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1. Introduction
With the proliferation of interactive computer environments, such
as simulations, tutorials and "edutainment," in a variety of
highly spatial content areas such as math (especially geometry), chemistry,
and physics, it is important to investigate the relationship between hands-on
interaction with computer programs and the acquisition of spatial visualization
skills. Typically educational situations involve both hands-on and observational
activities. For example, in a math class, students might first watch the
teacher solve problems on the board, then attempt to solve problems themselves.
Similarly in a class on Excel, students might first watch the teacher
create spreadsheets and then create spreadsheets themselves. Cooperative
learning groups in school computer labs often place one student at the
mouse and keyboard with one or more other students watching and advising;
an alternate model of cooperative learning in computer labs has students
taking turns at the controls. The comparative effectiveness of different
variations of hands-on interactivity (hands-on, observation, taking turns,
etc.) for learning spatial visualization is an important issue for the
pedagogy of computer-based learning.
Although measurable
by a number of standardized tests and accepted as a valid psychological
construct, because of its non-verbal nature, spatial visualization remains
elusive to unambiguous definition. I offer the following eclectic definition:
Spatial visualization is the ability to solve multi-step problems involving
configurations of shapes, primarily using mental imagery or other mental
representations and transformations of same which explicitly preserve
the topological and geometric relations of the problem, while optionally
involving additional logical, verbal and symbolic reasoning.
Spatial visualization
is an important factor in student success in a variety of spatial domains
such as geometry (Battista, 1990), other higher forms of mathematics (Battista,
1990; Smith, 1964), chemistry (Pribyl & Bodner, 1987) and physics
(Pallrand & Seeber, 1984).
Interestingly there
is a relationship between time and spatial visualization. Without time
pressure, people often resort to entirely non-spatial strategies for solving
spatial problems (Smith, 1964). Moreover, the amount of elapsed time as
well as success in solving the task provides a more accurate measure of
spatial skill. If someone takes an exceedingly long time to solve a spatial
problem, his/her success may be more indicative of patience or persistence
than spatial visualization skill. For the purposes of measurement, it
is more productive to record elapsed time, along with success rate, and
determine spatial visualization efficiency as the success rate divided
by elapsed time.
Additionally there
is a relationship, long posited by scientists, between acquisition of
spatial visualization skill and hands-on interaction. Piaget & Inhelder
(1948) suggested that a combination of hands-on touching and integration
of different viewpoints is instrumental in children's development of spatial
ability and mental models of spatial objects. There are similar connections
between spatial visualization and interaction with virtual shapes in computer
programs. Interactive computer graphics can facilitate improvements in
adolescents' and adults' spatial visualization (Okagaki and Frensch, 1994;
Gagnon, 1985).
The principle of spatial
weaning (Smith, 1998) suggests that hands-on, interactive situations
may initially be more beneficial to novices to a spatial domain who may
not be familiar enough with the geometry of that new spatial domain to
construct the mental imagery necessary for visualizing solutions. Once
students become more familiar with the geometry of the new domain, they
may benefit more from less interactive situations. They are now familiar
enough with the geometry of that domain to construct the mental imagery
necessary to visualize hypothetical solutions without the scaffolding
of hands-on stimuli.
However, the very
opposite of hands-on interaction, i.e., relatively more passive observation,
sometimes has the advantage in educational settings (Sweller, 1994). Hands-on
manipulation may divert short -term memory resources needed for students
to comprehend a new schema requiring the simultaneous mental manipulation
of a larger number of elements. When algebra or geometry students are
learning specific principles or techniques, it is often more beneficial
for them to observe the teacher working on a problem than to immediately
try to solve it themselves. Immediately solving problems by applying principles
only recently introduced imposes an extraneous "cognitive load"
on the students' short-term memory (Sweller, 1994). As students mentally
manipulate the elements of the problem, they must also hold in mind the
new principle that the problem illustrates, straining the capacity of
their short term memory.
Considering that there
are theoretical advantages for both interaction and observation, an important
question is 'How do interaction versus observation compare as learning
situations?' Smith (1998) provided some evidence that fifth-grade students,
less skilled in spatial visualization, benefit more from computer interaction,
while fifth-graders already skilled in spatial visualization benefit more
from observation. However, it is unclear how these results extend to other
age groups and other learning situations. Moreover, it is unclear how
alternating between interaction and observation, another possible variation
of spatial weaning, might affect acquisition of spatial visualization
skills. These questions have important implications for the pedagogy of
interactive computer programs in a variety of subjects involving spatial
visualization skills, such as geometry, chemistry, physics, etc.
The current study
seeks to statistically test the principle of spatial weaning discovered
with think-aloud methods on fifth graders (Smith, 1998) and extend it
to another age group, i.e., college undergraduates. Spatial weaning
predicts that students unfamiliar with a spatial domain will benefit most
from high interaction, while benefiting least from observation alone.
Furthermore, we are
interested in looking at these concepts from the point of efficiency in
spatial visualization. Timed spatial tests emphasize mental imagery and
provide a more accurate measure of spatial visualization skill than tests
with no time limits. Therefore we are interested in efficiency in spatial
visualization, i.e., how many problems can be solved divided by average
time to solve them.
Our main research
question is: How do a) hands-on interaction and b) observation compare
as collaborative computer-based situations for learning efficiency in
spatial visualization?
Since the pedagogy
of computer interaction and spatial visualization is relatively new, a
broader search of learning conditions is warranted. Perhaps some variation
of hands-on interaction might be most beneficial. Thus we examined another
variation on spatial weaning, i.e., alternating between interaction and
observation/consulting. A secondary research question focuses on variations
in hands-on interaction with a computer: How do a) exclusively hands-on
interaction, b) intermittent hands-on interaction (alternating between
hands-on and observation) and c) observation compare as learning situations
for efficiency in spatial visualization?
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