**The Use of Mathematical Formulae in an E-Learning Environment**

Josep Cuartero-Olivera, Antoni Pérez-Navarro and Teresa Sancho-Vinuesa *Universitat Oberta de Catalunya Spain* 

#### **1. Introduction**

106 E-Learning – Engineering, On-Job Training and Interactive Teaching

Galitz, W. O. (2007). *The Essential Guide to User Interface Design. An Introduction to GUI Design* 

Georgia Institute of Technology (n.d.), *Educational Matlab GUIs,* Date of access: July 31, 2011, Available from <http://users.ece.gatech.edu/mcclella/ matlabGUIs/> Hercog, R. D.; Jezernik, K. (2007). Advanced control course with teleoperation in the

KEM TU Kosice (2010). Virtual Laboratory of Mechatronic Systems Control, In: *web site of the project KEGA, No 3/4203/06*, Date of access: July 31, 2011, Available from

MeRLab (n.d.). Innovative Remote Laboratory in the Etraining of Mechatronics, Date of

Pipan, M.; Arh, T.; Blažič, B. J. (2008). Innovative Remote Laboratory in the Enhanced E-

Petropol-Serb, G.D.; Petropol-Serb, I.; Campeanu, A. & Petrisor, A. (2007). Using GUI of

Potkonjak, V.; Vukobratović, M.; Jovanović, K. & Medenica, M. (2010). Virtual

*Education archive,* Vol. 55 , Issue 2 (Sept. 2010), pp. 465-475, ISSN 0360-1315 Ruhr-Universität Bochum (2011), Lehrstuhl für Automatisierungstechnik und

Technical University of Kosice (n.d.). Students' Skills Development for Mechatronic Systems

Wong, H.; Kapila, V. & Tzes A. (2001). Mechatronics/Process Control Remote Laboratory.

*Proceedings of the 2001 American Society for Engineering Education, Annual Conference* 

*Electronics*, EDPE 2007, The High Tatras, September 24-26, 2007

< http://andromeda.fei.tuke.sk/> (in Slovak)

access: July 31, 2011, Available from <www.merlab.eu>

Cruz, Canary Islands, Spain, December 15-17, 2008

software/MatlabPlugin/MatlabPlugin.html/> Saadat, H. (n.d.). MATLAB Graphical User Interface for EE Students. Date of access: July 31, 2011, Available from

Control. In: *Project KEGA 103-039TUKE-4/2010* 

*& Exposition*, Albuquerque, NM, 2001*.*

<http://people.msoe.edu/ ~saadat/matlabgui.htm>

Warsaw, September 9-12, 2007

Miskolc, March 18-20, 2010

Indianapolis, Indiana

*Section K: Electrotechnics and Electronics,* ISBN 978-963-661-925-1, University of

*Principles and Techniques,* Wiley Publishing, Inc., ISBN 978-0-470-05342-3,

mechatronics study, *Proceedings of 16th Int. Conf. on Electrical Drives and Power* 

training of Mechatronics, *Proceedings of the 7th WSEAS International Conference on Circuits, Systems, Electronics, Control and Signal Processing* (CSECS'08), Puerto De La

Matlab to create a virtual laboratory to study an induction machine. EUROCON, 2007. *The International Conference on Computer as a Tool,* ISBN 978-1-4244-0813-9,

Mechatronic/Robotic laboratory - A step further in distance learning, *Computers &* 

Prozessinformatik. Virtual Control Lab 3.1 MATLAB Plugin. Date of access: October 31, 2011, Available from <http://www.atp.ruhr-uni-bochum.de/VCLab/ The use of mathematical formulae in engineering studies is as important as the subject content itself, especially in online distance education. In engineering studies, which have a strong technical component, both students and teachers must use formulae to express and solve their doubts, prove their knowledge or even quote any given piece of support material. In addition, in online distance education, communicating mathematics is not as easy as writing on a piece of paper or on a blackboard. As well as mastering the language of mathematics to express them properly, which is a problem that also exists in on-site environments, there is the problem of *writing* mathematics mainly through text e-mails, which is the main way to communicate within an on-line environment. The data gathered for this research at the *Universitat Oberta de Catalunya* (UOC) involves 4 terms, 15 engineering-related subjects and more than 17,000 e-mails. Among this large volume of emails, the use of mathematical notation is present in over 4,000 of them, representing an average of 23% of the total. As this preliminary result is quite significant, the aim of this chapter is to analyse the use of all the different strategies for communicating ideas with a mathematical content through the Internet and studying the impact for each one of them in order to find usage patterns.

Regarding virtual learning environments, as it is not possible to find previous studies about the use of mathematical notation within them, this work presents research of the different methods used by teachers and students to communicate mathematics through the Internet, and the use patterns regarding different subjects and knowledge areas. In order to do so, the core of this chapter consists of exploratory research as to which are the mentioned use patterns and tries to find relationships between them.

This chapter is structured as follows: as a first step, Section 2 explains in detail the problem addressed by this research. In Section 3, different methods for expressing mathematical notation in the particular case of a virtual learning environment like UOC are described. Next, Section 4 will introduce the scenario in which this research has been conducted. After that, Section 5 will focus on the study of how every one of these notation methods is used. Some statistical measurements are presented in order to try to find behaviour patterns through the different subjects and/or knowledge areas. The chapter ends with the conclusions and future lines of work.

The Use of Mathematical Formulae in an E-Learning Environment 109

As we stated in Section 1, currently there is not much research into the particular context of a virtual learning environment, regarding the use of the mathematics language. The main communication method in this kind of environment is the use of e-mail, so students have to adapt their communications, including the mathematical notation within them, to this particular communication tool. Next, Section 3 shows how this is carried out by students

The teaching and learning activity in a virtual campus, like in the case of UOC, is developed mainly within the virtual classroom. The virtual classroom is a space where teachers and

Most of the interaction among the classroom members happens in the classroom forum or discussion board, where any of the members can send text messages and attach documents, while all the rest of members can read any of the messages and reply to them. Besides this communication space, students and teachers can also communicate by using their private email address or the delivery board, where students send their due work, like continuous assessment tests. In the case of the private e-mail or the delivery board those messages are private to the sender and the recipient. However, the message format within all of these communication spaces is the same one: an e-mail written with the virtual campus e-mail

As previously stated, there are several tools to improve mathematics communication in virtual learning environments, mostly formulae editors. Some of these formulae editors work as a standalone program, like the Wiris Editor (Wiris, 2011) or Microsoft Equation Editor (Microsoft, 2011), which can also be embedded into other software like Moodle. Some others are available directly on a website, like the LaTeX Equation Editor (The Number Empire, 2011) or sMArTh (sMArTH, 2011). Most of them use very common mathematical notation languages, like LaTeX (LaTeX, 2011) or the commonly known as MathML, Mathematical Markup Language (World Wide Web Consortium, 2011), which make them

At UOC, such a mathematical notation tool has been available only during the last few terms, and it is still considered to be in its early stages. In fact, several tools are being tested and it is still to be decided which one is the best option. Before this tool was available, students and teachers needed to use other communication methods. These methods can range from the virtual campus e-mail editor itself -either in its plain text or Rich Text

and teachers and also explains the different available methods.

**3. Writing mathematical notation within e-mails** 

students can communicate in a few different ways:

very feasible as plug-ins for other environments.

the combination and information about the expression constants and variables. Translating: In the last step, a recognized expression is produced and translated into a script or a source code suitable for being used in third-party software like TeX or

Mathematica.

 Classroom forums Discussion boards Delivery board Private e-mail

editor.

child relationships according to the expression semantics, the mathematical meaning of

#### **2. Engineering studies in a virtual learning environment**

Virtual learning environments are, in general, still challenging nowadays, as they have to deal with the barriers of time and distance. This is true not only for communication from teacher to students, but also among student workgroups or for students to communicate their queries to the teacher. The challenges become greater in engineering studies, where there are additional obstacles to overcome; for example the use of laboratories (having to become virtual laboratories) or granting access to high-profile computational tools. Focusing on the issue of knowledge transfer, one of the main problems regarding engineering studies is communication among university members, as a great part of this communication implies the use of a large amount of mathematical notation.

In the case of a virtual learning environment, the issue of learning and communicating mathematics can be compared to a disability such as visual impairment. Visually impaired students can listen to the reading of a given formula by the teacher, while they cannot easily learn how it is expressed visually, even in an on-site learning environment (Fitzpatrick, 2007). In reverse, a virtual learning environment allows students to see visual expression of formulae, but traditionally does not provide them with a verbal representation, which is also a handicap for visually impaired students. In addition, in some cases there is no auxiliary tool to help express mathematical notation, for example a formulae editor. When there is no such tool available, the methods for expressing mathematics are still computer aided, but they are as rudimentary as plain text or file attachments.

The issues of the use of mathematical notation regarding information systems has previously been stated and researched. For instance, there are differences in handling math expressions in one way or another for the indexing and retrieval of mathematics educational material in a search engine (Zhao, 2008). For that purpose, the author proposes the use of links between math expressions and text keywords. In this way, a semantic expression like "area of the function cosinus" can be linked to mathematics content about the resolution of integral functions for the particular cosinus function. From a different point of view, other authors propose a five step process for the recognition and semantic understanding of mathematical formulae, basically consisting of (Chen & Okada, 2001):


child relationships according to the expression semantics, the mathematical meaning of the combination and information about the expression constants and variables.

 Translating: In the last step, a recognized expression is produced and translated into a script or a source code suitable for being used in third-party software like TeX or Mathematica.

As we stated in Section 1, currently there is not much research into the particular context of a virtual learning environment, regarding the use of the mathematics language. The main communication method in this kind of environment is the use of e-mail, so students have to adapt their communications, including the mathematical notation within them, to this particular communication tool. Next, Section 3 shows how this is carried out by students and teachers and also explains the different available methods.

#### **3. Writing mathematical notation within e-mails**

The teaching and learning activity in a virtual campus, like in the case of UOC, is developed mainly within the virtual classroom. The virtual classroom is a space where teachers and students can communicate in a few different ways:


108 E-Learning – Engineering, On-Job Training and Interactive Teaching

Virtual learning environments are, in general, still challenging nowadays, as they have to deal with the barriers of time and distance. This is true not only for communication from teacher to students, but also among student workgroups or for students to communicate their queries to the teacher. The challenges become greater in engineering studies, where there are additional obstacles to overcome; for example the use of laboratories (having to become virtual laboratories) or granting access to high-profile computational tools. Focusing on the issue of knowledge transfer, one of the main problems regarding engineering studies is communication among university members, as a great part of this communication implies

In the case of a virtual learning environment, the issue of learning and communicating mathematics can be compared to a disability such as visual impairment. Visually impaired students can listen to the reading of a given formula by the teacher, while they cannot easily learn how it is expressed visually, even in an on-site learning environment (Fitzpatrick, 2007). In reverse, a virtual learning environment allows students to see visual expression of formulae, but traditionally does not provide them with a verbal representation, which is also a handicap for visually impaired students. In addition, in some cases there is no auxiliary tool to help express mathematical notation, for example a formulae editor. When there is no such tool available, the methods for expressing mathematics are still computer

The issues of the use of mathematical notation regarding information systems has previously been stated and researched. For instance, there are differences in handling math expressions in one way or another for the indexing and retrieval of mathematics educational material in a search engine (Zhao, 2008). For that purpose, the author proposes the use of links between math expressions and text keywords. In this way, a semantic expression like "area of the function cosinus" can be linked to mathematics content about the resolution of integral functions for the particular cosinus function. From a different point of view, other authors propose a five step process for the recognition and semantic understanding of

 Pre-processing: In this first step, the mathematical expression is scanned to obtain an image. This image is processed in order to remove any noise and then split into

 Character recognition: The individual symbols, digits and letters are processed through a character recognition system and then classified into dyadic operators, monadic

 Rule base: Any ambiguity in the mathematical expression is eliminated by using a rules system. This system consists of mathematical rules, a sense-based dictionary for handling layout-dependent ambiguity and an experience-based dictionary for handling

 Expression understanding: According to the layout of the mathematical expression, a layout tree is generated and parsed. This layout treecontains type and position of symbols, their sizes and centrelines and their parent-child relationships according to the expression layout. The result of this step is a semantic tree based on the mathematical rules used in step 3. This new semantic tree contains the types of symbols, their parent-

**2. Engineering studies in a virtual learning environment** 

aided, but they are as rudimentary as plain text or file attachments.

mathematical formulae, basically consisting of (Chen & Okada, 2001):

mathematical symbols, digits and letters.

operators or atom characters.

layout-independent uncertainty.

the use of a large amount of mathematical notation.

Private e-mail

Most of the interaction among the classroom members happens in the classroom forum or discussion board, where any of the members can send text messages and attach documents, while all the rest of members can read any of the messages and reply to them. Besides this communication space, students and teachers can also communicate by using their private email address or the delivery board, where students send their due work, like continuous assessment tests. In the case of the private e-mail or the delivery board those messages are private to the sender and the recipient. However, the message format within all of these communication spaces is the same one: an e-mail written with the virtual campus e-mail editor.

As previously stated, there are several tools to improve mathematics communication in virtual learning environments, mostly formulae editors. Some of these formulae editors work as a standalone program, like the Wiris Editor (Wiris, 2011) or Microsoft Equation Editor (Microsoft, 2011), which can also be embedded into other software like Moodle. Some others are available directly on a website, like the LaTeX Equation Editor (The Number Empire, 2011) or sMArTh (sMArTH, 2011). Most of them use very common mathematical notation languages, like LaTeX (LaTeX, 2011) or the commonly known as MathML, Mathematical Markup Language (World Wide Web Consortium, 2011), which make them very feasible as plug-ins for other environments.

At UOC, such a mathematical notation tool has been available only during the last few terms, and it is still considered to be in its early stages. In fact, several tools are being tested and it is still to be decided which one is the best option. Before this tool was available, students and teachers needed to use other communication methods. These methods can range from the virtual campus e-mail editor itself -either in its plain text or Rich Text

The Use of Mathematical Formulae in an E-Learning Environment 111

Formulae referencing is used whenever a certain formula or expression is cited within the text, whether it is in its most common way (i.e. the formula on the first paragraph of page

The last method consists of attaching a file containing the formulae referenced in the e-mail body (i.e. the attached formula is wrong), or even writing the whole body of the message in an attached file. The attachment might be an image, some kind of text document (RTF, Microsoft Word, OpenOffice.org Writer, etc.), or even a scan of handwritten formulae.

According to Zhao classification of mathematical educational resources and some math information indexing and retrieval systems analysed through his research (Zhao, 2008), mathematical expressions can be considered as syntactically math-aware whenever the retrieval system reads the syntactical structure of the math expression to be searched for. On the other hand, if the system is capable of also capturing the semantics of the expression, then it is considered as semantically math-aware. Other systems, incapable of recovering neither the math-related syntactic or semantic meaning, are considered as math-unaware. Following this classification, full mathematical formulae and mathematical symbols could be considered as syntactically math-aware, and formulae referencing as semantically mathaware. However, as we have seen, there are not many different ways of expressing mathematical notation, although as explained in this section they are quite different from one another. Therefore, the next sections address the scenario for this research and the analysis of how each method is used by students and teachers, what patterns can be found among different subjects and knowledge areas and what the possible reasons are for a

As described in section 3, there are several ways of including mathematical expressions in a digital text subject to be sent by email. As most of the communication between teachers and students takes place in the classroom forum, for this research we have only considered the emails sent to that communication space. Therefore, in this section an exhaustive analysis of over 17,000 e-mail messages is made in order to classify them according to the type of mathematical expression method used. These e-mail messages have been gathered from 15

The interaction among students at the UOC is mainly developed through the virtual campus. Therefore, it is very common to find e-mails not directly related to the subject, for example introductory messages, technical problems or Christmas greetings. In order to avoid any kind of noise in the results, all these e-mails have been carefully discarded. This cleansing leaves still more than 15,000 e-mails. In a first search through this data, it has been detected that the use of mathematical notation is present in over 4,000 of the 15,000 e-mails, representing an average of 27% containing some kind of mathematical expression. These 4,000 e-mails are the ones we are going to take into consideration for the rest of this work.

different subjects, all of them related to engineering degrees.

24) or by using a previously established citation system (i.e. formula 17).

**3.3 Formulae referencing** 

**3.4 Attachment** 

particular behaviour.

**4. Scenario under study** 

Format versions- to more evolved tools for attaching documents like Microsoft Word or OpenOffice.org Writer –where these tools can be considered as the transfer method of the formulae itself, instead of the e-mail body.

Two main methods for expressing mathematics in web-based environments have been covered: through pictures and through coding with MathML (Yue-sheng & Jia-yi, 2008). These methods are focused on the way a formula is usually represented in a web page, from a technological point of view. Since this research though is focused on how students write formulae, it has to respond to a different classification, based on the technique used to write them. For instance, a symbol can be written with any rich text editor (for example the ∑ symbol), or even with a plain text editor depending on the symbol (for example the + symbol). However, the construction of a given formula is frequently not possible using only text and needs other tools to help with its visual representation, for instance as shown in Figure 1:

Fig. 1. Sample formula

It is also possible to cite a formula by using any simple text editor, while in the case of a formula attached to an e-mail body an external tool is needed to generate the attachment itself. Therefore, a wider classification has been used, obtained from the observation of the behaviour of students and teachers: full mathematical formulae, mathematical symbols, formulae referencing and attachment. In order to better understand the results, all these different ways of communicating are explained and delimited through the next sections.

#### **3.1 Full mathematical formulae**

The first and most common method for expressing mathematical notation is through full mathematical formulae, understanding it as an equality (i.e. a=b+3), an inequality (i.e. a+2>5), or a mathematical expression consisting of a combination of more than one mathematical symbol (i.e. sin(ln(1)). Full mathematical formulae can also be expressed in any specific syntax delivered by programming languages or software commonly used in engineering environments. These variations are also considered in this group, for example specific mark-up codes like "\sqrt", which are meaningful for the LaTeX2 editor, converting the expression \sqrt{1-e^2} into <sup>2</sup> 1 *e* .

#### **3.2 Mathematical symbols**

The mathematical symbol method consists of writing just one mathematical symbol at a time, whether it is in plain text (i.e. lambda) or by using the symbol itself (i.e. λ), and exclusively when the symbol is not part of a whole mathematical formula. Numeric expressions have been considered into this group only if they are preceded (or followed) by a mathematical symbol (i.e. >10 or 10!). Hyper-index, sub-index, or commonly used abbreviations of mathematical expressions like SQR, TAN, etc. also fall into this group.

#### **3.3 Formulae referencing**

Formulae referencing is used whenever a certain formula or expression is cited within the text, whether it is in its most common way (i.e. the formula on the first paragraph of page 24) or by using a previously established citation system (i.e. formula 17).

#### **3.4 Attachment**

110 E-Learning – Engineering, On-Job Training and Interactive Teaching

Format versions- to more evolved tools for attaching documents like Microsoft Word or OpenOffice.org Writer –where these tools can be considered as the transfer method of the

Two main methods for expressing mathematics in web-based environments have been covered: through pictures and through coding with MathML (Yue-sheng & Jia-yi, 2008). These methods are focused on the way a formula is usually represented in a web page, from a technological point of view. Since this research though is focused on how students write formulae, it has to respond to a different classification, based on the technique used to write them. For instance, a symbol can be written with any rich text editor (for example the ∑ symbol), or even with a plain text editor depending on the symbol (for example the + symbol). However, the construction of a given formula is frequently not possible using only text and needs other tools to help with its visual representation, for instance as shown in

> <sup>0</sup> 1 lim *<sup>i</sup> <sup>x</sup> <sup>i</sup>*

It is also possible to cite a formula by using any simple text editor, while in the case of a formula attached to an e-mail body an external tool is needed to generate the attachment itself. Therefore, a wider classification has been used, obtained from the observation of the behaviour of students and teachers: full mathematical formulae, mathematical symbols, formulae referencing and attachment. In order to better understand the results, all these different ways of communicating are explained and delimited through the next sections.

The first and most common method for expressing mathematical notation is through full mathematical formulae, understanding it as an equality (i.e. a=b+3), an inequality (i.e. a+2>5), or a mathematical expression consisting of a combination of more than one mathematical symbol (i.e. sin(ln(1)). Full mathematical formulae can also be expressed in any specific syntax delivered by programming languages or software commonly used in engineering environments. These variations are also considered in this group, for example specific mark-up codes like "\sqrt", which are meaningful for the LaTeX2 editor,

The mathematical symbol method consists of writing just one mathematical symbol at a time, whether it is in plain text (i.e. lambda) or by using the symbol itself (i.e. λ), and exclusively when the symbol is not part of a whole mathematical formula. Numeric expressions have been considered into this group only if they are preceded (or followed) by a mathematical symbol (i.e. >10 or 10!). Hyper-index, sub-index, or commonly used abbreviations of mathematical expressions like SQR, TAN, etc. also fall into this group.

*f x x*

formulae itself, instead of the e-mail body.

Figure 1:

Fig. 1. Sample formula

**3.1 Full mathematical formulae** 

**3.2 Mathematical symbols** 

converting the expression \sqrt{1-e^2} into <sup>2</sup> 1 *e* .

The last method consists of attaching a file containing the formulae referenced in the e-mail body (i.e. the attached formula is wrong), or even writing the whole body of the message in an attached file. The attachment might be an image, some kind of text document (RTF, Microsoft Word, OpenOffice.org Writer, etc.), or even a scan of handwritten formulae.

According to Zhao classification of mathematical educational resources and some math information indexing and retrieval systems analysed through his research (Zhao, 2008), mathematical expressions can be considered as syntactically math-aware whenever the retrieval system reads the syntactical structure of the math expression to be searched for. On the other hand, if the system is capable of also capturing the semantics of the expression, then it is considered as semantically math-aware. Other systems, incapable of recovering neither the math-related syntactic or semantic meaning, are considered as math-unaware. Following this classification, full mathematical formulae and mathematical symbols could be considered as syntactically math-aware, and formulae referencing as semantically mathaware. However, as we have seen, there are not many different ways of expressing mathematical notation, although as explained in this section they are quite different from one another. Therefore, the next sections address the scenario for this research and the analysis of how each method is used by students and teachers, what patterns can be found among different subjects and knowledge areas and what the possible reasons are for a particular behaviour.

#### **4. Scenario under study**

As described in section 3, there are several ways of including mathematical expressions in a digital text subject to be sent by email. As most of the communication between teachers and students takes place in the classroom forum, for this research we have only considered the emails sent to that communication space. Therefore, in this section an exhaustive analysis of over 17,000 e-mail messages is made in order to classify them according to the type of mathematical expression method used. These e-mail messages have been gathered from 15 different subjects, all of them related to engineering degrees.

The interaction among students at the UOC is mainly developed through the virtual campus. Therefore, it is very common to find e-mails not directly related to the subject, for example introductory messages, technical problems or Christmas greetings. In order to avoid any kind of noise in the results, all these e-mails have been carefully discarded. This cleansing leaves still more than 15,000 e-mails. In a first search through this data, it has been detected that the use of mathematical notation is present in over 4,000 of the 15,000 e-mails, representing an average of 27% containing some kind of mathematical expression. These 4,000 e-mails are the ones we are going to take into consideration for the rest of this work.

The Use of Mathematical Formulae in an E-Learning Environment 113

between the methodology and the study materials of every subject, or also due to different student profiles. In both cases, the results now require us to take into consideration each individual subject. Therefore, as a further step, it is necessary to find out what the patterns are for every subject, which are in turn classified under different knowledge areas. The next

Algebra 332 235 71 77 23 29 9 24 7

**Subject Formulae Symbol Citation Attachment**

Languages I 128 57 45 63 49 2 2 9 7

Technology 287 175 61 101 35 6 2 11 4 Cryptography 224 155 69 49 22 36 16 10 4 Discrete Mathematics 244 158 65 71 29 29 12 12 5

Engineering Physics Fundamentals 228 107 47 52 23 127 56 10 4

Engineering 194 147 76 22 11 10 5 23 12 Linear Systems 316 224 71 60 19 14 4 30 9 Mathematical Analysis 425 307 72 120 28 66 16 55 13 Mathematics I 352 250 71 48 14 12 3 54 15 Probability and Statistics 218 170 78 21 10 13 6 24 11 Statistics 331 228 69 83 25 45 14 21 6 Technological Fundamentals I 216 136 63 73 34 4 2 9 4 Technological Fundamentals II 328 203 62 78 24 64 20 31 9 Wiris Laboratory (Algebra) 232 127 55 49 21 4 2 67 29

Table 2. Classification of e-mails according to the subject and the mathematical notation type

After these first results, and as we have observed thanks to the statistics in Table 2, the next questions deal with the behaviour of students and teachers according to a particular subject. The main goal is to find out if the same average behaviour can be applied to all of the studied subjects or, if not, what are the possible reasons why there is a different behaviour,

In order to calculate the next measurements, firstly we will consider the total number of emails for every subject, including the ones with no mathematical notation but directly related to that particular subject. We can see there is quite a significant difference between subjects regarding the type of mathematical notation used: depending on the subject, we find 17% of the total e-mails contain mathematical notation, while it can rise to 45% for other

If we consider only e-mails containing mathematical expressions for every subject, as we previously did in Table 2, we observe differences in the use of one or other type of

**# # %# %#%#%**

**Total**

section takes care of this matter.

Automata Theory and Formal

Introduction on Mathematics for

**5.2 Different subjects, different behaviour** 

by finding subject-related variables affecting that overall pattern.

used

subjects.

Computers Structure and

Having prepared the e-mails which are going to be processed, this work focuses first on statistically analysing the types and frequency of mathematical notation used in them. With this information, a careful search through the data will make it possible to detect any particular usage pattern or specific student behaviour depending on variables such as the subject, the knowledge area, the type of studying material and other subject-related variables. Therefore, the next section deals with processing and analysing all this data in order to explain different behaviours in different classrooms.

### **5. Analysis of the results**

Having agreed the motivation for this study, the characteristics of the research subject and the scenario in which it is developed, this section addresses the core of the research. We will first present a basic study of the way students and teachers communicate using mathematical expressions, consisting of the use frequency for every different expression type. Afterwards, the analysis will focus on determining some similarities and differences in the usage pattern for different subjects and/or knowledge areas. Finally, and in order to be able to better explain the reasons for those patterns, some of the most significant descriptive statistics will be developed.

#### **5.1 A basic classification**

The first question arising out of this study is to what degree mathematical expressions are used, regarding the different types of notation. We must bear in mind that students are not required to use any specific notation method, so they are free to use whichever method they think is most convenient for their communication needs. As previously noted, and unless it is stated differently, this research and its calculations will consider only the 4,000 e-mails containing some kind of mathematical notation. Therefore, Table 1 gathers the use percentage for every mathematical notation type, showing that around 66% of the e-mails include full mathematical formulae. The rest of the e-mails include, in order of use frequency, single mathematical symbols (24%), formulae citation (11%) and attachments with some mathematical notation (10%). It should be noted that e-mails may fall under more than one category if they use more than one of the different methods. Full results are shown in Table 1.


Table 1. Classification of e-mails according to the mathematical notation type used

Furthermore, we want to analyse if this same frequencies apply to individual subjects. The aim is to find out if those frequencies exist regardless of the knowledge area of a particular subject, its content or its methodology. As a first step we will analyse the data in Table 1 but this time grouped by subject. Table 2 shows these results.

As we can see in Table 2, not all the individual subjects have the same average percentages regarding the use of one or other type of mathematics expression. The overall pattern is the same, but there are subjects where full mathematical formulae is used less in favour of citation, or the use of many more mathematical symbols. This fact can be due to differences

Having prepared the e-mails which are going to be processed, this work focuses first on statistically analysing the types and frequency of mathematical notation used in them. With this information, a careful search through the data will make it possible to detect any particular usage pattern or specific student behaviour depending on variables such as the subject, the knowledge area, the type of studying material and other subject-related variables. Therefore, the next section deals with processing and analysing all this data in

Having agreed the motivation for this study, the characteristics of the research subject and the scenario in which it is developed, this section addresses the core of the research. We will first present a basic study of the way students and teachers communicate using mathematical expressions, consisting of the use frequency for every different expression type. Afterwards, the analysis will focus on determining some similarities and differences in the usage pattern for different subjects and/or knowledge areas. Finally, and in order to be able to better explain the reasons for those patterns, some of the most significant descriptive

The first question arising out of this study is to what degree mathematical expressions are used, regarding the different types of notation. We must bear in mind that students are not required to use any specific notation method, so they are free to use whichever method they think is most convenient for their communication needs. As previously noted, and unless it is stated differently, this research and its calculations will consider only the 4,000 e-mails containing some kind of mathematical notation. Therefore, Table 1 gathers the use percentage for every mathematical notation type, showing that around 66% of the e-mails include full mathematical formulae. The rest of the e-mails include, in order of use frequency, single mathematical symbols (24%), formulae citation (11%) and attachments with some mathematical notation (10%). It should be noted that e-mails may fall under more than one category if they use more than one of the different methods. Full results are shown in Table 1.

**# e-mails # e-mails Total % # e-mails Total % # e-mails Total % # e-mails Total %** 4055 2679 66 967 24 461 11 390 10

Furthermore, we want to analyse if this same frequencies apply to individual subjects. The aim is to find out if those frequencies exist regardless of the knowledge area of a particular subject, its content or its methodology. As a first step we will analyse the data in Table 1 but

As we can see in Table 2, not all the individual subjects have the same average percentages regarding the use of one or other type of mathematics expression. The overall pattern is the same, but there are subjects where full mathematical formulae is used less in favour of citation, or the use of many more mathematical symbols. This fact can be due to differences

Table 1. Classification of e-mails according to the mathematical notation type used

this time grouped by subject. Table 2 shows these results.

**Formulae Symbol Citation Attachment**

order to explain different behaviours in different classrooms.

**5. Analysis of the results** 

statistics will be developed.

**5.1 A basic classification** 

**Total**

between the methodology and the study materials of every subject, or also due to different student profiles. In both cases, the results now require us to take into consideration each individual subject. Therefore, as a further step, it is necessary to find out what the patterns are for every subject, which are in turn classified under different knowledge areas. The next section takes care of this matter.


Table 2. Classification of e-mails according to the subject and the mathematical notation type used

#### **5.2 Different subjects, different behaviour**

After these first results, and as we have observed thanks to the statistics in Table 2, the next questions deal with the behaviour of students and teachers according to a particular subject. The main goal is to find out if the same average behaviour can be applied to all of the studied subjects or, if not, what are the possible reasons why there is a different behaviour, by finding subject-related variables affecting that overall pattern.

In order to calculate the next measurements, firstly we will consider the total number of emails for every subject, including the ones with no mathematical notation but directly related to that particular subject. We can see there is quite a significant difference between subjects regarding the type of mathematical notation used: depending on the subject, we find 17% of the total e-mails contain mathematical notation, while it can rise to 45% for other subjects.

If we consider only e-mails containing mathematical expressions for every subject, as we previously did in Table 2, we observe differences in the use of one or other type of

The Use of Mathematical Formulae in an E-Learning Environment 115

**Area Subject # #%#%#%#%#%**

332

128

224

244

194

316

425

352

218

331

232

287

216 20

Table 3. Usage of mathematical notation types by subject and aggregations by knowledge

The second reason is that in the Physics area the use of a citation method is favoured as we

Still looking at full mathematical formulae and focusing on the Mathematics area, this same irregular behaviour can be verified. The average use percentage of full mathematical formulae for this knowledge area is around 69%, which is quite high, but the behaviour is

**Technological Fundamentals II** <sup>1230</sup> <sup>328</sup> 27 203 <sup>62</sup> <sup>78</sup> <sup>24</sup> <sup>64</sup> <sup>20</sup> <sup>31</sup> <sup>9</sup>

**Engineering Physics Fundamentals** <sup>581</sup> <sup>228</sup> 39 107 <sup>47</sup> <sup>52</sup> <sup>23</sup> <sup>127</sup> <sup>56</sup> <sup>10</sup> <sup>4</sup>

28 235

21 57

20 155

24 158

27 147

37 224

45 307

29 250

36 170

23 228

21 127

17 175

71 77

**notation Formulae Symbol Citation**

45 63

69 49

65 71

76 22

71 60

72 120

71 48

78 21

69 83

55 49

61 101

73

**AREA TOTALS 10788 2996 <sup>28</sup> 2058 69 663 22 260 9 329 11**

**AREA TOTALS 581 228 <sup>39</sup> 107 47 52 23 127 56 10 4**

136 63

**AREA TOTALS 3973 831 <sup>21</sup> 514 62 252 30 74 9 51 6**

23 29

**Attachment Math** 

49 2

22 36

29 29

11 10

19 14

28 66

14 12

10 13

25 45

21 4

35 6

34 4 9 24

2 9

16 10

12 12

5 23

4 30

16 55

3 54

6 24

14 21

2 67

2 11

2 9 7

7

4

5

12

9

13

15

11

6

29

4

4

**Total e-mails**

1020

1198

**Algebra** <sup>1170</sup>

**Cryptography** <sup>1122</sup>

**Linear Systems** <sup>846</sup>

**Mathematical Analysis** <sup>953</sup>

**Probability and Statistics** <sup>610</sup>

**Statistics** <sup>1413</sup>

**Wiris Laboratory (Algebra)** <sup>1120</sup>

**Technology** 1665

**Technological Fundamentals I** <sup>1078</sup>

**Computers Structure and** 

**Automata Theory and Formal Languages I** 610

**Introduction on Mathematics for Engineering** 726

**Discrete Mathematics**

**Mathematics I**

**Mathematics**

**Technology**

previously explained.

area

 **Physics**

expression. Table 3 shows the full results of this data, but as a main result it is possible to observe that the percentages are quite different from one subject to another:


As it can be seen, there are significant differences regarding both the percentage of e-mails containing mathematical notation and the use of one or another expression method. Considering these results, the next question that arises is about the relationship between similar behaviours. As subjects can be classified within different knowledge areas, Table 3 also contains the same statistics, this time calculated for each one of those areas.

The most significant fact regarding the differences between knowledge areas is about Physics. In that knowledge area there is, compared with the other areas, quite a significant increase in overall mathematical notation use: while for Mathematics this percentage is around 28% and for Technology it is around 21%, for the Physics area it increases to 39%. Analysing this fact in detail and if we have a closer look at the different notation methods, the increase is mostly related to citations: 56% against 9% in the other areas. The reasons for this behaviour pattern are two-fold:


Again, the usage figures for full mathematical formulae have an expected pattern, according to the results previously shown in Table 2. While for the Mathematics area it increases to 69%, very similar to the 62% for the Technology area, it drops to 47% for the Physics area. This behaviour is because of two main reasons: the first one is that the Technology area has a lower amount of formulae use within the subjects than the Mathematics and Physics areas.

expression. Table 3 shows the full results of this data, but as a main result it is possible to

Regarding full mathematical formulae, the results range from 45% in Automata Theory

 In the case of single mathematical symbols, the percentage varies from 10% in Probability and Statistics to 49% in Automata Theory and Formal Languages. Regarding formulae citations, the percentage ranges from 2% in Automata Theory and Formal Languages, Wiris Laboratory (Algebra) or Computers Structure and Technology

 For attachments containing mathematical notation, the percentages range from 4% in Cryptography, Engineering Physics Fundamentals, Computers Structure and Technology or Technological Fundamentals I to 29% in Wiris Laboratory (Algebra). As it can be seen, there are significant differences regarding both the percentage of e-mails containing mathematical notation and the use of one or another expression method. Considering these results, the next question that arises is about the relationship between similar behaviours. As subjects can be classified within different knowledge areas, Table 3

The most significant fact regarding the differences between knowledge areas is about Physics. In that knowledge area there is, compared with the other areas, quite a significant increase in overall mathematical notation use: while for Mathematics this percentage is around 28% and for Technology it is around 21%, for the Physics area it increases to 39%. Analysing this fact in detail and if we have a closer look at the different notation methods, the increase is mostly related to citations: 56% against 9% in the other areas. The reasons for

1. There is a well defined citation method in the subject falling under this knowledge area (Engineering Physics Fundamentals), which is responsible for this increase in the use of mathematical notation. This citation method consists of uniquely identifying with a number every single formula used within the subject. In every work document during the term, as well as within communications between students and teachers, formulae are referenced by using those unique numbers. Therefore, it can be easier and faster for both students and teachers referencing any of the formulae and thus the mathematical notation percentage increases. This same fact causes the rest of the notation types to be less used for the Physics area. Technological Fundamentals II (Circuit Theory) uses the same citation method and as we can see it is the second subject where the citation

2. The subject itself: in Physics there are many formulae that students have to learn and understand. This explains the difference with Technological Fundamentals II, where the

Again, the usage figures for full mathematical formulae have an expected pattern, according to the results previously shown in Table 2. While for the Mathematics area it increases to 69%, very similar to the 62% for the Technology area, it drops to 47% for the Physics area. This behaviour is because of two main reasons: the first one is that the Technology area has a lower amount of formulae use within the subjects than the Mathematics and Physics areas.

also contains the same statistics, this time calculated for each one of those areas.

observe that the percentages are quite different from one subject to another:

and Formal Languages to 78% in Probability and Statistics.

to 56% in Engineering Physics Fundamentals.

this behaviour pattern are two-fold:

method is used more, with a percentage of 20%.

number of formulae is very much smaller.


Table 3. Usage of mathematical notation types by subject and aggregations by knowledge area

The second reason is that in the Physics area the use of a citation method is favoured as we previously explained.

Still looking at full mathematical formulae and focusing on the Mathematics area, this same irregular behaviour can be verified. The average use percentage of full mathematical formulae for this knowledge area is around 69%, which is quite high, but the behaviour is

The Use of Mathematical Formulae in an E-Learning Environment 117

the other subjects because of their content type. That is also confirmed by this area having the overall highest standard deviations, especially concerning the most used notation types: full mathematical formulae (with a standard deviation of 9) and mathematical symbol (with

**Knowledge area Mean Min Max Standard** 

**Mathematics** 67 45 78 9 >= 70% - < 80%

**Physics** 47 47 57 - >= 40% - < 50%

**Technology** 62 61 63 1 >= 60% - < 70%

**Mathematics** 23 10 49 10 >= 20% - < 30%

**Physics** 23 23 23 - >= 20% - < 30%

**Technology** 31 24 35 5 >= 30% - < 40%

**Mathematics** 8 2 16 5 >= 0% - <10%

**Physics** 56 56 56 - >= 50% - < 60%

**Technology** 8 2 20 8 >= 0% - <10%

**Mathematics** 11 4 29 7 >= 0% - <10%

**Physics** 4 4 4 - >= 0% - <10%

**Technology** 6 4 9 3 >= 0% - <10%

**Mathematics** 5 1 14 4 >= 0% - <10%

**Physics** 1 1 1 - >= 0% - <10%

**Technology** 6 4 9 2 >= 0% - <10%

**Mathematics** 2 0 5 2 >= 0% - <10%

**Physics** 2 2 2 - >= 0% - <10%

**Technology** 5 1 10 4 >= 0% - <10%

**Mathematics** 28 20 45 8 >= 20% - < 30%

**Physics** 39 39 39 - >= 30% - < 40%

**Technology** 21 17 27 4 >= 20% - < 30%

Table 5 shows the same statistical measurements groups as in Table 4, but this time regardless of the knowledge area. As it can be seen in the results, the percentages are more

Table 4. Statistical analysis grouped by notation type and knowledge area

**deviation Mode**

a standard deviation of 10).

**Formula within** 

**Mathematical** 

**Citation**

**Attachament with formula**

**symbol**

**the e-mail body**

**Attachment** 

**Attachment** 

**Any kind of** 

**mathematical** 

**notation**

**with graphics**

**without** 

**formula**

not the same for all of the subjects in this area. While most of them fall into the range 65% to 75%, there are two subjects where the percentage drops dramatically to 45% and 55%. These subjects are, respectively, Automata Theory and Formal Languages I and Wiris Laboratory (Algebra). Similarly, as previously explained, these subjects do not contain as much mathematical formulae as the rest of the subjects and therefore the use percentage decreases. On the other hand, the use percentage of mathematical symbols in the subject Automata Theory and Formal Languages I is quite high, since this subject contains a high amount of single mathematical symbols instead of full mathematical formulae.

Besides these facts, as for the rest of the notation types there is no significant difference. Again, the conclusion we come to is that in some cases the use of one or other type of notation is highly dependant on the subject, depending on the content itself and on a previous agreement between teachers and students for using some specific notation method as we could see in the Physics subject. In this way, it seems that it is easier and more feasible for students and teachers to express mathematics by the use of a previously established citation system. But again, for the rest of the subjects, apparently the use of one or other method is more likely to be linked to the students' particular preferences.

In the next section we will develop more statistics in order to find yet more specific relationships between subjects and knowledge areas.

#### **5.3 A global statistical analysis**

The previous section has shown that there are significant differences in the use of notation between different subjects or knowledge areas. At this point it is important to develop some global descriptive statistics in order to better understand the links between different expression methods.

Table 4 shows the main statistical measurements, calculated for every notation type and knowledge area. For each of these groups, it shows the mean, the minimum and maximum, the standard deviation and the mode, all values represented in percentages. Regarding the special case of Physics, as there is just one subject under this knowledge area, we will not consider its standard deviation.

As it can be seen in Table 4, there are two cases in which the mean does not fall into the mode range:


In none of these cases, though, the difference between the mean and the mode is very significant. This might only be a symptom of an abnormal distribution, and it is not surprising because as we described in previous sections there is a very different pattern in a few subjects for using one or other mathematical notation type depending on the subject and area.

The Mathematics knowledge area is the one showing a larger difference overall between the minimum and maximum percentages for every notation type. This was already explained in a previous section, the reason being there are two subjects in this area (Automata Theory and Formal Languages I and Wiris Laboratory) which do not follow the regular pattern of

not the same for all of the subjects in this area. While most of them fall into the range 65% to 75%, there are two subjects where the percentage drops dramatically to 45% and 55%. These subjects are, respectively, Automata Theory and Formal Languages I and Wiris Laboratory (Algebra). Similarly, as previously explained, these subjects do not contain as much mathematical formulae as the rest of the subjects and therefore the use percentage decreases. On the other hand, the use percentage of mathematical symbols in the subject Automata Theory and Formal Languages I is quite high, since this subject contains a high amount of

Besides these facts, as for the rest of the notation types there is no significant difference. Again, the conclusion we come to is that in some cases the use of one or other type of notation is highly dependant on the subject, depending on the content itself and on a previous agreement between teachers and students for using some specific notation method as we could see in the Physics subject. In this way, it seems that it is easier and more feasible for students and teachers to express mathematics by the use of a previously established citation system. But again, for the rest of the subjects, apparently the use of one or other

In the next section we will develop more statistics in order to find yet more specific

The previous section has shown that there are significant differences in the use of notation between different subjects or knowledge areas. At this point it is important to develop some global descriptive statistics in order to better understand the links between different

Table 4 shows the main statistical measurements, calculated for every notation type and knowledge area. For each of these groups, it shows the mean, the minimum and maximum, the standard deviation and the mode, all values represented in percentages. Regarding the special case of Physics, as there is just one subject under this knowledge area, we will not

As it can be seen in Table 4, there are two cases in which the mean does not fall into the

In none of these cases, though, the difference between the mean and the mode is very significant. This might only be a symptom of an abnormal distribution, and it is not surprising because as we described in previous sections there is a very different pattern in a few subjects for using one or other mathematical notation type depending on the subject

The Mathematics knowledge area is the one showing a larger difference overall between the minimum and maximum percentages for every notation type. This was already explained in a previous section, the reason being there are two subjects in this area (Automata Theory and Formal Languages I and Wiris Laboratory) which do not follow the regular pattern of

single mathematical symbols instead of full mathematical formulae.

method is more likely to be linked to the students' particular preferences.

relationships between subjects and knowledge areas.

 Mathematics area, formula within the e-mail body Mathematics area, attachment with formula

**5.3 A global statistical analysis** 

consider its standard deviation.

expression methods.

mode range:

and area.

the other subjects because of their content type. That is also confirmed by this area having the overall highest standard deviations, especially concerning the most used notation types: full mathematical formulae (with a standard deviation of 9) and mathematical symbol (with a standard deviation of 10).


Table 4. Statistical analysis grouped by notation type and knowledge area

Table 5 shows the same statistical measurements groups as in Table 4, but this time regardless of the knowledge area. As it can be seen in the results, the percentages are more

The Use of Mathematical Formulae in an E-Learning Environment 119

while Physics has citations as its preferred type. Furthermore, Physics does not have mathematical symbols in second place as Mathematics and Technology do, but formula within the e-mail body instead. This means that for Physics, when citation is not being used,

As we have seen, these main statistical measurements neither completely explain the overall behaviour of students choosing a particular mathematics expression method. More information is needed, basically in the way of a much larger e-mail sample, so it is possible to understand why a student expresses mathematics in a particular way. Therefore, this research leads us to conclude that a deeper study is needed in order to analyse different

In this chapter it has been shown: 1) which strategies and methods students use to communicate mathematical formulae in a web based e-learning environment, by means of the analysis of 17,000 messages; and 2) how important each method is depending on the

This study has been developed exclusively using an e-mail web application that lacks a formulae editor, in order to explain the way students communicate using mathematical notation. In the course of this research, it has been seen that the use of mathematical formulae in virtual learning environments has to be carefully studied in order to provide students with better communication, as well as a better understanding of mathematics in

 Mathematical formulae appear in 30% of the e-mails for the analysed subjects. This shows that in the area of e-learning for technical and scientific degrees formulae play a key role in communication. When a technological solution is not available, which is the case, students manage to find a way to communicate mathematics. However, it has to be taken into account that this is an extra handicap for students in subjects that they traditionally find difficult. The challenge of communication, besides the inherent

Mathematical expressions appear in different ways: as a symbol, as a formula written in

For some subjects, the method used to communicate mathematical formulae depends

 The subject itself: some subjects have more formulae (like Physics) and others have more symbols (like Automata Theory and Formal Languages I). The complexity of the formulae and the role they play in the subjects will determine how much mathematical formulae will appear. Then, the overall amount of mathematical notation used by teachers and students seems to relate to the amount of mathematical notation content within the subject itself better than to some other

 The features of the study materials: some subjects, like Physics or Technological Fundamentals II, have a very good citation method since every formula is numbered. This makes it easier for students and teachers to cite formulae by their

difficulty of the subjects, can cause some students not to ask questions.

pseudocode (LaTeX style), as a cited formula and as an attachment.

the pattern reflects the one in Mathematics and Technology.

patterns linked to particular students.

subject and on the knowledge area.

From the study, it can be concluded that:

**6. Conclusion** 

engineering degrees.

on two factors:

external factors.

dispersed, showing a high standard deviation on all three most commonly used notation types: formula within the e-mail body, mathematical symbol and citation.

As it can be observed, the only group mismatching the mean into the mode range with a significant percentage is Formula within the e-mail body. But analysing the data in Table 3, we can see that it is only due to a very irregular use of mathematical formulae: while the mode stays at the range 70%-80%, the rest of the subjects not falling into this range belong to a few different ranges. Therefore, we can discard the statistics in Table 5 as they are not explanatory for this study.


Table 5. Statistical analysis grouped by notation type

Finally, Table 6 shows, according to the mode, the most popular notation types within each knowledge area. This rank also states that one or other notation type use highly depends on the subject and area, Physics being a good example of that: Mathematics and Technology areas both have formula within the e-mail body as the most commonly used notation type,


Table 6. Most commonly used citation methods by knowledge area

while Physics has citations as its preferred type. Furthermore, Physics does not have mathematical symbols in second place as Mathematics and Technology do, but formula within the e-mail body instead. This means that for Physics, when citation is not being used, the pattern reflects the one in Mathematics and Technology.

As we have seen, these main statistical measurements neither completely explain the overall behaviour of students choosing a particular mathematics expression method. More information is needed, basically in the way of a much larger e-mail sample, so it is possible to understand why a student expresses mathematics in a particular way. Therefore, this research leads us to conclude that a deeper study is needed in order to analyse different patterns linked to particular students.

### **6. Conclusion**

118 E-Learning – Engineering, On-Job Training and Interactive Teaching

dispersed, showing a high standard deviation on all three most commonly used notation

As it can be observed, the only group mismatching the mean into the mode range with a significant percentage is Formula within the e-mail body. But analysing the data in Table 3, we can see that it is only due to a very irregular use of mathematical formulae: while the mode stays at the range 70%-80%, the rest of the subjects not falling into this range belong to a few different ranges. Therefore, we can discard the statistics in Table 5 as they are not

**Formula within the e-mail body** 65 45 78 10 >= 70% - < 80% **Mathematical symbol** 24 10 49 10 >= 20% - < 30% **Citation** 11 2 56 13 >= 0% - <10% **Attachment with formula** 9 4 29 6 >= 0% - <10% **Attachment without formula** 5 1 14 4 >= 0% - <10% **Attachment with graphics** 3 0 10 2 >= 0% - <10% **Any kind of mathematical notation** 28 17 45 8 >= 20% - < 30%

Finally, Table 6 shows, according to the mode, the most popular notation types within each knowledge area. This rank also states that one or other notation type use highly depends on the subject and area, Physics being a good example of that: Mathematics and Technology areas both have formula within the e-mail body as the most commonly used notation type,

**Mathematics** Formula within the e-mail body Mathematical symbol

**Technology** Formula within the e-mail body Mathematical symbol

Table 6. Most commonly used citation methods by knowledge area

**Physics** Citation Formula within the e-mail body

**Mean Min Max Standard** 

**Most commonly used Second commonly used**

**deviation Mode**

types: formula within the e-mail body, mathematical symbol and citation.

explanatory for this study.

Table 5. Statistical analysis grouped by notation type

In this chapter it has been shown: 1) which strategies and methods students use to communicate mathematical formulae in a web based e-learning environment, by means of the analysis of 17,000 messages; and 2) how important each method is depending on the subject and on the knowledge area.

This study has been developed exclusively using an e-mail web application that lacks a formulae editor, in order to explain the way students communicate using mathematical notation. In the course of this research, it has been seen that the use of mathematical formulae in virtual learning environments has to be carefully studied in order to provide students with better communication, as well as a better understanding of mathematics in engineering degrees.

From the study, it can be concluded that:

	- The subject itself: some subjects have more formulae (like Physics) and others have more symbols (like Automata Theory and Formal Languages I). The complexity of the formulae and the role they play in the subjects will determine how much mathematical formulae will appear. Then, the overall amount of mathematical notation used by teachers and students seems to relate to the amount of mathematical notation content within the subject itself better than to some other external factors.
	- The features of the study materials: some subjects, like Physics or Technological Fundamentals II, have a very good citation method since every formula is numbered. This makes it easier for students and teachers to cite formulae by their

The Use of Mathematical Formulae in an E-Learning Environment 121

one of them and even the content of the e-mails itself can lead us to detect different student profiles from which we could have another very interesting point of view. For example, the use of a richer language or the development and discussion of a given formula through a thread of e-mails can help teachers identify the expected performance for a particular student and therefore help them focus on the students who are not

According to the results of this research, the contents and structure of a subject can lead students to communicate mathematics in a particular way, sometimes more frequently than the average. However, this does not necessarily mean a better overall performance in a subject, as students would perhaps perform better if the subject was, conversely, designed according to the preferences of the students, providing them with the necessary tools for this

Finally, the use of mathematical language within a virtual classroom is a handicap for e-learning since students and teachers are only able to express themselves by the use of email but, furthermore, we must take into account that this problem can be much worse for disadvantaged student groups – as for example students with visual impairments – especially when we consider the similar difficulties that both students in a virtual environment and students with visual impairments face on a daily basis (as was explained in Section 2). Therefore, these are the main aspects that will be explored in

Chen, Y. & Okada, M. (2001). Structural Analysis and Semantic Understanding for Offline

Fitzpatrick, D. (2007). Teaching Science subjects to Blind Students. Seventh IEEE International Conference on Advanced Learning Technologies (ICALT) LaTeX (2011). A document preparation system. Date of access: 01/05/2011. Available from:

Microsoft (2011). Microsoft Equation Editor. Date of access: 01/05/2011. Available from:

sMArTH (2011). An online equation editor for MathML and LaTeX. Date of access:

The Number Empire (2011). LaTeX Equation Editor. Date of access: 01/05/2011. Available from: http://www.numberempire.com/texequationeditor/equationeditor.php Wiris (2011). The global solution for maths education. Date of access: 01/05/2011. Available

World Wide Web Consortium (2011). MathML, W3C Math Home. Date of access:

Yue-sheng, G. & Jia-yi, Z (2008). Uploading Strategy of the Formula in the Web-based

Mathematics Testing System. International Conference on Computer Science and

*Intelligence*, Vol. 15, No. 6, pp. 967-988, Sept. 2001.

http://www.microsoft.com/education/en-us/teachers/how-

01/05/2011. Available from: http://smarth.sourceforge.net

01/05/2011. Available from: http://www.w3.org/Math

to/Pages/mathematical-equations.aspx

from: http://www.wiris.com/en/editor

Mathematical Expressions. *International Journal of Pattern Recognition and Artificial* 

following this pattern.

purpose.

future work.

**7. References** 

http://www.latex-project.org

Software Engineering.

number and therefore causes a significant boost to the use of formulae thanks to the simplicity of the citation method. Assuming that students and teachers use (or should use) mathematical notation whenever they need to, and regarding the increase of mathematical notation use in Physics, it can be concluded that the lack of such an easy pre-established notation method causes difficulties in communication among the members of a virtual classroom community.


All these conclusions show the importance of mathematical notation for students of technological subjects. For some subjects, this study has detected several key points as indicators for the use of a specific mathematics expression method. For example, in certain subjects, a well-established citation system makes it easier and faster for students to use citation instead of any other method. In the same way, other features like the structure of the study materials or even its content, can also affect the behaviour of students. As for other subjects, further work has to be developed in order to find proper key indicators, which apparently can be related to particular student profile or preferences.

In spite of the large volume of e-mails processed in this research, more than 17,000, the information gathered from them is not enough to identify these student profiles. Currently, the information related to one particular student through different subjects and terms is not significant enough, statistically speaking, to be able to determine if they are following a particular pattern. Therefore, future research must bear this in mind and target particular students behaviour instead of overall subject behaviour. Once this information is available, future studies can also try to find links between the academic performance of students and mathematical expressions use patterns. For example, it is possible to find out if a specific behaviour pattern, varying from the classroom average, leads to a different academic performance, either if that performance is reflected in the students' final marks or on a higher rate of students following continuous assessment during the term. Furthermore, not only the use of the communication method chosen by the student, but the variation in the use of different methods, the usage amount of each one of them and even the content of the e-mails itself can lead us to detect different student profiles from which we could have another very interesting point of view. For example, the use of a richer language or the development and discussion of a given formula through a thread of e-mails can help teachers identify the expected performance for a particular student and therefore help them focus on the students who are not following this pattern.

According to the results of this research, the contents and structure of a subject can lead students to communicate mathematics in a particular way, sometimes more frequently than the average. However, this does not necessarily mean a better overall performance in a subject, as students would perhaps perform better if the subject was, conversely, designed according to the preferences of the students, providing them with the necessary tools for this purpose.

Finally, the use of mathematical language within a virtual classroom is a handicap for e-learning since students and teachers are only able to express themselves by the use of email but, furthermore, we must take into account that this problem can be much worse for disadvantaged student groups – as for example students with visual impairments – especially when we consider the similar difficulties that both students in a virtual environment and students with visual impairments face on a daily basis (as was explained in Section 2). Therefore, these are the main aspects that will be explored in future work.

#### **7. References**

120 E-Learning – Engineering, On-Job Training and Interactive Teaching

communication among the members of a virtual classroom community. There is no pattern regarding the use of mathematical formulae which is valid for all the subjects and knowledge areas. When a concrete type of notation is considered, the results show there is an overall common pattern among all the subjects, full mathematical formula, symbol and citation being the most commonly used. The exception though occurs when a certain notation method is established beforehand, in which case it seems easier and more likely to be used by students and teachers according to the increase of use observed in the particular case of the Physics subject. Therefore, there are signs leading to the existence of student patterns and profiles, more than an overall pattern for every subject. In some cases, when a subject offers an easy and feasible method for expressing mathematics, such is the case for citation, students and teachers tend to adopt it and in that way increase the use of mathematics content within e-mail. In the rest of cases, the student preference seems to be the main reason for the selection. In that case, we need to analyse what leads a student to choose one or other method and if that choice can be linked to a better understanding of the subject, thus a better academic performance. Or furthermore, from a different point of view, if students that have a better academic performance are linked to one particular type of

All these conclusions show the importance of mathematical notation for students of technological subjects. For some subjects, this study has detected several key points as indicators for the use of a specific mathematics expression method. For example, in certain subjects, a well-established citation system makes it easier and faster for students to use citation instead of any other method. In the same way, other features like the structure of the study materials or even its content, can also affect the behaviour of students. As for other subjects, further work has to be developed in order to find proper key indicators, which

In spite of the large volume of e-mails processed in this research, more than 17,000, the information gathered from them is not enough to identify these student profiles. Currently, the information related to one particular student through different subjects and terms is not significant enough, statistically speaking, to be able to determine if they are following a particular pattern. Therefore, future research must bear this in mind and target particular students behaviour instead of overall subject behaviour. Once this information is available, future studies can also try to find links between the academic performance of students and mathematical expressions use patterns. For example, it is possible to find out if a specific behaviour pattern, varying from the classroom average, leads to a different academic performance, either if that performance is reflected in the students' final marks or on a higher rate of students following continuous assessment during the term. Furthermore, not only the use of the communication method chosen by the student, but the variation in the use of different methods, the usage amount of each

apparently can be related to particular student profile or preferences.

mathematical expressions.

number and therefore causes a significant boost to the use of formulae thanks to the simplicity of the citation method. Assuming that students and teachers use (or should use) mathematical notation whenever they need to, and regarding the increase of mathematical notation use in Physics, it can be concluded that the lack of such an easy pre-established notation method causes difficulties in


**8** 

Majda Krajnc

*Slovenia* 

**E-Learning Usage During Chemical** 

*University of Maribor, Faculty of Chemistry and Chemical Engineering* 

During the last century a lot of changes appeared within the education process. At the beginning of the 20th century, children went to school on foot. Sometimes their homes were very far from their schools, so they spent a lot of time per day just walking. Our grandmothers and grandfathers were such a generation. Sometimes sleepy and tired, they still had to listen very carefully to what the teachers said because they had to make notes for their homework. Teachers were strict and pupils had to obey them. Teachers were often the only people who gave children information about history, geography, mathematics, chemistry etc. Most the inhabitants of those times did not have a radio, and television did not exist yet. Despite this, some of the pupils of this generation went-on to universities and even became scientists. How was it possible? Did they have enough knowledge under such circumstances? They did not have computers and internet yet. In spite of all that, they had knowledge skills, and work ethics than the generations at the end of the 20th century. They spent a lot of time in libraries reading, learning and, writing about what they were learning. They discussed a lot about their problems with their colleagues and professors. They were

In the second half of the 20th century students, in general, did not need to go to school on foot anymore, whether they lived far from school or not. They could choose the bus or train, or even lived in student hostels. The evolution in technology also caused an evolution in the education process. The lectures became more practical. Lecturers did not only use a blackboard and chalk when lecturing but some of them started to use different technical equipment such as overhead projectors and slides for presenting the subject material to their students. Students could spend time in modern libraries, make notes in notebooks or even make copies of the course material. Many lecturers wrote their own books as course

At the beginning of the 21st century, a group of eminent professors of chemical engineering (Felder et al., 2000) announced that in the very near future, it would be almost impossible to carry-out the education process without incorporating better teaching methods. Different study reforms would change the traditional curricula and lecturers would simply have insufficient time for explaining all the material, within the classroom. This meant that students would need to take greater responsibility for their own knowledge and nontraditional methods, such as active learning, cooperative learning, problem-based learning, project-based learning, and e-learning would be the more important activities regarding a

**1. Introduction** 

very good listeners.

material, which students could then buy.

**Engineering Courses** 

Zhao, J. (2008). Towards a User-centric Math Information Retrieval System. Bulletin of IEEE Technical Committee on Digital Libraries, Vol. 4, issue 2, fall 2008, ISSN 1937-7266

## **E-Learning Usage During Chemical Engineering Courses**

#### Majda Krajnc

*University of Maribor, Faculty of Chemistry and Chemical Engineering Slovenia* 

#### **1. Introduction**

122 E-Learning – Engineering, On-Job Training and Interactive Teaching

Zhao, J. (2008). Towards a User-centric Math Information Retrieval System. Bulletin of

1937-7266

IEEE Technical Committee on Digital Libraries, Vol. 4, issue 2, fall 2008, ISSN

During the last century a lot of changes appeared within the education process. At the beginning of the 20th century, children went to school on foot. Sometimes their homes were very far from their schools, so they spent a lot of time per day just walking. Our grandmothers and grandfathers were such a generation. Sometimes sleepy and tired, they still had to listen very carefully to what the teachers said because they had to make notes for their homework. Teachers were strict and pupils had to obey them. Teachers were often the only people who gave children information about history, geography, mathematics, chemistry etc. Most the inhabitants of those times did not have a radio, and television did not exist yet. Despite this, some of the pupils of this generation went-on to universities and even became scientists. How was it possible? Did they have enough knowledge under such circumstances? They did not have computers and internet yet. In spite of all that, they had knowledge skills, and work ethics than the generations at the end of the 20th century. They spent a lot of time in libraries reading, learning and, writing about what they were learning. They discussed a lot about their problems with their colleagues and professors. They were very good listeners.

In the second half of the 20th century students, in general, did not need to go to school on foot anymore, whether they lived far from school or not. They could choose the bus or train, or even lived in student hostels. The evolution in technology also caused an evolution in the education process. The lectures became more practical. Lecturers did not only use a blackboard and chalk when lecturing but some of them started to use different technical equipment such as overhead projectors and slides for presenting the subject material to their students. Students could spend time in modern libraries, make notes in notebooks or even make copies of the course material. Many lecturers wrote their own books as course material, which students could then buy.

At the beginning of the 21st century, a group of eminent professors of chemical engineering (Felder et al., 2000) announced that in the very near future, it would be almost impossible to carry-out the education process without incorporating better teaching methods. Different study reforms would change the traditional curricula and lecturers would simply have insufficient time for explaining all the material, within the classroom. This meant that students would need to take greater responsibility for their own knowledge and nontraditional methods, such as active learning, cooperative learning, problem-based learning, project-based learning, and e-learning would be the more important activities regarding a

E-Learning Usage During Chemical Engineering Courses 125

learning course quality, perceived usefulness, perceived ease of use and diversity during assessments, are the critical factors. The effect of learning activities and students' satisfaction are influenced by their instructors' attitudes when handling learning activities. Active and positive attitudes do motivate students regarding e-learning usage. Pei-Chen et al. (2008) also discussed that course quality, which includes teaching material, interactive discussion, and course-scheduling, had the strongest association with satisfaction regarding e-learning. Furthermore, many e-learning users were discouraged from e-learning by those poor

Nowadays, a lot of e-tools are available for e-education e.g. internet tools (wikis), electronic or virtual learning environments (Blackboard, Webassign, WebCT, Moodle), and web labs. Through such tools the lecturers and students can communicate in two different ways: synchronous and asynchronous. A lot of experiences and supporting technologies on synchronous e-learning were presented by Granda et al. (2010). They pointed-out two major features of synchronous e-learning systems, i.e. audio and video-conferencing. The first one is used to allow participants to participate orally within learning sessions, whilst the second is used to reinforce a sense of user-presence. Floyd Smith et al. (2010) presented their experiences of a synchronous distance-education course for non-scientists, which was

Lectures and experts from many institutions worldwide who already use different kinds of e-learning tools within their education processes (Lau, 2005; Maurice, 2006; Selmer 2007; Hussman, 2004; Rodrígues et al., 2006) think that such technology stimulates and motivates students' interest in their subjects, improves their learning performances within the discipline of industrial engineering, and significantly improves the teaching and learning, whilst saving time and money regarding all aspects of the classroom. Web labs, for example, provide students with training for working with experimental equipment and help them to understand the fundamentals of unit operations e.g. distillation and drying (Dongil et al., 2009). Such laboratories drastically reduce the economic necessity of providing new equipment, and stimulate skills such as teamwork, communication, and presentation

Electronic tools could be successfully used in interdisciplinary learning courses in which e.g. students participate outside the classroom. Schaad et al. (2008) described such course in which students had the option of participating in either a service-learning exercise within an area ravaged by a natural disaster within Lousiana and North Carolina, or to research a topic related to natural disasters. All students attended the lecture component of the course and completed on-line quizzes on Blackboard in order to demonstrate their understanding of the presented material. The twice-weekly lectures were recorded and provided in the

Some educators use Internet tools e.g. wikis technology, to enhance creativity, communication, student interaction, collaboration, and the organization of information (Hadley & Debelak, 2009) when students work on projects, and as a replacement for traditional text-books where students add problems and edit the educational content (Richardson, 2006). When using wikis during projects, the supervisor can keep constant tabs on a student's progress, so the projects are completed on time and the results are valid. ICT has also been incorporated into some Chemical Engineering Courses at the Faculty of Chemistry and Chemical Engineering (FCCE), University of Maribor (UM), Slovenia. At the

technologies having slow response-times or frequent technical difficulties.

successfully carried out over two semesters and jointly by three universities.

(Selmer, 2007; Le Roux et al., 2010).

form of Webcasts for future reference.

more efficient education system (Krajnc, 2009). The solutions exist, it is upon the lecturer to decide which method to choose.

When the computer era began, computer experts started to develop information and communication technology (ICT), which created a huge revolution in the presentation of knowledge and information to the world, which then became a much smaller place with a lot more information. A basic ICT infrastructure needs computers, the internet, e-mail, and intranet. Using such structures, an electronic way of learning (e-learning) is possible and in a modern society all these tools are usually available.

E-learning could be used as part of traditional learning (blended-learning, hybrid-learning, mixed-learning) or just as online (virtual) education and incorporated into any course content i.e. the natural sciences or sociology. Maybe it is a little harder to use it in natural sciences because the mathematicians probably asses knowledge electronically less than the historian.

Nowadays, it is normal to use electronic slides, the internet, e-mails, electronic learning environments and e-course material during lectures presentation. When using ICT at lectures, it is the lecturers' responsibilities to present students with qualitative and important information. Many lecturers who use ICT say that when ICT is included within the traditional method of education, it facilitates lectures and the students' work, and the lectures became more dynamic and interesting. Different e-activities also enrich the subject content. E-learning presents an alternative for students and helps them to find a balance between their private lives, careers, and education. It is one of the more dynamic and enriching forms of learning, and reduces dependency on space and time (Paik et al., 2004). It offers both individual learning experiences, and opportunities for working together with colleagues (Peat, 2000).

A lot of statements have been made to date which have shown both positive and negative responses to e-learning. The following are some examples. Lecturers who have one hundred or more students at their lectures know that the lecturer my well spend more time on the final assessment than on lecturing, lecture preparation, and tutorials (Husssman et al.; 2004, Excell, 2004). Because assessment represents a significant part of a lecturer's workload, computer-assisted assessment has the potential for allowing an effective assessment regime to be maintained in the cases of large classes. E-learning assessment of knowledge is also of great benefit from the students' points of view. Rossiter et al. (2010) implemented online quizzes within a Chemical Process Principle Course in the freshman year. Such a new method of learning improved students' learning and success, particularly among weaker students and helped them to develop transferable skills regarding teamwork and communication. The quizzes helped them to do their homework, and to a certain extent, develop their core technical skills for problem-based learning activities.

On the one hand, e-learning brings a lot of advantages whilst, on the other, it does require the adoption of new skills and knowledge. At the beginnings of any e-learning incorporation into the education process, a lot of time is needed in order to learn new aspects regarding the adoption of new technologies, and their different tools. Some users stop using it after their initial experience. Pei-Chen Sun et al. (2008) investigated those critical factors affecting learners' satisfaction with e-learning. They discovered that learner computer-anxiety, instructor-attitude towards e-learning, e-learning course flexibility, e-

more efficient education system (Krajnc, 2009). The solutions exist, it is upon the lecturer to

When the computer era began, computer experts started to develop information and communication technology (ICT), which created a huge revolution in the presentation of knowledge and information to the world, which then became a much smaller place with a lot more information. A basic ICT infrastructure needs computers, the internet, e-mail, and intranet. Using such structures, an electronic way of learning (e-learning) is possible and in a

E-learning could be used as part of traditional learning (blended-learning, hybrid-learning, mixed-learning) or just as online (virtual) education and incorporated into any course content i.e. the natural sciences or sociology. Maybe it is a little harder to use it in natural sciences because the mathematicians probably asses knowledge electronically less than the

Nowadays, it is normal to use electronic slides, the internet, e-mails, electronic learning environments and e-course material during lectures presentation. When using ICT at lectures, it is the lecturers' responsibilities to present students with qualitative and important information. Many lecturers who use ICT say that when ICT is included within the traditional method of education, it facilitates lectures and the students' work, and the lectures became more dynamic and interesting. Different e-activities also enrich the subject content. E-learning presents an alternative for students and helps them to find a balance between their private lives, careers, and education. It is one of the more dynamic and enriching forms of learning, and reduces dependency on space and time (Paik et al., 2004). It offers both individual learning experiences, and opportunities for working together with

A lot of statements have been made to date which have shown both positive and negative responses to e-learning. The following are some examples. Lecturers who have one hundred or more students at their lectures know that the lecturer my well spend more time on the final assessment than on lecturing, lecture preparation, and tutorials (Husssman et al.; 2004, Excell, 2004). Because assessment represents a significant part of a lecturer's workload, computer-assisted assessment has the potential for allowing an effective assessment regime to be maintained in the cases of large classes. E-learning assessment of knowledge is also of great benefit from the students' points of view. Rossiter et al. (2010) implemented online quizzes within a Chemical Process Principle Course in the freshman year. Such a new method of learning improved students' learning and success, particularly among weaker students and helped them to develop transferable skills regarding teamwork and communication. The quizzes helped them to do their homework, and to a certain extent,

On the one hand, e-learning brings a lot of advantages whilst, on the other, it does require the adoption of new skills and knowledge. At the beginnings of any e-learning incorporation into the education process, a lot of time is needed in order to learn new aspects regarding the adoption of new technologies, and their different tools. Some users stop using it after their initial experience. Pei-Chen Sun et al. (2008) investigated those critical factors affecting learners' satisfaction with e-learning. They discovered that learner computer-anxiety, instructor-attitude towards e-learning, e-learning course flexibility, e-

develop their core technical skills for problem-based learning activities.

decide which method to choose.

historian.

colleagues (Peat, 2000).

modern society all these tools are usually available.

learning course quality, perceived usefulness, perceived ease of use and diversity during assessments, are the critical factors. The effect of learning activities and students' satisfaction are influenced by their instructors' attitudes when handling learning activities. Active and positive attitudes do motivate students regarding e-learning usage. Pei-Chen et al. (2008) also discussed that course quality, which includes teaching material, interactive discussion, and course-scheduling, had the strongest association with satisfaction regarding e-learning. Furthermore, many e-learning users were discouraged from e-learning by those poor technologies having slow response-times or frequent technical difficulties.

Nowadays, a lot of e-tools are available for e-education e.g. internet tools (wikis), electronic or virtual learning environments (Blackboard, Webassign, WebCT, Moodle), and web labs. Through such tools the lecturers and students can communicate in two different ways: synchronous and asynchronous. A lot of experiences and supporting technologies on synchronous e-learning were presented by Granda et al. (2010). They pointed-out two major features of synchronous e-learning systems, i.e. audio and video-conferencing. The first one is used to allow participants to participate orally within learning sessions, whilst the second is used to reinforce a sense of user-presence. Floyd Smith et al. (2010) presented their experiences of a synchronous distance-education course for non-scientists, which was successfully carried out over two semesters and jointly by three universities.

Lectures and experts from many institutions worldwide who already use different kinds of e-learning tools within their education processes (Lau, 2005; Maurice, 2006; Selmer 2007; Hussman, 2004; Rodrígues et al., 2006) think that such technology stimulates and motivates students' interest in their subjects, improves their learning performances within the discipline of industrial engineering, and significantly improves the teaching and learning, whilst saving time and money regarding all aspects of the classroom. Web labs, for example, provide students with training for working with experimental equipment and help them to understand the fundamentals of unit operations e.g. distillation and drying (Dongil et al., 2009). Such laboratories drastically reduce the economic necessity of providing new equipment, and stimulate skills such as teamwork, communication, and presentation (Selmer, 2007; Le Roux et al., 2010).

Electronic tools could be successfully used in interdisciplinary learning courses in which e.g. students participate outside the classroom. Schaad et al. (2008) described such course in which students had the option of participating in either a service-learning exercise within an area ravaged by a natural disaster within Lousiana and North Carolina, or to research a topic related to natural disasters. All students attended the lecture component of the course and completed on-line quizzes on Blackboard in order to demonstrate their understanding of the presented material. The twice-weekly lectures were recorded and provided in the form of Webcasts for future reference.

Some educators use Internet tools e.g. wikis technology, to enhance creativity, communication, student interaction, collaboration, and the organization of information (Hadley & Debelak, 2009) when students work on projects, and as a replacement for traditional text-books where students add problems and edit the educational content (Richardson, 2006). When using wikis during projects, the supervisor can keep constant tabs on a student's progress, so the projects are completed on time and the results are valid.

ICT has also been incorporated into some Chemical Engineering Courses at the Faculty of Chemistry and Chemical Engineering (FCCE), University of Maribor (UM), Slovenia. At the

E-Learning Usage During Chemical Engineering Courses 127

Students also stated, that they could print-out, for example, solution manuals, questions for traditional oral exams, chapters of the text-books, whenever they wanted to. The lecturer

In 2009, ELEUM was replaced by Moodle, a internationally-known open-source (course) learning management system also called "Virtual Learning Environment" (VLE) (Dougiamas, 1999). In comparison with ELEUM, Moodle was fairly sophisticated and provided more aids than ELEUM. When Moodle became available for educational purposes, it caused stress among lecturers. It was a novelty once again. For this reason, the lecturers were only capable of putting on it mainly electronic documents and exam results, as at the time of ELEUM's beginning. The Computer Centre of the University of Maribor, Department for e-learning, prepares learning workshops every year because of the problems. By such an education of the pedagogic staff, Moodle has advanced into the

In spite of many useful electronic tools, being available online, there are some which particularly help to decrease the lecturers' workloads and increase efficiency when studying. The following, presents only two of them i.e. electronic tests (quizzes) for the electronic assessment of knowledge and multimedia e-chapter which helps students to

From almost the beginning of the ELEUM's usage, electronic tests (quizzes) were prepared for students who were willing to choose them instead of the traditional oral exam. Some people would say that creating a bank of questions takes a lot of time and effort, and the final result is a greater lecturer workload. This was true at the beginning of e-assessment but after a year or two the workload decreases because it is unnecessary to create a new bank of questions every year but only to add new or edit old questions. It is certainly true that lecturers engaged in such work have a lot of enthusiasm for their work and want to offer

The students' responses to e-test usage were different in comparison with other available functionalities. In this case, knowledge was assessed using an appropriate mark after finishing each e-test. For these reasons, students did not decide to use them in as greater

The first electronic test was realized at the Process Synthesis Course during the academic year 2004/2005, and since then every following academic year without interruption. Some

students have seen a lot of advantages in such a choice, such as (Krajnc, 2008):

They pointed-out the following advantages: updated information about the Course, all the data collected in one place,

pedagogical process from year to year.

**3. Efficient tools for e-learning** 

**3.1 Electronic assessment of knowledge** 

students new ideas.

numbers as for other tools.

could correct the data, and update the manuals and text-books.

prepare for electronic or classical assessments of knowledge.

electronic text-books.

beginning, this novelty confused the majority of the teaching staff. Some lecturers thought that the students' knowledge would decrease by incorporating e-learning into their courses. Only a few enthusiasts believed that new learning methods and tools will produce better and efficient study results, and that some activities will expand both the lecturers' and students' knowledge. The results of their efforts are described in this Chapter.

This Chapter is organized as follows: Section 2 introduces the incorporation of e-learning at the FCCE in Maribor. Section 3 illustrates the efficient tools of e-learning i.e. electronic tests for the e-assessment of knowledge and multimedia e-chapters. The students' and teaching staffs' responses to e-learning are also presented in this section. Section 4 concludes the chapter describing their experiences of e-learning usage from both the students and teaching staffs' points of view, and ends with the challenges for the future.

#### **2. Incorporation of e-learning at FCCE, University of Maribor**

E-learning at the Faculty of Chemistry and Chemical Engineering (FCCE) in Maribor was incorporated into the education process for the first time during the academic year 2004/2005. The pedagogical staff started to adopt the electronic learning environment called ELEUM, which was developed at the Faculty of Electrical Engineering and Computer Science, in Maribor. It was available to all members of the University free of charge. It was a simple but effective electronic learning environment, which could be used by all lecturers and students as a communication tool.

ELEUM advanced into the pedagogical process very slowly, because the introduction of anything new is hard and painstaking work. However, the first experiences showed that it could improve the quality of the process. Only one lecturer from one Course used it at the beginning. Only certain activities were used in the first year because this was a new method of learning, teaching and communicating. In general, lecturers put on ELEUM electronic documents of the Course material, the criteria of the Course, dates for exams and colloquiums, and information about lectures, practical work etc. Then new functionalities were added from year to year.

Although the pedagogical staff became acquainted very slowly with this new method of working, the students adopted it almost immediately. Their responses to e-learning and the ELEUM were collected by means of a questionnaire (Krajnc, 2006, 2009). The questionnaires were filled by students at the Process Synthesis Course, where e-learning was introduced for the first time at FCCE. The course was carried-out in the second semester of the third year as a professional higher programme.

The questionnaire results showed that during the academic year 2004/2005 e-learning was almost unknown to students, by the next academic year approximately one half of students knew or partly-knew e-learning, but by the 2006/2007 academic year, all the students knew it well or fairly-well. Thus, information about e-learning within the education process has advanced from year to year (Krajnc, 2009). At the beginning, the lecturer was the main source of initial information about e-learning but over the following academic years, the students received information from their friends and other colleagues who had used an electronic learning environment in previous years, too. Students thought that ELEUM was an effective tool and helped them to improve the qualities and efficiencies of their studies.

They pointed-out the following advantages:


126 E-Learning – Engineering, On-Job Training and Interactive Teaching

beginning, this novelty confused the majority of the teaching staff. Some lecturers thought that the students' knowledge would decrease by incorporating e-learning into their courses. Only a few enthusiasts believed that new learning methods and tools will produce better and efficient study results, and that some activities will expand both the lecturers' and

This Chapter is organized as follows: Section 2 introduces the incorporation of e-learning at the FCCE in Maribor. Section 3 illustrates the efficient tools of e-learning i.e. electronic tests for the e-assessment of knowledge and multimedia e-chapters. The students' and teaching staffs' responses to e-learning are also presented in this section. Section 4 concludes the chapter describing their experiences of e-learning usage from both the students and teaching

E-learning at the Faculty of Chemistry and Chemical Engineering (FCCE) in Maribor was incorporated into the education process for the first time during the academic year 2004/2005. The pedagogical staff started to adopt the electronic learning environment called ELEUM, which was developed at the Faculty of Electrical Engineering and Computer Science, in Maribor. It was available to all members of the University free of charge. It was a simple but effective electronic learning environment, which could be used by all lecturers

ELEUM advanced into the pedagogical process very slowly, because the introduction of anything new is hard and painstaking work. However, the first experiences showed that it could improve the quality of the process. Only one lecturer from one Course used it at the beginning. Only certain activities were used in the first year because this was a new method of learning, teaching and communicating. In general, lecturers put on ELEUM electronic documents of the Course material, the criteria of the Course, dates for exams and colloquiums, and information about lectures, practical work etc. Then new functionalities

Although the pedagogical staff became acquainted very slowly with this new method of working, the students adopted it almost immediately. Their responses to e-learning and the ELEUM were collected by means of a questionnaire (Krajnc, 2006, 2009). The questionnaires were filled by students at the Process Synthesis Course, where e-learning was introduced for the first time at FCCE. The course was carried-out in the second semester of the third year as

The questionnaire results showed that during the academic year 2004/2005 e-learning was almost unknown to students, by the next academic year approximately one half of students knew or partly-knew e-learning, but by the 2006/2007 academic year, all the students knew it well or fairly-well. Thus, information about e-learning within the education process has advanced from year to year (Krajnc, 2009). At the beginning, the lecturer was the main source of initial information about e-learning but over the following academic years, the students received information from their friends and other colleagues who had used an electronic learning environment in previous years, too. Students thought that ELEUM was an effective tool and helped them to improve the qualities and efficiencies of their studies.

students' knowledge. The results of their efforts are described in this Chapter.

staffs' points of view, and ends with the challenges for the future.

and students as a communication tool.

were added from year to year.

a professional higher programme.

**2. Incorporation of e-learning at FCCE, University of Maribor** 

Students also stated, that they could print-out, for example, solution manuals, questions for traditional oral exams, chapters of the text-books, whenever they wanted to. The lecturer could correct the data, and update the manuals and text-books.

In 2009, ELEUM was replaced by Moodle, a internationally-known open-source (course) learning management system also called "Virtual Learning Environment" (VLE) (Dougiamas, 1999). In comparison with ELEUM, Moodle was fairly sophisticated and provided more aids than ELEUM. When Moodle became available for educational purposes, it caused stress among lecturers. It was a novelty once again. For this reason, the lecturers were only capable of putting on it mainly electronic documents and exam results, as at the time of ELEUM's beginning. The Computer Centre of the University of Maribor, Department for e-learning, prepares learning workshops every year because of the problems. By such an education of the pedagogic staff, Moodle has advanced into the pedagogical process from year to year.

#### **3. Efficient tools for e-learning**

In spite of many useful electronic tools, being available online, there are some which particularly help to decrease the lecturers' workloads and increase efficiency when studying. The following, presents only two of them i.e. electronic tests (quizzes) for the electronic assessment of knowledge and multimedia e-chapter which helps students to prepare for electronic or classical assessments of knowledge.

#### **3.1 Electronic assessment of knowledge**

From almost the beginning of the ELEUM's usage, electronic tests (quizzes) were prepared for students who were willing to choose them instead of the traditional oral exam. Some people would say that creating a bank of questions takes a lot of time and effort, and the final result is a greater lecturer workload. This was true at the beginning of e-assessment but after a year or two the workload decreases because it is unnecessary to create a new bank of questions every year but only to add new or edit old questions. It is certainly true that lecturers engaged in such work have a lot of enthusiasm for their work and want to offer students new ideas.

The students' responses to e-test usage were different in comparison with other available functionalities. In this case, knowledge was assessed using an appropriate mark after finishing each e-test. For these reasons, students did not decide to use them in as greater numbers as for other tools.

The first electronic test was realized at the Process Synthesis Course during the academic year 2004/2005, and since then every following academic year without interruption. Some students have seen a lot of advantages in such a choice, such as (Krajnc, 2008):

E-Learning Usage During Chemical Engineering Courses 129

The following are some examples of those e-test questions included in the electronic

Example 1 represents the essay-type question. The Table presents data for a four-component mixture which should be separated into pure components. Students need to focus on the properties of the components i.e. boiling points, corrosiveness and toxicity, and on this basis determine the appropriate separation sequence. They have to take into consideration two

Example 2 is more exact because certain calculations need to be done before selecting the correct answer. A student has to know the proper value and unit of ideal gas constant (in this case 8,314 J/(mol · K)) by heart, and then calculate activation energy. He/she must pay attention to the activation energy unit which must be in kJ/mol. When he/she establishes all

a. questions with one correct answer from two possible answers,

assessment of knowledge during the Process Synthesis Course.

a. remove the corrosive and hazardous material early, and

Example 2: The multiple-choice type question with one correct answer.

Their findings are written in the box below the question.

b. difficult separations are best saved for last.

d. true/false questions, e. the essay-type questions.

heuristic rules:

Example 1: The essay-type question

b. questions with one correct answer from among several possible answers, c. questions with several correct answers from among many possible answers,


Since the academic year 2004/2005, more and more students have chosen this assessment of their knowledge, instead of the classical oral examinations (Krajnc, 2008), as shown Fig. 1.

Fig. 1. Students' applications for e-tests during the Process Synthesis Course.

The middle-curve shows the interest for e-tests during the seven academic years of the Process Synthesis Course. The curve shows the increase in e-test applications until the academic year 2007/2008. The next academic year the interest stayed the same, i.e. all students chose e-tests, but in the academic years 2009/2010 and 2010/2011 some students did not choose e-tests instead of the classical oral exam. The lower curve represents the number of students who finished e-tests successfully. It can be seen, that in the academic years 2007/2008 and 2008/2009, all the regular enrolled students chose e-tests and also finished them successfully. It is evident that the number of sceptical students decreased gradually from the academic year 2004/2005 to 2007/2008 but increased again during the academic year 2009/2010. The fluctuation in e-tests applicability among students during the seven year time period was mainly about their ignorance of the new way of learning, and an unwillingness to become acquainted with the knowledge in so short a time i.e. chapter after chapter.

E-tests were prepared for each chapter of the course material separately and were composed of different numbers and kinds of questions. They were executed approximately twice a month. Students had one week to prepare for each e-test. When the e-test was turned on, they came to the Faculty's computer room.

All e-tests included about 70 questions. Students had to focus on each question very carefully since the answers sometimes seemed very similar. A student was successful if the fraction of correct answers was at least 60 %. There were different types of questions in each e-test:


Since the academic year 2004/2005, more and more students have chosen this assessment of their knowledge, instead of the classical oral examinations (Krajnc, 2008), as shown Fig. 1.

they can avoid the embarrassment of confronting their lecturer face to face,

Fig. 1. Students' applications for e-tests during the Process Synthesis Course.

The middle-curve shows the interest for e-tests during the seven academic years of the Process Synthesis Course. The curve shows the increase in e-test applications until the academic year 2007/2008. The next academic year the interest stayed the same, i.e. all students chose e-tests, but in the academic years 2009/2010 and 2010/2011 some students did not choose e-tests instead of the classical oral exam. The lower curve represents the number of students who finished e-tests successfully. It can be seen, that in the academic years 2007/2008 and 2008/2009, all the regular enrolled students chose e-tests and also finished them successfully. It is evident that the number of sceptical students decreased gradually from the academic year 2004/2005 to 2007/2008 but increased again during the academic year 2009/2010. The fluctuation in e-tests applicability among students during the seven year time period was mainly about their ignorance of the new way of learning, and an unwillingness to become acquainted with the knowledge in so short a time i.e. chapter after

E-tests were prepared for each chapter of the course material separately and were composed of different numbers and kinds of questions. They were executed approximately twice a month. Students had one week to prepare for each e-test. When the e-test was turned on,

All e-tests included about 70 questions. Students had to focus on each question very carefully since the answers sometimes seemed very similar. A student was successful if the fraction of correct answers was at least 60 %. There were different types of questions in each

 they can concentrate better on the questions, the results of the e-tests are known immediately.

chapter.

e-test:

they came to the Faculty's computer room.

e. the essay-type questions.

The following are some examples of those e-test questions included in the electronic assessment of knowledge during the Process Synthesis Course.

Example 1: The essay-type question

Example 1 represents the essay-type question. The Table presents data for a four-component mixture which should be separated into pure components. Students need to focus on the properties of the components i.e. boiling points, corrosiveness and toxicity, and on this basis determine the appropriate separation sequence. They have to take into consideration two heuristic rules:


Their findings are written in the box below the question.

Example 2: The multiple-choice type question with one correct answer.


Example 2 is more exact because certain calculations need to be done before selecting the correct answer. A student has to know the proper value and unit of ideal gas constant (in this case 8,314 J/(mol · K)) by heart, and then calculate activation energy. He/she must pay attention to the activation energy unit which must be in kJ/mol. When he/she establishes all

E-Learning Usage During Chemical Engineering Courses 131

Course and 33 % in the Process Calculation Course took e-tests before the oral exam (Krajnc,

they would suggest such assessment of knowledge for the following generations of

The Bologna study programmes at FCCE started during the academic year 2009/2010. Each year the results show that a lot of students register in the first study year, which causes a lot of pedagogic workload for the staff. As the application of IC learning environments is particularly useful when a lot of students are enrolled, Moodle was incorporated within some Bologna Courses i.e. Computer Science in Chemistry Course (CSC), and Process Calculation I Course (PC I) in the first semester, and Process Calculation II Course (PC II), Chemical Calculation II Course (CC II), and Process Balances Course (PB) in the second semester. On the basis of the previous experiences from the Process Synthesis Course, the electronic assessment of knowledge was also incorporated into the mentioned Bologna courses. Lectures at all courses were given once a week (3 hours every week). The lecturer explained the main points of the material, and the students learned the rest by themselves.

At the Computer Science in Chemistry Course and Process Calculation I Course of the first semester, electronic assessment was introduced to the freshman three times, half an hour before regular lectures, and in a computer room of the Faculty. Each e-test was administrated only once. It was forbidden to write down the questions on the paper. A

In order to obtain freshman's feedback on the applicability, usefulness, and efficiency of e-assessment, at the end of the semester students filled-in a questionnaire and answered certain questions. It was comprised of 16 questions, 13 of which were multiple-choice type questions and three were essay-type questions. The questionnaire was classified into four

109 of the students filled-in the questionnaire. The results showed that 10 % of students used the electronic-learning environment Moodle every day, 82 % once a week, and the rest (8 %)

The following explains the electronic assessment procedures at some courses.

student was successful if at least 60 % of the answers were correct.

parts where students gave their opinions on:

 reasons for e-environment usage, electronic-assessment and the new way of learning.

electronic-learning environment applicability,

**3.1.1 Electronic assessment of knowledge for the Bologna study-program courses**  When Slovenia in 2004 became a full member of the European Union and the European University Area, the Bologna Process started, to which the members of this area are bound. It encompasses a unique model regarding studies. This has meant reassessing and changing the traditional curricula towards a single-study structure within European Universities

with e-tests they learned what was the essence of each chapter,

the marks and results of the e-tests were known at once and

e-tests gave them a critique about the knowledge,

2009) . They said that:

students.

(Krajnc, 2009).

correct answers were available,

the requirements, the correct answer is selected (the third one in this case). Obviously in this case the student chose the wrong answer. The message »*The answer is incorrect. You should pay more attention to R constant unit*!« reminds student as to what mistake he/she has probably made.

Example 3: True/false question.


Example 3 shows a sentence which is written correctly or incorrectly. Students have to read it word by word and very carefully because sometimes only one word has a significant meaning. After deciding the student chooses only one possibility i.e. true (if the sentence is written correctly) or false (if the sentence is written incorrectly). In this case, the student chose the second possibility i.e. false, which was the wrong decision.

Students have the interesting comments on questions with the different kinds of correct and wrong answers. They think that questions with several possible answers are the most pretentious because they have to know the theory in detail. They should focus on answers very carefully because they sometimes seem similar. If they are somewhat unacquainted with the theory of the course, they usually do not select all the correct answers.

Before starting the first e-test, the lecturer explains how e-tests are conducted e.g. that they have time-limits, the questions and answers for each implementation are mixed, how many questions are contained in each e-test, and incorrect answers are estimated with negative points. Students are usually very nervous before the first e-test. This is understandable particularly in those cases where they have not had such a kind of knowledge evaluation up to that moment. In the Process Synthesis Course, the lecturer accepts a failure in one e-test, but they must be successful in the following. The theory of the chapter, in which the student fails, would he/she passes traditional.

The non-traditional way of learning i.e. co-operative work (when doing homework and solving problems in teams) and e-learning, produced good study results during the Process Synthesis Course. Almost all students finished their course obligations within the course time or within one or two weeks after finishing the lectures. The students stated that, in such a manner, more time was left for other courses and obligations where they did not have such work opportunities.

During the academic year 2006/2007, the electronic assessment of knowledge was also incorporated in the second study year within the Process Balances and Process Calculation Courses. During this study year e-tests were prepared for the self-assessment of knowledge before the oral exam. Electronic tests were active from the 1st June until the 1st October of that year, i.e. throughout whole summer examination time. Students who passed all e-tests successfully got an extra bonus towards the final mark of the exam, as a stimulus award. Almost half of the regular enrolled students (46 %) who needed to pass the Process Balances Course and 33 % in the Process Calculation Course took e-tests before the oral exam (Krajnc, 2009) . They said that:


130 E-Learning – Engineering, On-Job Training and Interactive Teaching

the requirements, the correct answer is selected (the third one in this case). Obviously in this case the student chose the wrong answer. The message »*The answer is incorrect. You should pay more attention to R constant unit*!« reminds student as to what mistake he/she has

Example 3 shows a sentence which is written correctly or incorrectly. Students have to read it word by word and very carefully because sometimes only one word has a significant meaning. After deciding the student chooses only one possibility i.e. true (if the sentence is written correctly) or false (if the sentence is written incorrectly). In this case, the student

Students have the interesting comments on questions with the different kinds of correct and wrong answers. They think that questions with several possible answers are the most pretentious because they have to know the theory in detail. They should focus on answers very carefully because they sometimes seem similar. If they are somewhat unacquainted

Before starting the first e-test, the lecturer explains how e-tests are conducted e.g. that they have time-limits, the questions and answers for each implementation are mixed, how many questions are contained in each e-test, and incorrect answers are estimated with negative points. Students are usually very nervous before the first e-test. This is understandable particularly in those cases where they have not had such a kind of knowledge evaluation up to that moment. In the Process Synthesis Course, the lecturer accepts a failure in one e-test, but they must be successful in the following. The theory of the chapter, in which the student

The non-traditional way of learning i.e. co-operative work (when doing homework and solving problems in teams) and e-learning, produced good study results during the Process Synthesis Course. Almost all students finished their course obligations within the course time or within one or two weeks after finishing the lectures. The students stated that, in such a manner, more time was left for other courses and obligations where they did not have

During the academic year 2006/2007, the electronic assessment of knowledge was also incorporated in the second study year within the Process Balances and Process Calculation Courses. During this study year e-tests were prepared for the self-assessment of knowledge before the oral exam. Electronic tests were active from the 1st June until the 1st October of that year, i.e. throughout whole summer examination time. Students who passed all e-tests successfully got an extra bonus towards the final mark of the exam, as a stimulus award. Almost half of the regular enrolled students (46 %) who needed to pass the Process Balances

chose the second possibility i.e. false, which was the wrong decision.

with the theory of the course, they usually do not select all the correct answers.

probably made.

Example 3: True/false question.

fails, would he/she passes traditional.

such work opportunities.


#### **3.1.1 Electronic assessment of knowledge for the Bologna study-program courses**

When Slovenia in 2004 became a full member of the European Union and the European University Area, the Bologna Process started, to which the members of this area are bound. It encompasses a unique model regarding studies. This has meant reassessing and changing the traditional curricula towards a single-study structure within European Universities (Krajnc, 2009).

The Bologna study programmes at FCCE started during the academic year 2009/2010. Each year the results show that a lot of students register in the first study year, which causes a lot of pedagogic workload for the staff. As the application of IC learning environments is particularly useful when a lot of students are enrolled, Moodle was incorporated within some Bologna Courses i.e. Computer Science in Chemistry Course (CSC), and Process Calculation I Course (PC I) in the first semester, and Process Calculation II Course (PC II), Chemical Calculation II Course (CC II), and Process Balances Course (PB) in the second semester. On the basis of the previous experiences from the Process Synthesis Course, the electronic assessment of knowledge was also incorporated into the mentioned Bologna courses. Lectures at all courses were given once a week (3 hours every week). The lecturer explained the main points of the material, and the students learned the rest by themselves. The following explains the electronic assessment procedures at some courses.

At the Computer Science in Chemistry Course and Process Calculation I Course of the first semester, electronic assessment was introduced to the freshman three times, half an hour before regular lectures, and in a computer room of the Faculty. Each e-test was administrated only once. It was forbidden to write down the questions on the paper. A student was successful if at least 60 % of the answers were correct.

In order to obtain freshman's feedback on the applicability, usefulness, and efficiency of e-assessment, at the end of the semester students filled-in a questionnaire and answered certain questions. It was comprised of 16 questions, 13 of which were multiple-choice type questions and three were essay-type questions. The questionnaire was classified into four parts where students gave their opinions on:


109 of the students filled-in the questionnaire. The results showed that 10 % of students used the electronic-learning environment Moodle every day, 82 % once a week, and the rest (8 %)

E-Learning Usage During Chemical Engineering Courses 133

From among the 109 students who started the electronic-assessment of their knowledge at CSC and PC I, 78 students (72 %) finished all e-tests successfully, 19 students (17 %) resigned from electronic-assessment because of negative grades, and 12 students (11 %) resigned from e-assessment because they changed their mind about such a kind of assessment or study, in general. Some students also realised that such a kind of work is too difficult for

The analysis of 116 active students i.e. those who finished the experimental computer work in the computer room, after completing the lectures at CSC and PC I, showed that 78 of them completed all the e-tests successfully. The others (38 of the active students or 33 %) had to move to the classical oral exam. The results showed that the lecturers' workloads regarding oral examinations decreased by 67 %. So, what does this mean in hours regarding lecturers' workloads? When you consider that one student needs approximately half an hour for a classical oral examination, 78 students meant 39 less hours needed for oral examinations, which is almost one working week. Within such a time-period, a lecturer could do other things e.g. research work, additional notes regarding course material, prepare new problems for written exams etc. It is also important to point out that the students saved time, too. They did not need extra time at the Faculty for the examination, so

Enthusiasm for introducing new methods into the educational process is not as great amongst the teaching staff as with the students. This was already apparent at the time of the ELEUM application. The first responses from the lecturers and assistants were obtained at the end of the academic year 2005/2006, on the basis of a questionnaire which was sent to all teaching staff at the Faculty. The results showed that half of the teaching staff was completely disinterested in e-learning or they were so occupied with other duties that they had no time to answer the questionnaire (Krajnc, 2009). The other half showed resistance to

Anyway, awareness of electronic-teaching and learning has expanded among the staff from year to year. The more experienced lecturers in e-learning are constantly encouraging colleagues towards the new method of working. The application of different activities within e-learning are presented every year at the "*Slovenian Chemical Days, Conference"* which takes place at the FCCE in Maribor every autumn. The Computer Centre of the UM, Department for e-learning, prepares learning workshops three times a year. Recently, in December 2010, a Workshop on the electronic-teaching environment Moodle's usage was held at FCCE in Maribor. The Workshop was led by a lecturer of the Faculty who has many years experiences in e-learning. The participation of the teaching staff was very low. Only six lecturers and assistants were interested in Moodle application during the pedagogical process. At the end of the Workshop, participants filled-in an electronic questionnaire which included six questions concerning Moodle's application. On the question »*How often do you use Moodle*?« one answered several times a year, two of them replied never, and three of them said once a week. Their knowledge of Moodle was estimated at a 1,7 grade on a five point scale (1-insufficient, 2-sufficient, 3-well, 4-very good, 5-excellent). They said, they used

they saved time and money on bus or train tickets, or fuel if they had a car.

**3.2 The response of the teaching staff to e-learning** 

use of electronic-teaching tools within their courses.

reading the question wrongly.

them.

Moodle:

once a month. They also said that the combination of traditional and electronic method of learning suited them and that they also wanted such a kind of work in other courses.

More than 71 % of the students' replies were the same as their older colleagues in the Process Synthesis Course, i.e. that they chose the electronic-assessment of knowledge because they had to become acquainted with smaller portions of the course material at once, the other students (29 %) chose the e-test because they wanted to avoid the oral exam in the professor's office. Three quarters of the students (74 %) said that after the first e-test they could better prepare for the others because after the first one they acquired a feeling for such a kind of examination. Almost all students (94 %) thought that they had enough time to answer all the questions in the e-assessment.

The lecturer also received a significant response about the intelligibilities and difficulties of the questions. The result showed that almost half the students (42 %) thought that the questions were always clear and easy to understand, and 50 % thought they were almost always understandable. 8 % of students replied that questions were sometimes understandable and sometimes not. Furthermore, 79 % of students said that questions were medium-difficult, 13 % thought they were easy, and 8 % that they were tough questions.

In one of the questions, the students compared electronic-assessment with the traditional oral exam. Almost half of the students (46 %) thought that the electronic-assessment of knowledge was easier than the classical one, 45 % said that it was easier and of higher quality, one student said it was of higher quality but difficult, and four students replied that it was easier but of a lesser quality than the classical oral exam. More than half of the students (68 %) felt less stressed at an e-examination as they had to confront the lecturer at a classical oral exam but more than a quarter of the students did not feel psychological burdened themselves by the e-test.

For the essay-type questions students gave their opinions on:


The students mainly said that the information was clear enough, effective, and practical. They wanted to have such information at other courses. The reasons for failures in e-tests were the lack of learning, reluctance at the exam, superficiality, difficult questions, and absence from lectures.

The advantages of the e-examination were:


The disadvantages were:


reading the question wrongly.

132 E-Learning – Engineering, On-Job Training and Interactive Teaching

once a month. They also said that the combination of traditional and electronic method of

More than 71 % of the students' replies were the same as their older colleagues in the Process Synthesis Course, i.e. that they chose the electronic-assessment of knowledge because they had to become acquainted with smaller portions of the course material at once, the other students (29 %) chose the e-test because they wanted to avoid the oral exam in the professor's office. Three quarters of the students (74 %) said that after the first e-test they could better prepare for the others because after the first one they acquired a feeling for such a kind of examination. Almost all students (94 %) thought that they had enough time to

The lecturer also received a significant response about the intelligibilities and difficulties of the questions. The result showed that almost half the students (42 %) thought that the questions were always clear and easy to understand, and 50 % thought they were almost always understandable. 8 % of students replied that questions were sometimes understandable and sometimes not. Furthermore, 79 % of students said that questions were medium-difficult, 13 % thought they were easy, and 8 % that they were tough questions.

In one of the questions, the students compared electronic-assessment with the traditional oral exam. Almost half of the students (46 %) thought that the electronic-assessment of knowledge was easier than the classical one, 45 % said that it was easier and of higher quality, one student said it was of higher quality but difficult, and four students replied that it was easier but of a lesser quality than the classical oral exam. More than half of the students (68 %) felt less stressed at an e-examination as they had to confront the lecturer at a classical oral exam but more than a quarter of the students did not feel psychological

The students mainly said that the information was clear enough, effective, and practical. They wanted to have such information at other courses. The reasons for failures in e-tests were the lack of learning, reluctance at the exam, superficiality, difficult questions, and

learning suited them and that they also wanted such a kind of work in other courses.

answer all the questions in the e-assessment.

burdened themselves by the e-test.

The advantages of the e-examination were:

instant feedback of the results,

ambiguous questions and answers,

no possibility of repeating e-tests,

e-test failure,

absence from lectures.

on-going learning,

 less time to learn, you are not under stress.

The disadvantages were:

quickly forget the theory,

For the essay-type questions students gave their opinions on: information about the Course activities through Moodle,

advantages and disadvantages of e-assessing knowledge.

From among the 109 students who started the electronic-assessment of their knowledge at CSC and PC I, 78 students (72 %) finished all e-tests successfully, 19 students (17 %) resigned from electronic-assessment because of negative grades, and 12 students (11 %) resigned from e-assessment because they changed their mind about such a kind of assessment or study, in general. Some students also realised that such a kind of work is too difficult for them.

The analysis of 116 active students i.e. those who finished the experimental computer work in the computer room, after completing the lectures at CSC and PC I, showed that 78 of them completed all the e-tests successfully. The others (38 of the active students or 33 %) had to move to the classical oral exam. The results showed that the lecturers' workloads regarding oral examinations decreased by 67 %. So, what does this mean in hours regarding lecturers' workloads? When you consider that one student needs approximately half an hour for a classical oral examination, 78 students meant 39 less hours needed for oral examinations, which is almost one working week. Within such a time-period, a lecturer could do other things e.g. research work, additional notes regarding course material, prepare new problems for written exams etc. It is also important to point out that the students saved time, too. They did not need extra time at the Faculty for the examination, so they saved time and money on bus or train tickets, or fuel if they had a car.

#### **3.2 The response of the teaching staff to e-learning**

Enthusiasm for introducing new methods into the educational process is not as great amongst the teaching staff as with the students. This was already apparent at the time of the ELEUM application. The first responses from the lecturers and assistants were obtained at the end of the academic year 2005/2006, on the basis of a questionnaire which was sent to all teaching staff at the Faculty. The results showed that half of the teaching staff was completely disinterested in e-learning or they were so occupied with other duties that they had no time to answer the questionnaire (Krajnc, 2009). The other half showed resistance to use of electronic-teaching tools within their courses.

Anyway, awareness of electronic-teaching and learning has expanded among the staff from year to year. The more experienced lecturers in e-learning are constantly encouraging colleagues towards the new method of working. The application of different activities within e-learning are presented every year at the "*Slovenian Chemical Days, Conference"* which takes place at the FCCE in Maribor every autumn. The Computer Centre of the UM, Department for e-learning, prepares learning workshops three times a year. Recently, in December 2010, a Workshop on the electronic-teaching environment Moodle's usage was held at FCCE in Maribor. The Workshop was led by a lecturer of the Faculty who has many years experiences in e-learning. The participation of the teaching staff was very low. Only six lecturers and assistants were interested in Moodle application during the pedagogical process. At the end of the Workshop, participants filled-in an electronic questionnaire which included six questions concerning Moodle's application. On the question »*How often do you use Moodle*?« one answered several times a year, two of them replied never, and three of them said once a week. Their knowledge of Moodle was estimated at a 1,7 grade on a five point scale (1-insufficient, 2-sufficient, 3-well, 4-very good, 5-excellent). They said, they used Moodle:

E-Learning Usage During Chemical Engineering Courses 135

During the academic years 2008/2009, 2009/2010 and 2010/2011, a group of students who had the possibility of using the multimedia e-chapter on the Process Synthesis Course, gave feedback about its usage to the lecturer on the basis of a questionnaire. It consisted of 8 questions, 5 of which were multiple-choice questions, and 3 essay-type questions. The questionnaire was filled-in by 53 students. Among these were also those who had not used the e-chapter. The main reason why they had not used it was that they did not know that such a kind of chapter even existed, because they had not followed the news and

The results showed that students mainly used both possibilities for learning i.e. the chapter in classical text-book, which is available, and the multimedia electronic chapter (72 %). Of those students who used the multimedia e-chapter, 77 % thought that such a kind of chapter was more appropriate for learning than the classical chapter because it consists of modules for dynamic learning, and 88 % said that they needed less time for studying the chapter material with the e-chapter in comparison with the classical one. More theory was retained in the memory. The same number of students realised that the multimedia e-chapter usage

On the question as to why they did or did not use the multimedia e-chapter, students gave

One student said: »*The content in the multimedia e-chapter is more transparent and regulated.* 

One student thought: »*I prefer the classic way of learning from my notes where I can underline the* 

The answer of one student was interesting: »*Such learning is tiring for the eyes. You have to look* 

Undergraduate-study reforms have placed the student at the centre of the education process. The curricula have been mainly reduced, so that students themselves undertake more responsibilities for better study results. For this reason, the traditional methods of teaching and learning should now be supplemented by non-traditional methods and technologies. These include active and cooperative learning, project work, and e-learning, which help students achieve better results. Students at the FCCE in Maribor, Slovenia now have significant experience with non-traditional learning methods, especially with elearning. They use electronic-learning environments and e-materials, which enable communication between lecturer-student and the assessment of knowledge. Different kinds of e-tools enable the students to obtain good study results. Since the Chapter focuses on the experiences of e-learning usage from both the students' and pedagogic staffs' points of view, the electronic environments, and their functionalities were not presented in detail. They

have already been described in other sources (Krajnc, 2006; Krajnc, 2009).

was a good preparation for the electronic-assessment of knowledge.

Another replied: »*It is great because you can check your knowledge*.«

Another replied: »*I like the colour-coded words in the e-chapter*.«

instructions on Moodle, regularly.

different answers.

*Learning is more friendly*.«

*at the screen continuously*.«

**4. Conclusion** 

*important things, and annotate the notes*.«


On the question »*Do you mean that Moodle facilitates the implementation of work and saves time*?« three of them agreed, one said it does not save time but facilitates the implementation of the pedagogic process, two of them could not agree or disagree with the statement as they had not used Moodle yet. Four participants of the Workshop knew that UM organises educational workshops on Moodle application three times a year but they had not participated in any of them yet. Two participants knew and already participated to them. The answers on the question »*Why don't you use Moodle more often*?« were similar i.e. they did not have enough time for additional education and they did not know enough about the Moodle application.

#### **3.3 Multimedia e-text-books (e-material)**

Because at e-learning, students' educations are largely left to them, text-books should be prepared in appropriate forms. Beside electronic learning environments and its tools and activities, which could be used within the learning process, multimedia electronic textbooks are useful tools, which additionally implement the education process. A lot of sources and modules can be inserted into such text-books such as: video, animations, internet links, short quizzes with different type of questions etc. In general, learning with multimedia e-materials is more motivated and successful compared with live lessons or other media (video, simulation, and a combination of graph and audio presentations), which enable easier learning. Such material adapts students to various learning styles and facilitates a constructive and enquiry-based approach to learning (Clark & Feldon, 2005; Krnel & Bajd, 2009). When students use multimedia e-text-books, they can better prepare themselves for examinations. Usually, they easily pass e-tests, oral, and written exams and colloquiums.

A quality multimedia e-text-book may only be prepared by the lecturer who teaches the subject. The preparation of an e-text-book is a great challenge, but interesting and responsible work, which takes a lot of time and effort. The lecturer often asks himself/herself what information should be included in e-material. He/she needs to be aware that the content should be clear and concise. Because multimedia e-material may contain animations, quizzes, online links etc., the lecturer should know where and how to enter these tools. His/her skills and knowledge of using them should be comprehensive.

An example of a multimedia e-chapter has already been created for the Process Synthesis Course at the FCCE in Maribor. The chapter is entitled Reaction-path Synthesis and it is an electronic version of the chapter, which is included in the classic text-book, and is usually available to students. The lecturer wanted to know how students will accept this version and what the study results will be achieved. Different types of electronic modules are included within the e-material as: cloze activities, multi-choice type questions, external websites, true-false questions, wiki articles, and reading activities. The eXe-learning XHTML editor was used for creating the multimedia e-chapter (New Zealand Government Tertiary Education Commission et al., 2011).

On the question »*Do you mean that Moodle facilitates the implementation of work and saves time*?« three of them agreed, one said it does not save time but facilitates the implementation of the pedagogic process, two of them could not agree or disagree with the statement as they had not used Moodle yet. Four participants of the Workshop knew that UM organises educational workshops on Moodle application three times a year but they had not participated in any of them yet. Two participants knew and already participated to them. The answers on the question »*Why don't you use Moodle more often*?« were similar i.e. they did not have enough time for additional education and they did not know enough about the

Because at e-learning, students' educations are largely left to them, text-books should be prepared in appropriate forms. Beside electronic learning environments and its tools and activities, which could be used within the learning process, multimedia electronic textbooks are useful tools, which additionally implement the education process. A lot of sources and modules can be inserted into such text-books such as: video, animations, internet links, short quizzes with different type of questions etc. In general, learning with multimedia e-materials is more motivated and successful compared with live lessons or other media (video, simulation, and a combination of graph and audio presentations), which enable easier learning. Such material adapts students to various learning styles and facilitates a constructive and enquiry-based approach to learning (Clark & Feldon, 2005; Krnel & Bajd, 2009). When students use multimedia e-text-books, they can better prepare themselves for examinations. Usually, they easily pass e-tests, oral, and written exams

A quality multimedia e-text-book may only be prepared by the lecturer who teaches the subject. The preparation of an e-text-book is a great challenge, but interesting and responsible work, which takes a lot of time and effort. The lecturer often asks himself/herself what information should be included in e-material. He/she needs to be aware that the content should be clear and concise. Because multimedia e-material may contain animations, quizzes, online links etc., the lecturer should know where and how to enter these tools. His/her skills and knowledge of using them should be comprehensive.

An example of a multimedia e-chapter has already been created for the Process Synthesis Course at the FCCE in Maribor. The chapter is entitled Reaction-path Synthesis and it is an electronic version of the chapter, which is included in the classic text-book, and is usually available to students. The lecturer wanted to know how students will accept this version and what the study results will be achieved. Different types of electronic modules are included within the e-material as: cloze activities, multi-choice type questions, external websites, true-false questions, wiki articles, and reading activities. The eXe-learning XHTML editor was used for creating the multimedia e-chapter (New Zealand Government Tertiary

 for informing and sending exam grades, for the publication of study materials,

**3.3 Multimedia e-text-books (e-material)** 

for displaying a list of students.

for questionnaires,

Moodle application.

and colloquiums.

Education Commission et al., 2011).

During the academic years 2008/2009, 2009/2010 and 2010/2011, a group of students who had the possibility of using the multimedia e-chapter on the Process Synthesis Course, gave feedback about its usage to the lecturer on the basis of a questionnaire. It consisted of 8 questions, 5 of which were multiple-choice questions, and 3 essay-type questions. The questionnaire was filled-in by 53 students. Among these were also those who had not used the e-chapter. The main reason why they had not used it was that they did not know that such a kind of chapter even existed, because they had not followed the news and instructions on Moodle, regularly.

The results showed that students mainly used both possibilities for learning i.e. the chapter in classical text-book, which is available, and the multimedia electronic chapter (72 %). Of those students who used the multimedia e-chapter, 77 % thought that such a kind of chapter was more appropriate for learning than the classical chapter because it consists of modules for dynamic learning, and 88 % said that they needed less time for studying the chapter material with the e-chapter in comparison with the classical one. More theory was retained in the memory. The same number of students realised that the multimedia e-chapter usage was a good preparation for the electronic-assessment of knowledge.

On the question as to why they did or did not use the multimedia e-chapter, students gave different answers.

One student said: »*The content in the multimedia e-chapter is more transparent and regulated. Learning is more friendly*.«

Another replied: »*It is great because you can check your knowledge*.«

One student thought: »*I prefer the classic way of learning from my notes where I can underline the important things, and annotate the notes*.«

Another replied: »*I like the colour-coded words in the e-chapter*.«

The answer of one student was interesting: »*Such learning is tiring for the eyes. You have to look at the screen continuously*.«

#### **4. Conclusion**

Undergraduate-study reforms have placed the student at the centre of the education process. The curricula have been mainly reduced, so that students themselves undertake more responsibilities for better study results. For this reason, the traditional methods of teaching and learning should now be supplemented by non-traditional methods and technologies. These include active and cooperative learning, project work, and e-learning, which help students achieve better results. Students at the FCCE in Maribor, Slovenia now have significant experience with non-traditional learning methods, especially with elearning. They use electronic-learning environments and e-materials, which enable communication between lecturer-student and the assessment of knowledge. Different kinds of e-tools enable the students to obtain good study results. Since the Chapter focuses on the experiences of e-learning usage from both the students' and pedagogic staffs' points of view, the electronic environments, and their functionalities were not presented in detail. They have already been described in other sources (Krajnc, 2006; Krajnc, 2009).

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Students' feedback on the multimedia electronic-chapter of the text-book showed that such a kind of e-material contributes to a better understanding of the subject's content and can better prepare them for electronic and classical examinations. Students who choose the electronic manner for learning usually finish their course obligations within the course timeframe or within one or two weeks after finishing the lectures. For this reason, more time is left for other courses.

Good study results were obtained with on-going electronic-assessment of knowledge, especially at Bologna Courses within the first and second semesters of a study year, when a lot of students are enrolled. It is important that students are not forced into new ways of working because this can lead to stress, but rather allow them to always choose between the traditional way of learning with the text-books.

The pedagogic staff at the FCCE in Maribor already have seven years of experience in elearning. The results show that the incorporation of electronic-learning environments into education process improves lectures and the quality and efficiency of the study. E-learning leads to a heavier workload for the lecturer at the start, but this reduces over time.

Electronic-learning environments offer a lot of modules and activities that require the continuous enhancement of lecturers' knowledge. Pedagogic staff at the FCCE have the opportunity to enhance their skills through various workshops organised by the UM or the Faculty.

There are challenges for the future. The lecturers who already successfully use e-learning during their courses should encourage other colleagues to use new methods of learning. Sceptic lecturers should know about e-learning implemented lectures to make them more dynamic. The great challenge is to convince lecturers that pedagogic work is also research work like other scientific research. It is recommended that pedagogic staff focus their efforts and time on multimedia e-material production. The faster tempo of life namely shows that, it will be necessary to optimise study time, so the use of quality multimedia e-text-books will be inevitable in the future.

#### **5. References**


Students' feedback on the multimedia electronic-chapter of the text-book showed that such a kind of e-material contributes to a better understanding of the subject's content and can better prepare them for electronic and classical examinations. Students who choose the electronic manner for learning usually finish their course obligations within the course timeframe or within one or two weeks after finishing the lectures. For this reason, more time is

Good study results were obtained with on-going electronic-assessment of knowledge, especially at Bologna Courses within the first and second semesters of a study year, when a lot of students are enrolled. It is important that students are not forced into new ways of working because this can lead to stress, but rather allow them to always choose between the

The pedagogic staff at the FCCE in Maribor already have seven years of experience in elearning. The results show that the incorporation of electronic-learning environments into education process improves lectures and the quality and efficiency of the study. E-learning

Electronic-learning environments offer a lot of modules and activities that require the continuous enhancement of lecturers' knowledge. Pedagogic staff at the FCCE have the opportunity to enhance their skills through various workshops organised by the UM or the

There are challenges for the future. The lecturers who already successfully use e-learning during their courses should encourage other colleagues to use new methods of learning. Sceptic lecturers should know about e-learning implemented lectures to make them more dynamic. The great challenge is to convince lecturers that pedagogic work is also research work like other scientific research. It is recommended that pedagogic staff focus their efforts and time on multimedia e-material production. The faster tempo of life namely shows that, it will be necessary to optimise study time, so the use of quality multimedia e-text-books

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**5. References** 

York.

ISSN: 0018-9359.

traditional way of learning with the text-books.


**9** 

*Taiwan (R.O.C.)* 

**Interactive WhiteBoard:** 

Kai-Ti Yang1 and Tzu-Hua Wang2,\* *1National Taiwan Normal University 2National HsinChu University of Education* 

**Designs for Biology Teaching** 

**Effective Interactive Teaching Strategy** 

The goal of this chapter is to design interactive teaching strategies with Interactive WhiteBoard (IWB) and investigate their effectiveness on Biology teaching. In recent years, with the rapid development of Information Communication Technology (ICT), integrating multimedia presentation tools to perform better teaching has become easier in today's classroom. Among many ICT systems, the innovation and introduction of IWB has not only changed the traditional classroom but symbolizes a key revolution in the history of whiteboard development. Researchers have identified a number of advantages of using IWB in teaching and learning: flexibility and versatility, multimedia/multimodal presentation, improving teaching efficiency, supporting planning and the development of resources, improving students' skills of using ICT technology, interactivity and participation during course, improving students' learning motivation, and improving students' understanding (BECTA, 2007; Glover, Miller, Averis, & Door, 2005; Holmes, 2009; Northcote, Mildenhall, Marshall, & Swan,2010;Slay, Sieborger, & Hadgkinson-Williams, 2008; Smith, Higgins, Wall, & Miller, 2005; Wall, Higgins, Smith, 2005). The IWB realizes interactive operations between the whiteboard and the computer. It has become a new interface to consolidate all teaching resources in a traditional classroom. Many countries, such as the United Kingdom, Japan, Singapore, Malaysia, China, and Russia, have invested heavily in the IWB and attempted to implement it in schools of all levels. In Taiwan, the government also invests a large amount of money to introduce IWB into classrooms. Since 2006, the Taiwan's Ministry of Education officially announced that more than \$50 million NTD (roughly \$15 million USD) would be invested in promoting the preliminary integration of IWB into instruction. Following the trend of integrating IWB into teaching, this research tries to understand how to make good use of the advantages of IWB to make

students have better learning effectiveness on junior high school Biology.

Among the topics of junior high school Biology, cell division, photosynthesis, cell respiration, food chain, food web and evolution are the topics difficult to teach and learn. Both teachers

**1. Introduction** 

\* Corresponding Author

