QGM – A SYSTEM TO IMPROVE MATHS e-LEARNING

José Casimiro Pereira

and Joaquim Sousa Pinto

Instituto Politécnico de Tomar, Quinta do Contador, 2300-313 Tomar, Portugal

Universidade de Aveiro, Campus de Santiago, 3810-193 Aveiro, Portugal

Keywords: Learning Objects, LOM, MathML, XML.

Abstract: The main goal of Projecto Matemática Ensino (Mathematics Teaching Project) – PmatE – is to promote the

learning of mathematics. To achieve that, PmatE has been developing since 1990 an internet project

especially designed to increase the interest of students in the discipline. The core of the Project anchors on

the so-called “Questions Generator Model” (from the Portuguese “Modelo Gerador de Questões”). Each

“model” is a tool based on parameterized expressions, which usually allows thousands of different questions

to be generated (different formulations of the same “model”) formally equivalent in terms of pedagogic

content. The scope of this paper is to redesign the former “model” using the IEEE LOM’s structure to define

the learning object and redefine the model structure itself to allow for independence of the technological

platform used to support the Project.

1 INTRODUCTION

The Mathematics Department of Aveiro University

(Portugal) has been developing a project named

Projecto Matemática Ensino (Mathematics Teaching

Project) – PmatE since 1990 which aims at

promoting the learning of mathematics using new

information technologies. The central focus of this

project is a structure called modelo gerador de

questões (questions generator model) (Vieira,

Carvalho et al., 2004).

Each questions generator model (QGM) is a

piece of software that generates questions about a

predefined theme, based upon scientific and learning

objectives. These questions are randomly generated

with parameterized expressions; the parameters

depend on the age and educational level of their

users. For each question, there are at least four

possible answers, again randomly chosen among a

set of possible answers.

Matching a question to an answer a true or false

statement is obtained. All questions may be true or

false. The user’s task is to answer correctly to each

statement. The QGM’s may be organized in

“competition mode” or in “evaluation and learning

mode”. In the competition mode, a collaborative

competition is suggested. In the learning and

evaluation mode, the cooperation among

schoolmates and teacher is an intrinsic aspect of the

process (Isidro, Pinto et al., 2005). Whatever the

mode, the evaluations to be performed by the

students will use, approximately, 20 models.

The randomness of the QGM’s is the key of this

project. In fact, for the same QGM thousands of

different formulations with the same pedagogical

and scientific value can be formulated. This feature

enables two computers running side-by-side to have

different questions and a different set of possible

answers while using the same QGM. Combining the

previous statement with the fact that the time to

perform the evaluation is restricted, makes almost

impossible for two students to practise any form of

plagiarism (Pinto, Oliveira et al., 2007).

To materialise this project, PmatE has

continuously developed an information system that

offers a set of contents related with the several

disciplines of Mathematics. Portuguese and Biology

QGM’s are also available recently. These learning

materials are, however, prisoners of the technology

used in their creation. They are all coded in Visual

Basic 6.0 and stored in ActiveX dynamic link

libraries (dll’s). The content of these libraries are

used to generate the questions that will be presented

in a browser, using the ASP technology (Isidro,

Fernandes et al., 2003). Such technological

260

Pereira J. and Sousa Pinto J. (2009).

QGM – A SYSTEM TO IMPROVE MATHS e-LEARNING.

In Proceedings of the First International Conference on Computer Supported Education, pages 259-265

DOI: 10.5220/0001976302590265

 SciTePress

dependency implies that sharing or reusing QGM’s

is very difficult, if not impossible.

The next two pictures show the system look and

feel. They represent two distinct formulations of the

QGM with ID 76.

Figure 1: Using QGM number 76 (Pinto, Oliveira et al.,

2007).

Figure 2: Another formulation of QGM number 76 (Pinto,

Oliveira et al., 2007).

The pictures above show the power of the

QGM’s. To make it possible for the QGM’s to be

shared throughout Portuguese and international

networks of Learning Objects, PmatE is promoting

their adaptation. To do that, we are dealing with two

distinct concerns: the QGM’s must become

independent from the technological platform and

must comply with the international standards used to

describe Learning Objects.

In this article, a description is given of the efforts

made to transform the QGM’s. First, we present the

QGM LOM structure and the arrangements made to

adapt it. Then we present the new QGM structure

and syntax and finally we present the efforts done to

test it.

2 LEARNING OBJECTS

There is no consensus on the definition of Learning

Objects (LO) (Daniel and Mohan, 2004). Therefore,

we will use the IEEE definition: “a learning object is

defined as any entity, digital or non-digital, that may

be used for learning, education or training” (IEEE,

2002).

According to that definition, we can consider that

the QGM’s defined and built by PmatE are suitable

to be viewed as learning objects.

2.1 Learning Objects Metadata (LOM)

Before we start, just a few introductory questions:

What is a Learning Object? In a simple way, a

Learning Object is the conjunction of metadata

about a learning object and the learning object itself.

What is metadata? Metadata is knowledge about

knowledge (Taylor, 2003)) or information about

information. Why is metadata so important? The

major reason is that with such information we are

able to understand the usefulness of a learning

object.

In 15 July 2002, the IEEE published the final

“Draft Standard About Learning Objects Metadata”

(IEEE, 2002). This was the end of a long journey

that started in 1997 with the efforts of the IMS

Project, a non-profit consortium of US institutions of

higher education (Consortium, 2006). They aimed to

develop a specification for learning content metadata

and an open market-based standard for online

learning. One year later, IMS and ARIADNE

(Alliance of Remote Instructional Authoring and

Distribution Networks for Europe) proposed

together to the IEEE, a new proposal of the Learning

Objects Metadata. After four years of development,

the final release was published (IEEE, 2002). This

final release proposed a structure to represent the

metadata about an LO. This strongly hierarchical

XML-based structure has nine sessions:

• General – describes the general information of

the LO;

• Lifecycle – specifies the actual state of the LO

and its evolution;

• Meta-Metadata – specifies the knowledge

about the LOM, not about the LO;

• Technical – describes the technical

requirements and technical characteristics of

LO;

• Educational – describes the pedagogical and

educational characteristics of the LO;

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261

• Rights – describes the copyrights and terms of

use of the LO;

• Relation – describes the kind of links that this

LO could have with other LOs;

• Annotation – in this session comments on the

educational use of the LO can be provided;

• Classification – specifies the classification

system of the LO, if any.

Together they form the LOMv1.0 Base Schema.

Figure 3: The LOM structure (Barker 2005).

Every element has sub-elements, and several of

them have, again, new sub-elements. All the

elements have their predefined data type. There are

two kinds of data types: aggregate data elements and

simple data elements. Simple data elements have

individual values, defined by scope and data type.

For aggregate data elements, LOM v1.0 Base

Schema does not define individual values.

Whenever possible, the LOM v1.0 Base Schema

restricts the values a user can choose to a predefined

list. This is useful to increase the interoperability of

the LOM within several systems.

For IEEE, LOM can be defined as strictly

conforming if it complies with all the rules and has

no extended elements or, as conforming, if it has

extended elements. Extended elements should have

their own namespace, instead of using the LOM’s

namespace.

2.2 The LOM Models

As mentioned above, the QGMs are captive of the

technological solution that had made them grow.

Bearing that in mind, PmatE started to redefine the

structure of the QGMs. This new model follows the

Learning Object architecture: the QGM has two

distinct sections:

• the metadata about the QGM, described using

the LOM structure;

and

• the QGM itself.

The metadata section will contain the necessary

to process information to allow compliance with the

LOM’s structure. Almost every LOM elements will

be used.

The QGM internal structure will be completely

rebuilt. The new structure is one of the scopes of this

article and will be further discussed in Session 5.

2.3 The <bibliography> Element

Besides the LOM architecture, it accomplishes

almost everything. However, during the process of

QGMs implementation in LOM, we faced a

problem: where to place the bibliographic references

necessary to produce and support scientifically a

QGM?

Our first attempt was to describe the

bibliographic issues in the

<annotation> element of

the LOM’s structure. Nevertheless, that solution

conflicts with the nature of the LOMs – the

interoperability between several metadata systems.

Therefore, we decided to create a new element

(the 10

) in the LOM’s proposed structure – the

<bibliography> element. Our goal is to define the

<bibliography> element accordingly to leading

software in this area that represents the bibliography.

This procedure will allow to export/import

bibliographic information to/from LOM’s structure.

This new element follows the Portuguese

standard for bibliographic references. We also

studied other formats used to describe bibliographic

references, in XML: EndNote (EndNote, 2007) and

BibTex (Patashnik and Feder, 2006; Gundersen and

Hendrikse, 2007).

2.3.1 The <bibliography> Structure – 1

The <bibliography> element has one sub-element

<item> that could be used once or several times.

Each

<item> element represents one bibliographic

reference. This element has one attribute named id,

which is mandatory. The attribute aims to identify

uniquely each

<item> element.

This element is then divided into 9 (nine) sub-

elements: type, authors, titles, publisher, edition

Number, updatedDate, normalizedNumber, accessed

URL, comment. All elements can be used only once.

The

<type>, <authors> and <titles> elements are

mandatory. The others are optional.

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The

<type> element identifies the class of

bibliographic item and has a list of predetermined

options. Those options are almost every types

defined by (EndNote, 2007): Ancient Text,

Audiovisual Material, Book, Book Section, Chart or

Table, Computer Program, Conference Paper,

Conference Proceedings, Dictionary, Encyclopedia,

Figure, Journal Article, Magazine Article,

Manuscript, Newspaper Article, Online Multimedia,

Personal Communication, Report, Thesis,

Unpublished Work, Web Page. To allow other types

not specified in that set, we have the option Other

Type.

The

<authors> element represents the

bibliographic reference authors. The

section has, at least, one sub-element, named

<author>. If the bibliographic reference has more

than one author, one

<author> element must be

filled by author. The order of the

<author> element

in the

<authors> section follows the order used in

the source. We consider that the first author is the

most important.

The

<titles> element stores the title of the

bibliographic item. It has four sub-elements: title,

chapter, pages and language. As the name suggests,

<title> represents the title of the bibliographic

item. This element is mandatory. <chapter> and

<pages> represent the sections of the book that is

important to be noted. If the bibliography is

something written, it should be important to express

the

<language>. The data type of this element is

LangString.

The

<publisher> element represents the editor’s

name of the bibliography. It has three sub-elements:

editorName, editionYear and local. The

<editorName> element expresses the editor’s name

of the bibliography. If

<publisher> element is used,

this sub-element is mandatory.

<editionYear> and

<local> represents the date and local where the

bibliographic item was published. The data type for

<editionYear> is DateTime.

<editionNumber> expresses the edition’s number

of the bibliographic item.

<updateDate> records the date of last update of

the bibliographic item. Its data type is DateTime.

The

<normalizedNumber> element is the place to

represent the kind of standard number that is used to

identify the bibliography. This element has an

attribute named type. This attribute uses a list of

predetermined options corresponding to six different

standards: ISBN, ISSN, LCCN, PCN, CIP and DOI.

If the bibliography was accessed in the Internet,

the element

<accessedURL> expresses that url. This

element has two sub-elements: url and visitedDate.

<accessedURL> is used, the two sub-elements are

mandatory. As their names suggest, url represents

the URL of the bibliography, and visitedDate

represents the date when the reference was visited.

For this last sub element, the data type is DateTime.

The last element,

<comment>, allows the possible

recording of comments about the bibliographic item.

Its data type is LangString.

The default data type is text.

2.3.2 The <bibliography> Structure – 2

The next code presents the <bibliography> structure:

Figure 4: The <bibliography> structure definition.

2.3.3 <bibliography> Example

Here is an example of the use of this new element:

<type>type of bibliography</type>

<author>Name of first

Author</author>

<author>Name of

Author</author>

</authors>

<title>Book’s title</title>

<chapter>Chapter’s name</chapter>

<pages>consulted pages</pages>

<language>Book’s language</language>

</titles>

<editorName>Editor’s name</editorName>

</editionYear>

<local>Edition place</local>

</publisher>

<editionNumber>Edition number</editionNumber>

</updatedDate>

<normalizedNumber type="ISBN">ISBN Number

</normalizedNumber>

</visitedDate>

</accessedURL>

<string language="en">possible comment about

this bibliographic item</string>

</comment>

</item>

</bibliography>

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263

Figure 5: A <bibliography> example.

2.3.4 The <bibliography> Validation

Since this is an element that was added to the

LOM’s structure, to allow the validation of such

element it was necessary to write a new Schema and

integrate it with the Schema provided by IEEE

(IEEE, 2005). With that integration, we are now able

to perform a total validation of the new LOM’s

structure.

To support this extension, we defined a new

namespace: http://PmatE.ua.pt/lomExtended.xsd.

4 MATHML

MathML is the acronym for Mathematical Markup

Language. This markup language is especially

suitable for representing mathematical notation. It

can represent the structure and capture the content of

a mathematical expression (Ausbrooks, Bos et al.,

2007). MathML, like other markup languages, is an

XML file. It is possible to write MathML documents

with two distinct notations: presentation and content.

Presentation markup is a more pleasant way to write

but this version only encodes the notational

structure. If it is necessary to encode the functional

structure of an expression, the content markup is the

best option. Nevertheless, this version is very hard to

code. When both presentation and content markup

are required, MathML allows the mix of the two

markups.

The QGMs started to be mathematical learning

objects, so the use of the MathML occurred

naturally. With the new version of the QGMs,

MathML gained a new importance. As will be

explained in the next section, MathML will be used

to represent mathematical expressions and to

represent the validation expressions of the QGMs.

Here the representation is necessary, but the

knowledge about what is represented is crucial. That

was the reason why we use the MathML content

markup version.

5 A QGM AS LEARNING OBJECT

The new QGM uses the XML as a description

language. With that, we intend to create a structure

that is suitable to be represented by a browser or

perhaps used in another system. By writing their

learning materials in XML, PmatE promotes the

content exchange with several platforms of Learning

Objects. At this moment, PmatE is making an effort

to diversify the subjects of their QGMs. The

majority of them are about mathematics, but the

number of QGMs in physics, biology and

Portuguese are increasing. This structure is

independent of the QGM subject.

A QGM has three sections:

• parameters (<dominioParametros>),

•

text (<texto>), and

•

answers (<respostas>).

Figure 6: A QGM structure.

The <dominioParametros> element has several

sub-elements. Each one describes the set of possible

...

</dominioParametros>

<texto>

...

</texto>

...

</respostas >

</modelo>

<author>Duval, Erik</author>

<author>Wason, Tom</author>

<author>Hodgins, Wayne</author>

<author>and others</author>

</authors>

<title>Draft Standard for

Learning Object Metadata

</title>

</titles>

</editionYear>

</publisher>

<editionNumber>IEEE 1484.12.1-2002

</editionNumber>

</updatedDate>

<url>http://ltsc.ieee.org/wg12/

files/LOM_1484_12_1_v1_Final

_Draft.pdf

</url>

</visitedDate>

</accessedURL>

</item>

</bibliography>

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values to each variables and the options that are

required to use the QGM. All values are represented

in MathML.

All elements have several attributes, needed to

format the values they represent. We use the

<![CDATA[ element to isolate the MathML code and

avoid inconsistencies with the Schema.

Figure 7: Example of a <operador> element.

The <texto> element contains the text used to be

presented as question in the normal usage of the

QGM. If the question has options, they are

represented also in MathML.

The last section,

<respostas> contains the set of

possible answers that can be presented to the user

when a QGM is instantiated. Since each question

always has four possible answers, this set must have

at least four answers. The necessary information to

each answer is stored in three sub-elements: answer

text (

<textoResposta>), validation (<validacao>)

and additional objectives (

<objAdicional>). The

<textoResposta> and <validacao> sub-elements

use MathML. In

<textoResposta> the MathML is

used to prepare the information that will be

presented to the user. In

<validacao> the MathML

is used to implement the validation expression that

will determine whether the response of the user is

valid or not.

6 THE QGM PARSER

The entire system required has three modules:

• the LOM’s editor;

• the QGM editor;

• and the QGM parser.

So far, only the first version of the QGM parser

is available.

The parser has the following architecture:

Figure 8: Parser architecture.

As referred, a QGM Learning Object uses

XML as description language, and has a set of

possible answers. In order to instantiate a new

question and present it to a user, a parser is required.

Such parser will select the possible answers and the

difficulty level according to some parameters such

as the user age.

Figure 9 shows the instantiation of the QGM

number 290. It is possible to see the MathML code

required to produce the answers that a user has to

choose. Figure 10 shows the instantiation of the

QGM number 1594 about the Portuguese language.

Figure 9: Parser result of math QGM.

Figure 10: A Portuguese language QGM.

<opcao varDependente="false"

calcular="true">

<![CDATA[<math>

</math>]]>

</opcao>

<opcao varDependente="false"

calcular="true">

<![CDATA[<math>

</math>]]>

</opcao>

</operador>

QGM - A SYSTEM TO IMPROVE MATHS e-LEARNING

265

The parser uses an XML Schema to validate the

QGM and XSLT files to extract the information.

A QGM is a very complex document, with many

options that the parser has to choose. Most of these

options are coded in MathML. However, MathML is

a complex language too and making a good parser

for it would be very difficult. So, we decided to

extend our own parser with WebMathematica. This

leading software in the math’s domain would be

accessed through a web service and would be

responsible for validating the choices made by the

parser. The code produced in step 1 of the parser is

complete but step 2 was impossible to test so far due

to the high cost of WebMathematica’s license. To

test phase 3 we were able to solve the MathML

manually.

7 CONCLUSIONS

At the beginning of this work we were confronted

with two problems: How to pass on our long-term

experience to Portuguese and international networks

of Learning Objects? How to make our Learning

Objects independent from the technological

structure?

Although the PmatE project was older than the

LOM proposal, the QGM metadata have evolved

due to the efforts of its staff. Therefore, the

adjustment of QGM’s metadata to the LOM

structure occurred straight. The only problem found

was the lack of bibliography references in the LOM

reference model. That limitation was overcome by

adding the

<bibliography> element.

The definition of the QGM structure through

XML makes it freely available for other uses. In

fact, now with a XSLT file it is possible to extract

information from them rapidly. That was not

possible with the older structure.

Another major advantage of this new architecture

is the speed of development. Actually, due to the

volume of material to be developed, it took us two to

three months to be able to generate questions with a

QGM. With the QGM editor, it will be possible to

reduce that time by 90%, because we do not have to

code and we can try it immediately.

In the whole work we had a remarkable setback:

the inability to test our parser with the

WebMathematica. Despite this setback, we believe

that our new structure will be the future and it will

work.

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