Information Technology Reference
In-Depth Information
The model described in this section focuses on
simplicity and reuse. The first point is more im-
portant for designers and authors, as experience
shows that complex tools tend not to be used very
much. The second point is important to designers
and teachers alike, as every practitioner will be
interested in the opportunity of profiting from
other people's work (and vice versa), lowering
the effort needed to get personalised sequences
of learning content. This is especially true in the
case of systems designed for lifelong learning, as
they tend to be large and costly to build, unless
material can be shared from different sources.
A common problem that appears when design-
ing educational systems for lifelong learning is
how to handle a large number of learning activities.
Courses usually include a significant number of
resources such as manuals, documents, exercises,
etc. In the goal of designing a practical system,
one of the issues that needs to be addressed is how
to allow the learning content author to organize
and manipulate a significantly large number of
possible resources. The strategy proposed here
confronts this problem by using a hierarchical
structure. In many cases, this structure is already
present (sometimes inherently) in the learning
units that are used. This facilitates the definition
of sequencings of learning material.
point at the same time if that fits the pedagogical
objectives of the sequences defined by a graph.
Sequencing graphs have a simple hierarchy: the
parent node of each node is unique. This type of
hierarchical transition structures are not a new
concept since they have been already used in a
number of areas such as system design (Harel,
1987; Girault et al., 1999), video compression
(Albert et al., 1997), and hypermedia systems (de
Oliveira et al., 2001).
Every edge in the hierarchical graph may
contain a condition and a set of actions. The
condition is an arbitrary boolean expression
over a previously defined set of variables. These
variables (that we call the environment) relate to
the history of the students, their competencies,
and other information that the system might have
stored before about them. The actions represent a
set of operations to be performed over the values
of these variables. The semantics of this pair of
elements is that the transition represented by the
edge is suitable to be performed if the condition
is true; and, if finally executed, the actions are
reflected in the set of variables.
The idea behind a Sequencing Graph (Figure 1
shows a small example) is to provide a sequential
structure that captures a large set of possible node
sequences over a large number of learning objects.
These sequences are decided based on the answers
obtained from the students in previous nodes and
their current position in the graph. This information
is stored in the environment of the student. In our
experience, expressing a sequence by means of
a graph is relatively easy to understand for most
people, which is the first of our four goals.
Description
A sequencing graph can be briefly described as an
oriented multigraph, without isolated nodes. Some
of these nodes are bound to actual basic learning
resources (exercises, documents, videos, audio,
etc.) and some are logical containers that hierar-
chically contain another sequencing sub-graph.
In order to enable sequences that interoperate on
different levels of the hierarchy, each graph has
one or more of its nodes defined as input nodes.
Input nodes are the entry points from a higher
level of hierarchy. Exit points are in the form of
directed edges that connect nodes to their parent
nodes. A node can be an input node and have an exit
Formal Definition
A Sequencing Graph SG is recursively defined
as follows:
A sequencing graph SG = (N, E, Φ, Π
, I, V,
η, Υ) is an eight tuple where elements of the set
N are nodes, elements of the set E are edges, Φ
N is the set of entry nodes of SG, Π
is the set of
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