PCMAT – Mathematics Collaborative Educational System

A. Peña-Ayala (Ed.): Intelligent and Adaptive ELS, SIST 17, pp. 183–212. springerlink.com © Springer-Verlag Berlin Heidelberg 2012

Chapter 8 PCMAT – Mathematics Collaborative Educational System

Constantino Martins1, Luiz Faria1, Marta Fernandes1, Paulo Couto1, Cristina Bastos1, and Eurico Carrapatoso2

1 GECAD – Knowledge Engineering and Decision Support Group / Institute of Engineering – Polytechnic of Porto R. Dr. António Bernardino de Almeida, 4200-072 Porto, Portugal {acm,lef,mmaf,pjco}@isep.ipp.pt, [email protected]

2 Faculty of Engineering of the University of Porto R. Dr. Roberto Frias 4200-465 Porto, Portugal [email protected]

Abstract. PCMAT (Mathematics Collaborative Learning Platform) is a collabora-tive adaptive learning tool based on progressive assessment for Mathematics in Basic Schools. The learning platform is based on a constructivist approach, assess-ing the user knowledge and presenting contents and activities adapted to the characteristics and learning style of the student. The intelligent behavior of such platform depends on the existence of a tentative description of the student – the student model (SM). The contents of this model and the student most prominent learning style are used by a domain and interaction model to select the most ap-propriate response to student actions. The SM is used to select the more appropri-ate learning object according the student learning stage. However, this selection demands for the access to metadata describing the contents of the learning object. This need leaded to the application of a standard to describe the learning objects (LO). The authoring of LO corresponds to one major maintenance costs present in these applications. PCMAT is able to generate several instances of the same learn-ing object through the parameterization of some features of the learning object. The platform is also able to process student responses in natural language. This project shows how techniques from Adaptive Hypermedia System (AHS) field can improve e-learning based systems in a basic school environment.

8.1 Introduction

The main goal of Educational Adaptive Systems (EAS) is to achieve applications able to adequate its relation with the student in terms of content presentation, na-vigation, and interface according to a predefined but updatable SM (Brusilovsky 2001, De Bra et al. 2004).

184 C. Martins et al.

In this kind of systems, the emphasis is placed on the student knowledge about the domain application and his learning style, in order to allow him to reach the learning objectives proposed in his training (Chepegin et al. 2004).

Although numerous research and already developed systems have provided good results, more development, experimentation and implementation are still ne-cessary to conclude about the adequate features and effectiveness of these systems (Martins et al. 2008a, Martins et al. 2008b).

The aims of this document are: to define what is a SM, to present existing and well known SM, to compare existing intelligent systems in the scientific area of student modeling and to present the project: PCMAT.

PCMAT is a collaborative learning platform based on a constructivist approach, assessing the user knowledge and presenting contents and activities adapted to the characteristics and learning style of the student of mathematics in basic schools.

This chapter is organized as follows. The first three sessions present a brief state of the art concerning the major concepts involved in an EAS. In particular, Sect. 8.2 provides a general approach to AHS, Sect. 8.3 defines SM and its role in the adaptation process, and Sect. 8.4 deals about the learning styles concept. In Sect. 8.5 some standards used to describe metadata about LO are described. Sect. 8.6 presents some issues regarding PCMAT implementation. Finally, Sect. 8.7, and 8.8 present some results and conclusions.

8.2 Adaptive Hypermedia Systems

AHS term is generally referred as a crossroad in the re-search of Hypermedia and User Model (UM) (De Bra et al. 2004, Brusilovsy, 1996, Brusilovsky, 2001). An AHS builds a model of the objectives, preferences and knowledge of each user and uses it, dynamically, through the Domain Model and the Interaction Model, to adapt its contents, navigation and interface to the user needs.

(Chepegin et al. 2004) indicate: “These systems must present the functionality to change content presentation, links structure or links annotation with the follow-ing objectives: guiding the user to relevant information and keep him away from the irrelevant one, or pages that he still would not be able to understand”. This ob-jective is generally known as link adaptation; supplying, in the content (page), ad-ditional or alternative information to certify that the most relevant information is shown. It is generally known as content adaptation.

The global architecture proposed by (Benyon 1993) and (De Bra et al. 2004) indicates that AHS must have three essential parts:

• The UM that describes the information, knowledge, and preferences of the user. This component allows extracting and expressing conclusions on the user characteristics,

8 PCMAT – Mathematics Collaborative Educational System 185

• The Domain Model represents a set of domains concepts; in different AHS these concepts can have distinct functions, weights and meanings; most com-monly, each concept is connected/related with other concepts, representing a semantic net,

• The Interaction Model, which represents and defines the interaction between the user and the application.

In educational adaptive hypermedia, the emphasis is placed on students’ know-ledge in the domain application and learning style, in order to allow them to reach the learning objectives proposed in their training (Martins et al. 2008b).

8.3 Student Model

The beginning of user modeling is dated to 1978/1979 with the first work by Al-len, Cohen, Perrault, and Rich (Kobsa 1993). In the next 10 years, numerous ap-plications or systems were developed to store different types of user information to allow distinct adaptation models. Morik, Kobsa, Wahlster, and McTear present an extensive survey of these systems (Kobsa 1993). In these initial systems, user modeling was embedded and there was not a clear distinction from other compo-nents of the system (Kobsa 1993).

In 1990, Kobsa was the first author to use the term “User Modeling Shell Sys- tem”. Since then, different systems have been developed with the ability to reuse UM (Kobsa 1993, Martins et al. 2008b).

In generic AHS, the UM allows changing several aspects of the system, in reply to certain characteristics (given or inferred) of the user (Brusilovsky 2001). These characteristics represent the knowledge and preferences that the system assumes the user (individual, group of users or no human user) has (Martins et al. 2008a, Martins et al. 2008b).

In educational adaptive hypermedia systems, the UM (or SM) has increased re-levance: when the student reaches the objectives of the course, the system must be able to re-adapt, for example, to his knowledge (Brusilovsky 2001, Martins et al. 2008a, Martins et al. 2008b).

A SM includes information referring to the specific knowledge that the system judges that the user possesses on the domain, known as the Domain Dependent Data (DDD). The components of the DDD correspond to the Domain Model with three-level functionality (Benyon 1993):

1. Task level: with the objectives/competences of the domain that the user will have to master. In this case, the objectives or intermediate objectives can be al-tered according to the evolution of the learning process,

2. Logical Level: which describes the user knowledge of the domain and is up-dated during the students learning process,

3. Physical Level: it registers and infers the profile of the user knowledge.


The Domain Independent Data (DID) is composed of two elements: the Psycho-logical Model and the Generic Model of the Student Profile, with an explicit re-presentation (Kobsa 1993). The psychological data are related with the cognitive and affective aspects of the student. Some studies have demonstrated that the dif-ference between the cognitive capacities and personality aspects affects the quality of some models or styles of interaction (Kobsa 1993). This data are more perma-nent which allows the system to know beforehand that it must adapt to which the characteristics are (Benyon 1993, Vassileva 1996).

The data related to the user interests, common knowledge and background is kept in the Generic Model of the Student Profile. The DID includes the following aspects (Benyon 1993, Kobsa 1993, Martins et al. 2008b): Initial user knowledge, Objective and plans, Cognitive capacities, Learning styles, Preferences, Academic profile (technological studies versus economical studies and management, know-ledge of literature, artistic capacities, etc.), Age and type of student, Cognitive style (affective, impulsive, etc.), and personality aspects (introverted, extroverted, etc.).

As expressed before, some of these characteristics are relevant for a determined type of UM and not for others (Brusilovsky 1996, Brusilovsy 2001, Martins et al. 2008b). Therefore, for each AHS it will be necessary to define the characteristics and relevant parameters of the user to be kept (Martins et al. 2008a).

The following list tries to address the most common aspects that support adap-tation (Martins et al. 2008b):

• DID:

− Generic profile: Personal information (name, email, password, etc.), demographic data (age, etc.), academic background, qualifications, background knowledge, deficiencies: visual or others, the Domain of Application, and inheritance of characteristics (creation of user stereotypes),

− Psychological profile: Learning style (taxonomy), cognitive capacities, per-sonality; inheritance of characteristics.

• DDD: objectives, plan, complete description of the navigation, knowledge ac-quired, results of evaluations, context model, aptitude; interests (definition of the interests of the individual with the objective to adapt the navigation and contents), and deadline extend (long, short, or normal stated period).

Two different types of techniques are used to implement the SM: knowledge and behavioral based (Martins et al. 2008b). The knowledge-based adaptation typical-ly results for data collected through questionnaires and studies of the user, with the purpose to produce a set of initial heuristics. The behavioral adaptation results from the monitorization of the user during his activity.

The use of stereotypes classifies users in groups and generalizes student charac-teristics to that group (Martins et al. 2008b). The definition of the necessary cha-racteristics for the classification in stereotypes must take to consideration the gra-nularity degree wanted.


The behavioral adaptation can be implemented in two forms: the Overlay and the Perturbation methods (Martins et al. 2008b).

Those methods relate the student’s knowledge level with the learning objectives that he intends to reach (Martins et al. 2008b). Table 8.1 represents some characte-ristics present in AHS UM. Further, some systems based on the overlay model will be described. Some AHS that use the overlay model for UM are the next:

• The Adaptive Hypermedia Architecture System (AHA) is an Educational AHS. The purpose of this system is to deliver courses over the web. The UM is based on concepts knowledge that the user acquires by solving tests and reading the hypermedia pages of the course,

• The XAHM system in which the adaptation depends on the users level of ex-pertise about the known concepts of the system domain (which are a subset of all domain concepts),

• The ISIS-TUTOR is a system intended for learning the print formatting lan-guage of an information retrieval system CDS/ISIS/M which uses the overlay model with a set of integer counters,

• The HYPERFLEX, which is an adaptive hypertext browser. This system asks the user to specify his objectives and plans and uses a connected semantic net-work (Brusilovsky 1996).

Table 8.1 Some UM characteristics of some existing AHS

Systems \ Characteristics

User knowledge

Stereotypes User objectives

Prerequisite and

expertise

Preferences User

interests

History

ADAPTWEB X X X

AHA X X X X

AVANTI X X X

C-BOOK X

ANATOM-TUTOR

X X

ELM-ART X X X X

INTERBOOK X X X X X X

KBS HYPERBOOK

X X X X X X

INSPIRE X X X

HYPADAPTER X X

HYPERFLEX X X X

HYPLAN X

HYNECOS X X X X

ISIS-TUTOR X

KN-AHS X

METADOC X X

XAHM X X X X


Many systems use stereotypes for describing the user. HYPERTUTOR is a system that uses stereotypes for describing the user. This system employs exercises to obtain information about the users and uses stereotypes for UM. The student can belong to one of three groups: novice, medium or expert (Kavcic 2000).

Many times one method alone does not allow the modeling needs of the system and the combination of diverse methods has to be chosen (Martins et al. 2008b).

8.4 Learning Styles

The key of constructivism theory is that the student must be actively involved in the learning process. It is important that teachers understand that the construction of knowledge acquisition occurs from knowledge that the student already pos-sesses and differs from student to student. The role of the teachers is now to be a guide for the student (Jonassen 1991, Martins et al. 2008a). Students learn in dif-ferent ways and depend upon many different and personal factors (Kolb 2005).

The emphasis in students individual differences is also important in a context to recognize, design and support students activities (tasks). In constructivism learn-ing theory, students have different learning styles. Also, the capacity of adaptation in different social contexts and the constructive social aspect of knowledge must be taken in consideration (Jonassen 1991, Martins et al. 2008a).

Generally, learning styles is understood as something that intent to define mod-els of how a person learns. The application of strategies compatible with the pre-ferred learning style usually leads to better results. Some case studies have been proposed that teachers should assess the learning styles of their students and adapt their classroom and methods to best fit each student’s learning style (Kolb 2005, Stash et al. 2005). There are different learning styles models (based on different psychological theories) such as for example models based on (Kolb 2005):

• Personality (Ritu and Sugata 1999), • Information processing approach (Schmecks 1983), • Social Interaction (Reichmann and Grasha 1974), • Multidimensional factors (Ritu and Sugata 1999).

VARK Strategies is a questionnaire that provides users with a profile of their learning preferences. These preferences are about the ways that they want to access and select information. These models/strategies describe three basic learn-ing styles: visual learning (learn by seeing), auditory learning (learn by reading or hearing), and kinesthetic learning (learn by doing) (Martins et al. 2008a).

The model proposed by Kolb is the most commonly used inventory and is based on Piaget’s model on cognitive and learning development (Kolb 2005). Kolb Learning Styles Model is based on the four stages of the learning cycle: Concrete Experience (CE), Reflective Observation (RO), Abstract Conceptualiza-tion (AC) and Active Experimentation (AE) (Kolb 2005, Stash et al. 2005).


From these levels are defined the matrix to allow the classification of the Stu-dent Learning Styles (Table 8.2). The learning process must take into considera-tion the individual cognitive and emotional parts of the student. Student personal progress must be adapted and not generalized and repetitive (Jonassen 1991, Mar-tins et al. 2008b).

8.5 Metadata Standards

Inherent to the operation of PCMAT is the existence of a collection of digital LO and the need for these to be retrieved manually, to be managed by teachers and content developers, and automatically, to be presented to the students in accor-dance with the respective learning style and knowledge. To make this possible, a metadata record will be associated to each learning object. This metadata docu-ment will contain the information pertaining to the learning object creators, the learning object identification, such as title, short description and keywords to help the search and retrieval actions, and also information pertaining to the learning ob-ject pedagogical characteristics, to allow for the learning object to be retrieved by the system if found suitable to a particular students knowledge and learning style.

With these requirements in mind we were confronted with the option of devel-oping a PCMAT specific set of metadata or adopting an established standard. To be adopted, it was required that the metadata standard: 1) was extendable and ad-mitted the inclusion of alien elements; 2) admitted an eXtensible Markup Lan-guage (XML) document as a representation of a metadata instance, thus providing the necessary XML Schema.

As far as LO are concerned, there are two established metadata schemas cur-rently in use: the IEEE Learning Object Metadata (LOM) and the Dublin Core Metadata Element Set (DCMES) (Barker 2010, Currier 2008).

The IEEE LOM is a multi-part standard, currently consisting of a conceptual data schema (IEEE 2002) and its XML schema binding (IEEE 2005). This stan-dard defines a structured set of 76 data elements, covering a wide variety of cha-racteristics found to be relevant to define a learning object, and grouped in the fol-lowing categories (illustrated in Fig. 8.1):

Table 8.2 Kolb learning styles matrix (Kolb 2005)

Doing

Active Experimentation (AE)

Watching

Reflective Observation (RO)

Feeling

Concrete Experience (CE)

Accommodating (CE/AE) Diverging (CE/RO)

Thinking

Abstract Conceptualization (AC)

Converging (AC/AE) Assimilating (AC/RO)


Fig. 8.1 Elements and structure of the LOM conceptual data schema (from IMS Meta-data Best Practice Guide for IEEE 1484.12.1-2002 Standard for Learning Object Metadata, Version 1.3 Final Specification. http://www.imsglobal.org/metadata/mdv1p3/ immdbestv1p3.html)

• General information that describes the LO as a whole, as, for example, an iden-tifier, the title, a description, and a set of keywords,

• Life cycle information pertaining to the development of the learning object, • Meta-metadata information concerning the actual metadata document and not

the described learning object, • Technical information regarding technical requirements and technical characte-

ristics of the learning object, • Educational information about the LO educational and pedagogic aspects, • Rights information on the LO intellectual property rights and conditions of use, • Relation information that defines the relationship of the described learning ob-

ject with other learning objects, • Annotation space for storing comments on the learning objects usage, • Classification description of the learning object in accordance with different

classification systems.


Within each category an element or a group of elements may be repeated, if ne-cessary, and every element is optional. According to the standard, a LOM instance that contains no value for any of the LOM data elements is a conforming instance (IEEE 2002).

Nonetheless, if use is made of a LOM data element, this shall be made respect-ing its structure within the schema and its value should be in accordance with the data types and vocabularies defined in the schema. However, the LOM standard allows the insertion of elements, or even attributes to the LOM elements, other than the ones foreseen within the standard, provided that these are identified by a specific namespace. This possibility allows a community of users to specify which elements and vocabularies they will use, building a LOM application profile.

Perhaps due to its status as an international standard, or because it was devel-oped from the beginning with the purpose of characterizing a learning object, or maybe due to the possibility of developing specific application profiles, LOM has been widely implemented by repositories. ARIADNE, SMETE, Learning Matrix, iLumina, MERLOT, HEAL, CAREO, Learn Alberta Online Curriculum Reposito-ry and Lydia Inc. are some examples of repositories that implemented the LOM standard (Neven 2002).

The DCMES is a vocabulary of fifteen properties for use in resource descrip-tion (DCMI 2010). Standardized as ISO Standard 15836:2009, the core Element Set is intended to be broad and generic, usable for describing a wide range of re-sources and comprises the following elements: contributor, coverage, creator, date, description, format, identifier, language, publisher, relation, rights, source, subject, title and type. All these elements are optional and may be repeated if re-quired. Dated 1998, this core set in now part of a larger set of metadata vocabula-ries known as DCMI Meta-data Terms (DCMI-TERMS). Aware of the fact that the metadata needs of particular communities and applications are very diverse, the Dublin Core Metadata Initiative (DCMI) provides a framework for designing a Dublin Core Application Profile (DCAP). As stated in the Guidelines for DCAP (DCMI 2008), a DCAP is a generic construct for designing metadata records that does not require the use of DCMI-TERMS, a DCAP can use any terms that are de-fined on the basis of Resource Description Framework (RDF), combining terms from multiple namespaces as needed.

A DCAP is a document (or set of documents) that specifies and describes the metadata used in a particular application, including guidance for metadata creators and clear specifications for metadata developers, and it consists of the following components:

• Functional requirements (mandatory) describes what a community wants to ac-complish with its application,

• Domain model (mandatory) characterizes the types of things described by the metadata and their relationships,

• Description set profile (mandatory) enumerates the metadata terms to be used and the rules for their use,


• Usage guidelines (optional) describe how to apply the application profile, how the used properties are intended to be used in the application context,

• Syntax guidelines (optional) define the machine syntax that will be used to en-code the data.

Still in accordance with the aforementioned guidelines, application profiles should be developed by a team with specialized knowledge of the resources that need to be described, the metadata to be used in the description of those resources, as well as an understanding of the Semantic Web and the linked data environment. Thus, following this recommendation, the DC-Education Community (DC-Ed) decided at the DC-2007 Conference in Singapore to form a new Task Group in order to finish the DC-Education Application Profile by mid-2008 (DCMI 2007). Howev-er, in the meeting held by the DC-Ed on October 20th, 2010, in Pittsburgh, the de-velopment work was still being carried out on the domain model of the DC-Education Application Profile. At this meeting it was foreseen that the complete documentation would is available since July-August 2011 (DCMI 2007).

Notwithstanding, DCMES has been adopted in particular by libraries and arc-hives worldwide, mostly because it is an integral part of the Open Archives Initia-tive Protocol for Metadata Harvesting (OAI-PMH) (OAI 2008). The OAI-PMH allows for compliant metadata from different repositories to be harvested automat-ically in order to build a centralized point of search. The implementation of this protocol has been quite successful due to the availability of open source freeware like DSpace, Fedora or Greenstone.

In the view of characteristics and development of the IEEE LOM and DCMES, and since PCMAT is at an early stage, it was decided to adopt IEEE LOM as the basis for the development of PCMATs domain model, mainly because it defines a large set of metadata from which one can choose the elements found relevant to characterize a specific set of LO and also because it allows the insertion of non-LOM elements or attributes if deemed necessary.

8.6 PCMAT Platform

The PCMAT system allows students to autonomously create and consolidate knowledge, with permanent automatic feedback and support, through instructional methodologies and educational activities explored in a constructivist manner.

The adaptation of the application is based on progressive self-assessment exer-cises solved by the student that evolve in difficulty and domain topics. The curri-culum is defined by the teacher but is dynamically individualized to the student according to the current level of knowledge, competences, abilities, and learning path. The platform provides contextualized access to tutorials if the students fail a progression step.


Others goals of the PCMAT include:

1. To define a new strategies and architecture for the implementation of an Adap-tive Hypermedia Educational platform to support and improve Mathematics in basic schools,

2. To define the student model that describes the information, knowledge, prefe-rences, and learning style of the user (Sect. 8.6.2),

3. To define the process and tools to produce LO aligned with the LOM standard, and conceive a knowledge representation of the students attributes concerning the emotional characteristics and develop a set of adaptive and dynamic peda-gogical strategies to put forward this hybrid model (Sect. 8.6.3);

4. To develop the system functionalities for the interaction model (interface adap-tation) considering the objectives, profile and knowledge of the student and the Domain and Adaptation model (Sect. 8.6.4),

5. To improve results and knowledge in Mathematics in Basic Schools (Sect. 8.7 and 8.8).

8.6.1 System Architecture

The PCMAT platform application is based on AHA. AHA is a Web based adap-tive hypermedia system and is able to perform adaptation that is based on the us-er’s browsing actions (De Bra et al. 2004). However, our system has significant differences with AHA, namely:

• The definition and implementation of the SM (Sect 8.6.2), • The existence of an authoring tool for metadata for the LO (Sect. 8.6.3), • The definition and implementation of the domain model and adaptation rules, • The application for the creation of questions and automatic generation of tests

(Sect. 8.6.4), • The pedagogical model definition and implementation (Sect. 8.6.4).

PCMAT is a project built on Java Servlet technology, use XML, eXtensible HyperText Markup Language (XHTML) and Cascading Style Sheets (CSS). The PCMAT platform (Fig. 8.2) is based on a constructivist approach, and aims to as-sess the user knowledge and to present contents and activities adapted to the cur-rent needs and learning style of the student.

Several models have been used to implement AHS, such as the Dexter Model, Amsterdam Hypermedia Model, Adaptive Hypermedia Application Model (AHAM), or Munich Reference Model (Wu et al. 1999). The system architecture, presented in Fig. 8.3, is based on some strategies already used in the AHAM model.


Fig. 8.2 PCMAT – Mathematics collaborative educational system

Therefore, in our system, the user requests an activity by clicking on a link in a Web page. Every page corresponds to a domain concept or a cluster of domain concepts. The system checks the suitability of the requested page for the current user. The adaptation rules used to check if the page is suitable are defined in the adaptation model. Updates to the SM are inferred from the interaction between the user and the application. The answers of the user allow the system to estimate the users knowledge level about the concepts related with the requested content.

Fig. 8.3 System architecture


8.6.2 Student Model Implementation

Two different types of techniques can be used to implement the SM: Knowledge and Behavioral based (Kobsa 1993, Martins et al. 2008b). The Knowledge-based adaptation results for data collected through questionnaires and studies of the user, with the purpose to produce a set of initial heuristics. The behavioral adaptation results from monitoring of the user during his activity (Martins et al. 2008).

The use of stereotypes allows classifying users in groups and generalizes stu-dent characteristics to that group (Martins et al. 2008). The definition of the neces-sary characteristics for the classification in stereotypes must take in consideration the desirable granularity degree (Martins et al. 2008).

The approach used to build the UM is the Stereotype Model with the overlay model for the knowledge representation of the student. The representation of the stereotype is hierarchical. Stereotypes for users with different knowledge have been used to adapt information, interface, scenario, goals and plans.

The user modeling process starts with the identification of the user subgroup using questionnaires and learning styles (Fig. 8.4), then the identification of key characteristics (each one to identify the members of a user-subgroup), and finally the representation in hierarchical ordered stereotypes with inheritance. We also use the reliability analysis in Software for Statistical Analysis (SPSS) to compute the Cronbach’s alpha reliability coefficient in every questionnaire (Woodward et al. 1983). Related to the learning style questionnaire, the value of the Cronbach’s alpha coefficient is 0.91. So we can affirm that the internal consistency is very good, suggesting that the items have high internal consistency.

The user plan is a sequence of user actions that allows him to achieve a certain goal. The System observes the user actions and tries to infer all possible user plans. This goal is possible because our system has a library of all possible user actions and the preconditions of those actions.

A large number of criteria are established in the Stereotype definition depend-ing on the adaptation goals (Martins et al. 2008a, Martins et al. 2008b). The defi-nition of the characteristics of the student account the Domain Model and the con-structivist approach of the application. For example, Table 8.3 presents a generic student profile used by PCMAT. The tools used to collect data are (Fig. 8.5):

• For the DID:

− Questionnaires, − Certificates, − Curriculum Vitae, − Learning Styles, − Psychological exams.

• For the DDD:

− Questionnaires, − Exams.


Fig. 8.4 Questionnaires and learning preferences

Fig. 8.5 UM architecture

For the definition of the Learning Styles of the student we are using the Kolb Learning Styles Matrix (Table 8.2). Concerning that and the objective of Domain Dependent Data, users aptitude and assessments result will be monitoring (Fig. 8.6). For each student profile, PCMAT keep an XML file.


Table 8.3 Characteristics used in the SM

Model Profile Characteristics Domain Independent Data Generic Profile Personal information

Demographic data Academics background Qualifications Knowledge (background know-ledge) Deficiencies: visual or others Application domain

Psychological profile Learning style Cognitive capacities Traces of the personality Inheritance of characteristics

Domain Dependent Data Objectives Planning / Plan Complete description of the na-vigation Knowledge acquired Results of evaluations Context model Aptitude Interests Deadline extend

This XML file contain the data related to the DDD and DID. The structure and

type of the data are validated by the SM PCMAT Schema (see Sect. 8.1). Every activity corresponds to a set of concepts in the Domain Model and in the

UM (implemented through an overlay model). Each concept has an attribute to represent the student’s knowledge. The value of the knowledge attribute is an in-teger between 0 and 100. The knowledge value about each concept is updated by the interaction model (Sect. 8.6.4 - domain and interaction model). Also, the learn-ing style for each student is update by the interaction model as well.

Fig. 8.6 Domain dependent data architecture of our UM


The requested page presentation is adapted by adaptation rules in two ways:

• Information content of the page can be changed (e.g., by conditionally includ-ing or hiding fragments),

• Links in the page can be manipulated. Links to pages that are considered is not suitable and can be annotated (for example with a red marker) or can be hidden; in addiction, the link route can be changed as well.

System adaptation (adaptation to content or links) to the user can cause UM up-dates as well, as the code of SM schema outlined as follows:

<xsd:element name=” Student_Model ”> <xsd:complexType> <xsd:sequence minOccurs=”1” maxOccurs=”1”> <!−−definition of data related with DDD and DID −−> <xsd:element name=”Domain_Independent_Data” type=”TDomain_Independent_Data”/> <xsd:element name=”Domain_Dependent_Data” type=”TDomain_Dependent_Data” /> </xsd:sequence> </xsd:complexType> </xsd:element> <xsd:complexType name=” TDomain_Independent_Data ”> <xsd:sequence> <xsd:element name=”Generic_Profile” type=”TGeneric_Profile” /> <xsd:element name=”Cognitive_Profile” type=”TCognitive_Profile” /> </ xsd:sequence> </xsd:complexType> <xsd:complexType name=” TGeneric Profile ”> <xsd:sequence minOccurs=”1” maxOccurs=”1”> <xsd:element name=”Personal_Information” type=”TPersonal_Information” /> <xsd:element name=”Academic_Background” type=”TAcademic” /> <xsd:element name=”Demographic_data” type=”TDemographic_data” /> <xsd:element name=”Background_Knowledge” type=”TBackground_Knowledge” /> </xsd:sequence> </ xsd:complexType> <xsd:complexType name=” TDomain_Dependent_Data ”> <xsd:sequence>

<xsd:element name=”Domain_Knowledge” type=”TBackground_Knowledge” /> <xsd:element name=”Task made” type=”TTask_made” /> ... ... </xsd:sequence> </xsd:complexType> ...


8.6.3 Authoring Tool for Metadata for the Learning Objects

With the aim of teachers and developers to create metadata instances pertaining to the respective LO it was built a web application. There are tools available free-ware, as Reload (http://www.reload.ac.uk/) or LomPad (http://helios.licef.ca:8080/ LomPad/en/ in- dex.htm), which allow the writing of metadata instances com-pliant to IEEE LOM. However, they are desktop applications and do not hold a Portuguese version. Hence, we acknowledge the need to develop our own metada-ta authoring tool, as the one pictured in Fig. 8.7.

This application is developed in Java and uses an XML document as its confi-guration file. This XML file contains an instance of every element identified in the IEEE LOM and it may contain other elements alien to the standard. For instance, the element used to point out the compatibility of a learning object with a learning style is one of these alien elements. To each element, several attributes were added that determine several configurations options undertaken by the application and, one in particular, determines if a certain element will be used or not to character-ize a learning object. Whenever feasible some elements are present pre-filled with default values and others have a vocabulary list from where to choose one or more values, even if in some cases such is not foreseen in IEEE LOM.

Keyword is an example of such an element. In order to provide the users of the platform with the least noise possible during the process of searching the PCMAT LO database, the keywords associated with each learning object are selected from a list build from a mathematical thesaurus. Fig. 8.8 shows a screen of the popup window containing the keywords list.

Fig. 8.7 PCMAT metadata application


Fig. 8.8 PCMAT metadata application – keywords list

8.6.4 Domain and Interaction Models Development

The Domain Model represents concept hierarchies and the related structure used to represent an estimation of the user knowledge level, by means of a quantitative value. The Domain and Adaptation Models use the student characteristics represented in the SM. The knowledge about the user, represented in the SM, is used by the Adaptation Model to define a specific domain concept graph, adapted from the Domain Model, in order to address the current user needs.

The path used in the graph is defined by: the interaction with the student using a progressive assessment, the student knowledge representation defined by the Overlay Model and the user characteristics in the SM.

The system adaptation (adaptation of contents or links) to the user can produce UM updates as well. The results of Domain and Adaptation Models achieved are: The development of the concept graph by each user to use in the Adaptation rules and the Definition of the Adaptation Model using the characteristics of the student in the UM.

The Interaction Model represents and defines the interaction between the user and the application (Martins et al. 2008a). The Interaction Model enables the sys-tem to present the following functionalities, which are sketched in Fig. 8.9:

• To change the content presentation, • To manipulate the structure of links or the links annotation with the objective to

allow the students to reach the learning goals proposed in their training, • To guide the user to the relevant information and keep him away from the irre-

levant information or pages that he still would not be able to understand, it is used the technique generally known by link adaptation (hiding, disabling, and removal).


Fig. 8.9 Example of a PCMAT content

The platform in the content page supplies additional or alternative information to certify that the most relevant information is shown. The technique that is used for this task is generally known by content adaptation. The Domain Model represents concept graph hierarchies. The concept graph is set in a XML file as follows:

<concept_hierarchies> <concept_relation> <concept_name>A</ concept_name> <hierarchy> <firstchild>A1</ firstchild> <nextsibling>A2</ nextsibling> <!−− root element of the concept graph !−−> <parent>proporcionalidade</ parent> </hierarchy> <children> <concept_name>A1</ concept_name> <concept_name>A2</ concept_name> <concept_name>A3</ concept_name> <concept_name>A4</ concept_name> </children> ... </concept_relation> <concept_relation> <concept_name>A1</ concept_name> <hierarchy> <firstchild></ firstchild> <nextsibling> A2</ nextsibling> <parent>A</ parent> </hierarchy> <children></ children> </concept_relation> </ concept_hierarchies>


The knowledge about the user, represented in the SM, is used by the Adaptation Rules Model to define a specific domain concept graph, adapted from the Domain Model, in order to address the current user needs.

The path used in the graph is defined by:

• The interaction with the student using a progressive assessment, • The student knowledge representation defined by the Overlay Model, • The user characteristics in the SM.

The Adaptation Rules Model is defined in a XML file according to a couple of items: 1) for each concept PCMAT have a set of attributes; 2) each attribute is re-lated with a set of adaptation rules. As regards with the attribute concept, it con-tains: a default value and a list of rules (i.e., set of adaptation rules). A rule holds: a Boolean expression to involve attributes of concepts or attributes of the SM (i.e., this expression must be true for the resulting sequencing action to be triggered) and a rule action that can update some attributes of concepts or attributes of the SM.

When the user tries to access a resource page (concept) the next events are triggered:

• The access attribute of the concept is accessed, • All the rules of access attribute are evaluated and activated, • One of these rules must evaluate the value of the suitability attribute of the con-

cept, • Another of these rules is responsible to assign values to the resource visibility

attribute of the concept.

The suitability attribute is used to define if a page (concept) is suitable to the learner. The value of this attribute results from the evaluation of a condition expressing the prerequisites to access the current concept. These prerequisites are defined in the pedagogical model and are formed by the minimum knowledge levels the student attained in a set of concepts. This pedagogical model is defined by teachers and is also implemented through a XML file. The following rule shows the mechanism used to update the suitability attribute:

<rule> <condition> <!−− Condition definition </condition> <rule_effect> <concept> <name>concept_name</name> <attribute> suitability </attribute> <value>true</value> </concept> </rule_effect> </rule>


If the value of the attribute concept.suitability associated to a page content is false then the page is not shown. Being the case, the student is conducted to other con-tents or to specific content fragments. The attribute knowledge receives a value between 0 and 100, and is used to represent an estimative of the knowledge level about a particular concept.

This attribute is updated during student activities, and can be used, for instance, to make a decision about to show or hide fragments, or to adapt links (hiding links or adding annotations to links).

We rely on the constructivist approach to suggest contents and activities to the student according with his behavior in previous activities (Martins et al. 2008a). Each activity or content (page, content fragment, etc) is associated to a prominent learning preference. The learning preference associated to the student is also represented in the SM through the attributes personal.lst (learn by reading and hearing), personal.lsv (visual learning) and personal.lsp (practical learning). When the student uses the system for the first time, these attributes are initialized from the results of the learning styles questionnaire (Sect. 8.6.2).

When the student accomplishes successfully an activity in PCMAT, the know-ledge level of the concepts involved is updated by the following mechanism:

Let A1,A2,A3,...,An be the set of concepts associated with the activity For each i in {1,2,3,...,n} Ai.knowledge = min(Ai.knowledge+Ai.knowledge*0.25,100) Let B1,B2,B3,...,Bm be the set of concepts from which concept Ai depends For each i in {1,2,3,...,m} Bi.knowledge = min(Bi.knowledge+Bi.knowledge*0.1,100)

A similar mechanism is used to update the learning preference of the student. The following example shows how the learning preference attributes are updated when the prominent learning preference attribute associated to the activity is personal.lst:

personal.lst = min(personal.lst + 1,10)

If personal.lsv >= personal.lsp then personal.lsv= max(personal.lsv−1,0)

If personal.lsv < personal.lsp then personal.lsp = max(personal.lsp−1,0)

The same algorithm is used in case of an activity whose learning preference is personal.lsv or personal.lsp. In case of student failure in an activity, a similar ap-proach is used to downgrade the concept knowledge level and the learning prefe-rence attribute. The PCMAT has an authoring module to make questions and au-tomatic generation of tests. The front-end of the application is developed using XHTML, CSS and Javascript, and the back-end is developed in Java.

This feature allows users to make test questions which are simple or paramete-rized. All questions are related to at least one concept and at most to five concepts. Each question is classified according its compatibility to a learning preference.


The body of the question is directly inserted by the user (Fig. 8.10), but it is al-so introduced by uploading a text file with the question. A resource, such as an image file, may be added as well. The user decides whether the question will be a multiple choice question or a restricted answer question (Fig. 8.11). In the case of restricted answer questions, the correct answer can be given in several ways, that is to say the word order may differ. It is therefore necessary to parse the answer, using a probabilistic natural language parser, to verify if it is correct or not.

Fig. 8.10 User interface for the creation of questions

The creation of parameterized questions (Fig. 8.12) requires the user to comply with certain rules. For instance, he/she can only utilize a maximum of five differ-ent variables which must have specific names and structure. This makes it possible to find the variables in the text and replace them by the given parameters. A table is provided for the insertion of parameter values, thus ensuring each parameter will be correctly associated with each variable.

Aside from adding new questions to the system, the user can also use it to gen-erate tests. He/she must input the number of questions the test should be composed of and the concepts to which those questions are related. The system will create a test by randomly choosing and retrieving questions from the database (Fig. 8.13).


If a chosen question happens to be a parameterized question, the system will ran-domly choose one of the possible sets of parameters and replace the questions va-riables with their respective values. After all the questions have been chosen the system creates an XHTML file with the finalized test.

The results achieved with the PCMAT Domain and Adaptation Model are two: the development of the concept graph by each user to use in the adaptation rules and the Definition of the Adaptation Model using the characteristics of the student in the UM.

Fig. 8.11 Creation of a restricted answer question

Resuming, the features of PCMAT interaction model are: 1) show different content in different formats; 2) to define the structure of the links or the links an-notation; 3) to guide the student to the relevant information and keep him away from the irrelevant information or pages; 4) to supply, in the content (page), addi-tional or alternative information; 5) activities in different formats (Word, PDF, Flash and others), using LO; 6) assessments adjusted by difficulty, knowledge and profile of the student; 7) news about national mathematics events; 8) online references.


8.7 Results Analysis

The learning domain chosen by the teachers to perform the first evaluation of the system was Direct Proportion unit, included in the mathematics course in the 7th grade. The students are 12 and 13 years old. The first version of the framework was already implemented, tested and evaluated in learning processes in two ma-thematics basic schools: 1) one class with 26 students of the 7th basic year from the first school, 2) two classes, one with 24 students and the other with 27 students of the 7th grade from the second school.

Fig. 8.12 Creation of a parameterized question

None of the students have previous experience of using some kind of AHS, but more than 75% of them were familiar with personal computers (PC). Generally, they use PC for the Internet browsing and for the games playing.

The first step of the evaluation was to divide randomly each class into two groups: experimental and control group. The random process has some criteria to select and put the students in each group:


• If possible each group must have the same students number (or approximate), • If possible each group must have the same number (or approximate) of excel-

lent students. For this effect, the students have taken a diagnostics test, • Each group have a similar number of students with the same learning prefe-

rence; for this effect a learning style questionnaire was made (see Sect. 8.6.2), • Each group has a similar distribution of student gender.

Fig. 8.13 Example of a XHTML test composed of one question


The results of this first step were the following:

• Creation of two groups in the first school (experimental and control group); each group has 13 students. Also each group has one teacher to follow the learning process,

• Creation of two groups in the second school (experimental and control group). The group using PCMAT has 26 students. Also each group has one teacher to follow the learning process,

• Analyzing the data of each group related to the learning preference, 58% of students of the experimental group have a visual learning preference. In the control group the value of visual learning preference was 62%. Some case stu-dies have demonstrated that: learning style in Basic Schools is more visual.

Thus, 39 students of the experimental group used PCMAT to learn Direct Propor-tion during fifteen days; and 37 students (control group) learnt Direct Proportion with the traditionally learning methodology during fifteen days. Using 4 different teachers for reducing the correlation between the quality of the learning process and the competence of the teacher.

The second step was to use questionnaires to collect data for the PCMAT SM (DDD and DID, but some data have already been collected in the first evaluation step). The second step was applied to all the students with the goal to validate the data. The third evaluation step was to make a final test to all students. The test is the same for the entire students (experimental and control group).

The collected evaluation data showed the next findings:

• In the first school the average of student scores in the experimental group is higher than the average of student scores in the control group, mean μ = 62.0 (σ = 17.0 (standard deviation)) vs. μ = 55.3, but the observed differences are not statistically significant (p = 0.281). The two groups were statistically compared using a two sided, independent samples t test with a 0.05 (5%) critical level of significance (t = 1.10, degrees of freedom = 24),

• In the second school, the average of student scores in the experimental group is higher than the average of student scores in the control group; μ = 61.5 (σ = 21.5) vs. μ = 54.0 (σ = 14.9), but the observed differences are not statistically significant (p = 0.157). The two groups were statistically compared using a two sided, independent samples t test with a 0.05 (5%) critical level of significance (t = 1.44, degrees of freedom = 48),

• And, analyzing simultaneously both schools, the average of student scores in the experimental group is higher than the average of student scores in the con-trol group, μ = 61.7 (σ = 19.9) vs. μ = 54.4 (σ = 14.3). Although the observed differences are not statistically significant (p = 0.073) the difference between groups seems to be clear. Again, the two groups were statistically compared us-ing a two sided, independent samples t test with a 0.05 (5%) critical level of significance (t = 1.82, degrees of freedom = 74).

These values are good indicators and may allow us to conclude about the adequate features and effectiveness of PCMAT system. Nevertheless, additional results, with an increased sample size, will allow validating these assumptions.


Students also perceived this tool as very relevant for their learning, as a self- operating application to be integrated in a more global learning strategy that in-cludes also tutoring (direct contact with the teacher) and peer learning. Teachers agreed with these definitions of the platform, as well.

Also, the collected evaluation data showed that the development of two author-ing tools, the authoring tool for metadata of the LO (Sect. 8.6.3) and the authoring tool for the creation of questions and automatic generation of tests (Sect. 8.6.4), showed a very high degree of interest and motivation from teachers alike, result-ing from its use.

Another result was the definition of a new strategy and architecture for the im-plementation of an Educational AHS in basic schools in Portugal (see Sect. 8.6.1). The capacity of adaptation of these tools in relation to the different needs and the diversity of the background of each student is necessary for bigger effectiveness and efficiency of the learning process.

The main result of the present development is the definition and validation of the characteristics of the student to be stored and the selection of the techniques of the Overlay Model and stereotypes for the representation of the user knowledge in the SM (see Sect. 8.6.2). Moreover, the present work allowed defining an adapta-tion and interaction model (see Sect. 8.6.4). Next school year, PCMAT will be tested in another school and also in the two previous schools.

8.8 Conclusions

In the scientific area of UM, numerous research and developed systems already seem to promise good results (Kules 2000), but yet some experimentation and im-plementation are still necessary to conclude about the utility of the UM. That is, the experimentation and implementation of these systems are still very scarce to determine the utility of some of the referred applications.

The intelligent behavior of the learning platform is based on the existence of a tentative description of the student – the SM. The contents of this model and the student most prominent learning style are used by an interaction model to select the most appropriate response to student actions.

The difficulty in building a SM using an Overlay Model for a given student depends on the type of information we want to store in the model. The main result of the present development is the validation of a SM that will allow the support of adaptive functionalities based on the use of LOM standard to truly support a con-structivist learning and cognitive path. The number and type of characteristics to use in the SM depend on the finality of each system, but some relevance is in the cognitive part, learning styles and student knowledge.

The analysis, application, implementation, integration and evaluation of tech-niques used to adapt the presentation and navigation in educational AHS, using metadata for the LO and user modeling, will contribute to improve the value and implementation of e-learning in Basic Schools, in a way to make possible the edu-cational process more adaptive to the student learning preference.


The capacity of the adaptation of these tools, considering the different necessi-ties and the diversity of individual information source of each student will be ne-cessary, namely for more and more efficiency in the learning process.

It will also be possible to introduce more responsibility to the student in his learning process, namely in the individualization and adaptability of learning.

The PCMAT project allowed us to define new strategies for the implementation of an AHS to support and improve Mathematics in basic Schools context. Addi-tional contributes of the project includes the definition of a SM describing the in-formation, knowledge, preferences, and learning style of the user; the definition of a process and the tools needed to produce LO aligned with the LOM standard; and the implementation of a set of adaptive and dynamic pedagogical strategies.

The outcome results are good indicators and may allow us to conclude about the adequate features and effectiveness of an AHS to improve e-learning based systems in a basic school environment in mathematics. However, further experi-ments will be necessary to confirm these results.

One of the next steps in the development of the platform will be the inclusion of a chat environment that will allow capturing the messages changed between learners during the learning process. The goal is to infer learners’ doubts from the messages. For that we will use mechanisms able to explore natural languages sen-tences and clustering algorithms to identify difficulties among the students. This feature will turn the platform into a full collaborative platform, where students may share their difficulties and to get appropriate feedback.

Acknowledgments. The authors would like to acknowledge FCT, FEDER, POCTI, POSI, POCI and POSC for their support to GECAD unit, and the project PCMAT (PTDS/CED/ 108339/2008).

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Abbreviations

AHA Adaptive Hypermedia Architecture System AHAM Adaptive Hypermedia Application Model AHS Adaptive Hypermedia System CSS Cascading Style Sheets DCAP Dublin Core Application Profile DCMES Dublin Core Metadata Element Set DCMI Dublin Core Metadata Initiative DDD Domain Dependent Data DID Domain Independent Data LO Learning Object LOM Learning Object Metadata SM Student Model SPSS Software for Statistical Analysis UM User Modeling XHTML eXtensible HyperText Markup Language XML eXtensible Markup Language

PCMAT – Mathematics Collaborative Educational System

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