to be taught early, so one
can go on to other things. And it needs to be done well,
not by the whole word method; deducing the phonic rules
this way is at best likely to lead to errors which need
correcting.

The process they go through to learn things is
as important as the concepts they learn, because it's the
process that will fuel a lifetime of independent learning.

At this time, what concepts have they learned? They have
learned that letter combinations may represent sounds, and
that these sounds combine into words. Some may have
learned that there is a grammatical structure, but most
not; they have picked up something, but again with MAJOR
errors.

Even gifted kids who can accumulate concepts faster benefit
from more opportunities to really think about things and
push the limits of their understanding, even if it's in
an enrichment area rather than the core curriculum, even
if it's collecting leaves, even if doesn't get them out of
school years earlier.

As I said, what concepts? Addition and multiplication are
taught as rules, with possibly a few examples. We still
have teachers asking children what happens to be the
largest number they know, while the basic concepts say that
one can always find a larger number.

Concepts are not "accumulated". Facts and procedures
are what are accumulated. It took millennia before
the fundamental concepts of arithmetic were formulated,
and they were not well understood before.

As for knowing what gifted children can do, I myself am gifted,
as is my son, and I know others and have had communication with
them, and also with some of their parents. As to what they
should do, I do not see how anyone who is not gifted is in a
position to proscribe their progress.

You do, of course, realize that you've been carrying
on a conversation with quite a few gifted folks and/or parents of
gifted children who disagree with your assertions? And that's
before looking into what the research into gifted education has
to say about it.

There are a few gifted people posting, and I do not see
any strong opposition from them.

How would you characterize my responses?

If you are gifted, you are uneducated in basic concepts,
so you have difficulty in understanding the points I
am making. You can teach people concepts directly, but
the idea of learning concepts, or even just facts, by
generalization does not work well; I have found some
which surprised experts.

As for parents of
gifted, they appear to detect giftedness fairly well,

Actually, it is not uncommon for gifted
parents have difficulties detecting giftedness
in their children. Their children's behavior often seems
normal to them because that's what they're used to.

Unfortunately, you happen to be right. My parents
did recognize that I was bright, but they had nothing
to go by for giftedness, and the idea of academic
giftedness was not in common use.

In giving advice to gifted children, it is at least necessary
to understand the subjects, and to have some idea of what
they can do. Those who do not understand their subjects
are not even in a good position to teach anything; alas,
the current educationist curriculum almost makes in impossible
for teachers to get the understanding which can be taught
to children.

Again, what is this "educationist curriculum" you
keep talking about?

The educationist curriculum, among other things, states
that children should be with their age groups, that one
learns from special cases to general, concentrates on
teaching memorization and routine with the possible hope
that some understanding will come from it, etc. It also
teaches "teaching methods", and assumes that teachers
will be able to learn faster than children.
--
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
Phone: (765)494-6054 FAX: (765)494-0558

On Jun 11, 4:51 pm, Ericka Kammerer wrote:

snip

Again, what is this "educationist curriculum" you
keep talking about?

I don't know what Mr. Rubin has in mind, but some books I have read
describing poor but widely practiced methods of teaching are

Class Warfa Besieged Schools, Bewildered Parents, Betrayed Kids and
the Attack on Excellence by J. Martin Rochester
Encounter Books (2004)

Ed School Follies: The Miseducation of America's Teachers
by Rita Kramer

Inside American Education
by Thomas Sowell
Free Press

Beliavsky wrote:
On Jun 11, 4:51 pm, Ericka Kammerer wrote:

snip

Again, what is this "educationist curriculum" you
keep talking about?

I don't know what Mr. Rubin has in mind, but some books I have read
describing poor but widely practiced methods of teaching are

Class Warfa Besieged Schools, Bewildered Parents, Betrayed Kids and
the Attack on Excellence by J. Martin Rochester
Encounter Books (2004)

Ed School Follies: The Miseducation of America's Teachers
by Rita Kramer

Inside American Education
by Thomas Sowell
Free Press

There are certainly practices that leave something
to be desired, and some of them are more prevalent than
one would wish. However, the absolutist claims he makes about
education seem quite extreme and not at all consistent with
my experiences (either with my own schooling in more than half
a dozen different states or with my children's schooling).

Best wishes,
Ericka