Cognitive Development
Within a Three-Dimensional Space of
Content, Complexity and Time
Stefan von Aufschnaiter
and Claudia von Aufschnaiter
University of Bremen
Learners' cognitive development
is mainly discussed with respect to the
development of content dependent knowledge (conceptual change or growth). We
suggest to take time and complexity into account, too, and to describe learning in
all three dimensions. We will found these three dimensions of content, complexity,
and time theoretically and show empirically where such framework will lead to. Our
database are 27 students (nine groups of three students each) who work on
physics tasks during three double lessons in a laboratory study. All activities are
videodocumented and analysed in great detail.
Results show that students'
meanings always refer to a narrow area of content, are
developed bottom up with respect to complexity, and show time dependent
dynamics in which 30 seconds and 5 minutes are important time scales.
Cognitive Development Within
a Three-Dimensional Space of Content, Complexity
and Time
Stefan von Aufschnaiter
and Claudia von Aufschnaiter, University of Bremen
Subject
For more than 10 years we
have been investigating the dynamics of individual
cognitive processes. We videotape small groups of students acting or talking in
real learning environments and analyse the videotapes carefully. For the
interpretation of the empirical data, we have developed a neurobiologically oriented
theoretical frame. Neurobiological orientation means that cognitive interpretations
of students' actions or verbal descriptions should be consistent with the actual
findings and interpretations of neuronal processes and structures (Greenfield 1998;
Calvin 1997; Grossberg 1998; Roth, G. 1997).
Our theoretical frame deals
with the context dependency of acting and thinking and
is therefore similar to Roth's "situated cognition" perspective (Roth, W.-M. 1996;
see also Clancey 1993). In addition, we believe that meanings (concepts) are
always (in every situation) constructed anew. The dynamics of development of
meanings thus depend on changes of context as well as on ontogenesis of the
related cognitive structures. Learning (i.e. individual development of cognitive
structures as a consequence of development of meaning) depends on matching the
development of meaning to changes of situated context.
Apart from distinguishing
consequently between cognitive structures ("memory")
and the cognitive processes generated by these structures (construction of
meanings) we also think that cognitive processes have a dynamics depending on
time and complexity as well as a dynamics depending on content.
For the analysis of development
of meaning and learning processes we therefore
have to consider three dimensions:
1) Content: This
dimension refers to the material taught in the classroom. The main
question is what knowledge students need to have to deal adequately with specific
material and what they can or have to learn while dealing with the learning
environment.
Development in the dimension
of content is therefore characterised by learners
expanding their "available" knowledge.
2) Complexity: It
is generally accepted that knowledge can be constructed and used
with different degrees of complexity or abstraction. So far, however, it has hardly
been studied, how differently complex knowledge of a given area of content can be
described quantitatively and how differently advanced learners use knowledge of
different complexity in varying circumstances. During the last 10 years the analysis
of these questions has been our main focus. Based on Piaget's (cf. 1991) step
theory and Powers's (1973) classification scheme for mental operations, we
developed and probed a model for the quantitative description of the complexity of
situated meanings (cf. v. Aufschnaiter & Welzel 1996, 1997a/b; Welzel 1997). One
result of our research is that concepts must be described with respect to their
complexity dependent dynamics.
Development in the dimension
of complexity is characterised by learners
expanding their "available" knowledge with respect to complexity.
3) Time: It is a
common experience that the time needed to produce knowledge of
a specific content with a specific complexity varies. In a lot of learning situations
and especially in examinations learners need to produce knowledge in a minimal
amount of time. Investigations about time needs for producing specific knowledge
and what changes time dependent dynamics of knowledge production still have do
be carried out.
Amongst others Damasio (1994)
and Pöppel (cf. 1994) found out that the cognitive
system has only 3 seconds available to produce single coherent meanings. This
matches results about investigations of simple cognitive achievements that are
clearly made in less than 3 seconds (cf. Anderson 1995).
If students are not able
to produce knowledge of a specific content and complexity
within 3 seconds (that means they are not sure about this fact) they only have the
option to develop the necessary knowledge in a succession of meanings with
respect to the essential content and complexity. Our empirical findings indicate that
such developments take place on two time scales (cf. v. Aufschnaiter, C. 1999):
Development in the dimension
of time is characterised by learners needing less
time to develop their "available" knowledge with respect to content and complexity.
Thereby they can generate knowledge of larger content width and/or higher
complexity on a specific time scale.
We consider learning to
be a process accompanying the cognitive processes
described in 1)-3). This results in cognitive structures realising cognitive processes
with broader content, higher complexity and reduced time needs. We expect
learning to take place in small steps and predominantly at different "construction
sites" within this three-dimensional space. For bigger (visible) learning progress
interlocking augmentation in each of these dimensions (content, complexity, and
time) may be essential. For the analysis of development of meaning and learning
processes dynamics of all three dimensions have to be investigated in great detail.
Design, Procedure, and
Data Analysis
During our presentation
we want to present results of a laboratory study concerning
the three dimensions of learning (content, complexity and time). In this study (which
was funded by the German Science Foundation, DFG) we videotaped 9 groups
each of three 11th grade students doing the same experimental tasks and
explaining the results.
We had worked out 51 tasks
which were written on index cards, with enough space
for the students to write down their observations and explanations. The tasks were
of increasing complicatedness and normally were handled in a fixed order.
(Complicatedness of a task denotes the complexity of situated cognitions which is
necessary for successfully solving this task.) A teacher was present but she did not
give the students any hints concerning the tasks. However, at certain points (which
had been planned in advance) she offered them additional information about
physical laws of definitions, which were also written on index cards but did not have
the form of tasks (we called these cards 'intervention cards').
On the average the students
needed 180 minutes to solve the tasks, distributed
over three sessions. We administrated questionnaires during these sessions and
also undertook two extra sessions with concept maps and interviews but we will not
talk about them in this presentation. The sessions were videotaped and transcribed
and then we tried to reconstruct the students' ideas with respect to what diSessa
and Sherin call "physical qualities" (diSessa & Sherin 1998; v. Aufschnaiter &
Welzel 1996; 1997a/b; Welzel 1997).
Results
1. Area of content:
Meanings are always constructed anew (with slightly changing
content). We ascribe meanings that changed concerning the content if single
actions are sequenced differently, if mimic and gesture of actions change clearly,
and if words are combined differently in verbal and written expressions. With these
distinctions we find that all 27 students each produce a large number of different
meanings (ca. 150 to 250) for a single task. Individual students construct a large
number of different meanings (from 500 to 1000) for all tasks combined. Only 16
words or word combinations are used more than ten times by individual students.
We can show development of meanings concerning their content only with these
words. We therefore cannot confirm the hypothesis that students "use" (stable)
concepts for the construction of meanings.
2. Levels of complexity:
While working on the tasks students first of all start on a
relatively low level of complexity. They operate with or discuss about concrete
objects and their features. During these operations an increasing number of
contents are taken into account. After that students are able to ascribe common
(invariant) properties to different objects or situations. In discussions with other
students they can start to link such properties. Higher levels of complexity (the
construction and combination of variable properties) are not reached by the
students of our investigation.
3. Time scales: Students
are only very seldom able to solve our tasks or
instructions spontaneously (within 3 seconds). This does not even happen if
successive tasks are very similar. If students start working on tasks or instructions
(what they do for nearly 100% of tasks but only for about 50% of instructions), they
often need several development of meanings (each within 30 seconds) with slightly
different content and/or different levels of complexity to solve the task successfully.
Unless students find a solution that is successful from their point of view, they stop
working on tasks/instructions after approximately 5 minutes (or even less). Within
such situations dissatisfaction is very often expressed explicitly.
General Interest
The presented investigation
refers to a narrow subject. However, we have found
similar results within other laboratory and field studies:
- 30 seconds for the development
of one way to solve the task and
- 5 minutes to work on a
task.
From our point of view,
the presented theoretical framework and results are
important parameters for the usage of learning environments. We therefore suggest
to analyse learning processes and learning environments critically under such
perspectives.
3D (4D) Space | Content, Complexity, Time
The area of content that is developed by learners,
This dimension refers to the material taught in the classroom. The main question
is what
knowledge students need to have to deal adequately with specific material and what they can or
have to learn while dealing with the learning environment.
1. Area of content: Meanings are always constructed anew (with slightly changing
content). We
ascribe meanings that changed concerning the content if single actions are sequenced differently,
if mimic and gesture of actions change clearly, and if words are combined differently in verbal and
written expressions. With these distinctions we find that all 27 students each produce a large
number of different meanings (ca. 150 to 250) for a single task. Individual students construct a large
number of different meanings (from 500 to 1000) for all tasks combined. Only 16 words or word
combinations are used more than ten times by individual students. We can show development of
meanings concerning their content only with these words. We therefore cannot confirm the
hypothesis that students "use" (stable) concepts for the construction of meanings.
1. Area of content: Meanings are always constructed anew (with slightly changing
content). We
ascribe meanings that changed concerning the content if single actions are sequenced differently,
if mimic and gesture of actions change clearly, and if words are combined differently in verbal and
written expressions. With these distinctions we find that all 27 students each produce a large
number of different meanings (ca. 150 to 250) for a single task. Individual students construct a large
number of different meanings (from 500 to 1000) for all tasks combined. Only 16 words or word
combinations are used more than ten times by individual students. We can show development of
meanings concerning their content only with these words. We therefore cannot confirm the
hypothesis that students "use" (stable) concepts for the construction of meanings.
Development in the dimension of content is therefore characterised by learners expanding
their
"available" knowledge.
The level of complexity that is reached within single constructions of meaning,
It is generally accepted that knowledge can be constructed and used with different
degrees of
complexity or abstraction. So far, however, it has hardly been studied, how differently complex
knowledge of a given area of content can be described quantitatively and how differently advanced
learners use knowledge of different complexity in varying circumstances. During the last 10 years
the analysis of these questions has been our main focus. Based on Piaget's (cf. 1991) step theory
and Powers's (1973) classification scheme for mental operations, we developed and probed a
model for the quantitative description of the complexity of situated meanings (cf. v. Aufschnaiter &
Welzel 1996, 1997a/b; Welzel 1997). One result of our research is that concepts must be
described with respect to their complexity dependent dynamics.
2. Levels of complexity: While working on the tasks students first of all start
on a relatively low
level of complexity. They operate with or discuss about concrete objects and their features. During
these operations an increasing number of contents are taken into account. After that students are
able to ascribe common (invariant) properties to different objects or situations. In discussions with
other students they can start to link such properties. Higher levels of complexity (the construction
and combination of variable properties) are not reached by the students of our investigation.
2. Levels of complexity: While working on the tasks students first of all start
on a relatively low
level of complexity. They operate with or discuss about concrete objects and their features. During
these operations an increasing number of contents are taken into account. After that students are
able to ascribe common (invariant) properties to different objects or situations. In discussions with
other students they can start to link such properties. Higher levels of complexity (the construction
and combination of variable properties) are not reached by the students of our investigation.
Development in the dimension of complexity is characterised by learners expanding
their
"available" knowledge with respect to complexity.
The time a learner needs to reach this level in a specific situation
It is a common experience that the time needed to produce knowledge of a specific
content with
a specific complexity varies. In a lot of learning situations and especially in examinations learners
need to produce knowledge in a minimal amount of time. Investigations about time needs for
producing specific knowledge and what changes time dependent dynamics of knowledge
production still have do be carried out.
Amongst others Damasio (1994) and Pöppel (cf. 1994) found out that the cognitive
system has
only 3 seconds available to produce single coherent meanings. This matches results about
investigations of simple cognitive achievements that are clearly made in less than 3 seconds (cf.
Anderson 1995).
If students are not able to produce knowledge of a specific content and complexity
within 3
seconds (that means they are not sure about this fact) they only have the option to develop the
necessary knowledge in a succession of meanings with respect to the essential content and
complexity. Our empirical findings indicate that such developments take place on two time scales
(cf. v. Aufschnaiter, C. 1999):
Around 5 minutes for working on a problem or task.
Around 30 seconds to test a possible solution to solve the problem or task successfully.
3. Time scales: Students are only very seldom able to solve our tasks or instructions
spontaneously (within 3 seconds). This does not even happen if successive tasks are very similar.
If students start working on tasks or instructions (what they do for nearly 100% of tasks but only for
about 50% of instructions), they often need several development of meanings (each within 30
seconds) with slightly different content and/or different levels of complexity to solve the task
successfully. Unless students find a solution that is successful from their point of view, they stop
working on tasks/instructions after approximately 5 minutes (or even less). Within such situations
dissatisfaction is very often expressed explicitly.
3. Time scales: Students are only very seldom able to solve our tasks or instructions
spontaneously (within 3 seconds). This does not even happen if successive tasks are very similar.
If students start working on tasks or instructions (what they do for nearly 100% of tasks but only for
about 50% of instructions), they often need several development of meanings (each within 30
seconds) with slightly different content and/or different levels of complexity to solve the task
successfully. Unless students find a solution that is successful from their point of view, they stop
working on tasks/instructions after approximately 5 minutes (or even less). Within such situations
dissatisfaction is very often expressed explicitly.
1. Thoughts
SpaceContent,Complexity,TimeHyperlinkIcon.gif){kind=small}
