After a general overview in a previous paper [AMJ10b], in which we proposed Didactic Networks (DN) as a new way for developing and exploiting web-learning content, we offer here a deeper study showing how to use them for web-learning design and content generation based on Instructional Theory with the coherence guaranty of the RST [MT99].   By using a set of expressivity patterns, it is possible to obtain different final ¿products¿ from the DNs such as different level or different aspect web-learning lessons, depending on the target, documents or evaluation tests.  In parallel we are defining the Fundamental Cognitive Networks (FCN), in which we deal with the most common patterns human being uses to think and communicate ideas. This FCN set reuses the representation of Concepts, Procedures and Principles defined here, and it is the main topic of a paper we are working on for the very near future

Alamo Lobo, Francisco Javier del

Jaen Gallego, Jose Alberto

Martínez Fernández, Raquel

English

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Didactic Networks and exemplification 
F. Javier del Álamo1, Raquel Martínez1, José Alberto Jaén1 
1Department of Control, Electronics and Computer Science 
E.T.S. Ingenieros Industriales 
Universidad Politécnica de Madrid 
fjalamo@etsii.upm.es, raquelm@etsii.upm.es, jjaen@etsii.upm.es 
 
Abstract.  After a general overview in a previous paper [10], in which we 
proposed Didactic Networks (DN) as a new way for developing and exploiting 
web-learning content, we offer here a deeper study showing how to use them 
for web-learning design and content generation based on Instructional Theory 
with the coherence guaranty of the RST [3].  
By using a set of expressivity patterns, it is possible to obtain different final 
“products” from the DNs such as different level or different aspect web-
learning lessons, depending on the target, documents or evaluation tests. 
In parallel we are defining the Fundamental Cognitive Networks (FCN), in 
which we deal with the most common patterns human being uses to think and 
communicate ideas. This FCN set reuses the representation of Concepts, 
Procedures and Principles defined here, and it is the main topic of a paper we 
are working on for the very near future. 
Keywords: Concept map, Rhetorical-Semantic Relation Semantic Network, 
RST, Didactic Network, Knowledge network. 
1 Introduction 
The RSR (Rhetorical Semantic Relations) we have proposed in a previous paper [8], 
have been defined as a set of relations valid for representing any kind of knowledge. 
By combining this set of relations with knowledge nodes, we are able to represent 
knowledge by means of a certain kind of concept map [5], with a set of topological 
and semantic constraints [7] that we call “knowledge network” (KN). 
The KNs can be the origin of web pages and web site content, by applying some 
visual transformations such as what we are explaining here. Each of the knowledge 
nodes in any KN includes a set of attributes. For the present paper, the most important 
to take in account are a Title, a textual description, a set of graphics, a set of 
audiovisual sequences, a set of equations and, finally, a set of Synchronization 
parameters. Providing the adequate information for each one of the nodes in a KN, 
these visual transformations automatically produce web pages and web sites. 
Once we have defined the “Didactic Networks” (DNs) for representing didactic 
methodology for applications in web-learning [10], we are ready to provide a 
complete description of how DNs support each of the steps of the methodology. 
 1
 
 Node representation: TITLE 
 GRAPH 
EQUATION  
TEXT  
 
 
 
 
 
 
 
 
 
 
Fig. 1. Visual Pattern 
2 Didactic Networks for memorization and examples 
Reigeluth treats memorization as an invariant task, because we can see concepts, 
procedures and principles as a list of items (facts, steps and events, respectively), 
making a distinction between ordered and non-ordered lists.  
The three major tactics to facilitate memorizing are Chunking, Repetition and 
Mnemonics. The method consists of the following steps as well as some motivational 
tactics depending on the student’s needs, not considered in the general case [6]. ( The 
convention for RSR representation in DNs is by means of an arrow, labeled by means 
of an ellipse including action name and a content type specification. 
2.1 Presentation of the object to memorize 
The methodology simply requires a list of elements. We define three different DNs 
that will be generalized to be also a FCN: Parts Network, Principle Network and 
Procedure Network. 
Block representation  : (Father Node, RS relations and children) 
 
FATHER NODE 
Inlay 
 CHILD NODE 1 
 
CHILD NODE 2  
 CHILD NODE N 
 
TITLE 
GRAPH 
EQUATION 
TEXT 
 
 2
a. Concept b. Causal principle c. Natural principle 
This semantic network 
shows a concept as a 
set of elements (list or 
group of particulars).  
We have included 
additional information 
regarding causal RSR, not 
required by BMI.  [8] 
In a natural principle 
presentation, it is important 
to show the sequence of 
events, and no other relation 
 
 
Fig. 2. Presentation of Concepts and Principles. 
Some examples, corresponding to the basic concepts in the eigenvalues problem [4]: 
 
 
 
 
 
 
 
 
 
 
 
Fig. 3. Didactic Network for the Concept of Linear Transformation 
 3
By applying the visual pattern defined in Fig 1 we will automatically obtain the 
next appearance for the web page: 
 
LINEAR TRANSFORMATION in Rn  
 
 
 
 
 
 
Fig. 4. Application of a Visual Pattern to the Didactic Network 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 5. Didactic Network for the presentation of the Concept of eigenvalue 
d. Procedures 
For a procedure presentation, the first step is the Objective declaration followed 
(optionally) by the description of the sequence of steps required to achieve it. If 
necessary, it is possible to specify the condition and action corresponding to each 
step.  
transforms vectors  
 
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vr A 
 
A matrix 
wvA rr =⋅  ⎟
⎟⎟
⎠
⎞
⎜⎜
⎜
⎝
⎛
=
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aa
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,1,3
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In general, a linear transformation acts on a vector changing 
its magnitude and its direction. 
 4
  
 
 
 
 
 
 
Fig. 6. Procedure presentation 
Enrichment Tactics for difficult content 
In the case of long lists to memorize for concepts, procedures or principles, the use of 
power tactics, such as Chunking, Repetition and Mnemonics is recommended, by 
using the didactic network provided in the present section. 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 7. Enrichment Tactics for difficult content 
 5
. 
2 Prompting and Practice. 
In the last step, the methodology suggests requesting the learner for feedback about 
the knowledge transference. A software module will be responsible for an automatic 
test generation. Taking into account that all the information is ultimately a list which 
is independent of the knowledge nature, suitable questions include the following: 
- For a given element in a list, determine the next element 
- For a given element in a list, determine the previous element 
- If a list of associations, for a given element, determine its associated one 
3. Didactic networks for concept application (classification) 
3.1 Presentation 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 9. Concept classification 
The proposed network includes all sections required by BMI: The Prototype 
formation (common characteristics), Generalization (variable characteristics) and 
Discrimination (critical characteristics). 
 6
3.2. Exemplification 
The objective is to provide a useful guide for a suitable exemplification. We should 
create examples that are as divergent as possible, by specifying common variable 
features (dimension of divergence). The contrast with a non-example showing a non-
fulfillment of critical characteristics is a useful resource to complete the concept 
transmission. The didactic network supporting this phase is based on the concept 
classification: 
 
Fig. 10. Exemplification of concept application 
3.3. Presentation of the process of Concept classification (application). 
In most cases, the classification procedure is very simple: however there are situations 
in which it is not so easy, and it is necessary to carry out a strategy to do that. For 
both situations, the didactic network supporting this phase is related to the two 
alternatives: looking for unreliable critical features for the candidate exclusion and 
looking for matching for the candidate acceptation. (Fig 10) 
 7
3.4. Practice, Classification Test and Feedback 
Based on the same Fig.10, in this phase, the automatic suitable questions obtained 
from the database suitable are: For a given element X, does X belong to class 
/subclass/ super-class Y? A software module will be the responsible for this part of 
the sequence of learning. 
 
 
 
 
 
 
 
 
 
 
 
Fig. 11. Process of concept classification 
4. Didactic networks for procedure application 
4.1 Presentation 
In BMI [6] a procedural task is basically a sequence of physical or mental actions. It 
can be a linear procedure or a branching one that can be interpreted as so many linear 
procedures as combinations of possible branches. But a procedure can be seen in a 
more generic point of view, as a set of non-sequential productions (rules) which, 
depending on preconditions, are enabled or disabled [2]. The methodology suggests a 
presentation showing the dimensions of divergence, an exemplification and practices. 
Adapting the general procedure definition, our proposal is based on the following 
steps: 
1. Presentation of the procedure application, with two options and three networks. 
- Sequential Procedure (see procedure presentation, fig 1). 
 8
- General Procedure. It is the transcription of the general complex problem- 
solving studied in the ACT-R theory of Anderson.[2], including both sequential 
as well as rule based procedures. 
 
 
 
 
 
 
 
Fig. 12. General procedure presentation 
- Method: The method is a relevant part of the procedure network, and it is 
important enough to be treated independently in order to be reused, because it is 
used often. 
 
 
 
 
 
 
 
 
 
 
Fig. 13. Method presentation 
4.2. Dimensions of divergence 
Dimensions of divergence represent the different ways to solve a problem depending 
on different constraints, such as simplified methods, see Fig 15. 
 9
One of the most common examples for the dimensions of divergence is the simplified 
method for solving the determinant of a 2x2 or a 3x3 matrix. Fig 16. Shows the 
presentation of the corresponding didactic network. 
 
 
 
 
 
 
Fig. 14. Presentation of Dimensions of Divergence 
4.3 Exemplification of the use of the procedure. 
Demonstration of the use of the procedure rules for a specific set of data, by using the 
procedure presentation with a set of concrete data 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 15. Procedure exemplification didactic network 
 10
4.4 Test phase support. 
It is based on automatically generated questions about the procedure use, such as 
“what is the first step?”, “what is the next step to do?” or “what is the condition for an 
action?” 
4.5 Practice and Simulation.  
In some cases it is interesting to generate the same kinds of questions over different 
sets of data. A software module will be the responsible for this part of learning. 
5. Didactic networks for principle application (classification) 
Applying natural principles implies generalization and prediction of new cases. For 
causal principles there are two phases (acquisition and application) and three 
behaviors: Prediction, Explanation and Solution. The proposed method for learning 
principle applications based is: 
1. Presentation. (causes and effects or sequence of events for natural principles) 
 
 
 
 
 
 
 
Fig. 16. Presentation of principle application 
2. Exemplification of applications (as divergent as possible) 
3. Demonstration by using divergent examples on the same didactic network 
4. Test and practices. automatic questions: what is the cause/effect of ----? 
 11
 12
6. Future research lines 
Different research lines in which we are intensifying our activity are opened today, 
pointing in different directions. First of all, our main objective is to go deeper into the 
understanding and development of the theoretical framework, by means of: 
- The formulation of a molecular structure of knowledge by using the patterns 
often used.  (Fundamental Cognitive Networks and DNs for Understanding). 
- Developing visualization patterns for web transformation design. 
- Operations on RSR (plurals, inverses, combinations, verbal tenses, synonyms). 
- After completing the knowledge model definition, a computing data model will 
be the main issue both for interchange and storage objectives, consisting of: 
- The creation of an interchange computing data model both for representation and 
storage objectives, able to support FCNs and DNs.  
- Software selection / development for e-learning generation and compatible tools. 
- Definition of tests, practices and simulations.  
- Elaboration of a Knowledge Representation Methodology, by using KNs. 
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Didactic Networks and exemplification

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