[From Bruce Gregory (2003.0511.1724)]
Marc Abrams (2003.05.11.1554)
>
>
> I am really not trying to bust chops or be difficult here but I am
> perplexed. Quantitative data = numbers. The use of numbers = mathematics.
> Mathematics is _not_ empirical according to your definition.
Frankly I have never met or read a mathematician who thought mathematics
was empirical.
> How does this
> square with your last sentence? What are you empirically testing with
> a`model that is represented by non-empirical data?
Huh? You test the model, not the mathematics. Say you test a large
number of people and the resulting scores are _not_ normally
distributed. This does not lead you conclude that there is something
wrong with the mathematics of normal distributions, but rather there is
something wrong with the model that predicted that the scores would be
normally distributed. No matter how the chess game turns out, nobody
says, "Well, that outcome disproved the rules of chess!" You can cheat,
but you can't play a legitimate game of chess without following the
rules. Mathematics are the rules.
>>otherwise, you are simply telling just-so stories.
>
> Am I hearing you say that if everyone tells the same just-so story,
that the
> story has worthless "data"?,
I am not sure what you are asking. What does the popularity of a just-so
story have to do the quality of the data? The data is the data. The
story is told about the data. In order for the story to be empirical,
the data must be able to conflict with it. The salient feature of
just-so stories are that they are fashioned to accommodate the data
whatever it may be.
Or say 95% of the people tell the same story?
> How are numbers gathered and interpreted to mean any differently then
words
> are? how do you know that the numbers you gathered do in fact
represent the
> variables they are replacing?
Numbers don't represent variables, variables represent numbers. Are you
asking me how do I know that the numbers recorded by a digital
thermometer represent the temperature? By using an independent measure
of the temperature and comparing it with the output of the thermometer.
(A process called calibration).
> Can you give me an example of a problem that might be useful in
generating
> PCT data, besides a tracking task?
It depends on what you mean by a tracking task. Is matching cards in a
suit a tracking task? Catching a fly-ball? Flying an airplane on
instruments? Driving a car in heavy traffic? Each of these has been or
could be a good way to collect data to model via PCT.
> Skills require understanding ( i.e prior knowledge ) whether they are
part
> of the model or not. If not part of the model and not connected in
some way
> to the model, then skills cannot be explained by the model.
Sorry, I don't follow you. How is flying a plane on instruments part of
the PCT model? To the extent understanding is verbal and many skills are
not, it is possible to be able to exercise a skill, e.g., riding a
bicycle without being able to explain how you do it. I daresay very few
people can explain how they ride a bicycle.
>>The closest that I have come to exploring understanding as a
>>skill is to ask students to explain their understanding. How such
>>explanations evolve over time remains unexplored territory.
>
> Not totally. I believe Argyris might have some data that might prove
useful.
That would be very nice.
···
--
Bruce Gregory lives with the poet and painter Gray Jacobik in the future
Canadian Province of New England.
www.joincanadanow.org