Discussion:
Maths problems 'too hard for kids to read'
Tomasso
2007-07-31 01:46:07 UTC
From ABC News (July 31, 2007)
A leading educational researcher has called for a major overhaul of maths
teaching in Australian schools.
Ken Rowe from the Australian Council for Educational Research (ACER)
says maths questions in both primary and high schools require students to
have a literacy level that is often beyond their skills.
He has outlined his concerns in a submission to the national numeracy review.
Mr Rowe says it is turning students off maths.
"For grade three students for example, they have to read the problem and
then translate it into an algorithm and solve it," he said.
"Now that requires in most cases a Grade Five level of literacy before they
can even engage with the Year Three mathematics.
"The problem is usually put, well Jane has 52 pieces of fruit, Alex has 24
pieces of fruit, how many pieces of fruit do they have?
"So in other words you've got to be able to read what the problem is asking
before you can actually do the mathematics."
I guess I agree with the sentiment, but not with the example. I've noticed that a
lot of exercises for primary school kids are sloppily worded. It's not that the
expression is complex or uses advanced vocabulary, it's that it is often
ambiguous and imprecise.

A couple of years ago I took some primary maths questions apart, and compared
what they appeared to say (ie, what a natural interpretion was) with what they
were actually asking for and what they problem details they were actually
providing. That is IMHO more of a problem for the kids than "read the problem
and then translate it into an algorithm and solve it".

Problem analysis is a special skill, but one well summarised by George Polya half a
century ago as:

1 Identify what you are asked to find out.
2 Identify what information you are told/given.
3 Identify what other information you need to use (assumptions, background knowledge).
4 Build a plan to use the information to determine what you are asked.

In practice, much of problem solving is an artform rather than a recipe (at least for
people who solve problems rather than talk about it). However, the problem analysis
is a necessary and fairly painstaking part. It's similar to gap analysis where you work
out what's present and what's missing (out of what's required). If a kid is determined
to address the first three points above the twenty or thirty words that are the "question",
in my experience they can get there, unless the person who wrote the question has
done the kid the injustice of writing badly.

If the raw material for the problem (exercise X in the textbook) is sloppily written,
it's not a problem with grammar or term, it's an impediment due to fuzziness.

At least when you deal with problems in the real world, you don't have to put up
with a poorly posed problem. You write the problem spec or requirements for
yourself. You know when you've finished that part of the work because it no
longer sounds sloppy.

Tomasso.

OBs literacy: The "reading" involved in reading more complex problems is quite
different from what is normally meant by literacy (in the junior school sense).
It can be more like the "reading" involved in digesting a Shakespeare sonnet,
and take the same amount of time.
--
Oh Really?
Don H
2007-07-31 21:58:17 UTC
Post by Tomasso
From ABC News (July 31, 2007)
A leading educational researcher has called for a major overhaul of maths
teaching in Australian schools.
Ken Rowe from the Australian Council for Educational Research (ACER)
says maths questions in both primary and high schools require students to
have a literacy level that is often beyond their skills.
He has outlined his concerns in a submission to the national numeracy review.
Mr Rowe says it is turning students off maths.
"For grade three students for example, they have to read the problem and
then translate it into an algorithm and solve it," he said.
"Now that requires in most cases a Grade Five level of literacy before they
can even engage with the Year Three mathematics.
"The problem is usually put, well Jane has 52 pieces of fruit, Alex has 24
pieces of fruit, how many pieces of fruit do they have?
"So in other words you've got to be able to read what the problem is asking
before you can actually do the mathematics."
I guess I agree with the sentiment, but not with the example. I've noticed that a
lot of exercises for primary school kids are sloppily worded. It's not that the
expression is complex or uses advanced vocabulary, it's that it is often
ambiguous and imprecise.
A couple of years ago I took some primary maths questions apart, and compared
what they appeared to say (ie, what a natural interpretion was) with what they
were actually asking for and what they problem details they were actually
providing. That is IMHO more of a problem for the kids than "read the problem
and then translate it into an algorithm and solve it".
Problem analysis is a special skill, but one well summarised by George Polya half a
1 Identify what you are asked to find out.
2 Identify what information you are told/given.
3 Identify what other information you need to use (assumptions, background knowledge).
4 Build a plan to use the information to determine what you are asked.
In practice, much of problem solving is an artform rather than a recipe (at least for
people who solve problems rather than talk about it). However, the problem analysis
is a necessary and fairly painstaking part. It's similar to gap analysis where you work
out what's present and what's missing (out of what's required). If a kid is determined
to address the first three points above the twenty or thirty words that are the "question",
in my experience they can get there, unless the person who wrote the question has
done the kid the injustice of writing badly.
If the raw material for the problem (exercise X in the textbook) is sloppily written,
it's not a problem with grammar or term, it's an impediment due to fuzziness.
At least when you deal with problems in the real world, you don't have to put up
with a poorly posed problem. You write the problem spec or requirements for
yourself. You know when you've finished that part of the work because it no
longer sounds sloppy.
Tomasso.
OBs literacy: The "reading" involved in reading more complex problems is quite
different from what is normally meant by literacy (in the junior school sense).
It can be more like the "reading" involved in digesting a Shakespeare sonnet,
and take the same amount of time.
--
Oh Really?
# Back in my time at primary school (1930s-40s), maths had two aspects (a)
Processes, and (b) Problems. The former dealt with basic aspects, such as
addition, subtraction, etc. while the latter was couched in literary terms,
and involved problems in daily life.
The whole point of a "problem" was to extract the maths from the literary
context, and applying Processes, solve it. Otherwise, we merely have:
52+24=? assuming we are dealing with "both".
Fortunately, I was educated prior to introduction of the moronic Whole
Word "method", so didn't have much trouble in reading the relatively simple
text, such as posed in your example.
"Grade (whatever) level of literacy" would have been matched with same
level of maths quite easily, as all children could read and write by Grade
Two, and all that remained was refinement of grammar, and expansion of
vocabulary.
I never had any trouble with either Processes or Problems. If literacy
Tomasso
2007-08-01 10:06:56 UTC
Post by Tomasso
From ABC News (July 31, 2007)
A leading educational researcher has called for a major overhaul of
maths
Post by Tomasso
teaching in Australian schools.
Ken Rowe from the Australian Council for Educational Research (ACER)
says maths questions in both primary and high schools require students
to
Post by Tomasso
have a literacy level that is often beyond their skills.
He has outlined his concerns in a submission to the national numeracy
review.
Post by Tomasso
Mr Rowe says it is turning students off maths.
"For grade three students for example, they have to read the problem and
then translate it into an algorithm and solve it," he said.
"Now that requires in most cases a Grade Five level of literacy before
they
Post by Tomasso
can even engage with the Year Three mathematics.
"The problem is usually put, well Jane has 52 pieces of fruit, Alex has
24
Post by Tomasso
pieces of fruit, how many pieces of fruit do they have?
"So in other words you've got to be able to read what the problem is
Post by Tomasso
before you can actually do the mathematics."
I guess I agree with the sentiment, but not with the example. I've noticed
that a
Post by Tomasso
lot of exercises for primary school kids are sloppily worded. It's not
that the
Post by Tomasso
expression is complex or uses advanced vocabulary, it's that it is often
ambiguous and imprecise.
A couple of years ago I took some primary maths questions apart, and
compared
Post by Tomasso
what they appeared to say (ie, what a natural interpretion was) with what
they
Post by Tomasso
were actually asking for and what they problem details they were actually
providing. That is IMHO more of a problem for the kids than "read the
problem
Post by Tomasso
and then translate it into an algorithm and solve it".
Problem analysis is a special skill, but one well summarised by George
Polya half a
Post by Tomasso
1 Identify what you are asked to find out.
2 Identify what information you are told/given.
3 Identify what other information you need to use (assumptions, background
knowledge).
Post by Tomasso
4 Build a plan to use the information to determine what you are asked.
In practice, much of problem solving is an artform rather than a recipe
(at least for
Post by Tomasso
people who solve problems rather than talk about it). However, the problem
analysis
Post by Tomasso
is a necessary and fairly painstaking part. It's similar to gap analysis
where you work
Post by Tomasso
out what's present and what's missing (out of what's required). If a kid
is determined
Post by Tomasso
to address the first three points above the twenty or thirty words that
are the "question",
Post by Tomasso
in my experience they can get there, unless the person who wrote the
question has
Post by Tomasso
done the kid the injustice of writing badly.
If the raw material for the problem (exercise X in the textbook) is
sloppily written,
Post by Tomasso
it's not a problem with grammar or term, it's an impediment due to
fuzziness.
Post by Tomasso
At least when you deal with problems in the real world, you don't have to
put up
Post by Tomasso
with a poorly posed problem. You write the problem spec or requirements
for
Post by Tomasso
yourself. You know when you've finished that part of the work because it
no
Post by Tomasso
longer sounds sloppy.
Tomasso.
quite
Post by Tomasso
different from what is normally meant by literacy (in the junior school
sense).
Post by Tomasso
It can be more like the "reading" involved in digesting a Shakespeare
sonnet,
Post by Tomasso
and take the same amount of time.
--
Oh Really?
# Back in my time at primary school (1930s-40s), maths had two aspects (a)
Processes, and (b) Problems. The former dealt with basic aspects, such as
addition, subtraction, etc. while the latter was couched in literary terms,
and involved problems in daily life.
The whole point of a "problem" was to extract the maths from the literary
52+24=? assuming we are dealing with "both".
Fortunately, I was educated prior to introduction of the moronic Whole
Word "method", so didn't have much trouble in reading the relatively simple
text, such as posed in your example.
"Grade (whatever) level of literacy" would have been matched with same
level of maths quite easily, as all children could read and write by Grade
Two, and all that remained was refinement of grammar, and expansion of
vocabulary.
I never had any trouble with either Processes or Problems. If literacy
Well, yes. Mathematics is a language, too, with tighter requirements for
structure. The semantics of terms is whatever you want it to be (and
for operators, is what you chose to use).

The mathematics can be wrong too, if it doesn't reflect the problem (even if you
can "solve it"). Getting that act right is something a lot of people (adults)
have trouble with.

If the (English) problem description is sloppy, it's harder for kids (and adults)
to produce maths that reflects the problem.

At an advanced level, part of this is done with model validation, but even that
has a problem with identifying missing details. It can become philosophical
at that point, or, peer review with reliable peers.

Kids need to develop some kind of intuitive version of those "validation/review"
practices.

Sadly, a lot of "problem solving" in education is about pasting words onto
recipe approaches.

Tomasso.
Don H
2007-08-01 20:04:01 UTC
Post by Tomasso
Post by Tomasso
From ABC News (July 31, 2007)
A leading educational researcher has called for a major overhaul of
maths
Post by Tomasso
teaching in Australian schools.
Ken Rowe from the Australian Council for Educational Research (ACER)
says maths questions in both primary and high schools require students
to
Post by Tomasso
have a literacy level that is often beyond their skills.
He has outlined his concerns in a submission to the national numeracy
review.
Post by Tomasso
Mr Rowe says it is turning students off maths.
"For grade three students for example, they have to read the problem and
then translate it into an algorithm and solve it," he said.
"Now that requires in most cases a Grade Five level of literacy before
they
Post by Tomasso
can even engage with the Year Three mathematics.
"The problem is usually put, well Jane has 52 pieces of fruit, Alex has
24
Post by Tomasso
pieces of fruit, how many pieces of fruit do they have?
"So in other words you've got to be able to read what the problem is
Post by Tomasso
before you can actually do the mathematics."
I guess I agree with the sentiment, but not with the example. I've noticed
that a
Post by Tomasso
lot of exercises for primary school kids are sloppily worded. It's not
that the
Post by Tomasso
expression is complex or uses advanced vocabulary, it's that it is often
ambiguous and imprecise.
A couple of years ago I took some primary maths questions apart, and
compared
Post by Tomasso
what they appeared to say (ie, what a natural interpretion was) with what
they
Post by Tomasso
were actually asking for and what they problem details they were actually
providing. That is IMHO more of a problem for the kids than "read the
problem
Post by Tomasso
and then translate it into an algorithm and solve it".
Problem analysis is a special skill, but one well summarised by George
Polya half a
Post by Tomasso
1 Identify what you are asked to find out.
2 Identify what information you are told/given.
3 Identify what other information you need to use (assumptions, background
knowledge).
Post by Tomasso
4 Build a plan to use the information to determine what you are asked.
In practice, much of problem solving is an artform rather than a recipe
(at least for
Post by Tomasso
people who solve problems rather than talk about it). However, the problem
analysis
Post by Tomasso
is a necessary and fairly painstaking part. It's similar to gap analysis
where you work
Post by Tomasso
out what's present and what's missing (out of what's required). If a kid
is determined
Post by Tomasso
to address the first three points above the twenty or thirty words that
are the "question",
Post by Tomasso
in my experience they can get there, unless the person who wrote the
question has
Post by Tomasso
done the kid the injustice of writing badly.
If the raw material for the problem (exercise X in the textbook) is
sloppily written,
Post by Tomasso
it's not a problem with grammar or term, it's an impediment due to
fuzziness.
Post by Tomasso
At least when you deal with problems in the real world, you don't have to
put up
Post by Tomasso
with a poorly posed problem. You write the problem spec or requirements
for
Post by Tomasso
yourself. You know when you've finished that part of the work because it
no
Post by Tomasso
longer sounds sloppy.
Tomasso.
quite
Post by Tomasso
different from what is normally meant by literacy (in the junior school
sense).
Post by Tomasso
It can be more like the "reading" involved in digesting a Shakespeare
sonnet,
Post by Tomasso
and take the same amount of time.
--
Oh Really?
# Back in my time at primary school (1930s-40s), maths had two aspects (a)
Processes, and (b) Problems. The former dealt with basic aspects, such as
addition, subtraction, etc. while the latter was couched in literary terms,
and involved problems in daily life.
The whole point of a "problem" was to extract the maths from the literary
52+24=? assuming we are dealing with "both".
Fortunately, I was educated prior to introduction of the moronic Whole
Word "method", so didn't have much trouble in reading the relatively simple
text, such as posed in your example.
"Grade (whatever) level of literacy" would have been matched with same
level of maths quite easily, as all children could read and write by Grade
Two, and all that remained was refinement of grammar, and expansion of
vocabulary.
I never had any trouble with either Processes or Problems. If literacy
Well, yes. Mathematics is a language, too, with tighter requirements for
structure. The semantics of terms is whatever you want it to be (and
for operators, is what you chose to use).
The mathematics can be wrong too, if it doesn't reflect the problem (even if you
can "solve it"). Getting that act right is something a lot of people (adults)
have trouble with.
If the (English) problem description is sloppy, it's harder for kids (and adults)
to produce maths that reflects the problem.
At an advanced level, part of this is done with model validation, but even that
has a problem with identifying missing details. It can become
philosophical
Post by Tomasso
at that point, or, peer review with reliable peers.
Kids need to develop some kind of intuitive version of those
"validation/review"
Post by Tomasso
practices.
Sadly, a lot of "problem solving" in education is about pasting words onto
recipe approaches.
Tomasso.
# What do we have here? Language (English) is descriptive; Mathematics is
enumerative; and Logic is connective.
A "problem" must be described, and its content analysed for number
content, which can only be located if the logic is coherent and clear.
So, kids must be taught how to think, and add up, and write a
description of conclusions they come to. It's up to teachers to pose a
problem in a logical manner, one which makes sense, or it is a case of
garbage in / garbage out.
Language, Maths, and Logic may be said to coincide somewhat in the
Equation. In Logic, we have Subject, copula, and Object, as in "All swans
are (=) white" (ignoring black swans, for the moment). In Language, we have
similar in any Definition. While in Maths, 2+2=4; or 70% of swans (white) +
30% of swans (black) = 100% swans. (whatever the true percentages are).
Logic is the prime factor in all thinking (unless completely
daydreaming), and while quality is necessary for descriptive purposes and
communication, quantity has its place too.
Ned Latham
2008-04-18 01:18:37 UTC
Don H wrote:

----snip----
Post by Don H
Back in my time at primary school (1930s-40s), maths had two aspects (a)
Processes, and (b) Problems. The former dealt with basic aspects such as
addition, subtraction, etc, while the latter was couched in literary
terms and involved problems in daily life.
----snip----
Post by Don H
I never had any trouble with either Processes or Problems. If literacy
I guess you missed the teacher's campaign in the 70's to reduce their
workload and responsibility ... er, sorry: reduce the stress on pupils.

I had a monumentally dismaying experience in 1975. I saw a spokesman
for the VPTA explain on TV why they shouldn't hurt kids' feelings by
correcting their vocabulary, grammar or spelling. What she said was
so shocking that it burnt itself into my memory: "As long as they
understand each other, that's all that matters".

They used to aim higher than that.
David Moss
2007-08-03 05:29:19 UTC
Post by Tomasso
OBs literacy: The "reading" involved in reading more complex problems is quite
different from what is normally meant by literacy (in the junior school sense).
It can be more like the "reading" involved in digesting a Shakespeare sonnet,
and take the same amount of time.
--
Oh Really?
Really. Maths is quite like poetry in that one symbol can represent a
concept that can fill a book of its own. An equation can represent
concepts that would fill a multi-volume encyclopedia. Yet we can learn
to deal with all these things using abstract symbols, ignoring the
underlying richness when we need to solve a practical problem, or
studying it in minute detail if that is where our interest lies.

When I first came to Australia at the age of 5 I was assessed by a
specialist teacher. This bloke presented me with some coloured rods,
which I had never encountered before, and asked me questions like "how
many red ones make a yellow one". I had no idea and gave him a glazed
look. Several other problems were presented in this fashion. The
assessor was all set to mark me down as intellectually impaired when my
mother said "David, whats three times nine?" I immediately replied "27".
The assessor was flabbergasted. "What? He knows his multiplication
tables already? exclaimed the assessor. "Of course", replied my mother,
bits of wood you would have known that right away".

Asking kids questions to determine their knowledge of maths is useless
if they don't comprehend the language of the question.

This might be frustrating for someone keen to get kids on the road to
numeracy, but literacy must come first if you use a problem approach.

There are many concepts you can teach in the meantime however. Just
don't try to use a language that is not familiar to your students unless
you are willing to teach that first.

DM
personal opinion only
Tomasso
2007-08-03 05:57:11 UTC
Post by David Moss
Post by Tomasso
OBs literacy: The "reading" involved in reading more complex problems is quite
different from what is normally meant by literacy (in the junior school sense).
It can be more like the "reading" involved in digesting a Shakespeare sonnet,
and take the same amount of time.
--
Oh Really?
Really. Maths is quite like poetry in that one symbol can represent a
concept that can fill a book of its own. An equation can represent
concepts that would fill a multi-volume encyclopedia. Yet we can learn
to deal with all these things using abstract symbols, ignoring the
underlying richness when we need to solve a practical problem, or
studying it in minute detail if that is where our interest lies.
When I first came to Australia at the age of 5 I was assessed by a
specialist teacher. This bloke presented me with some coloured rods,
which I had never encountered before, and asked me questions like "how
many red ones make a yellow one". I had no idea and gave him a glazed
look. Several other problems were presented in this fashion. The
assessor was all set to mark me down as intellectually impaired when my
mother said "David, whats three times nine?" I immediately replied "27".
The assessor was flabbergasted. "What? He knows his multiplication
tables already? exclaimed the assessor. "Of course", replied my mother,
bits of wood you would have known that right away".
Asking kids questions to determine their knowledge of maths is useless
if they don't comprehend the language of the question.
This might be frustrating for someone keen to get kids on the road to
numeracy, but literacy must come first if you use a problem approach.
There are many concepts you can teach in the meantime however. Just
don't try to use a language that is not familiar to your students unless
you are willing to teach that first.
DM
personal opinion only
Good story David. Should keep you off most watch lists for a while, unless
mathematical thinking gets demonised as part of some political ploy... :-).

The most woeful experience I can recall from primary school was a teacher in
third class instructing a class to construct a title page - some text or other
around a circle. There were several (maybe four) circles as guides for letter
boundaries, and then marking off various arcs with a compass (aka, a "pair of
compasses") as letter boundaries, and finally the curved parts of letters drawn
with compass, and straight edge to draw the straight parts. Letters had thickness,
which was to be coloured in later.

The instruction was verbal. The whole fucking class really messed up their attempts
and there was no example of a finished or partial title page. The "motivation"
(aka intention) was not made clear, and the teacher's waffling was about as
useful as a blind drunk trying to reverse park a truck up hill.

I kept my title page for a few years as a memory that if "you're told to do something
by an idiot, the outcome might well be idiotic".

Luckily we all survived and went on to fourth class the next year, while the teacher
was made to repeat year three. Or that's the way we chose to see it.

A bit of robustness in the face of bad teaching, is about as good as a bit of joy
at receiving some good teaching.

Tomasso.

PS: I don't mind Shakespeare sonnets when I have a few hours to reflect.
--
Oh Really?
Noddy
2008-04-15 03:37:08 UTC
test
Post by Tomasso
From ABC News (July 31, 2007)
A leading educational researcher has called for a major overhaul of maths
teaching in Australian schools.
Ken Rowe from the Australian Council for Educational Research (ACER) says
maths questions in both primary and high schools require students to have
a literacy level that is often beyond their skills.
He has outlined his concerns in a submission to the national numeracy review.
Mr Rowe says it is turning students off maths.
"For grade three students for example, they have to read the problem and
then translate it into an algorithm and solve it," he said.
"Now that requires in most cases a Grade Five level of literacy before
they can even engage with the Year Three mathematics.
"The problem is usually put, well Jane has 52 pieces of fruit, Alex has
24 pieces of fruit, how many pieces of fruit do they have?
"So in other words you've got to be able to read what the problem is
asking before you can actually do the mathematics."
I guess I agree with the sentiment, but not with the example. I've noticed that a
lot of exercises for primary school kids are sloppily worded. It's not that the
expression is complex or uses advanced vocabulary, it's that it is often
ambiguous and imprecise.
A couple of years ago I took some primary maths questions apart, and compared
what they appeared to say (ie, what a natural interpretion was) with what they
were actually asking for and what they problem details they were actually
providing. That is IMHO more of a problem for the kids than "read the problem
and then translate it into an algorithm and solve it".
Problem analysis is a special skill, but one well summarised by George Polya half a
1 Identify what you are asked to find out.
2 Identify what information you are told/given.
3 Identify what other information you need to use (assumptions, background knowledge).
4 Build a plan to use the information to determine what you are asked.
In practice, much of problem solving is an artform rather than a recipe (at least for
people who solve problems rather than talk about it). However, the problem analysis
is a necessary and fairly painstaking part. It's similar to gap analysis where you work
out what's present and what's missing (out of what's required). If a kid is determined
to address the first three points above the twenty or thirty words that are the "question",
in my experience they can get there, unless the person who wrote the question has
done the kid the injustice of writing badly.
If the raw material for the problem (exercise X in the textbook) is sloppily written,
it's not a problem with grammar or term, it's an impediment due to fuzziness.
At least when you deal with problems in the real world, you don't have to put up
with a poorly posed problem. You write the problem spec or requirements for
yourself. You know when you've finished that part of the work because it no
longer sounds sloppy.
Tomasso.
quite different from what is normally meant by literacy (in the junior
school sense). It can be more like the "reading" involved in digesting a
Shakespeare sonnet, and take the same amount of time.
--
Oh Really?
Tomasso
2008-04-16 11:52:47 UTC
Are you sure it was just a test?

Let x = y
=> x^2 = x.y
=> x^2 - y^2 = x.y - y^2
=> (x+y).(x-y) = y.(x-y)
=> x+y = y

Instantiating x = 1 we have 1+1 = 1.

T.
test
Post by Tomasso
From ABC News (July 31, 2007)
A leading educational researcher has called for a major overhaul of maths
teaching in Australian schools.
Ken Rowe from the Australian Council for Educational Research (ACER) says
maths questions in both primary and high schools require students to have
a literacy level that is often beyond their skills.
He has outlined his concerns in a submission to the national numeracy review.
Mr Rowe says it is turning students off maths.
"For grade three students for example, they have to read the problem and
then translate it into an algorithm and solve it," he said.
"Now that requires in most cases a Grade Five level of literacy before
they can even engage with the Year Three mathematics.
"The problem is usually put, well Jane has 52 pieces of fruit, Alex has
24 pieces of fruit, how many pieces of fruit do they have?
"So in other words you've got to be able to read what the problem is
asking before you can actually do the mathematics."
I guess I agree with the sentiment, but not with the example. I've noticed that a
lot of exercises for primary school kids are sloppily worded. It's not that the
expression is complex or uses advanced vocabulary, it's that it is often
ambiguous and imprecise.
A couple of years ago I took some primary maths questions apart, and compared
what they appeared to say (ie, what a natural interpretion was) with what they
were actually asking for and what they problem details they were actually
providing. That is IMHO more of a problem for the kids than "read the problem
and then translate it into an algorithm and solve it".
Problem analysis is a special skill, but one well summarised by George Polya half a
1 Identify what you are asked to find out.
2 Identify what information you are told/given.
3 Identify what other information you need to use (assumptions, background knowledge).
4 Build a plan to use the information to determine what you are asked.
In practice, much of problem solving is an artform rather than a recipe (at least for
people who solve problems rather than talk about it). However, the problem analysis
is a necessary and fairly painstaking part. It's similar to gap analysis where you work
out what's present and what's missing (out of what's required). If a kid is determined
to address the first three points above the twenty or thirty words that
are the "question",
in my experience they can get there, unless the person who wrote the question has
done the kid the injustice of writing badly.
If the raw material for the problem (exercise X in the textbook) is sloppily written,
it's not a problem with grammar or term, it's an impediment due to fuzziness.
At least when you deal with problems in the real world, you don't have to put up
with a poorly posed problem. You write the problem spec or requirements for
yourself. You know when you've finished that part of the work because it no
longer sounds sloppy.
Tomasso.
quite different from what is normally meant by literacy (in the junior
school sense). It can be more like the "reading" involved in digesting a
Shakespeare sonnet, and take the same amount of time.
--
Oh Really?
Phred
2008-04-16 13:28:59 UTC
Post by Tomasso
Are you sure it was just a test?
Let x = y
=> x^2 = x.y
=> x^2 - y^2 = x.y - y^2
=> (x+y).(x-y) = y.(x-y)
=> x+y = y
Instantiating x = 1 we have 1+1 = 1.
Reminds me of the time back in about 1950 when I was first introduced
to the concept x^2 = (-x)^2. That led me to show that any number
could be made equal to any other number. :-)

But your algebraic form got me wondering: "Where's the fallacy."

I assume it's when we get to this bit:

x^2 - y^2 = x.y - y^2

Given x = y, then the above becomes 0 = 0 and trying to factor zero is
absurd. (Well, that's my take on it anyway. 8-)

Cheers, Phred.
--
***@THISyahoo.com.INVALID
Barb Knox
2008-04-17 01:39:56 UTC
Post by Phred
Post by Tomasso
Are you sure it was just a test?
Let x = y
=> x^2 = x.y
=> x^2 - y^2 = x.y - y^2
=> (x+y).(x-y) = y.(x-y)
=> x+y = y
Instantiating x = 1 we have 1+1 = 1.
Reminds me of the time back in about 1950 when I was first introduced
to the concept x^2 = (-x)^2. That led me to show that any number
could be made equal to any other number. :-)
But your algebraic form got me wondering: "Where's the fallacy."
x^2 - y^2 = x.y - y^2
Given x = y, then the above becomes 0 = 0 and trying to factor zero is
absurd. (Well, that's my take on it anyway. 8-)
Having a 0 factor is fine, e.g.
(x+y).(x-y) = y.(x-y)

but *dividing* by 0 (here in the form of x-y) is not.
Post by Phred
Cheers, Phred.
--
---------------------------
| BBB b \ Barbara at LivingHistory stop co stop uk
| B B aa rrr b |
| BBB a a r bbb | Quidquid latine dictum sit,
| B B a a r b b | altum viditur.
| BBB aa a r bbb |
-----------------------------
Phred
2008-04-18 12:35:24 UTC
Post by Barb Knox
Post by Phred
Post by Tomasso
Are you sure it was just a test?
Let x = y
=> x^2 = x.y
=> x^2 - y^2 = x.y - y^2
=> (x+y).(x-y) = y.(x-y)
=> x+y = y
Instantiating x = 1 we have 1+1 = 1.
Reminds me of the time back in about 1950 when I was first introduced
to the concept x^2 = (-x)^2. That led me to show that any number
could be made equal to any other number. :-)
But your algebraic form got me wondering: "Where's the fallacy."
x^2 - y^2 = x.y - y^2
Given x = y, then the above becomes 0 = 0 and trying to factor zero is
absurd. (Well, that's my take on it anyway. 8-)
Having a 0 factor is fine, e.g.
(x+y).(x-y) = y.(x-y)
but *dividing* by 0 (here in the form of x-y) is not.
"Trying to factor zero" is not the same as "Having a 0 factor."
(But I agree that dividing by zero is not acceptable. :-)

My objection went back to the step before the bit you quoted:

x^2 - y^2 = x.y - y^2

which is 0 = 0 for the condition x = y.

Cheers, Phred.
--
***@THISyahoo.com.INVALID
Barb Knox
2008-04-18 21:11:41 UTC
Post by Phred
Post by Barb Knox
Post by Phred
Post by Tomasso
Are you sure it was just a test?
Let x = y
=> x^2 = x.y
=> x^2 - y^2 = x.y - y^2
=> (x+y).(x-y) = y.(x-y)
=> x+y = y
Instantiating x = 1 we have 1+1 = 1.
Reminds me of the time back in about 1950 when I was first introduced
to the concept x^2 = (-x)^2. That led me to show that any number
could be made equal to any other number. :-)
But your algebraic form got me wondering: "Where's the fallacy."
x^2 - y^2 = x.y - y^2
Given x = y, then the above becomes 0 = 0 and trying to factor zero is
absurd. (Well, that's my take on it anyway. 8-)
Having a 0 factor is fine, e.g.
(x+y).(x-y) = y.(x-y)
but *dividing* by 0 (here in the form of x-y) is not.
"Trying to factor zero" is not the same as "Having a 0 factor."
(But I agree that dividing by zero is not acceptable. :-)
x^2 - y^2 = x.y - y^2
which is 0 = 0 for the condition x = y.
What's wrong with that? 0 = 0 is true, after all.
Post by Phred
Cheers, Phred.
--
---------------------------
| BBB b \ Barbara at LivingHistory stop co stop uk
| B B aa rrr b |
| BBB a a r bbb | Quidquid latine dictum sit,
| B B a a r b b | altum viditur.
| BBB aa a r bbb |
-----------------------------
Phred
2008-04-19 09:24:31 UTC
Post by Barb Knox
Post by Phred
Post by Barb Knox
Post by Phred
Post by Tomasso
Are you sure it was just a test?
Let x = y
=> x^2 = x.y
=> x^2 - y^2 = x.y - y^2
=> (x+y).(x-y) = y.(x-y)
=> x+y = y
Instantiating x = 1 we have 1+1 = 1.
Reminds me of the time back in about 1950 when I was first introduced
to the concept x^2 = (-x)^2. That led me to show that any number
could be made equal to any other number. :-)
But your algebraic form got me wondering: "Where's the fallacy."
x^2 - y^2 = x.y - y^2
Given x = y, then the above becomes 0 = 0 and trying to factor zero is
absurd. (Well, that's my take on it anyway. 8-)
Having a 0 factor is fine, e.g.
(x+y).(x-y) = y.(x-y)
but *dividing* by 0 (here in the form of x-y) is not.
"Trying to factor zero" is not the same as "Having a 0 factor."
(But I agree that dividing by zero is not acceptable. :-)
x^2 - y^2 = x.y - y^2
which is 0 = 0 for the condition x = y.
What's wrong with that? 0 = 0 is true, after all.
True. :-) But I don't see how you can sensibly factor zero.

Cheers, Phred.
--
***@THISyahoo.com.INVALID
Barb Knox
2008-04-19 23:49:04 UTC
Post by Phred
Post by Barb Knox
Post by Phred
Post by Barb Knox
In article
Post by Tomasso
Are you sure it was just a test?
Let x = y
=> x^2 = x.y
=> x^2 - y^2 = x.y - y^2
=> (x+y).(x-y) = y.(x-y)
=> x+y = y
Instantiating x = 1 we have 1+1 = 1.
Reminds me of the time back in about 1950 when I was first introduced
to the concept x^2 = (-x)^2. That led me to show that any number
could be made equal to any other number. :-)
But your algebraic form got me wondering: "Where's the fallacy."
x^2 - y^2 = x.y - y^2
Given x = y, then the above becomes 0 = 0 and trying to factor zero is
absurd. (Well, that's my take on it anyway. 8-)
Having a 0 factor is fine, e.g.
(x+y).(x-y) = y.(x-y)
but *dividing* by 0 (here in the form of x-y) is not.
"Trying to factor zero" is not the same as "Having a 0 factor."
(But I agree that dividing by zero is not acceptable. :-)
x^2 - y^2 = x.y - y^2
which is 0 = 0 for the condition x = y.
What's wrong with that? 0 = 0 is true, after all.
True. :-) But I don't see how you can sensibly factor zero.
Why not? What's wrong with (e.g.) 0 = 0*42 ?

*Every* number is a factor of 0, n'est-ce pas?
Post by Phred
Cheers, Phred.
--
---------------------------
| BBB b \ Barbara at LivingHistory stop co stop uk
| B B aa rrr b |
| BBB a a r bbb | Quidquid latine dictum sit,
| B B a a r b b | altum viditur.
| BBB aa a r bbb |
-----------------------------
Phred
2008-04-20 09:14:38 UTC
Post by Barb Knox
Post by Phred
Post by Barb Knox
Post by Phred
Post by Barb Knox
In article
Post by Tomasso
Are you sure it was just a test?
Let x = y
=> x^2 = x.y
=> x^2 - y^2 = x.y - y^2
=> (x+y).(x-y) = y.(x-y)
=> x+y = y
Instantiating x = 1 we have 1+1 = 1.
Reminds me of the time back in about 1950 when I was first introduced
to the concept x^2 = (-x)^2. That led me to show that any number
could be made equal to any other number. :-)
But your algebraic form got me wondering: "Where's the fallacy."
x^2 - y^2 = x.y - y^2
Given x = y, then the above becomes 0 = 0 and trying to factor zero is
absurd. (Well, that's my take on it anyway. 8-)
Having a 0 factor is fine, e.g.
(x+y).(x-y) = y.(x-y)
but *dividing* by 0 (here in the form of x-y) is not.
"Trying to factor zero" is not the same as "Having a 0 factor."
(But I agree that dividing by zero is not acceptable. :-)
x^2 - y^2 = x.y - y^2
which is 0 = 0 for the condition x = y.
What's wrong with that? 0 = 0 is true, after all.
True. :-) But I don't see how you can sensibly factor zero.
Why not? What's wrong with (e.g.) 0 = 0*42 ?
*Every* number is a factor of 0, n'est-ce pas?
Exactly. There is no "solution" as such.

Cheers, Phred.
--
***@THISyahoo.com.INVALID
Barb Knox
2008-04-20 22:02:13 UTC
Post by Phred
Post by Barb Knox
Post by Phred
Post by Barb Knox
Post by Phred
Post by Barb Knox
In article
Post by Tomasso
Are you sure it was just a test?
Let x = y
=> x^2 = x.y
=> x^2 - y^2 = x.y - y^2
=> (x+y).(x-y) = y.(x-y)
=> x+y = y
Instantiating x = 1 we have 1+1 = 1.
Reminds me of the time back in about 1950 when I was first introduced
to the concept x^2 = (-x)^2. That led me to show that any number
could be made equal to any other number. :-)
But your algebraic form got me wondering: "Where's the fallacy."
x^2 - y^2 = x.y - y^2
Given x = y, then the above becomes 0 = 0 and trying to factor zero is
absurd. (Well, that's my take on it anyway. 8-)
Having a 0 factor is fine, e.g.
(x+y).(x-y) = y.(x-y)
but *dividing* by 0 (here in the form of x-y) is not.
"Trying to factor zero" is not the same as "Having a 0 factor."
(But I agree that dividing by zero is not acceptable. :-)
x^2 - y^2 = x.y - y^2
which is 0 = 0 for the condition x = y.
What's wrong with that? 0 = 0 is true, after all.
True. :-) But I don't see how you can sensibly factor zero.
Why not? What's wrong with (e.g.) 0 = 0*42 ?
*Every* number is a factor of 0, n'est-ce pas?
Exactly. There is no "solution" as such.
(1) There's a world of difference between "no solution" and "a whole
huge heap of solutions".

(2) *Every* real number has multiple factorisations:
1.23 = 12.3 * 0.1; 1.23 = .41 * 3; etc. etc.

(3) Natural numbers have multiple factorisations too:
42 = 6*7; 42 = 21*3; etc.

Face facts: the problem with the above "paradox" is exactly and only
that there is a division by 0, which is an undefined operation. Every
other step is perfectly fine, including the factorisation of x^2 - y^2
and of x*y - y^2.
Post by Phred
Cheers, Phred.
--
---------------------------
| BBB b \ Barbara at LivingHistory stop co stop uk
| B B aa rrr b |
| BBB a a r bbb | Quidquid latine dictum sit,
| B B a a r b b | altum viditur.
| BBB aa a r bbb |
-----------------------------
Phred
2008-04-21 10:31:26 UTC
Post by Barb Knox
Post by Phred
Post by Barb Knox
Post by Phred
Post by Barb Knox
Post by Phred
Post by Barb Knox
In article
Post by Tomasso
Are you sure it was just a test?
Let x = y
=> x^2 = x.y
=> x^2 - y^2 = x.y - y^2
=> (x+y).(x-y) = y.(x-y)
=> x+y = y
Instantiating x = 1 we have 1+1 = 1.
Reminds me of the time back in about 1950 when I was first introduced
to the concept x^2 = (-x)^2. That led me to show that any number
could be made equal to any other number. :-)
But your algebraic form got me wondering: "Where's the fallacy."
x^2 - y^2 = x.y - y^2
Given x = y, then the above becomes 0 = 0 and trying to factor zero is
absurd. (Well, that's my take on it anyway. 8-)
Having a 0 factor is fine, e.g.
(x+y).(x-y) = y.(x-y)
but *dividing* by 0 (here in the form of x-y) is not.
"Trying to factor zero" is not the same as "Having a 0 factor."
(But I agree that dividing by zero is not acceptable. :-)
x^2 - y^2 = x.y - y^2
which is 0 = 0 for the condition x = y.
What's wrong with that? 0 = 0 is true, after all.
True. :-) But I don't see how you can sensibly factor zero.
Why not? What's wrong with (e.g.) 0 = 0*42 ?
*Every* number is a factor of 0, n'est-ce pas?
Exactly. There is no "solution" as such.
(1) There's a world of difference between "no solution" and "a whole
huge heap of solutions".
I didn't say "no solution". If you had read carefully you would have
noted I said "no 'solution' ".
Post by Barb Knox
1.23 = 12.3 * 0.1; 1.23 = .41 * 3; etc. etc.
42 = 6*7; 42 = 21*3; etc.
Face facts: the problem with the above "paradox" is exactly and only
that there is a division by 0, which is an undefined operation. Every
Miss Murphy (was it?) told me the result of division by zero is
infinity. But that was >50 years ago. So, if Mr T is listening, I
would be interested to hear what he has to say about the modern
approach.
Post by Barb Knox
other step is perfectly fine, including the factorisation of x^2 - y^2
and of x*y - y^2.
Cheers, Phred.
--
***@THISyahoo.com.INVALID
Tomasso
2008-04-20 01:32:20 UTC
Post by Phred
...
"Trying to factor zero" is not the same as "Having a 0 factor."
(But I agree that dividing by zero is not acceptable. :-)
Why is "dividing by zero" not acceptable, in this case, Phred?

Is it a real reason?

Or is it that "everyone knows you can't divide by zero"?

Or "Miss Murphy told me in Grade 4, and I never forgot it"?

The fundamental reason (in this case) is about factors and a product of value zero.

A simple theorem like: B = C => A*B = A*C, but not A*B = A*C => B = C is the core.

T.
Phred
2008-04-20 09:30:59 UTC
Post by Tomasso
Post by Phred
...
"Trying to factor zero" is not the same as "Having a 0 factor."
(But I agree that dividing by zero is not acceptable. :-)
Why is "dividing by zero" not acceptable, in this case, Phred?
Because it's irrelevant.
Post by Tomasso
Is it a real reason?
Or is it that "everyone knows you can't divide by zero"?
Or "Miss Murphy told me in Grade 4, and I never forgot it"?
I can't remember if Miss Murphy taught me in Grade 4; but, if she had,
I'm sure she would have mentioned it. :-)
Post by Tomasso
The fundamental reason (in this case) is about factors and a product of value zero.
I think that's what I pointed out initially -- or maybe it was only in
response to Barb's first comment?
Post by Tomasso
A simple theorem like: B = C => A*B = A*C, but not A*B = A*C => B = C is the core.
Thank you.

Cheers, Phred.
--
***@THISyahoo.com.INVALID
2008-04-17 05:49:53 UTC
Post by Tomasso
Are you sure it was just a test?
Let x = y
=> x^2 = x.y
=> x^2 - y^2 = x.y - y^2
=> (x+y).(x-y) = y.(x-y)
=> x+y = y
Instantiating x = 1 we have 1+1 = 1.
T.
Naughty old Tom. Teasing the youngsters.

I like this one....

-2 = -2
4 - 6 = 1 - 3
4 - 6 + 9/4 = 1 - 3 + 9/4
(2 - 3/2)2 = (1 - 3/2)2
2 - 3/2 = 1 - 3/2
2 = 1

Marky.
Post by Tomasso
test
Post by Tomasso
From ABC News (July 31, 2007)
A leading educational researcher has called for a major overhaul of maths
teaching in Australian schools.
Ken Rowe from the Australian Council for Educational Research (ACER) says
maths questions in both primary and high schools require students to have
a literacy level that is often beyond their skills.
He has outlined his concerns in a submission to the national numeracy review.
Mr Rowe says it is turning students off maths.
"For grade three students for example, they have to read the problem and
then translate it into an algorithm and solve it," he said.
"Now that requires in most cases a Grade Five level of literacy before
they can even engage with the Year Three mathematics.
"The problem is usually put, well Jane has 52 pieces of fruit, Alex has
24 pieces of fruit, how many pieces of fruit do they have?
"So in other words you've got to be able to read what the problem is
asking before you can actually do the mathematics."
I guess I agree with the sentiment, but not with the example. I've noticed that a
lot of exercises for primary school kids are sloppily worded. It's not that the
expression is complex or uses advanced vocabulary, it's that it is often
ambiguous and imprecise.
A couple of years ago I took some primary maths questions apart, and compared
what they appeared to say (ie, what a natural interpretion was) with what they
were actually asking for and what they problem details they were actually
providing. That is IMHO more of a problem for the kids than "read the problem
and then translate it into an algorithm and solve it".
Problem analysis is a special skill, but one well summarised by George Polya half a
1 Identify what you are asked to find out.
2 Identify what information you are told/given.
3 Identify what other information you need to use (assumptions, background
knowledge).
4 Build a plan to use the information to determine what you are asked.
In practice, much of problem solving is an artform rather than a recipe (at least for
people who solve problems rather than talk about it). However, the problem analysis
is a necessary and fairly painstaking part. It's similar to gap analysis
where you work
out what's present and what's missing (out of what's required). If a kid
is determined
to address the first three points above the twenty or thirty words that
are the "question",
in my experience they can get there, unless the person who wrote the question has
done the kid the injustice of writing badly.
If the raw material for the problem (exercise X in the textbook) is sloppily written,
it's not a problem with grammar or term, it's an impediment due to fuzziness.
At least when you deal with problems in the real world, you don't have to put up
with a poorly posed problem. You write the problem spec or requirements for
yourself. You know when you've finished that part of the work because it no
longer sounds sloppy.
Tomasso.
quite different from what is normally meant by literacy (in the junior
school sense). It can be more like the "reading" involved in digesting a
Shakespeare sonnet, and take the same amount of time.
--
Oh Really?- Hide quoted text -
- Show quoted text -
Ned Latham
2008-04-18 01:28:51 UTC
----snip----
Post by Tomasso
Let x = y
=> x^2 = x.y
=> x^2 - y^2 = x.y - y^2
=> (x+y).(x-y) = y.(x-y)
Fallacy. Division by zero.
Post by Tomasso
=> x+y = y
Instantiating x = 1 we have 1+1 = 1.
Naughty old Tom. Teasing the youngsters.
I like this one....
-2 = -2
4 - 6 = 1 - 3
4 - 6 + 9/4 = 1 - 3 + 9/4
(2 - 3/2)2 = (1 - 3/2)2
False.
(2 - 3/2)/2 == +1/4
(1 - 3/2)/2 == -1/4
2 - 3/2 = 1 - 3/2
2 = 1
----snip----
2008-04-18 11:20:12 UTC
Post by Ned Latham
----snip----
Post by Tomasso
Let x = y
=> x^2 = x.y
=> x^2 - y^2 = x.y - y^2
=> (x+y).(x-y) = y.(x-y)
Fallacy. Division by zero.
Post by Tomasso
=> x+y = y
Instantiating x = 1 we have 1+1 = 1.
Naughty old Tom. Â Teasing the youngsters.
I like this one....
-2 = -2
4 - 6 = 1 - 3
4 - 6 + 9/4 = 1 - 3 + 9/4
(2 - 3/2)2 = (1 - 3/2)2
False.
(2 - 3/2)/2 == +1/4
(1 - 3/2)/2 == -1/4
2 - 3/2 = 1 - 3/2
2 = 1
Well done Noddy! How are ya BTW?
Slip an ABS in there and it gets a trifle less obvious!

Post by Ned Latham
----snip----
Ned Latham
2008-04-19 13:54:24 UTC
----snip----
Post by Ned Latham
I like this one....
-2 = -2
4 - 6 = 1 - 3
4 - 6 + 9/4 = 1 - 3 + 9/4
(2 - 3/2)2 = (1 - 3/2)2
False.
(2 - 3/2)/2 == +1/4
(1 - 3/2)/2 == -1/4
2 - 3/2 = 1 - 3/2
2 = 1
Well done Noddy! How are ya BTW?
Stayin' alive.

Been busy. Harrassed, even. But I'm now just a couple of months
short of retirement and things are easing up.

I'm doing a bit of development work at home these days, and for
separating jobs I create a user account for the employer. I can
then switch from job to job with CTL ALT F<whatever>. I've been
looking for a way to log those switches for timesheet purposes,
but can't find anything applicable. Got any ideas?
Slip an ABS in there and it gets a trifle less obvious!
Actually, I reckon that'd make it more, not less, obvious.
As it is, I had to do sums to see it.

What puzzles me is what steps you take to get from 4 - 6 + 9/4
to (2 - 3/2)2.

Ned
2008-04-19 14:21:28 UTC
Post by Ned Latham
----snip----
Post by Ned Latham
I like this one....
-2 = -2
4 - 6 = 1 - 3
4 - 6 + 9/4 = 1 - 3 + 9/4
(2 - 3/2)2 = (1 - 3/2)2
False.
(2 - 3/2)/2 == +1/4
(1 - 3/2)/2 == -1/4
2 - 3/2 = 1 - 3/2
2 = 1
Well done Noddy! How are ya BTW?
Stayin' alive.
Goodo.
Post by Ned Latham
Been busy. Harrassed, even. But I'm now just a couple of months
short of retirement and things are easing up.
Lucky bastard. I moved up to Cairns to have a rest and ended
up with more work than three men can do.....
Post by Ned Latham
I'm doing a bit of development work at home these days, and for
separating jobs I create a user account for the employer. I can
then switch from job to job with CTL ALT F<whatever>. I've been
looking for a way to log those switches for timesheet purposes,
but can't find anything applicable. Got any ideas?
Not really, and not in the Linux world. You could write a script,
./start < who am i
./stop < who am i

and shoot it into /var/log

I know a few lawyers that have a Widoze system that allows them
to bill by the minute.
Post by Ned Latham
Slip an ABS in there and it gets a trifle less obvious!
Actually, I reckon that'd make it more, not less, obvious.
As it is, I had to do sums to see it.
What puzzles me is what steps you take to get from 4 - 6 + 9/4
to (2 - 3/2)2.
It's a rounding fallacy. sticking it in an abs() would make it
moreso.

Later,
Mark.
Ned Latham
2008-04-20 02:37:42 UTC
----snip----
Post by Ned Latham
Been busy. Harrassed, even. But I'm now just a couple of months
short of retirement and things are easing up.
Lucky bastard. I moved up to Cairns to have a rest and ended
up with more work than three men can do.....
Mm. Yair. Too much is as bad as not enough.
Post by Ned Latham
I'm doing a bit of development work at home these days, and for
separating jobs I create a user account for the employer. I can
then switch from job to job with CTL ALT F<whatever>. I've been
looking for a way to log those switches for timesheet purposes,
but can't find anything applicable. Got any ideas?
Not really, and not in the Linux world. You could write a script,
./start < who am i
./stop < who am i
But I'd have to remember to execute them. Not reliable.

I have one machine dedicated to development work, and I'm permanently
logged on to my personal user account and any unfinished employer jobs
(I'm thinking of creating separate accounts for my personal projects
too, because I keep time for them as well). I hit CTL ALT F<whatever>
to start work, and CTL ALT F<something else> to finish. Nice and simple,
and with F7 to F12, I can have up to six jobs in the loop at any time.

(Yair, I know: it's a bit sooky using X, but I like having four
different source files visible at the same time. And with a single
mouse click, a different four, or a web browser.)
and shoot it into /var/log
I've been looking for a keystroke logger that I can rewrite to do
the timekeeping for me. I figure that if I can get a local-only
daemon to recognise the three-finger salute and log that with the
username (or alternatively, check every keystroke against the
previous one and log username changes), I'll have a reliable
record and updating timesheets will be simple and easy. And I
won't have to remember to do stuff.

Problem is, all I've found is xsniff, and I don't understand how it
works. (Well, yet: if there's no easier alternative, I guess I'll
just have to nut it out.)
I know a few lawyers that have a Widoze system that allows them
to bill by the minute.

----snip----

Ciao,

Ned
Ned Latham
2008-04-22 07:41:06 UTC
----snip----
Post by Ned Latham
Post by Ned Latham
I'm doing a bit of development work at home these days, and for
separating jobs I create a user account for the employer. I can
then switch from job to job with CTL ALT F<whatever>. I've been
looking for a way to log those switches for timesheet purposes,
but can't find anything applicable. Got any ideas?
Not really, and not in the Linux world. You could write a script,
./start < who am i
./stop < who am i
But I'd have to remember to execute them. Not reliable.
'Mazing how talking it through can help: I had a think about X 'cos
it *has* to know when the switches occur, and there in /var/log are
Xorg logfiles for each display. I couldn't find a way to make it
update them with time and username info, but each switch changes the
m_time of the logfile for the display reopened, so I have a solution.

----snip----
Tomasso
2008-04-18 12:07:25 UTC
Post by Ned Latham
----snip----
Post by Tomasso
Let x = y
=> x^2 = x.y
=> x^2 - y^2 = x.y - y^2
=> (x+y).(x-y) = y.(x-y)
Fallacy. Division by zero.
I wrote out a proof of why this is a fallacy, but without requiring division.

I expect it was too confusion for most readers, so didn't post it.

The proof is based on A = 0 /\ B = 0 <=> A*B = 0, which is easy to establish by cases (in the forward direction), and by

Also, I agree with Ned that a non-rigorous education is a largely waste of time. Babysitting, in fact. People can survive it, but it
is wrong nonetheless.

Luckily there are plenty of teachers who agree, and teach what they want to...

Potter's law of education: Bad students learn because of their education, but good students in spite of it.

T.
Ned Latham
2008-04-19 14:32:10 UTC
Post by Tomasso
Post by Ned Latham
----snip----
Post by Tomasso
Let x = y
=> x^2 = x.y
=> x^2 - y^2 = x.y - y^2
=> (x+y).(x-y) = y.(x-y)
Fallacy. Division by zero.
I wrote out a proof of why this is a fallacy, but without requiring division.
I expect it was too confusion for most readers, so didn't post it.
The proof is based on A = 0 /\ B = 0 <=> A*B = 0, which is easy to
establish by cases (in the forward direction), and by contradiction
for the converse.
Now you have me floundering. I presume <=> means equivalence, but if
so, there's no forward direction and no converse.

Given <=> means equivalence, /\ has to mean OR. What am I missing?
Post by Tomasso
Also, I agree with Ned that a non-rigorous education is largely a
waste of time. Babysitting, in fact.
I think it's worse than that: I think it alienates people from the
learning experience and sets them up to fail at life.

Inevitably, many students reach a stage when they can't cope with
the course. They are being *taught* to be failures, and no amount
of handholding or eqo-stroking can make up for that.
Post by Tomasso
People can survive it, but
it is wrong nonetheless.
Luckily there are plenty of teachers who agree, and teach what they want to...
Well, I see evidence that there are *some*, but "plenty"?

The NSW Teacher's Federation have recently been advertising for
public support for their campaign for "qualified" teachers.

The vision I get from that is diploma-shop time-servers.
Post by Tomasso
Potter's law of education: Bad students learn because of their
education, but good students in spite of it.
Wonder what (s)he means by "bad" and "good"?
Tomasso
2008-04-19 23:10:32 UTC
Post by Ned Latham
Post by Tomasso
Post by Ned Latham
----snip----
Post by Tomasso
Let x = y
=> x^2 = x.y
=> x^2 - y^2 = x.y - y^2
=> (x+y).(x-y) = y.(x-y)
Fallacy. Division by zero.
I wrote out a proof of why this is a fallacy, but without requiring division.
I expect it was too confusion for most readers, so didn't post it.
The proof is based on A = 0 /\ B = 0 <=> A*B = 0, which is easy to
establish by cases (in the forward direction), and by contradiction
for the converse.
Now you have me floundering. I presume <=> means equivalence, but if
so, there's no forward direction and no converse.
Given <=> means equivalence, /\ has to mean OR. What am I missing?
My typo. Sorry. Should have been: A = 0 \/ B = 0 <=> A*B = 0.

<=> means logically equivalent (ie, if and only if). \/ means OR.

The gist is that is one of the two factors is zero, there is no reasoning
to tell you about the other factor. [Deeper into this, is thinking about
multiple, distinct roots, which lies at the heart of very many problems].
Post by Ned Latham
Post by Tomasso
Also, I agree with Ned that a non-rigorous education is largely a
waste of time. Babysitting, in fact.
I think it's worse than that: I think it alienates people from the
learning experience and sets them up to fail at life.
Cafes, pubs, bush walks can be more useful.

Sadly, many workplaces are "learning averse", too.
Post by Ned Latham
Inevitably, many students reach a stage when they can't cope with
the course. They are being *taught* to be failures, and no amount
of handholding or eqo-stroking can make up for that.
Yerse. Keep succeeding up to the point of failure. Getting a PhD means
not failing and not getting rich (and often not pragmatic to catch a taxi)..

Bit like the Peter Principle. Inevitably taking students to a bad destination.
But if they catch the taxi and decide where to get off, there is hope. They
can get back on later if they like, or read a book.
Post by Ned Latham
Post by Tomasso
People can survive it, but
it is wrong nonetheless.
Luckily there are plenty of teachers who agree, and teach what they want to...
Well, I see evidence that there are *some*, but "plenty"?
I've met a fair few teachers recently who do this. One kid in year 9 and
one in year 7. Maybe I'm just coming across good ones by luck.

The administrators are either useless self-promotors, or inspirational
and very human. It would be worthwhile finding out how they ended
up like this (in both cases) in positions of influence and control, and
whether they started off similar to the way they are now.
Post by Ned Latham
The NSW Teacher's Federation have recently been advertising for
public support for their campaign for "qualified" teachers.
Reminds me of someone I knew who was reprimanded for being
"unprofessional". "Unprofessional" meant "not being loyal to a
colleague". And "not being loyal to a colleague" meant covering
up serious issues that should have been addressed (and ultimately
they were).

"Professional" and "qualified". Yes, I've watched Monty Python, too.
Post by Ned Latham
The vision I get from that is diploma-shop time-servers.
IMO, there are issues, but they are mainly about the curricula and
Post by Ned Latham
Post by Tomasso
Potter's law of education: Bad students learn because of their
education, but good students in spite of it.
Wonder what (s)he means by "bad" and "good"?
He. Professor Potter now. In his case, students would sometimes
come back years later to say, "it was a hard subject, but I'm still
using what I learnt then... ...not like much of the other stuff".

"Bad" student meant those whose learning had to be forced on them and
propped up. "Good" ones were natural learners and/or self-motivated.

Potter meant that it was more important to find ways to transform
the students to the latter kind (transform in the sense of guide, not
force), OR encourage them to do something else (where they'd be
happier, healthier and better off). Part of the modern problem is
that the bit after the OR is ignored.

Tomasso.
Ned Latham
2008-04-20 01:01:12 UTC
Post by Tomasso
Post by Ned Latham
Post by Tomasso
Post by Ned Latham
----snip----
Post by Tomasso
Let x = y
=> x^2 = x.y
=> x^2 - y^2 = x.y - y^2
=> (x+y).(x-y) = y.(x-y)
Fallacy. Division by zero.
I wrote out a proof of why this is a fallacy, but without requiring division.
I expect it was too confusion for most readers, so didn't post it.
The proof is based on A = 0 /\ B = 0 <=> A*B = 0, which is easy to
establish by cases (in the forward direction), and by contradiction
for the converse.
Now you have me floundering. I presume <=> means equivalence, but if
so, there's no forward direction and no converse.
Given <=> means equivalence, /\ has to mean OR. What am I missing?
My typo. Sorry. Should have been: A = 0 \/ B = 0 <=> A*B = 0.
<=> means logically equivalent (ie, if and only if). \/ means OR.
Ok. So I guessed that part correctly. Still left with no forward direction
and no converse.

Shouldn't it be A = 0 \/ B = 0 => A*B = 0?
Post by Tomasso
The gist is that is one of the two factors is zero, there is no reasoning
to tell you about the other factor.
Which is why I think =>, not <=>.
Post by Tomasso
[Deeper into this, is thinking about
multiple, distinct roots, which lies at the heart of very many problems].
Post by Ned Latham
Post by Tomasso
Also, I agree with Ned that a non-rigorous education is largely a
waste of time. Babysitting, in fact.
I think it's worse than that: I think it alienates people from the
learning experience and sets them up to fail at life.
Cafes, pubs, bush walks can be more useful.
A wide range of learning experiences in a wide range of environments?
That's what Cubs and Cadets and involving the kids in life activities
like working in the kitchen and the garage, and taking them fishing
and hunting, and sending them out to play, are about, right?

Oops. Using TV and computers as bebaysitters has put an end to that.
Post by Tomasso
Sadly, many workplaces are "learning averse", too.
Do what you're told and don't ask questions? Yair, I've seen a lot of
that. It's easy to blame it on lazy/incompetent management (or in the
spook world, "need to know"), but ISTM that in some cases its roots
lie in the worker's lack of "comprehension skills", and that that's
a legacy of their schooling.

----snip----
Post by Tomasso
Post by Ned Latham
Post by Tomasso
Luckily there are plenty of teachers who agree, and teach what they want to...
Well, I see evidence that there are *some*, but "plenty"?
I've met a fair few teachers recently who do this. One kid in year 9
and one in year 7. Maybe I'm just coming across good ones by luck.
The administrators are either useless self-promotors, or inspirational
and very human.
was a working teacher as well, and the school was administered by clerks
working under his direction.

"Management" is becoming something of a disease in modern society.
Post by Tomasso
It would be worthwhile finding out how they ended
up like this (in both cases) in positions of influence and control,
and whether they started off similar to the way they are now.
King oath. But those are psychological questions, and unless psychology
becomes a science, they won't be answered.
Post by Tomasso
Post by Ned Latham
The NSW Teacher's Federation have recently been advertising for
public support for their campaign for "qualified" teachers.
Reminds me of someone I knew who was reprimanded for being
"unprofessional". "Unprofessional" meant "not being loyal to a
colleague". And "not being loyal to a colleague" meant covering
up serious issues that should have been addressed (and ultimately
they were).
That's not uncommon. Except that the coverup often exacerbates the
harmful effects.
Post by Tomasso
"Professional" and "qualified". Yes, I've watched Monty Python, too.
Post by Ned Latham
The vision I get from that is diploma-shop time-servers.
IMO, there are issues, but they are mainly about the curricula
the union.
I agree in principle, but there's a lot of devil in the detail:
everyone I've encountered who was born after about 1970 has been
subliterate, and ISTM that's because their primary education was
inadequate. It's highly visible in the media, but its effects are
there to be seen in the education system too. The blind leading
the blind. Sloppily.

It doesn't stop the talented from being productive, but it does
keep others down. As I've said before, our mother tongue is the
most important research tool any of us will ever have: we need
a deep understanding of it, not just a working knowledge of
street talk.

As I see it, the insistence of "qualification" (by which I assume
a BE is meant) won't solve the problem: what's needed is rigourous
teaching by primary school teachers who are highly accomplished in
the teaching language: here in Oz, English.

(I see a side issue to that: English Grammar texts are faulty.)
Post by Tomasso
Post by Ned Latham
Post by Tomasso
Potter's law of education: Bad students learn because of their
education, but good students in spite of it.
Wonder what (s)he means by "bad" and "good"?
He. Professor Potter now. In his case, students would sometimes
come back years later to say, "it was a hard subject, but I'm still
using what I learnt then... ...not like much of the other stuff".
"Bad" student meant those whose learning had to be forced on them and
propped up. "Good" ones were natural learners and/or self-motivated.
Potter meant that it was more important to find ways to transform
the students to the latter kind (transform in the sense of guide, not
force), OR encourage them to do something else (where they'd be
happier, healthier and better off). Part of the modern problem is
that the bit after the OR is ignored.
LOL. The bit before it, too.
Tomasso
2008-04-20 01:50:36 UTC
Post by Ned Latham
Post by Tomasso
Post by Ned Latham
Post by Tomasso
Post by Ned Latham
----snip----
Post by Tomasso
Let x = y
=> x^2 = x.y
=> x^2 - y^2 = x.y - y^2
=> (x+y).(x-y) = y.(x-y)
Fallacy. Division by zero.
I wrote out a proof of why this is a fallacy, but without requiring division.
I expect it was too confusion for most readers, so didn't post it.
The proof is based on A = 0 /\ B = 0 <=> A*B = 0, which is easy to
establish by cases (in the forward direction), and by contradiction
for the converse.
Now you have me floundering. I presume <=> means equivalence, but if
so, there's no forward direction and no converse.
Given <=> means equivalence, /\ has to mean OR. What am I missing?
My typo. Sorry. Should have been: A = 0 \/ B = 0 <=> A*B = 0.
<=> means logically equivalent (ie, if and only if). \/ means OR.
Ok. So I guessed that part correctly. Still left with no forward direction
and no converse.
Shouldn't it be A = 0 \/ B = 0 => A*B = 0?
No. A = 0 \/ B = 0 <= A*B = 0 (or A*B = 0 => A=0 \/ B=0) is certainly true, too.

The missing part is that A*B=0 => B=0 is invalid.

[Counterexample, when A = 0, B = 1, fundamental definition of \/, that T \/ F = T. ].

This means we can't use A*B = A*C => B = C (whenever A = 0, or consequently A*B = 0).

In this problem, A = (x-y), B = (x+y), C = y.

Phred and others were thinking that if something was false, and they nominated a
reason for the falsity, then they must be right. That's another kind of fallacy!
Post by Ned Latham
Post by Tomasso
The gist is that is one of the two factors is zero, there is no reasoning
to tell you about the other factor.
Which is why I think =>, not <=>.
Post by Tomasso
[Deeper into this, is thinking about
multiple, distinct roots, which lies at the heart of very many problems].
Post by Ned Latham
Post by Tomasso
Also, I agree with Ned that a non-rigorous education is largely a
waste of time. Babysitting, in fact.
I think it's worse than that: I think it alienates people from the
learning experience and sets them up to fail at life.
Cafes, pubs, bush walks can be more useful.
A wide range of learning experiences in a wide range of environments?
That's what Cubs and Cadets and involving the kids in life activities
like working in the kitchen and the garage, and taking them fishing
and hunting, and sending them out to play, are about, right?
Yes. Books too. Holidays. Cubby houses. Etc.

Learning a musical instrument is also a good idea.
Post by Ned Latham
Oops. Using TV and computers as bebaysitters has put an end to that.
Yerse.
Post by Ned Latham
Post by Tomasso
Sadly, many workplaces are "learning averse", too.
Do what you're told and don't ask questions? Yair, I've seen a lot of
that. It's easy to blame it on lazy/incompetent management (or in the
spook world, "need to know"), but ISTM that in some cases its roots
lie in the worker's lack of "comprehension skills", and that that's
a legacy of their schooling.
Yerse. But someone hired them...
Post by Ned Latham
----snip----
Post by Tomasso
Post by Ned Latham
Post by Tomasso
Luckily there are plenty of teachers who agree, and teach what they want to...
Well, I see evidence that there are *some*, but "plenty"?
I've met a fair few teachers recently who do this. One kid in year 9
and one in year 7. Maybe I'm just coming across good ones by luck.
The administrators are either useless self-promotors, or inspirational
and very human.
was a working teacher as well, and the school was administered by clerks
working under his direction.
"Management" is becoming something of a disease in modern society.
It can be successful, given the right objectives and right people. Sometimes
the strategic plan (or whatever it gets called) is defective (solving heaps of
non-problems for administrators, but not giving any direction). Sometimes
the general directions aren't followed. Sometimes self-interest over-rides
the directions and what starts out seeking X ends up with Y. Good upper
management keeps an eye on this possibility..
Post by Ned Latham
Post by Tomasso
It would be worthwhile finding out how they ended
up like this (in both cases) in positions of influence and control,
and whether they started off similar to the way they are now.
King oath. But those are psychological questions, and unless psychology
becomes a science, they won't be answered.
Examples I've seen stemmed from nepotism and poor job descriptions.
Post by Ned Latham
Post by Tomasso
Post by Ned Latham
The NSW Teacher's Federation have recently been advertising for
public support for their campaign for "qualified" teachers.
Reminds me of someone I knew who was reprimanded for being
"unprofessional". "Unprofessional" meant "not being loyal to a
colleague". And "not being loyal to a colleague" meant covering
up serious issues that should have been addressed (and ultimately
they were).
That's not uncommon. Except that the coverup often exacerbates the
harmful effects.
Post by Tomasso
"Professional" and "qualified". Yes, I've watched Monty Python, too.
Post by Ned Latham
The vision I get from that is diploma-shop time-servers.
IMO, there are issues, but they are mainly about the curricula
the union.
everyone I've encountered who was born after about 1970 has been
subliterate, and ISTM that's because their primary education was
inadequate. It's highly visible in the media, but its effects are
there to be seen in the education system too. The blind leading
the blind. Sloppily.
Primary maths seems to be back on track (even taking ideas from
George Polya - "How to solve it", etc).
Post by Ned Latham
It doesn't stop the talented from being productive, but it does
keep others down. As I've said before, our mother tongue is the
most important research tool any of us will ever have: we need
a deep understanding of it, not just a working knowledge of
street talk.
As I see it, the insistence of "qualification" (by which I assume
a BE is meant) won't solve the problem: what's needed is rigourous
teaching by primary school teachers who are highly accomplished in
the teaching language: here in Oz, English.
(I see a side issue to that: English Grammar texts are faulty.)
I had a research student in the 90s who used a large English grammar
(ie, thousands of rules). More basic texts cover this well (Strunk and
White, Fowler, ..) and should be given free to all HS students (and all
teachers). It may not fix all the communication problems, but would
clean up a lot of the basics.

[BTW, the research student was a mature Lebanese, fluent in Arabic,
French, Italian and English].
Post by Ned Latham
Post by Tomasso
Post by Ned Latham
Post by Tomasso
Potter's law of education: Bad students learn because of their
education, but good students in spite of it.
Wonder what (s)he means by "bad" and "good"?
He. Professor Potter now. In his case, students would sometimes
come back years later to say, "it was a hard subject, but I'm still
using what I learnt then... ...not like much of the other stuff".
"Bad" student meant those whose learning had to be forced on them and
propped up. "Good" ones were natural learners and/or self-motivated.
Potter meant that it was more important to find ways to transform
the students to the latter kind (transform in the sense of guide, not
force), OR encourage them to do something else (where they'd be
happier, healthier and better off). Part of the modern problem is
that the bit after the OR is ignored.
LOL. The bit before it, too.
Cheese.
Ned Latham
2008-04-22 07:25:41 UTC
Post by Tomasso
Post by Ned Latham
Post by Tomasso
Post by Ned Latham
Post by Tomasso
Post by Ned Latham
----snip----
Post by Tomasso
Let x = y
=> x^2 = x.y
=> x^2 - y^2 = x.y - y^2
=> (x+y).(x-y) = y.(x-y)
Fallacy. Division by zero.
I wrote out a proof of why this is a fallacy, but without requiring
division.
I expect it was too confusion for most readers, so didn't post it.
The proof is based on A = 0 /\ B = 0 <=> A*B = 0, which is easy to
establish by cases (in the forward direction), and by contradiction
for the converse.
Now you have me floundering. I presume <=> means equivalence, but if
so, there's no forward direction and no converse.
Given <=> means equivalence, /\ has to mean OR. What am I missing?
My typo. Sorry. Should have been: A = 0 \/ B = 0 <=> A*B = 0.
<=> means logically equivalent (ie, if and only if). \/ means OR.
Ok. So I guessed that part correctly. Still left with no forward direction
and no converse.
And therefore no possibility of contradiction.
Post by Tomasso
Post by Ned Latham
Shouldn't it be A = 0 \/ B = 0 => A*B = 0?
No. A = 0 \/ B = 0 <= A*B = 0 (or A*B = 0 => A=0 \/ B=0) is certainly true, too.
Oops. My bad. Here I am talking OR and (when I wrote that) thinking AND.

Let me use C symbols for OR and AND:

A = 0 || B = 0 <=> A*B = 0 has no forward direction and no converse.

A = 0 && B = 0 <=> A*B = 0 is false because
A = 0 && B = 0 => A*B = 0 is true but A = 0 && B = 0 <= A*B = 0 is false.

----snip----
Post by Tomasso
Post by Ned Latham
Post by Tomasso
Sadly, many workplaces are "learning averse", too.
Do what you're told and don't ask questions? Yair, I've seen a lot of
that. It's easy to blame it on lazy/incompetent management (or in the
spook world, "need to know"), but ISTM that in some cases its roots
lie in the worker's lack of "comprehension skills", and that that's
a legacy of their schooling.
Yerse. But someone hired them...
Same problem with that someone? No better choice available?
Post by Tomasso
Post by Ned Latham
Post by Tomasso
The administrators are either useless self-promotors, or inspirational
and very human.
was a working teacher as well, and the school was administered by clerks
working under his direction.
"Management" is becoming something of a disease in modern society.
It can be successful, given the right objectives and right people.
Or a protected market. Or a monopoly. Or an oligopoly.

Or similarly incompetent competition.
Post by Tomasso
Sometimes the strategic plan (or whatever it gets called) is defective
(solving heaps of non-problems for administrators, but not giving
any direction). Sometimes the general directions aren't followed.
Sometimes self-interest over-rides the directions and what starts
out seeking X ends up with Y. Good upper management keeps an eye
on this possibility.
So *that's* why they get sqillion-dollar emoluments!
Post by Tomasso
Post by Ned Latham
Post by Tomasso
It would be worthwhile finding out how they ended
up like this (in both cases) in positions of influence and control,
and whether they started off similar to the way they are now.
King oath. But those are psychological questions, and unless psychology
becomes a science, they won't be answered.
Examples I've seen stemmed from nepotism and poor job descriptions.
And mendacious application followed by poor performance monitoring.
But those are about "ended up like this" in relation to "in positions
of influence and control": I was thinking about it in relation to
"useless self-promotors" vs "inspirational and very human".
Post by Tomasso
Post by Ned Latham
Post by Tomasso
Post by Ned Latham
The NSW Teacher's Federation have recently been advertising for
public support for their campaign for "qualified" teachers.
----snip----
Post by Tomasso
Post by Ned Latham
As I see it, the insistence of "qualification" (by which I assume
a BE is meant) won't solve the problem: what's needed is rigourous
teaching by primary school teachers who are highly accomplished in
the teaching language: here in Oz, English.
(I see a side issue to that: English Grammar texts are faulty.)
I had a research student in the 90s who used a large English grammar
(ie, thousands of rules). More basic texts cover this well (Strunk and
White, Fowler, ..)
IIRC, I've read a Fowler, and was unfavourably impressed. The ghost
of classicism is still present (especially in the discussions of the
so-called prepositon), and he got it wrong on spelling the plurals
of words ending in "o".
Post by Tomasso
and should be given free to all HS students (and all
teachers). It may not fix all the communication problems, but would
clean up a lot of the basics.
Mmm. Well, even a faulty grammar consistently applied would be better
than the present confusion.
Post by Tomasso
[BTW, the research student was a mature Lebanese, fluent in Arabic,
French, Italian and English].
O, the irony!

----snip----
Tomasso
2008-04-22 10:55:28 UTC
Post by Ned Latham
Post by Tomasso
Post by Ned Latham
Post by Tomasso
Post by Ned Latham
Post by Tomasso
Post by Ned Latham
----snip----
Post by Tomasso
Let x = y
=> x^2 = x.y
=> x^2 - y^2 = x.y - y^2
=> (x+y).(x-y) = y.(x-y)
Fallacy. Division by zero.
I wrote out a proof of why this is a fallacy, but without requiring
division.
I expect it was too confusion for most readers, so didn't post it.
The proof is based on A = 0 /\ B = 0 <=> A*B = 0, which is easy to
establish by cases (in the forward direction), and by contradiction
for the converse.
Now you have me floundering. I presume <=> means equivalence, but if
so, there's no forward direction and no converse.
Given <=> means equivalence, /\ has to mean OR. What am I missing?
My typo. Sorry. Should have been: A = 0 \/ B = 0 <=> A*B = 0.
<=> means logically equivalent (ie, if and only if). \/ means OR.
Ok. So I guessed that part correctly. Still left with no forward direction
and no converse.
And therefore no possibility of contradiction.
Post by Tomasso
Post by Ned Latham
Shouldn't it be A = 0 \/ B = 0 => A*B = 0?
No. A = 0 \/ B = 0 <= A*B = 0 (or A*B = 0 => A=0 \/ B=0) is certainly true, too.
Oops. My bad. Here I am talking OR and (when I wrote that) thinking AND.
A = 0 || B = 0 <=> A*B = 0 has no forward direction and no converse.
A = 0 && B = 0 <=> A*B = 0 is false because
A = 0 && B = 0 => A*B = 0 is true but A = 0 && B = 0 <= A*B = 0 is false.
----snip----
Post by Tomasso
Post by Ned Latham
Post by Tomasso
Sadly, many workplaces are "learning averse", too.
Do what you're told and don't ask questions? Yair, I've seen a lot of
that. It's easy to blame it on lazy/incompetent management (or in the
spook world, "need to know"), but ISTM that in some cases its roots
lie in the worker's lack of "comprehension skills", and that that's
a legacy of their schooling.
Yerse. But someone hired them...
Same problem with that someone? No better choice available?
Post by Tomasso
Post by Ned Latham
Post by Tomasso
The administrators are either useless self-promotors, or inspirational
and very human.
was a working teacher as well, and the school was administered by clerks
working under his direction.
"Management" is becoming something of a disease in modern society.
It can be successful, given the right objectives and right people.
Or a protected market. Or a monopoly. Or an oligopoly.
Or similarly incompetent competition.
Post by Tomasso
Sometimes the strategic plan (or whatever it gets called) is defective
(solving heaps of non-problems for administrators, but not giving
any direction). Sometimes the general directions aren't followed.
Sometimes self-interest over-rides the directions and what starts
out seeking X ends up with Y. Good upper management keeps an eye
on this possibility.
So *that's* why they get sqillion-dollar emoluments!
But they get paid when the stuff it too. Call it mates, maybe, to denigrate a
term with better meanings. NSW govt is trying to organise the same thing
for itself.
Post by Ned Latham
Post by Tomasso
Post by Ned Latham
Post by Tomasso
It would be worthwhile finding out how they ended
up like this (in both cases) in positions of influence and control,
and whether they started off similar to the way they are now.
King oath. But those are psychological questions, and unless psychology
becomes a science, they won't be answered.
Examples I've seen stemmed from nepotism and poor job descriptions.
And mendacious application followed by poor performance monitoring.
But those are about "ended up like this" in relation to "in positions
of influence and control": I was thinking about it in relation to
"useless self-promotors" vs "inspirational and very human".
Post by Tomasso
Post by Ned Latham
Post by Tomasso
Post by Ned Latham
The NSW Teacher's Federation have recently been advertising for
public support for their campaign for "qualified" teachers.
----snip----
Post by Tomasso
Post by Ned Latham
As I see it, the insistence of "qualification" (by which I assume
a BE is meant) won't solve the problem: what's needed is rigourous
teaching by primary school teachers who are highly accomplished in
the teaching language: here in Oz, English.
(I see a side issue to that: English Grammar texts are faulty.)
I had a research student in the 90s who used a large English grammar
(ie, thousands of rules). More basic texts cover this well (Strunk and
White, Fowler, ..)
IIRC, I've read a Fowler, and was unfavourably impressed. The ghost
of classicism is still present (especially in the discussions of the
so-called prepositon), and he got it wrong on spelling the plurals
of words ending in "o".
OK, agree. Needs a modern Fowler...
Post by Ned Latham
Post by Tomasso
and should be given free to all HS students (and all
teachers). It may not fix all the communication problems, but would
clean up a lot of the basics.
Mmm. Well, even a faulty grammar consistently applied would be better
than the present confusion.
Post by Tomasso
[BTW, the research student was a mature Lebanese, fluent in Arabic,
French, Italian and English].
O, the irony!
----snip----
Ned Latham
2008-04-18 00:58:08 UTC
Post by Tomasso
From ABC News (July 31, 2007)
A leading educational researcher has called for a major overhaul of
maths teaching in Australian schools.
Ken Rowe from the Australian Council for Educational Research (ACER)
says maths questions in both primary and high schools require students
to have a literacy level that is often beyond their skills.
He has outlined his concerns in a submission to the national numeracy review.
He should take them to the national literacy review.

----snip----
Post by Tomasso
I guess I agree with the sentiment, but not with the example.
The example could well be real. Teachers and students are *both*
subliterate.

No surprise there. Accomplishment was removed from primary school
curricula way back in 1975.

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