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lows variables from the lower level to be used in
upper levels. For example, the time spent to read
some texts and do some exercises on a lower level
can be used to influence the sequencing of related
topics on higher levels.
On the other hand, the existence of entry edges
is not necessary. First, allowing edges coming
“from above” is contrary to the philosophy of
having sequencing graphs that are autonomous;
the presence of entry edges would mean a higher
degree of coupling between levels and would hin-
der reusability. Without entry edges, a container
node is an autonomous entity that can be easily
reused. The upwards interface hides the complex-
ity of the internal activities, their sequencing, and
their variables.
Second, it can be seen that a graph has to be
always initialized in the same way. If a graph is
to be reused, the sequencing of activities within
cannot depend on how or where the student en-
ters in it. That is why there are not entry edges,
but just entry nodes and initialization phases,
explained bellow.
but it has opened the door for automatic testing of
sequencing graphs. The details are omitted here
for the sake of space, but the interested reader is
referred to (Prieto-Linillos et al., 2008).
The Issue of Reusability
Reusability is encouraged in Sequencing Graphs
in a double sense: from the point of view of
the activities and from the point of view of the
graphs. From the point of view of the activities,
a Sequencing Graph does not change if one of
the activities in its nodes does, as long as the in-
terface of the activity (the set of variables that it
introduces in the environment) is the same. This
implements a logical separation between learn-
ing content (i.e. in the nodes) and its sequencing
(i.e. the graph), allowing for different experts to
specialize in these two aspects of learning design.
For example, activities could be modified to have
a more interesting appearance or more complex
interaction with the user. As long as the exported
variables (e.g. time of interaction, mark obtained)
are the same, the graph remains unchanged, as
well as the instructional design that it defines.
From the point of view of the graphs, the clear
separation between levels of hierarchy permits
to reuse a whole sequencing graph as it was an
atomic activity. Different graphs can be combined
with a graph of a higher level of hierarchy that
establishes how they should be sequenced. The
interested reader is referred to (Gutierrez Santos,
2007), where a complete example is described
in pages 87-90, and cannot be included here for
the sake of space. Several graphs, each of them
implementing an instructional strategy for a
domain, are combined together within a broader
sequencing graph. The result is a tutoring system
of a high-level domain that includes them all.
This is performed at a very low cost: only the
variables exported (the upwards interface) need
to be known on the higher level. The rest of the
information is hidden.
Initialization Phase and the
Intra-Level Interface
An initialization section for each graph is neces-
sary. It defines the intra-level interface, that is, the
variables that can be used in this level of hierarchy.
Explicit declaration of variables is a common
strategy in programming languages and it is a
useful approach to prevent many mistakes. This
feature makes it possible to perform automatic
error detection at design time (Prieto-Linillos et
al., 2008). Early detection of errors improves the
reusability of the graphs, as a designer can use
a sequencing created by a different author with
confidence. It also improves scalability, which is
one of our four goals, because many mistakes are
confined to a local scope, and detected earlier.
Besides, the initialization phase provides a
coherent initial state for each graph. This is not
only relevant from the instructional point of view,
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