Hi everybody,
I think that we are talking about two related issues (at least): the
"theoretical/practical knowledge" and "direct instruction/guided discovery". I
agree with Gordon that:
"It is this interplay between theory and practice, involving different and
complementary modes of knowing, that is one of the key features of the
inquiry approach to classroom activities that I proposed [in earlier
messages]."
In fact I think that it is not always easy to make a distinction between
practical and theoretical knowledge. The theory "driving" practical knowledge
may not always be explicit, or universal, or "right" but it has to be there in
some form. What we call theoretical knowledge is always some abstraction from a
concrete situation. However, this abstraction may not always be generalized or
even generalizable. Theoretical knowledge can be incomplete even when "right".
By "incomplete" I mean that it may contain "holes" or missing links. For
instance you may know what is "square root", be able to give a right definition
of it and understand the concept and, yet, not be able to make a connection
between this knowledge and the actual set of procedures you were taught in
school to calculate a square root (without a calculator). Moreover, you also may
know when and why to apply this set of procedures (or use a calculator). So in
fact you have both the theoretical knowledge and the practical knowledge about
square roots but not necessarily a complete knowledge that thoroughly connects
the two.
The other issue is the teaching mode: direct instruction or guided discovery. I
think that they do not represent a dichotomy but two extremes in the social
distribution of the active part of the learning (thinking) process. Both of them
may be used for teaching both "theoretical" and "practical" knowledge. However,
depending on a concrete situation they will have different (not necessarily
better or worse) social and practical implications. Here is an anecdote from the
time I was in high school which brings together (at least for me) the
multidimensionality of the learning processes and teaching styles: Our class had
the so called "projective geometry" (I am not sure of the right term in English,
but this subject deals with learning to project a three dimensional object to
the three orthogonal planes of the three dimensional space and vice versa, to
draw a three dimensional object given the three projections). Our teacher taught
this subject as a set of rules or practical steps you had to do in a certain
order to get the right drawing. That went like that for about a year and a half.
Some students understood these rules (in a sense that they could "see" the
"theory" or reasons for these rules) and other students did not understand them
but were able to learn and apply them and still get a good grade. Our teacher
was very patient and nice and always helped anyone who needed help and would
repeat these rules as many times as we wanted. In other words, she was very
co-operative. In the middle of the second year she became ill and had to be
absent for about three months and we got a substitute. He was a young architect
who just graduated from the school of architecture. He was funny and much more
appealing to us as a person, but almost nobody understood a word of what he was
saying. There were just two students in the class who could follow his lectures.
He did not teach a set of practical steps or rules of how you draw a projection
of an object. He taught relationships in space! He was "talking" theory. And he
tried to let us discover the rules by bringing wire objects, paper screens and
lights into the classroom. The first reaction of most of the students and
especially of the all-"A" students was a total panic. He did not want you just
to draw a correct picture, he wanted you to know WHY this should be so? He would
bring his wire objects, lamps and strings to you and arrange them in some way
and ask questions or point out something. The only way you could answer was if
you were able to discover relationships between the three dimensional space and
a two dimensional projection.
I would call the teaching style of our first teacher: direct instruction and of
the second one, guided discovery. Moreover, our first teacher taught "practical
knowledge" - a set of steps that you have to do to get the correct result. Our
second teacher taught "theoretical knowledge" - what is three dimensional
space, how does it relate to the two dimensional space etc. The "set of rules"
to draw a correct drawing was something to be discovered, in fact they became
the result of the theoretical knowledge.
However, most of the students did not like, did not want and could not
understand the teaching of the second teacher. They were quite satisfied with
being given a direct instruction on what to do. They could manage the set of
prescribed steps even without understanding them. For them it meant that they
could get a good grade in an efficient and manageable way.
One can argue that they really did not get anything from this class (except a
good grade). With one teacher they got a lot of practical knowledge on
geometrical drawing without understanding it. With the other teacher they did
not get even that. Both teachers were cooperative, and tried in their own ways
to teach us.
Eugene Matusov wrote:
> "the findings seem to suggest teachers' using
> hands-on activities is a way (at least) to get away from their own lack of
> motivation and excitement about curriculum they have to teach.
>
Both of our teachers had some idea of what should be "hands-on" activities. But
their ideas were totally different. With the first teacher we got to do a lot of
"hands-on" drawing but no discovery, no thinking nor understanding. With the
second teacher we got a lot of "hands-on" concrete objects and their shadows. We
were given a chance to discover relations in space, but that chance was not a
chance for everyone, even though this teacher seemed really excited about the
subject and was very enthusiastic to make everyone really know. What he couldn't
do, however, was to motivate everyone to do the discovery.
I have often thought about this example. It was puzzling to me why did this
teaching method fail with so many students when according to our theory it
should work "better" because: it gives a chance to a student to be curious,
doesn't punish wrong answers, is based in the interactive and distributed
inquiry and is aimed at construction of concepts (theoretical knowledge) rather
than merely at a concrete practical set of rules which have to be followed
without understanding. Moreover - these so called "rules" of drawing, are in
fact a product of the theory of (three-dimensional) space. They are very
abstract and at the same time very concrete.
Any ideas?
Ana
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Hi everybody,
I think that we are talking about two related issues (at least): the "theoretical/practical knowledge" and "direct instruction/guided discovery". I agree with Gordon that:
The other issue is the teaching mode: direct instruction or guided discovery.
I think that they do not represent a dichotomy but two extremes in the
social distribution of the active part of the learning (thinking) process.
Both of them may be used for teaching both "theoretical" and "practical"
knowledge. However, depending on a concrete situation they will have different
(not necessarily better or worse) social and practical implications. Here
is an anecdote from the time I was in high school which brings together
(at least for me) the multidimensionality of the learning processes and
teaching styles: Our class had the so called "projective geometry" (I am
not sure of the right term in English, but this subject deals with learning
to project a three dimensional object to the three orthogonal planes of
the three dimensional space and vice versa, to draw a three dimensional
object given the three projections). Our teacher taught this subject as
a set of rules or practical steps you had to do in a certain order to get
the right drawing. That went like that for about a year and a half. Some
students understood these rules (in a sense that they could "see" the "theory"
or reasons for these rules) and other students did not understand them
but were able to learn and apply them and still get a good grade. Our teacher
was very patient and nice and always helped anyone who needed help and
would repeat these rules as many times as we wanted. In other words, she
was very co-operative. In the middle of the second year she became ill
and had to be absent for about three months and we got a substitute. He
was a young architect who just graduated from the school of architecture.
He was funny and much more appealing to us as a person, but almost nobody
understood a word of what he was saying. There were just two students in
the class who could follow his lectures. He did not teach a set of practical
steps or rules of how you draw a projection of an object. He taught relationships
in space! He was "talking" theory. And he tried to let us discover the
rules by bringing wire objects, paper screens and lights into the
classroom. The first reaction of most of the students and especially of
the all-"A" students was a total panic. He did not want you just to draw
a correct picture, he wanted you to know WHY this should be so? He would
bring his wire objects, lamps and strings to you and arrange them in some
way and ask questions or point out something. The only way you could answer
was if you were able to discover relationships between the three dimensional
space and a two dimensional projection.
I would call the teaching style of our first teacher: direct instruction
and of the second one, guided discovery. Moreover, our first teacher taught
"practical knowledge" - a set of steps that you have to do to get the correct
result. Our second teacher taught "theoretical knowledge" - what is
three dimensional space, how does it relate to the two dimensional space
etc. The "set of rules" to draw a correct drawing was something to be discovered,
in fact they became the result of the theoretical knowledge.
However, most of the students did not like, did not want and could
not understand the teaching of the second teacher. They were quite satisfied
with being given a direct instruction on what to do. They could manage
the set of prescribed steps even without understanding them. For them it
meant that they could get a good grade in an efficient and manageable way.
One can argue that they really did not get anything from this class
(except a good grade). With one teacher they got a lot of practical knowledge
on geometrical drawing without understanding it. With the other teacher
they did not get even that. Both teachers were cooperative, and tried in
their own ways to teach us.
Eugene Matusov wrote:
"the findings seem to suggest teachers' usingBoth of our teachers had some idea of what should be "hands-on" activities. But their ideas were totally different. With the first teacher we got to do a lot of "hands-on" drawing but no discovery, no thinking nor understanding. With the second teacher we got a lot of "hands-on" concrete objects and their shadows. We were given a chance to discover relations in space, but that chance was not a chance for everyone, even though this teacher seemed really excited about the subject and was very enthusiastic to make everyone really know. What he couldn't do, however, was to motivate everyone to do the discovery.
hands-on activities is a way (at least) to get away from their own lack of
motivation and excitement about curriculum they have to teach.
I have often thought about this example. It was puzzling to me why did this teaching method fail with so many students when according to our theory it should work "better" because: it gives a chance to a student to be curious, doesn't punish wrong answers, is based in the interactive and distributed inquiry and is aimed at construction of concepts (theoretical knowledge) rather than merely at a concrete practical set of rules which have to be followed without understanding. Moreover - these so called "rules" of drawing, are in fact a product of the theory of (three-dimensional) space. They are very abstract and at the same time very concrete.
Any ideas?
Ana
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