A related but less fundamental question is what are successful methods
to teach abstraction anyway?
------------------------------------
Bill Kerr said:-
> yang yin
Brian Harvey said:-
:These are useful ideas when applied as I believe they were originally
:intended: to call attention to opposing tendencies *within everyone*.
:But not to establish categories of "yang people" and "yin people,"
:and least of all to suggest that it's a desirable educational goal
:to leave a person entirely in one column.
What Papert and Turkle say is that some people prefer a Planner learning
style and others prefer a bricoleur or tinkerer learning style. This is
true in my experience even though I agree that all generalisations are
dangerous. I suppose I'm saying that this abstraction is useful ;-) from
my perspective, anyway. They also say that the canonical style for
teaching computer programming is that of the Planner. Bricoleurs exclude
themselves (from programming courses) because the dominant computing
culture does not make them welcome. They are forced into "not me" or
alienated relations with the way the teaching materials are presented to
them.
Brian:-
:Where am I in this categorization?
I think you correctly point out that just lists of dichotomies are
simplistic. I did qualify that in my original post as well. It is true
that there are opposing tendencies within everyone. But to just leave it
at that would be an unhelpful generalisation too. Clearly different people
lean more one way on certain characteristics and if this happens for a
cluster of characteristics on the lists then this would add up to a
different preferred learning style. Some may feel comfortable in either
learning style (Planner or Bricoleur) but for those who don't we need to
explore ways for them to learn without being alienated.
Bill:-
> opaque transparent
Brian:-
:If anything, I'd put these in the other order. Yin is about
:mysteries; yang about what-you-see-is-what-you-get.
There is quite a lengthy discussion on this point in the Epistemological
Pluralism (EP) paper. They refer to two women (Lisa and Robin) who are
doing the Harvard University introductory programming course. Lisa is a
poet and wants to manipulate the computer language the way she writes a
poem. She likes to "feel her way from one word to another", sculpting
the whole. She experiences language as transparent, she knows where
everything is at every point in the development of her poetry. She wants
her relationship to computer language to be similarly transparent. When
she builds large programs she prefers to write her own, smaller building
block procedures even though she could use prepackaged ones from a
program library. Her teachers chide her insisting that her demand for
transparency is making her work more difficult.....
Robin, a pianist, has a similar story about becoming alienated from the
Harvard programming course .... this is why I put opaque (or black
boxing) under yang and transparent under yin.
However, EP elaborates further supporting the point you make Brian and
also making a mockery of my shorthand lists ----->>>>
When dealing with programs made by others the situation is reversed. Now
the bricoleurs are happy to get to know an object by interacting with
it, learning about it through its behaviour the way you would learn
about a person. But the planners more analytical approach demands
knowing how the program works before interacting with it.
Bill:-
> mathematicican poet
> scientist artist
Brian:-
:This commonly held view is just plain wrong. Research says that
:virtually all great mathematicians report that they mentally see
:and feel the ideas they work with; later, they use formal systems
:to communicate those ideas to each other.
OK, point taken.
Bill:-
> (eg. object oriented programming is more like telling
>actors on the stage what to do, or shifting around the furniture in a
>room, than traditional structured programming).
Brian:-
:I don't understand this at all. OOP has been most enthusiastically
:endorsed by the people who manage teams of 500 mediocre programmers
:and want very rigid control over their method of work! They refer to
:it as a further extension of structured programming, not as a reversal.
Interesting, not being very up to date with programming trends, this is
news to me.
Brian:-
:(Now, you can use OOP in a different, more flexible way, too. That was
:the original Smalltalk vision of OOP. But if you're going to talk about
:contemporary trends in the real world, that's not one.)
A friend uses Smalltalk to prototype (until recently) and I think the
flexibility is what appeals to him. My original comments were, once
again, lifted from the EP paper. I think it is a substantial point
because there is an attempt in EP (and more recent writings by Papert)
to make the word "object" a focus word from a number of learning domains
(psychology, programming, learning theory). I see it as fairly central
to our current discussion.
If we have a substantial group of people (mainly women) whose preferred
thinking mode is bricolage and not planning then put bluntly there are
two choices:-
a) tell them they have to learn how to abstract and become more logical
for their own good, eg. if they want to learn computer programming.
b) find alternatives to abstraction and logic that work well
Papert I think is making concerted explorations to do (b). He is
exploring the idea of a diversity of ways in which the mind can think
with objects as a viable alternative to the rules of logic.
He has been using the slogan "objects to think with" for some time, eg.
turtle as computational object that makes the abstract concrete.
Clearly, in MicroWorlds (Papert's preferred Logo version) the "objects
to think with" multiply (turtles, sliders, buttons, textboxes, colours)
although the OOPs features are incomplete, unfortunately.
The word "object" comes in from a psychological perspective when Turkle
makes the connection with the object relations school of psychoanalysis
as a developmental process whereby objects (people and things) come to
live within us. This can be connected to Minsky's theory of how mind
works, although he calls them agents not objects.
In EP, Turkle and Papert, suggest that the growing popularity of icons
in computer interfaces might be part of a larger shift towards an
acceptance of concrete ways of thinking. They do say it is open to
different interpretations. In this context they talk about object
orientated programming: "In OOP the unit of thought is creating and
modifying interactive agents within a program for which the natural
metaphors are biological and social rather than algebraic. The elements
of the program interact as would actors on a stage....."
How does this relate to the point you make about the 500 mediocre
programmers being controlled by the big companies? These companies
surely would be selling OOPs short, I believe, acting through their
compulsion to control and keep a tight check on their workforce. I see
this as part of a general historical trend. Computing technology is not
the natural ally of the capitalist class at all. They limit and restrict
its development continually because of their obsession to control it.
In a more recent article (in the new international Maths Journal) Papert
takes his "objects" analysis a step further. He elaborates the thingness
principle, objects before operation. He then talks about "MicroChild
(which I haven't seen) a version of MicroWorlds made by A.Sopranov in
which Logo like instructions and even procedures are constructed by
putting "blocks" together like making a Lego house.... with a little
more development, ideas of function, composition of functions,
definition of functions, transformations of functions can become
perfectly natural to pre school children ... they would be accustomed to
thinking of functions as thing-like: you put them somewhere, you move
them from one place to another, you build with them, you give them
names." (101)
This approach to programming seems to be a growing trend and one that
opens doors for the Bricoleur to do things that previously would have
been very difficult for them (without learning to be better at logic).
An example I saw the other day was Visual Cafe (by Symantec?) which
enables the user to program all these cute web applets all by visual
connections and menu choices without having to write a single line of
code.
Brian:-
:That's not what (I think) we're arguing about; it's about whether the
:process of abstraction is harmful or valuable.
Papert and Turkle are saying that the process of abstraction is harmful
(alienating) for people like Lisa and Robin at the Harvard introductory
programming course. They are saying there are alternatives for those
with a bricolage style. They are not trying to force those who prefer
abstraction and logic to change their style but saying lets design
courses to include other learning styles not just the dominant one.
EP has influenced the way I teach. As introduction I like to use Barry
Newell's brilliant little book 'Turtle Confusion' because of all the
open ended tasks that can be completed in so many different ways. If
kids do spagetti code or "inefficient" code then more often than not
I'll let it go. I do have sessions (individual or group) where I show my
preferred way of doing it but if some or many chose not to follow that
then that's OK. I feel this approach actually works much better and that
I need a theoretical justification (mainly for myself but also others)
to do something which from a Planners viewpoint is just plain sloppy.
This is just one example but let me say this, though. I don't think that
I'm ever trying to teach abstraction by using abstraction (by your
definition). What I'm doing is either:-
a) teaching rules, eg. MTM=P, because I'm not aware of concrete ways to
get them across
b) trying to construct rich down to earth, concrete, constructionist
learning environments, eg. like Idit's fraction environment
(and I have seen kids spontaneously come up with abstract ideas when
immersed in these environments)
As a teacher I feel quite liberated by the idea that I don't have to
insist for *all* students that they must demonstrate the ability to
abstract *whatever* as an endpoint of their learning. And the bottom
line here is Papert / Turkle assertion that Bricolage is a different
style of work, not better not worse than the logic and abstraction of
the Planner.
Idit Harel in her Fractions study cites previous research that "found
that children did not understand the meaning or purpose of a super
procedure and rarely used superprocedures or subprocedures in their
programs unless they were very explicitly instructed to do so." Harel
found that "Debbie" did eventually use super and sub procedures without
pressure due to the much larger amount of programming time in her study
compared with previous studies. ie. when the procedures became too long
Debbie decided on her own to modularise them.
If Idit Harel's learning environment is a good example of how to teach
abstraction then my conclusion would be this. We teach abstraction by
designing constructionist, concrete learning environments. The only
alternative would be to give rules which you say is not abstraction but
just bad teaching.
Brian:-
:Galileo (and then Newton and Kepler) wanted to find commonalities in
:all these diverse physical events. Their big insight was that the
:stars and the feathers and so on are *all* obeying the *same* laws of
:physics, as they work out in different situations.
Newton's laws would be a useful abstraction by a masterly abstract
thinker. Today's question would be how can we explain Newton's laws
using computers to those who do not feel comfortable with abstract
thinking? Are there alternatives using objects to think with?
Brian:-
:Much the same is true in other areas too. Biology started out as
:enumerating species; then all that information was put to work to
:discover abstractions such as genetics. The geneticists needed to
:know and appreciate the specifics! But they also had to know and
:appreciate the abstractions.
Barbara McClintock (geneticist, Nobel laureate)is cited by feminist
critics of the standard notion of scientific objectivity as someone who
practised science essentially as a conversation with the materials.
Abstraction without detail is dogma. Perhaps she succeeded where others
failed because her preferred mode of thinking was concrete.
Bill:-
>Now a lot of mathematics as taught is schools is abstract, rule driven
>and impersonal. You need to memorise these things kids:-
>
>minus * minus = plus
>to divide by a fraction you invert and multiply
>to add fractions make a common denominator
>
>These are abstractions, fragile, almost meaningless single chains of
>learning. When they are made more concrete (like MTM=P has been on this
>list) then they become more meaningful, less abstract.
Brian:-
:This is really unfair, and it's why I keep talking about you using
:"abstraction" as a curse word. What you are describing is BAD TEACHING!
:Plain and simple bad teaching, the *same* kind of bad teaching that has
:kids memorize dates (concrete, specific dates) in history class. The
:process of abstraction, as carried out by mathematicians, is not in the
:least like "invert and multiply"!!! Those things are not abstractions
:at all; they are quasi-religious rituals chanted by people who find
:themselves teaching math but who don't understand any themselves.
How then can we teach abstraction, except by constructing very concrete,
constructionist self directed learning environments, eg. like Idit
Harel's fraction environment?
Brian (in reply to Jim Baker):-
:But what if the kid wants to invent a new, similar game? I claim that
:now the kid *needs* *abstraction*! If you just pick game elements to
:sort-of match elements of the games you know, the result will certainly
:be boringly derivative, and very likely will turn out unplayable.
:To make a good game, the would-be designer must come to understand
:ideas of the form "feature A and feature B go together, because either
:one alone would make the game unbalanced." (I'm being vague here
snip
The problem I have with this is that it seems to suggest that only
abstract thinkers are creative and that concrete thinkers (bricoleurs)
are not.
One point that EP makes is that Bricoleurs do construct theories but
that they do it in a different way from Planners. They do it by arranging and rearranging by negotiating and renegotiating with the materials at hand. There are some really
nice instances given where the Bricoleurs use materials in innovative
ways because they don't look at them logically.
One instance was Alex, working with LEGO, who used a wheel as a flat
shoe and a motor as a vibrator of that shoe. That's like a new game!
Another was Anne writing a Logo animation with birds. At one point she
wanted to hide the birds (different colours). Rather than do it
algebraically (by making and manipulating a list of variables) she did
it like a painter would, by creating a sky coloured screen and hiding the birds at the right
time behind the screen. That's creative!
I get the same sense from reading Hofstadter (eg. Variations on the
theme is the crux of creativity in Metamagical Themas) that creativity
is a concrete rather than an abstract process. Maybe its both.
----------------------------
I would urge those interested to read up on the Papert / Turkle article
on "Epistemological Pluralism" which made a huge impact on me when I
first read it 5 years ago (and still does). This article can be found in
either one of these sources:-
Signs: Journal of Women in Culture and Society 1990 vol. 16, no. 1
,or,
Constructionist Learning (edited by Idit Harel) 1990, from MIT
Bill Kerr
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