Mars 2005
Image
manipulating capabilities by students of secondary schools
By
Yacov Levi -qualified instructor for woodworking
“ The logical picture of the facts is the thought”
L.Wittgenstein 1919
Introduction
I’m a carpenter. My
professional life span stretches from 1937 till 1988, the year of my
retirement. More than thirty years ago I was recruited to teach children. My
lack of formal training in teaching led me to a unique instruction method. All
my observations were done during the period of 1973 – 1995 while teaching 7th
and 8th grades in a public school and a special education school
simultaneously. Total it involved 1200 children.
To my notice there was no
significant difference between those two groups of children at the initial
stage of instruction and working process. The big difference came in the
learning curve later. I was facing the question why both groups had a common
ground at the early stage. Was it because we didn’t occupy ourselves with subjects
of knowledge but with objects of reality? And that, in turn, brought up how we
see objects and how we describe them.
In each school I had a fully
equipped workshop, including small machinery. My method was to make students
decide for themselves what object to choose for a work project. That was
uncommon practice in the framework of a school, but was very effective in terms
of learning and helpful in creating a work-like discipline. All the common
disciplinary problems of the school evaporated. I had shifted the
responsibility for proper performance from the teacher to the students.
All that is written here concerns half of the school population.
When in the text the term
“students” is used, it refers to half of the pupils in each class.
Also, all written here needs verification by
systematic scientific inquiry, which I was not able to do.
In this article i have tried to describe one of the
main obstacles in the process of education of ordinary students in secondary
schools. Proper valuation of my findings, and then acting accordingly, could
improve the achievements of many ordinary students. There is an illusion that
the present school system fits the needs of the average pupil. I personally
doubt this, because 50 – 60 % of students demonstrate that their achievements
are less than average. In fact, it is common knowledge that with the transition
to a higher school class, the studying is going to be harder for most of the
students.
That is in sharp contrast to every other known
activity of men. It is a general rule that the performances in every field of
activity become easier and automated; the longer people occupy themselves with
a given activity. Why is school different in this respect then? Two reasons are
normally given: adolescence, and
the gradual increase in the difficulty of the learning subjects. It sounds
convincing. But I doubt it is the whole answer.
Definitions
It is very difficult to write in well-defined terms
about the representation of the seen world in one’s mind. Each school of
thought works with his own terms and concepts. There is no agreement how to
call the perceived ”picture” of the visual input. It can be picture, image,
imagination, presentation, and representation in English; Darstellung and
Vorstellung in German. Each term describes a station of the conscious visual
perception system. (beside fantasies, dreams, hallucinations rooted more in the
unconsciousness).
I incline to describe the phenomena I discuss here
with the German term “Vorstellung”. That is the nearest equivalent to the
English term “representation” The term Vorstellung was coined by the German
philosopher K.L. Reinhold (1758-1827), who tried to clarify the legacy of
Kant’s writing and making a distinction between the perception of the real and
the products of the mind itself. I use here the term “Image” as the nearest
equivalent to the German term, in spite of the many different uses of the term
“image” in psychological and technical professions.
Images of the mind can be of many types, I limit
myself to those, which originate in direct visual perception. Visual perception
is a very dynamic system, capable to give the mind orientation and basic for
motor activity. (J.J.Gibson 1961) Piaget made the basic inquiry how small
infants develop their notions of the constant and changing in the visual field.
(J.Piaget 1953) I found that those basic notions of constancy of amounts and
sizes, in spite changing images don’t prevail in more complex situations
presented to adolescents in my workshop.
Image manipulation versus
fronto-parallel view
The main problem
If
disciplinary problems disappeared, learning problems arose, especially in the
initial stage of “planning”. Those problems didn’t go away in the different
stages of the working process. It can be assumed that a child, introduced to
new environment, needs time to adjust to the unknown condition.
After a while, however, I found out that at this stage creating smooth
communication with each pupil had an inherent obstacle. Some children could not
convey to me their wishes by any verbal or pictorial tool. That sounds
strange. Of course they could say, “ I want to make a model airplane; I want to
sculpt a horse” and so on. But how does an airplane or a horse look? What are
the parts, and what are the proportions and the relations between the different
parts of small objects? They had no tools to “analyze” the images and
presentations of their mind. They could not give a proper description of the
desired object and its parts.
The children had before their eyes a huge collection of executable
objects, a collection of books with pages showing small wooden objects, some of
them as plain photographs, some of them as simple drawings. In addition, part
of the desired object has been seen elsewhere; the objects had to be
constructed using memory. But the contents of the children’s memory were poor
and insufficient for planning.
I found it necessary to initialize the work-process by asking the
students to make a sketch. Any sketch that could give information about the
students’ real intentions would do. I thought at the same time that the sketch
could prime technical thinking. The children refused to cooperate, however, totally and without exception.
Then I asked for a verbal description of their intentions (size.
material, form and color). That helped to synchronize their and my view of the
planning phase, choosing the appropriate material and so on. But there was
always a fundamental difference in our approaches. I had in mind to start with
the construction of the main body; they started with the front view. If the
front view of a small object was a door, the child wanted to start initial
stage of planning and choosing material for with the door. The next part of the
object they used to deal with was the back or the bottom part of the object.
This phenomenon, known in vision-science, as the
fronto-parallel view is the heart of this discussion. To be restricted to
perceive the world through this rigid lens puts severe limits to the process of
education. (J.Brunner 1965)
This problem of how to “see” or to plan an non-existing object was not
restricted to the initial planning phase of executing. Rather it repeated
itself in each stage of the working process. I will attempt to describe it in
detail.
PART ONE
How to make
a wooden box?
Two different modes of woodwork
To people not familiar with the proceedings of a workshop, who may find
my observations exaggerated, I will add in short another issue that may
emphasize my observations.
Creative work with wood can be done in two ways:
1. Reducing from a wooden block
(sculpting).
2.
Creating parts and assembling them to create a desired object.
I tried both ways and quickly found out that only a handful of students
are able to create an object by cutting away pieces of wood from a block. The
necessary imaginative tool is much more complicated in this approach. Nothing
can be done without sketching a view of the desired object on two faces of the
block, or, better, three: the front view, the side view, and the view from
above. Sculpted objects don’t have straight, linear boundaries; the boundaries
are curved. (Imaging an animal “trapped”
in a wooden block.) The children’s
frustration in trying to create super-simple sculptures was so prominent that I
discourage them from using this method. The only objects that could possibly be
executed satisfactorily were flat bowls or trays. (The chance of creating a
useable tray by chipping away the excess wood depends heavily on the quality of
the available wooden block and the intuition of the pupil to grasp the
direction of the grain of the wood.)
To simplify the results of my observation of
children I will give a description of the way a wooden box is made. Most small
wooden objects are boxes in disguise, such as wooden quadrilateral objects for
the use in a household, like small containers, shelves, tables etc. Next most
popular objects were crossbows, rifles, boomerangs and musical instruments,
like guitars and flutes, followed by rocking chairs and canoes.
The planning phase:
1.) I noticed that children could not properly
describe an object, and instead preferred to start the working process by
locating the door or the lid before considering construction of the box itself.
2.) Children had no idea how to use
numbers. No connections emerged between the math studied in the classroom and
the reality expressed in centimeters. This is a pity, but acceptable. Children
could never tell me what should be the desired size, say of a shelf, in terms
of centimeter; it was my task to question them and make decisions, such as what
width or length would be appropriate. Maybe practical training later in life
can correct this.
3.) It was a strange idea to all of my
students that one has to locate a wooden plank whose width corresponds to the
height or depth of the box. The students accepted it only after they were
instructed to mark two pairs of identical pieces representing the two opposite
sides of the box. Only after executing my instructions did the students
understand what I was speaking about.
(Fig.
0)
Measuring
Most children at this age can use the number system
and can calculate by multiplifying and dividing. They could not, however, do it
with more complex numbers that didn’t divide smoothly. To divide a number like
37.5 centimeter by two in order to find its middle point was always a problem
that required my help. If I suggested dividing it into two identical parts
without using a ruler they were perplexed. I demonstrated how to do it by
taking a string and folding it in two or three. That was something outside the
mathematical reason they learned, but they got the point quickly.
Then I found out that small number of children had a real problem. They
couldn’t measure a square; they never got the common notion, used almost unconsciously
by everyone, that we project onto our space and onto every object a lattice of
coordinates that meet in angles of 90degree. This practice is so obvious to
people growing up in a developed society, so common, that it does not need to
be explained, but a small portion of students who attended the classroom for
several years had not internalized this basic fact. It may be that their image system projected
three-dimensional views in a distorted perspective relationship. I don’t really
know whether such children need special training in order to synchronize their
image system with collective accepted system. Needless to say, such students
could not master mathematics even in its rudimentary form of counting as well
as basic mathematical operations.
The most extreme situation in this respect that I had experienced was
during a demonstration of how to draw a rectangle out on a big sheet of
plywood. I demonstrated how to measure two points from the edge of the sheet
and then draw a line through these two points. I was asked by one of my
students (age 10): “Why do I have to measure two points in the other direction
from the one I need to draw my line from?”
My easy answer: “If you do
as instructed, you always will get the desired result.” That is a practical
answer, but it didn’t answer his question at all about the nature of the
procedure. J.Brunner (1965) wrote
that a teacher has to be able to answer students’ questions in an
intellectually honest and correct way. In this case, I could not. It took me a long
time to figure out the answer, that is quoted as: We use Euclidean geometry
that projects onto our field of view a grid of parallel lines, and this grid
projects the lines into our eyes in a way that help us to orient ourselves and
behave accordingly. In the geometric theory, all those lines meet in angles of
90 degrees, even if we conceive them in a perspective view, which projects a
virtual reality with virtual lines on our retina and brain.
The ten-year-old boy, who posed the question probably, had a distorted
projection or different “philosophy” of visual perception. Proper measuring is
a problem for all students but can be learned to a certain degree without many
problems. Only students who learn well can obtain the degree of accuracy needed
for fitting complex or delicate structures.
The most annoying problem was always the construction of a right angle.
The problem has to be divided into two parts: grasping the importance of the
right angle and manually executing a right angle.
Executing a right angle
The core problem in woodwork is to overcome this obstacle. A pair of two
identical wooden parts constructs a box. If one of the 8 sides in the corner
deviate from 90 degree the box will be distorted.
I
found that all the work would be in vein if I had let the children cut the wood
by themselves. They never attained a right angle, or two identical pieces.
Machinery didn’t help much. The common solution – the teacher is doing the
actually cutting on a precise electrical saw bench. That was not my idea of a proper
work process, but was the only available solution.
Wood
is a comparatively flexible material. Applying pressure can repair small
deviation from the right angle. Three years I tried to force children to stick
to right angles. I tried to work with rigid plastic sheets (Perspex) instead of
plywood. If a box made of rigid plastic is not executed in right angles, the
sidepieces can’t be glued. This experiment was a complete failure. Children in
this age group could not bring themselves to cut and handle parts of the
objects in a proper right angle. I gave up and continued to work with wood.
But
that is not the end of the story. The next obstacle to make a box was much more
significant. This stage revealed something much more fundamental.
We
proceed from the second stage of preparing 4 sides of a box to the stage to
link those pieces to a simple frame. I will describe what happened in most of
the cases, where perfectly normal and fit children were involved. They prepared
those 4 pieces in an acceptable manner. They knew by their own experiences that
they prepared 2 identical pairs and got my OK to proceed by nailing the pieces
together. Simple? You wish.
3
new obstacles raised:
1.) In most cases after nailing three pieces the
nailing was not perfect and by turning the three pieces the under laying
structure was not identical with the length of the remaining piece. Or the
structure was too open or too close and the last pieces didn’t fit. The
reaction of all the children was a mixture of disbelief and riddle. They could
not understand what had happened. They forgot in most cases that they had a
moment ago identical pieces and couldn’t figure out what happened. (Figures
1-4) 
This is an exact repetition of
J. Piaget’s experiment with very small children. He could proof that
small children acquire by a natural trial and error process, without verbal
instruction, the notion, that the amount of liquid will not change, regardless
of its form or containing vessel.
This situation, as described here is a proof that was learned in early
childhood can’t be transferred to another situation. It proofs that even simple
notions like the ability to distinguish correctly between constant and changing
objects in visual representation have to be learned again during each stage of
children's growing process.
Directions of measuring
This
situation repeated itself over and over again and without my help, children
couldn’t continue. I remember vividly, a 16-year-old boy in this situation. His
4th piece was “too long”. He took a hammer and axed away the
protruding wood. That was an extreme reaction and it took me some time to
figure out why he did what he did. He wasn’t the aggressive type, but he came
from a social milieu where it is a custom to solve problems by using force. He
simply didn't know how else to react in problematic situations.
Proper
training of the image understanding would have prevented such situation. If
children’s image understanding is exposed to 2-D material only, as in a common
school, it is reduced to evaluate the front view only. No one of my students
had the ability while having 2 identical pair of wood to apply it to 3-D
situation.
2.)
The next obstacle is connected to a situation where the two identical pieces
nailed weren't exactly parallel. The box was twisted and to finish it became a
difficulty. The lid never closed tightly. But that was an unproblematic
situation; the result is just sloppy work. (Fig 5)
3.) What size of nails to use? Easy to solve by
telling the pupil take nails no. X. But that is not a proper teaching. How can
you formulate the answers in a way that will help the pupil to make his choice
in a similar but different situation?
Real life-situations are never schematically. One of
our means to handle them is to create a clear picture of its components in our
mind and figure out how to act. The success in any complex situation depends on
this ability. This ability can be trained. This discussion is devoted to
training 3-D situation in a real working process.
This
problem is connected to another activity of depicturing in a practical
situation.
Estimate.
No one is walking around with a measuring instrument
in his pocket. But proper estimating is a part of daily life. Each child learns
quickly to estimate distances as part of leaning to walk erect. Children learn
to estimate distances by play, mostly ball playing. School should concern
themselves with teaching students how to build connections between the natural
acquired abilities and estimating distances to estimate and handle abstract and
semi-abstract issues. Proper estimation as a task, concrete or abstract, has to
be formed in a proper medium of instruction. A proper estimation of effort and
means to execute a practical task or to execute an academic task is the first
step of a planning process. Proper planning is a visual and imagery process,
prior to abstract thinking processes, which are better to fill-in in the
different cells of content, like the structure and the content of an ”Excel”
worksheet. The list of failed task is endless, but without proper visual outlay
no task will be executed properly. Such visual outlays and schemata can be
acquired by simple procedural learning. The computer programs that assist such
planning are not more than a complex visual form, specializing in a certain
field of activity. They fill-in the vacuum created by the absence of ability to
organize and form a visual representation of what lay ahead.
Because
the ability to estimate is vital, we need tools to handle the reality where
exact data is absent. Von Bayer (1993) gives such a marvelous description of
how science works by telling how E.Fermi, the Italian physicist, took an
estimated account of the power of the first detonated Atomic device by using
nothing more than some pieces of confetti.
Cutting a straight line ,
cutting a circle.
Children
not always can use a handsaw properly. They have not enough control and power
to move their forearm in a straight line. To obtain movement in a straight line
we need to make so many adjustments in the movements of the different joints
and parts of the shoulder, the arm and the wrist that it can’t be expected from
children at this age. The easy solution – use an electrical jigsaw. The jigsaw
was the main instrument of woodcutting. But mechanical saws work in an opposite
manner of the arm and hand. They can cut in a straight line only. Every
deviation from the straight line results in a stalling of the blade.
To
overcome this obstacle it is necessary to plan the approach of using the saw
for all actions, that are not executed in a single straight line.
A
situation, that repeated itself was cutting a circle from a rectangular piece
of wood.
(Figure
6 - 7)
The
common approach is to make a short, straight cut from the edge of the plywood
to the circumference of the circle. But from there you can’t continue. It is
impossible to force the saw to make a 90-degree bend. The solution is easy if
people are trained properly to use their visual perception for executing the
task. To cut a circle is possible only by imagining a couple of tangenting
lines, which touch the circumference of the circle.(Fig 6-7) For children this
was one of the riddles of the working process.
If
students grasped the principle involved and learned to apply it in other
situation then something had been achieved. If students had the ability to
depict what they saw and remember to use this ability later, they learned an
important lesson. But, again, half of the students struggled with this
technique of imagining a correct action, not an easy task. (Fig 8-9)
Assembling
Not
all objects are so simple as a box, there are objects like shelves, a table, a
rocking chair that have parts to be joined properly. The first task is to
calculate overlapping, a common practice in carpentry but hard to depict.
Professional drawings include 3 elements:
Exact measure and size of each part;
The
cross section of each part;
The
overall measure of the whole object;
Only
an experienced carpenter can read such drawing, calculate the necessary
overlapping in the corners where the parts meet. But the exact process is done
thanks to personal knowledge acquired by the craftsmen.
So,
part of my work was to give detailed instruction.
In
cases of making simple boxes, what has to be calculated for obtaining the
desired measure is a simple reduction of the thickness of the wooden part from
the lengths of the joined part. Otherwise the thickness of the parts will add
length to the whole box. It could be expected from a student to master this simple
practical geometry. After some experience most students got the point, but not
always.
The
matter was more complicated if the “box” or a similar object was not a straight
square. I know that students could not calculate properly such objects measurements
and make a simple list of it for the required part. This part demanded time and
lengthy discussion imagining and analyzing the composed object.
But
the real obstacle was in the next phase of the task. The necessary wooden parts
were ready, joints were made, and all the parts were on the bench. How would
they fit together? My students couldn’t figure out how parts laying on the
bench could be assembled in the different directions of the view field; that
means in their proper place of the whole object. If it was necessary to make a
simple wooden joint and during the working process parts changed their location
it was a great effort to imagine how they would meet in a different direction.
This was a problem that could not be easily eliminated, because they had not
the necessary mental abilities to rotate and change the position of the parts
and assemble them in their mind as parts of the whole. In a school this lengthy
process of preparing all the parts of complex structure is interrupted by the
restricted time devoted to each lesson. Suddenly the lesson is over. The
results are that at the beginning of a new lesson the parts lay on the bench
and the whole process of arranging the parts in the right order and direction
for finding, what meets what and where, started from anew.
I can only stress again: it
does matter to obtain orientation in an existing environment and outlay. All
the research in orientation, in the way different people act according to their
personal mode of orientation, is done in labs in a preconstructed physical
outlay. I’m dealing with a situation of creating a new outlay, visually and
real, from different parts, each of them has each own dimension and they have
to fit together and create the desired (imagined) object.
Coordination of lines and
objects
Wooden parts, that don’t
meet at the right angle, complicate the matter and demand a higher degree of
depicting. If students learned to master how to adhere to the fact that a right
angle is necessary for a construction, they could go one step further. But not
always parts of an object meet at the right angles. So the degree of possible
complications rises again.
The joining process
To find the right angle in both joined pieces is not easy. The two adjoining pieces have not the
same (perspective) view in two possible situations. Laying flat on the bench in
random direction or joined in space on their proper location.
In each case you have to separate the joining pieces
and make the necessary angle on each of the two pieces in a separate working
process. The matter became even more complicated if it was necessary to use
machinery, like a sandpaper machine. This situation repeated itself over and
over again. If the desired angle was only a light deviation from 90-degree
students could do it. But they could not achieve a steeper angle, because they
could not make the necessary adjustment between three different directions of
action:
-The fixed working direction of the machine.
-The adjusting of their arms and hands to the
desired angle.
-The direction of viewing the angle, that changes
instantly from the frontal view to another view-direction by the necessity to
hold the work piece in not a frontal-view direction. The steeper the angle the greater the difficulty to execute a given
task properly. During many years of practice I didn’t find a student that
could properly sharpen a wooden stick on a sandpaper machine.
The
fact students had difficulties to handle properly 3-D real objects and to
create simple objects that have to be assembled from some parts in a
hierarchical character has some significance. First of all it is the overall
inability to imagine correctly a simple object, then the problem, that an
object is grasped properly if it can be imagined from several advantage-
points, not only from the front view. To create pivot points for mental
operation, to set a starting point for motor execution; lines and directions;
coordination of direction, directions of the object; directions of coordinating
hand, object and tool, and uneasy part to know the effects of proper applying
of force and timing.
Part two
Correlation
between imagining and learning
I’m not qualified to make statements about brain
functions and the learning process. Sot I will give only a crude sketch of the
results of my observations.
I can say without
restrictions there is a correlation between the abilities of students to
describe correctly the objects in their mind, to manipulate the parts in the
different stages of the working process, and their performance in the
classroom, not only in mathematics but in other subjects as well.
This correlation between classroom performance and workshop activity is the topic of many contemporary research – “Acquisition of Intellectual and perceptual-motor skills” (D.A.Rosenblum; R.A.Careson & R.O.Gilmore 2001) – It is agreed upon that they are acquired in similar ways Not be able to handle the contents of the mind in a dynamically mode is the main obstacle for advancement in High-school learning. Rote learning has its merit too, but as principle tool in education it hamper high-level abstractions.
Without having any specially knowledge in psychology I was always able to give other teachers correct information about what a particular student can learn or not. Those correlations existed even in students whose measured IQ was above the norm, but who had learning problems nevertheless. It is common knowledge that a part of gifted children has tendency to unequal distribution of their capabilities.
I learned to manipulate the failure of students for
my purposes (be able to divide my attention between the students.) I had always
the strange feeling to have a look into the working process of somebody other’s
mind.
I can’t claim that I was teaching students in the
manner it is expected in school. I certainly didn’t add any vital knowledge,
but adding knowledge without creating a support structure to use it is
inexpedient and complete impossible for certain kinds of students. That is the
opinion of G.Furth and G.Wachs (Furth&Wachs 1971). On page 12 they write,
”The learning aspect is subordinated in importance and emphasis to the thinking
aspect, the primary reason for all activity”. Thinking is done in abstract and
individual way. So they add 2 levels of abstraction: (ibid p.16)
-Low-level abstractions derived from objects
-High-level abstractions derived from actions
And
on p.20: “Intellectually challenging opportunities for children in primary
school invariably require action-orientated activities in physical and concrete
thinking”.
My
conclusions, found by observation of children’s action, are identical to their
findings. I will describe how objects are handle by 12 – 15 year olds in a
faulty way for lack of internal imagination. Those faults are primary in
structure and very important for handling abstract contents. What really is
important is the ability to handle those objects in a dynamic and effortless
way. To acquire this ability is the most important phase for students, who are
not inclined by habit or inborn constitution to read a lot by themselves and
acquire abstract contents and subjects as natural function of their mind.
Low-level abstractions are fundamental in themselves and prior to
high-level abstraction. But the core and the essentials of my teaching was not
to create wooden objects, or to recognize the underlying structures of geometry
and perspective, but to open a window to higher level of mental activity by
assisting children to act intelligently even in a simple concrete situation.
The
behavior of students with learning difficulties, who had no access and
experience in high-level abstraction, can be strange. They were always eager to
act, to do something. But in this age they were depended totally on
step-to-step instruction as consequence of their school experience. They all
were very good in dismantling. Because they were unable to create a structure
from parts, so they went the opposite way. One extreme case is vividly in my
mind. A small group of boys dismantled an abandoned and hidden from sight
tractor into its parts, to the last screw! Not a small endeavor. In another
case a 12-year-old boy got the electrical parts for his wooden lamp that he had
made. He didn’t know what to do with them exactly, so he dismantled it and even
the wire he stripped to each layer.
Educational consideration
Children depend for their development on this basic
mental system, to perceive and react, that may be a genetically and biological
one developed during the rise of the human species. Children relay heavily on
their visual input, and learn with little outside help to react quickly and
efficiently. To get perfection in this realm is their main occupation in
childhood and sometime it is connected to visual fantasies and other contents
of their mentality. But they don’t acquire knowledge by their own and so they
go to school. They start studying verbal functions, reading, writing, grammar,
language, meanings and syntax etc. They acquire knowledge in many fields,
especially in the realm of social sciences.
Only a part of the students can express and
formulate their thoughts properly after 12 years of study. The knowledge they
acquire in school is not properly organized. Each piece of knowledge and
information is stored on its own. The
relations and connections created by the innumerable bits of knowledge are
weak. Relations and connections have a strong spatial content. Those structures
have to be learned and assimilated too.
Knowledge
is superficial and unusable without structure. Verbal training can’t do this
easily because of its 2-Dimentional character. This quasi-visual thinking has
to be learned in its proper realm, in a surrounding that trains manipulation of
3-D objects for a start and then uses this base as a foundation to handle
knowledge in general. Part of students need special training to create a
biofeedback system for handling knowledge in its proper structure. It’s like we
have many books but no catalog to access their content. The associations of
such students are ruled by “sound bites”. (Ask a regular student, what subject
he learned in the former school year?) He will not give an answer instantly.
The first stage is achieved by proper depicting of the outer world
through the visual system. The second stage is achieved by manipulating the
seen objects in the mind. The third stage is the discarding of the visual
crutches and handling knowledge instantaneously, automatically. In other words:
obtain control and mastery. Every field of knowledge is acquired. By this
mechanism, from simple automated motored performances to mastering the
specifics of a profession.
Proper
use of one’s knowledge depends on creating a process of thinking that is
overextending the basic biological functions like seeing, orientating, catching
and aiming. Executing simple manual tasks may be the border area between the
biologic-genetic apparatus of man and higher learning. The basic principles of
such an instruction system are not formulated yet. There exists a gap between
all learning theories and their proper application.
The attempt of our educational system to teach mathematics with the help
of concrete elements (a box containing wooden units in different color) was
abandoned. A number can’t be both, abstract and real in the same time. Each
man, even uneducated, can act in a 3-dimensional reality, that is part of his
biology, but the proper understanding of dimension is no more than 400 years
old.
Practical considerations
The
thinking process of man is not restricted to substances that can be or have to
be depicted in his own mind. But certain actions depend on the ability to
predict and to plan movements for meeting vital needs. All body movements, even
if they are fully automated, need time and control by a mental apparatus
including in his core a phase of estimation of direction and targeting. (Fitts
and Posner 1967). Between the perception of a sign and responding to it, is a
time delay that varies from man to man. Proper execution of a motor movement
contains a phase of coordination that is done with the help of short term
imaginary and control system. (Pribram, Gallacher, Miller 1970) The important
point for me was proper execution of motor movements including a short phase of
imaginary. If the individual was sure of his movements, this phase was
shortened, if he was unsure this interim phase was longer.
The
fact that imagination plays a role in executing and controlling movement can be
confirmed by the fact that an imaginary movement of a body part and the real
movement need the same time for execution. The brain mechanism for real
movement and imaginary movement uses the same nerve pathways. The execution of
real movements and imaginary movements requires the same time span.
This
primary system of movement is the main instrument for children to meet the
world. Most of them, without a source of stimulating other, higher mentally
needs, will train their bodily function through an almost endless play. Because
schools are instruments of educations, the development of movement-depended
function plays a secondary role. This sounds convincing and is common
knowledge. The disregard of child’s basic developments/needs has a price, paid
by child and dysfunctional school. Schools are, in principle, vehicle for 2-D
presentations to the mind through flat surfaces.(Books, blackboards and
copybooks and paper.) Body movements of all kinds are executed by a mechanism
that needs the elaborating 3-D visual input. The only instrument that we have
to refine, and to control this coordination between eye and body is the hand. The hand is the tool for training and,
possibly, enlarging the eye’s visual capabilities.
I found, without any reservation, that for the main body of students,
learning is possible only by a gradual passage from a mental process based on
real, depictable objects to abstract thought. It is not the depictable object,
that is important, but the ability to manipulate it mentally. The moment this
stage of mental development is achieved, the image and the imagining process
can be forgotten, but the manipulating abilities remain.
I
repeat this in another way. The content of our mental system is divided between
depicting contents, real objects and pictures, (Wittengenstein 1922 pp 30-43)
and verbal contents that can be grasped and understood with the help of other
simpler words. These notions have a life of their own, they change their
meaning and have to be explained and adjusted all the time.
We have a way as humans to deepen our understanding by using images and
words, and sounds in a way that converge in our mind and are able to create a
virtual world beside the real world.
In
this context I relate to the realm of
mental imagination as the part of the mind where everything is converging and
everything is elaborated before responses are created. This is true for
motor action too. For many children intelligent and creative motor action is
the first step to achieve more than instrumental, formal education.
Human
movements can’t be executed in a simple straight movement. We move with limbs
that are attached to the body and can move only in a circular way. Straight
movements are executed by coordination of series of calibrated circular
movements. (Pribram, Gallagher, Miller 1970) (Legge&Barber 1976), which
originate in a coordination between eye (seeing the target), the brain
(imagining and controlling) and the hands (executing).
It
is not in the realm of this article to go into the details of this basic
biological system. I will tell only what I found through observing my students,
especially those who had not a smooth executing system.
I
found that the coordination system needs adjustment for quite a big part of
children. The only way to refine motor eye-hand coordination is through guided
training. What is overlooked is the
fact, that the only tool to train the eye, to give reality, control and
feedback to mind's image system is the hand. The other way to obtain the same
goal is to perform with closed eyes, to train executions of bodily functions by
imagining them. These two contradicting modes can complement each other.
It
is not enough to see to enable intelligent execution. If the eye is not trained
in manipulating real 3-D objects, its ability to do so will shrink and the
depicting of the real world will be restricted to see a virtual 3-D world,
which is in fact a 2-D world. In this virtual world everybody can move
passively. This virtual electronic world is now ubiquitous. It did the brain
one important service. It trained the brain to grasp images incoming in very
quick intervals. That is the main difference in the perceptions abilities
between the older generation and the younger one.
For
those reasons I got the impression that half
of my very normal students had a kind of regression
that restricted the visual input and they could process to its frontal view
input only. Every line that appears on the retina in an angle, as required by
perspective perception, is seen but they could not make any mental operation
with it. (Estimate, rotate and bring them into their final position, if some
imagination or action was required) The steeper the angle was to the frontal
view, the bigger was the difficulty to act accordingly.
Memory training
Without
describing the basic working system of short and permanent memory (A.Lurie
1953) I will point to the fact that all methods of memory improvements use the
existing imagining system as a basic tool for attaining this goal. The
imagining system is able to create a bond between abstract words and ideas and
the virtual world, as seen by the eye and depicted by the brain. In other
words: A good functioning imagining system is important for remembering, for
learning. The method to achieve this will be discussed later.
Can 3-D imagination be acquired by learning?
My
answer is yes. The common notion is:
1)
Everyone learns to see by himself by a natural biological conditioned way.
2) Handling reality images has nothing to do with advanced education,
but in some cases an occupation required a higher level of observance and
analysis qualities. Artist of all kinds need such awareness in the visual realm
just as poets and writers need it in their verbal realm.
These
notions are partly true if students have natural abilities to learn in a
abstract 2-D mode. Or to put it another way, a portion of children has a mental
system that responds to teaching as practiced everywhere. This generates the
illusion, that there are good students and not bad students. Today everyone has
to be educated in a way, that in earlier centuries was the privilege of a part
of the general population only. The ratio of 50 % of students, that have a
problem with acquiring advanced education, is a constant, which appears in many
publications on education. People have two perceptive mental modes; one
inclined to hearing and verbal priorities, the other one inclined to seeing and
bodily executions.
3-D imagination can be acquired by all kinds of art
education and guided usage of images.
Arts use imagination and motor action simultaneously. Today there is no
direct connection between arts and general teaching and how it can serve the
requirements of the curriculum. This is not only a matter of research; it
requires a change in the general attitude and relation to this subject. It is
assumed and taken for granted that arts are a desirable supplement to the
school curriculum. Arts, properly
incorporated into the learning process can be the base to learn abstract and
verbal subjects. It can serve this purpose if the proper taxonomy of its
contents will be known. The
emphasis has to be on 3-D media, but not exclusively. It is obvious that you
can teach exact science satisfactory only with the help of a laboratory. So it
should be done in all others fields of knowledge.
The 2 dimensional school
Today
the trend in education is to introduce computers as part of the learning
process. Knowledge is processed, like in assisted learning systems, into small
bits. But the computer screen reveals its content for a short period only; The
computer can assist in procedural learning but a computer in the classroom is
no substitute for building tools of thinking. The school supervising system is
occupied with standardization of knowledge to synchronize the curriculum with
the advantages offered by the computer. The knowledge of students is quantified
by a list of items, which the students have to know and remember (at least
until the examination). In certain subjects the Israeli Ministry of Education
concentrates the knowledgeable Items in a list of 100. But that is not enough
to buy an entrance ticket to a college or a university. Universities do not
accept the results of secondary education even if students pass the final
examination successfully. Students are sent to a special course of
Psychometrics. Why? In these psychometric courses students are trained to pass
a number of additional tests. Those tests measure the different aspects of what
is called IQ. This practice proofs that IQ can be changed and can be improved by
specific learning. If a short preparatory course for college admission can have
such an impact on all students, why then should schools not disregard the
principles of these courses and concentrate on accumulation of knowledge in
some subjects only, considered critically for general education.
All
plastic arts can be the vehicle in training the imagination. Not all people
have the same kind of imagination or use their imagination in the same way.
There are converger and diverger, (Liam Hudson 1967) or according to A.Petrie
enhancer and reducer. (A.Petrie 1975). There are children and adults whose
imagination has no proper frame to serve specific purpose. A proper organized
imagination system is a natural gift not given to everyone. I learned later that
this problem of unorganized imagination system is the problem of many gifted
children too, their mind works above average in many aspects but not in all of
them. This fact points to another feature of the imagery system. The
imagination system has to be seen as the central part of all conscious brain
activity in a given moment, every sensory input and every verbal and motor
action is attached to this central part. I consider imagination as a pooling
and testing system for achieving efficiency in action.
Only rote learning can be done without imagination.
That is the reason that so many teaching systems are based on learning of
procedures. Teaching systems that concentrate on accumulating bits of
information or different kinds of procedures not always support learning and
thinking. Hannah Arendt, (H.Arendt 1959) the American philosopher made once a
remark that:
“We are messing up between two brain
activities: the quest for knowledge and the ability to think.”
Probably that is right, but
not the whole truth. Knowledge and thought are interlocked mental capacities.
The acquiring of knowledge in school is a process that enhances the thinking
process in itself. The handling of 3-D objects in a process of creation helps
to augment the ability to imagine and replace objects in your mind and in your
view field. In its first stage this is a kind of pictorial thinking. This is
one of the preferred pathways of young children to learn and internalize
reality. It is used in preschool and early school as vehicle of learning. The
same vehicle has to be used at the higher level of learning as well but not by
passive absorbing of graphical material. The goal should be to get access to a
3-D-realm, adjusted to the needs of students that are over whelmed by the
requirement of the demands of the higher school classes. Today’s' schools have
no facilities for such activity, except a few laboratories.
What makes me claim that it is
desirable and possibly fruitful to expose students of high school to creative
activity in a 3-D medium is the limited ability of a part of children to learn
and act intelligently in concrete connection. What the school lacks is an intermediate step to help
students to achieve high-level abstraction by actions in the visual field.
These are impossible in a school that is 2-D orientated in all its activities.
A school deals with flat surfaces only.
I
know that my findings have a negative character. I have tried to demonstrate
that students, which can’t act in a 3-D medium can’t learn easily and are
dropping out from high school. I know that the exact data have to be assembled
by systematic survey and research. So I have made an effort to build taxonomy
of mental capabilities as I observed in my workshop.
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Yacov
Levi Beth-
Shaarim 30046
ISRAEL
yacle@netvision.net.il