John M. Kennedy
Department of Psychology
Division of Life Sciences
Scarborough Campus
University of Toronto
1. Tracy drew very competently, but occasionally included
some puzzling lines, such as arcs at the corner of a
square showing a cube, and an arc across the top of
two attached squares, also showing a cube. What role
do these puzzling devices play in drawing
development? Are these devices specific to the blind?
2. Does drawing development occur in the blind and the
sighted in the same way?
3. How do sighted children draw at different ages?
4. Overall - earliest drawings are unrecognizable and
later ones are quite recognizable.
5. ASIDE: Points 5 - 7. Many factors influence particular
drawings
e.g. a)purely esthetic or design factors (Kellogg studied
these as influences on infants drawing)
e.g. b) styles, especially in adult's drawings
e.g. c) conventions, things we teach in a culture
e.g. d) the medium e.g. basket weaving, or "bacon-
strip" noses and "fried-egg" eyes on a lunch
plate!
e.g. e)types of objects - some having "prototypical"
drawings: Wilson and Wilson point out sighted
children in the late Nineteenth century, aged 7-11,
typically drew "two-eyed profiles" (e.g. more than 80%
in 1880). This fell to about 30% by about 1930. Now
it is rare (except in, say, Egypt). Another device is the
"ladder mouth". It has waned in popularity. Children
have "prototypes" that vary in frequency, depending on
their influences e.g. children's comic books are readily
available now, but were not in 1880 (or in Egypt today
in poorer sections)
6. The result of independent influences is independent
schemas, leading to children's comments like "This is
how you draw an ear" or "I don't know how to draw a
nose, or a giraffe".
7. Schemas build up a vocabulary, but not a general
principle - like a meandering river that leaves oxbow
lakes, cut off from the main flow of development.
8. General influences are more important than local
influences and their schemas - and the most general
influences are:
a. the nature of representation
b. the elements to be employed
c. the configuration rules
9. Nature of Representation: A represents B because A
is intended to make a person think of B and user and
recipient share this idea about the use of A. This
involves intention or will, awareness of other minds,
and a regress.
10. Elements: In pictorial representation, elements create
impressions, e.g. a line creates an impression of an
edge of a surface. This was the key discovery of cave
artists.
11. Configuration rules: The relative location of elements
in pictures is a PROJECTION of the relative location
of the parts of the object. There is usually some
relation to the observer's vantage point (which can
produce convergence, for example).
12. The Nature of Representation is such that it allows
anything to represent anything else (at one extreme)
and the nature of pictures is more restrictive, such that
only some elements are suitable for given purposes -
which sets limits on attempts to use pictures in
extreme ways (e.g. it won't let just any shape show any
other shape). Usefully, these powers of the elements
leave perception relatively free from a need for
detailed specificity, even in simple sketches that
optically are quite ambiguous.
13. Development is shaped by these 3 general principles.
14. One possible theory is "Inadvertent actions eventually
lead to specificity" in drawing development. That is,
a. motor actions
b. become complex, and produce specificity by
chance
c. specificity is reinforcing, leading to repetition.
d. further accidental discoveries lead to a dictionary
of schemas
e. schemas can be combined, accidentally, and lead
to complex pictures
f. finally, abbreviated schemas can be recognized -
abstraction has been attained
15. A more tenable theory is - we begin abstractly!
a. abstract will or "fiat"
b. later, we use some resemblance (suitable
elements, and some "shape similarity" of curves
and angles)
c. only finally, specificity (with a. and b. still active
and available when needed)
16. Evidence: To test Lowenfeld and Brittain's motoric
theory: 14-16m infants
Mueller and Kennedy: finger painting study
Results: infants proceed from very restricted, with
visual attention, to complex
NOT very general and random to very controlled,
detailed, small
17. Evidence: To test the role of perception and attention
on motor's results: 18m -36m infants:
Gibson and Yonas: Marking & non-marking pens
Results: Non-markers are non-interesting
18. Evidence on "will": To show role of intention prior to
shape similarity
Golomb; Wolf: Study verbal accompaniment
Results: At about 2 years, children announce what is
shown in a picture, when making marks with no
apparent shape in common with the referent: They
LIST the referents, we might say.
19. Evidence on emergence of shape similarity:
Golomb: Study on dictation
Subjects: Two year olds
Procedure:Dictate parts in random order e.g. head,
feet, tummy - in that order
Results: Two year olds distribute marks on the page
along a spatial dimension.
20. ASIDE: Freeman and others argue children distribute
marks as convenient, not to reflect projection from a
vantage point. To draw a cube with a cubic corner
using a Y junction, children draw right angles as Vs
and as obliques - when these are "put together
conveniently" they form a Y. (J.K.: This is only part of
the story).
21. ASIDE: Freeman argues children draw "tadpole
figures" for people because they think of the first
feature (head) and the last feature (feet). (J.K. :
There are cognitive limitations in the number of
features being controlled, but first and last is not a
major principle governing selection of parts.)
22. ASIDE: J.K.: My aim is to discover the overall spatial
principles at work.
23. Evidence on emergence of spontaneous shape
similarity
Golomb: study 3-year olds and dimensions of objects
Results: 80% of 3 year olds make the spatial
distribution of parts reflect spatial distribution in the
referent.
24. ASIDE: Points 24-30: Theory: Willats: How do
young children use spatial dimensions on the page, to
show spatial dimensions in the object?
Answer: The EXTENDEDNESS Theory. Objects are
extended in 1,2 or 3 dimensions.
Dimensions on the page Dimensions on the
object
Round mark - extended in 2-D MEANS Lump-extended in 3D
Long mark - extended in 1-d MEANS Stick-Extended in 2D
Dot mark - extended in 0-d MEANS Pebble-Extended in
Od chiefly
Special note from Willats: This extendedness system has a
drawback. It cannot be used to draw SLABS (like books,
planks, answering machines, files....) that are chiefly extended
in 2 dimensions. Round marks seem "too bulky" to be slabs.
And long marks seem "too rod-like" to be slabs.
25. Are young children restricted to using this
"extendedness" system? J.K. Recent evidence. No -
they also use shape.
Evidence: The snake study: If Ss are only able to use
extendedness, they will draw a long straight snake and
a long curved snake with the same kind of line - a long
line to show the extendedness of the snakes.
Subjects: 3-5 year olds who draw cubes as round
marks
Procedures: Ask the subjects to draw a long straight
snake and a long, very curved snake (S shaped)
Results: Besides using a long line (in keeping with
extendedness) they also curve the mark more to show
the S-shaped snake.
26. Is the extendedness theory accurate to some extent?
Yes to distinguish a slab from a boulder, the contour
has to be given L-junctions at suitable locations.
Children of 3-5 do have trouble controlling the
contour details. They also have some troubles with
orientation, for the snakes study found children often
drew horizontal snakes for snakes in any orientation.
(Could do another study with X vs. + shapes of
snakes: J.K.).
27. It has been argued, by Willats and others, that initially
the outline is used just to shape a REGION.
For example: Cubes are drawn by 3 year olds as
round regions and as squares by 4,5 and 6 year olds to
show the whole cube. Evidence: A cubic die has all its
numbers on faces added within the square region. A
coloured die has all its coloured faces added within
the square region.
(J.K.'s later studies find: Children who draw a cube as
a square identify the lines as showing the corners
between one of the cube's faces, and are using
outline.)
28. a). If the line is not functioning as an outline, it is free
to do other things e.g. to draw a square as + or X i.e.
its major dimensions or as its diagonals. Or the line
could be used in a drawing of a glass as the front of a
glass. This is rare, however.
b). Willats argues not only is a whole cube shown by a
square region, but later, when children come to draw
several faces of the cube, they mean the square region
stands for the face, but the lines do not stand for the
edges of the faces i.e. the corners between the faces.
For example, occasionally children draw two squares
side by side NOT touching. When asked "Where is
the corner?" they add ANOTHER LINE, midway
between the two squares. This third line shows the
corner, while its two flanking lines merely show
borders of REGIONS which show faces of the cube.
This is a "THREE LINE CORNER" one might say, if
Willats's interpretation is correct.
29. Caron-Pargue found occasional children draw many
squares to show a cube, distributed widely over the
page. Here the distribution of the faces ignores the
major dimensions or extendedness of the object.
30. But do note the squares in Caron-Pargue's study do
show shapes that are similar to the parts of the object.
31. Willats's three-line corner and Caron-Pargue's
distributed-cube do not show Connections: In the next
development in drawing, each part at roughly age 6-7
is connected by a line that means a surface edge.
32. The result initially is a FOLDOUT version of an
object - the set of faces being chosen, and their
distribution being a problem preoccupying children for
several years.
33. One distribution decision: Goodnow points out the
form added second should not interfere with the first
(e.g. legs of tables or chairs should not interfere with
lines showing the table top or the chair's seat.)
Drawing a cylinder, a rectangle may be drawn first,
and completely (or emphasized, Caron-Pargue says).
The circular tops and bottoms of the cylinder are then
added, but incompletely e.g. as semi-circles at the top
and bottom of the rectangle.
Alternatively, this system in which "emphasis" is
changed from one feature to another can produce
complete circles, at the top and bottom of the cylinder,
and only two sides of the rectangle would then be
shown.
34. ASIDE: Several commentators have pointed out
connections are the subject of a geometry called
TOPOLOGY.
Other features of topology are "enclosure" and
"crossing over". However, topology is too broad a
geometry to describe what children are using.
35. ASIDE: Topology is too broad because in topology, a
square or a circle can become a waving-flag shape, a
crescent shape, a pin-cushion shape or a long thin
shape. But these are distinct for the child, and the
child uses some shape-similarity e.g. number of curves,
and number of straight sections.
36. The foldout system has drawbacks.
37. So children shift to vantage point systems at age 8-10
using obliques to show receding sides, and also begin
to use foreshortening or convergence.
38. The simple version of a vantage point system is
DRAW WHAT FACES YOU. The advanced version
is DRAW WHAT FACES YOU, ON A PICTURE
SURFACE
CONSIDERED TO BE AT A CERTAIN PLACE
WITH A PARTICULAR ORIENTATION
BETWEEN YOU AND THE OBJECT.
39. ASIDE: When your vantage point, the picture's
location and orientation, and the object's proportions
are all appreciated then the rules are clear: The rules
were first appreciated by Brunelleschi in the
Renaissance.
He noted something about surfaces at 45o to the
picture's plane. These have a vanishing point on the
horizon. This is at a particular distance from the foot
of the normal from the observer's vantage point to the
picture plane. He measured the distance from the
vantage point to the foot of the normal. It equalled
the distance from the foot to the vanishing point on
the pictured horizon. This enabled him to draw
objects correctly objectively for the first time in
history.
40. The sighted do not usually offer formal rules like
Brunelleschi. Rather they have
- some general rules e.g. (1) if distance increases, the
size on the picture decreases
- e.g. (2) there is a horizon, with vanishing points on
it
- e.g. (3) receding parallels can be drawn converging,
but some parallels can be drawn as parallels
(these are ones parallel to the picture plane)
- e.g. (4) the picture can be checked by eye
41. But a complication is that vision's use of "perspective"
is imperfect.
(a) We accept parallels for surfaces receding from the
picture plane - - which is improper!
(b) We accept drawings of objects using about 10o -
15o angular subtense from a wide range of angular
subtenses e.g. the 15o drawing can be looked at close
up (25o subtense) or far away (2o angular subtense),
and it still looks good! (It is "robust" over a wide
variety of angles).
42. We use an angle law for cubic corners e.g. the two
smaller angles in the drawing should sum to over 90o.
43. Despite using parallels for receding sides of cubes, we
use foreshortening - generally preferring 0.65-0.70
foreshortening of the side.
44. Thus we have rough inspection laws - perception's
rules - which are not exactly Realism's perspective.
(J.K.: We may be influenced by perspective's lack of
change as far objects approach and recede by distances
equal to many times their width).
45. Evidence: How do children come to use connection,
foldout and vantage point principles in making their
drawings?
Nicholls and Kennedy study: On close to 1,000
sighted children and 1,000 sighted adults with aid from
*****Carol Flynn*****
Procedure: Ask subjects to make their "best drawing"
of a cube.
Basic results: Children develop from single square to
three faces around a Y vertex.
46. Details:
Subjects: Aged 4 -15: 789
Aged 16 up: 945
Categories used: From J. Willats plus others.
Willats 1: Rough circle: pre-single aspect
Willats 2: Square: Single aspect
Willats 3: Connected squares: Multiple aspect or
foldout
Willats 4: Two squares attached: If stacked-up,
vertical "oblique". If side-by-side,
horizontal "oblique". These
use the vertical or horizontal dimensions
to show depth
Willats 5: A central Y vertex, but a straight-line
inverted-T on the base. "Near oblique"
Category 6: Square with obliques that are parallel
(using obliques to show depth)
Category 7: Central line, and all faces shown by
obliques that are parallel
Category 8: Square with obliques that converge
Category 9: Central line, all faces shown by obliques
that converge
Category 10: Square form internally dissected (a type
noted by Caron-Pargue)
Category 11: other
47. Results A. There were very few category 8 and 9
drawings : So these were combined with others - 6
with 8, 7 with 9. The mean ages of the types increase
steadily from age 4 (Willats 1) to 12.3 (Convergent,
Category 7 plus 9).
48. Results B: However, only two phases were dominant.
Willats 2: Square - single aspect: 83% at age 5
Categories 6,7,8,9 combined (Willats 6, as it happens):
83% at age 14.
49. Results C: Generally the Willats stages enter, reach a
single peak, and then decline.
50. Results D: In the middle childhood years of 8-10
there is no dominant stage, and the "other" category
reaches a peak of 23%.
51. The other drawings can be categorized into square
with thin rectangles (mean age 8.2) and an arc added
to two rectangles (9.2). No adults drew like this
except for Tracy! Also, on occasion triangles were
added (10.3 - and some adults), or obliques were
added (10.3 - and some adults).
This suggests foreshortening is used before
convergence, which requires obliques (and obliques
may be related to the triangles being added).
52. Adult drawings were very like drawings by 14 and 15
year olds - often to within 2%.
53. In sum - the order is region, shape similarity,
connected features, foreshortening, obliques. But
overall the key factors are, first, shape similarity (age
5), and, second, the parts that face the observer with a
suggestion of their relation to the vantage point.
54. Drawing development also involves metaphor -
deliberate violations of a dimension (e.g. exaggeration)
to show a referent non-literally. This can be done to
show a referent that cannot be shown within the limits
of a system.
55. Do many of the hallmarks of drawing development
occur in drawings by the blind? Consider three young
children - the youngest in each site (Haiti, Phoenix,
Tucson) - and an older child from each site.
56. Cel-Haiti: Aged 6: Chiefly uses outline. Shape
similarity evident. Often connects features (but not
always - see table).
57. Ros-Haiti: Aged 16: Shows shape similarity and
connections ("foldout" table). Note: She improved
rapidly from her first drawing of a glass.
58. Di - Phoenix, aged 6: Possibly some use of outline
and some use of distribution of marks in a spatial
dimension. Several uses of "fiat" - very basic drawings.
59. Hal - Phoenix, aged 10 - similarity, foldout (including
disconnected parts), vantage point (table), metaphor
(for spinning wheel and moving wheel).
60. Lu - Tucson age 5 - shape similarity, disconnected
parts, fiat.
61. Raf - Tucson, aged 12 - shape similarity, vantage
point.
62. Summary: Haiti:
Coat hanger - shape similarity & recognizable - 13 of
15
Bracelet - single rounded form - 12 of 13
Thick ring - two concentric circles - 12 of 14
Table - closed shape with 4 legs in 14 of 15
63. Summary: Phoenix
Coat hanger - shape similarity, recognizable - 5
parts of the hanger - 5
Box - 3 use lines for sides of the box not edges
- 7 draw faces of the box (note Ted's use of
"angling off", a vantage-point effect)
- 6 indicated the lines stand for edges or corners
64. Summary: Tucson
Coathanger - 5 with recognizable similarity
- 5 draw ring with 2 concentric circles
- 5 use square for cube (shape similarity)
65. Summary overall - the typical response is in keeping
with outline style, some foldout, some vantage point.
Younger children showed "fiat". One use of metaphor.
66. Tracy - a later drawing of a cube showed
foreshortening. Thus, a first drawing is like a 5 year
old's, a later one is like a 9.2 m "other" drawing, and a
still later one shows foreshortening. The small arcs
are conventions for "angles".
67. In a test of a "folded card" drawing, with one side of
the card receding, Tracy used foreshortening again.
68. Kathy R. (blind adult) also advanced rapidly from pre-
single aspect to foldout. She also draws people
standing and lying down using shape similarity,
recognizably.
69. The hallmarks of drawing development are common to
the sighted and the blind. Older blind subjects draw
in a developmentally more-advanced fashion, even
though they have had no practice.
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