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Advances in E-learning-Experiences and Methodologies

Integrating Technology and Research in Mathematics Education IntroductIon The main concern of this chapter is the integration of technology and research in the field of mathematics education. Currently technology is too often used with little or no concern for the results of educational research, despite the fact that they could provide valuable help to both magnify the outcomes and keep away from some unwelcome washback. Conversely, too often research in mathematics education disregards the impressive opportunities technology could provide. Through the chapter we focus on e-learning as a domain appropriate for integrating technology and educational research. We argue that nowadays technology is flexible enough to be used within different theoretical frameworks (such as the constructivist and the socio-cultural ones) and at different levels (cognitive, metacognitive, noncognitive). We also show that technology can provide matchless opportunities for dealing with most of the learning problems related to language and representations. In the section “Background” we give: • A concise overview of some outcomes of research that underline the complexity of educational processes, and in particular the need for taking into account not just cognitive, but also metacognitive and noncognitive aspects; • An overview of research on individual and personal learning processes related to the use of technology; • A sketch of the main features of constructive and cooperative methods and their feasibility in an e-learning platform; • A framework for dealing with language and representations in order to effectively interpret students’ behaviors. In the section “Teaching and Learning Opportuinities,” we show examples of teaching activities which fulfil some of the requirements sketched and apply some of the ideas and methods discussed there. The section “Future Trends and Conclusions” includes some discussion of the opportunities for future research. In all the examples described in this chapter we refer either to Moodle (Moodle, 2006) or to IWT (Intelligent Web Teacher, 2006). The latter is a distance-learning platform designed to lay the foundation for the next generation e-learning (for details, see Albano, Gaeta, & Salerno, 2006, or Intelligent Web Teacher, 2006). BAckground technology and research on mathematics education Currently information and communication technology (ICT) is not strictly linked to any theoretical framework in mathematics education. This was not the case in the past, as sometimes it was naively associated to some specific cognitive framework (e.g., information-processing theory) or even to some interpretation of mathematics (e.g., computational ones). This may account for the relatively poor role played by ICT in most studies in the psychology of mathematics education. We also assume that the use of ICT is not a simple matter but requires the development of detailed teaching paths and much research to fully exploit the opportunities provided and to keep away from any potential drawbacks. Research on mathematics education, conversely, has widely shown the complexity of teaching and learning processes, and thus the inadequacy of one-dimensional models, including the belief that the simple addition of some technology to standard teaching practices could provide considerable improvements of the outcomes. In particular any model for mathematics education has to consider that students’ performances are affected by factors belonging to at least three different levels:

Integrating Technology and Research in Mathematics Education • The cognitive level, which involves the learning of the specific concepts and methods of the discipline, also related to the obstacles recognized by research and practice; • The metacognitive level, which involves learners’ control of their own learning processes; • The noncognitive level, which involves beliefs, emotions, and attitudes, and all affective aspects, which are most often critical in shaping learners’ decisions and performances. As we will see below, ICT can play a part in each of these levels, including the noncognitive one, as it from the one hand can deeply influence learners’ beliefs, emotions, and attitudes related to mathematics, and from the other hand is itself the object of deep-rooted beliefs and can produce effects at the noncognitive level. So any study integrating ICT and research on mathematics education has to take into account noncognitive factors related to technology as well as to mathematics. In the next sections we will focus on some issues which are regarded as critical by research in mathematics education and could be dealt with in a more appropriate way with the help of an e-learning platform: constructive learning, cooperative learning, language and representations, and noncognitive implications. Of course, although we examine each of them separately, in teaching practice these issues cannot be dealt with in isolation. individual and Personal teaching and Learning The individualisation of teaching is one of the most critical issues in instructional practice. It is well known that some instructional strategies are more or less effective for particular individuals depending upon their specific abilities. According to Cronbach and Snow (1997), the best learning achievements occur when the instruction is exactly matched to the aptitudes of the learner. At first, we can say that individualisation regards how much the instruction fits students’ characteristics, creating learning situations suitable to different students. In particular we refer to the individualisation at the teaching level which, according to Baldacci (1999), means the adjustment of the teaching to the individual students’ characteristics, by means of specific and concrete teaching practices. Another major goal is the personalisation of the teaching, which refers to the set of activities directed to stimulate each specific person in order to achieve the maximum intellectual capability. It is clear that neither individualisation nor personalisation are possible at undergraduate level, especially with large classes of freshman students, if teaching is still based on standard lectures. The didactical transposition carried out by the teacher is based on general parameters, which arise from the average of sets of data regarding, for example, previous curriculum and knowledge, attitude to mathematics, metacognitive awareness, and so forth, and which can hardly suit the actual needs or problems of the individuals. On the contrary, the modality of blended learning, that is the support by online activities to standard lectures, seems to give a considerable contribution in the right direction. The belief that there exist teaching methods which produce the best outcomes has been long discarded, and learning is now regarded as the result of a process whose core is the pair person-situation, which is influenced by both teaching methods and individual differences (Jonassen & Grabowski, 1993). In particular the support of diversity in student’s methods is also viewed as the guide of mathematical learning (Balacheff & Sutherland, 1999). From the viewpoint of individualisation, the teaching procedures included in the platform should get the students to attain the basic skills by means of a choice of different learning paths, whereas from that of personalisation teaching activities should be planned in order to allow the

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    Advances in E-Learning: Experiences

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    Table of Contents Preface .........

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    Chapter XIV Open Source LMS Customi

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    Chapter III Philosophical and Epist

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    of constructive and cooperative met

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    Chapter XIV Open Source LMS Customi

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    contents, learning contexts, proces

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    xv these organizations do not get a

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    xvii QuALIty In e-LeArnIng Before t

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    allow that the teachers in training

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    xxi ISO. (1986). Quality-Vocabulary

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    Chapter I RAPAD: A Reflective and P

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    RAPAD in fields such as law, engine

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    RAPAD mystery to the new student. B

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    RAPAD example, whereas Laurillard h

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    RAPAD Ontologically, systems philos

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    RAPAD information related processes

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    RAPAD methods and techniques accord

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    RAPAD 2. An introduction to learnin

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    RAPAD then asked to reflect on and

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    RAPAD Figure 4. A rich picture to h

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    RAPAD Again using techniques from t

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    RAPAD university preparation course

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    RAPAD The third interface is at the

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    RAPAD Knight, P.T., & Trowler, P. (

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    RAPAD AddItIonAL reAdIngs Goodyear,

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    A Heideggerian View on E-Learning t

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    A Heideggerian View on E-Learning (

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    A Heideggerian View on E-Learning M

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    Philisophical and Epistemological B

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    Philisophical and Epistemological B

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    Philisophical and Epistemological B

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    Philisophical and Epistemological B

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    Philisophical and Epistemological B

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    Philisophical and Epistemological B

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    Philisophical and Epistemological B

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    Chapter IV E-Mentoring: An Extended

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    E-Mentoring However, what is unders

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    E-Mentoring baugh, & Williams, 2004

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    E-Mentoring Table 2. Contact. Diffe

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    E-Mentoring Table 10. Ethical impli

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    E-Mentoring Table 15. Technology st

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    E-Mentoring Table 21. Coaching. Bes

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    E-Mentoring Table 27. Moment. Best

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    E-Mentoring Moreover, existing rese

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    E-Mentoring Kasprisin, C. A., Singl

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    E-Mentoring Ensher, E. A., Heun, C.

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    Knowledge Discovery from E-Learning

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    Knowledge Discovery from E-Learning

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    Knowledge Discovery from E-Learning

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    Knowledge Discovery from E-Learning

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    Knowledge Discovery from E-Learning

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    Knowledge Discovery from E-Learning

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    Knowledge Discovery from E-Learning

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    Knowledge Discovery from E-Learning

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    Chapter XI Swarm-Based Techniques i

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    Swarm-Based Techniques in E-Learnin

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    Swarm-Based Techniques in E-Learnin

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    Swarm-Based Techniques in E-Learnin

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    Swarm-Based Techniques in E-Learnin

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    Swarm-Based Techniques in E-Learnin

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    Swarm-Based Techniques in E-Learnin

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    Chapter XII E-Learning 2.0: The Lea

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    E-Learning 2.0 Table 1. Different s

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    E-Learning 2.0 Figure 1. Difference

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    E-Learning 2.0 where the blog is al

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    E-Learning 2.0 process. Along this

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    E-Learning 2.0 forth, and, of cours

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    E-Learning 2.0 Finally, it is impor

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    E-Learning 2.0 never be a hotchpotc

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    E-Learning 2.0 McPherson, K. (2006)

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    E-Learning 2.0 Rosen, A. (2006). Te

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    Telematic Environments and Competit

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    Telematic Environments and Competit

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    Telematic Environments and Competit

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    Telematic Environments and Competit

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    Telematic Environments and Competit

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    Telematic Environments and Competit

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    Telematic Environments and Competit

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    Telematic Environments and Competit

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    Telematic Environments and Competit

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    Open Source LMS Customization Intro

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    Open Source LMS Customization or ev

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    Open Source LMS Customization compa

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    Open Source LMS Customization Figur

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    Open Source LMS Customization Figur

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    Open Source LMS Customization Haina

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    Evaluation and Effective Learning p

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    Evaluation and Effective Learning H

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    Chapter XVI Formative Online Assess

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    Formative Online Assessment in E-Le

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    Formative Online Assessment in E-Le

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    Formative Online Assessment in E-Le

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    Formative Online Assessment in E-Le

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    Formative Online Assessment in E-Le

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    Formative Online Assessment in E-Le

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    Formative Online Assessment in E-Le

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    Formative Online Assessment in E-Le

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    Formative Online Assessment in E-Le

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    Formative Online Assessment in E-Le

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    0 Chapter XVII Designing an Online

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    Designing an Online Assessment in E

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    Designing an Online Assessment in E

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    Designing an Online Assessment in E

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    Designing an Online Assessment in E

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    Designing an Online Assessment in E

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    Designing an Online Assessment in E

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    Designing an Online Assessment in E

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    Designing an Online Assessment in E

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    Quality Assessment of E-Facilitator

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    Quality Assessment of E-Facilitator

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    Quality Assessment of E-Facilitator

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    Quality Assessment of E-Facilitator

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    Quality Assessment of E-Facilitator

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    Chapter XIX E-QUAL: A Proposal to M

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    E-QUAL is proposed to evaluate the

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    E-QUAL provide competent, service-o

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    E-QUAL 2004; Scalan, 2003) and qual

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    E-QUAL benchmarks address technolog

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    E-QUAL E-learning added two differe

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    E-QUAL Table 6. Application of the

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    E-QUAL Future trends The future of

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    E-QUAL (EQO) co-located to the 4 th

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    E-QUAL SMEs: An analysis of e-learn

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    E-QUAL Meyer, K. A. (2002). Quality

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    Compilation of References Argyris,

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    Compilation of References Biggs, J.

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    Compilation of References Cabero, J

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    Compilation of References Comezaña

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    Compilation of References Downes, S

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    Compilation of References Fandos, M

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    Compilation of References national

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    Compilation of References Hudson, B

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    Compilation of References Harbour.

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    Compilation of References Little, J

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    Compilation of References Metros, S

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    Compilation of References ONeill, K

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    Compilation of References Preece, J

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    Compilation of References Sadler, D

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    Compilation of References Shin, N.,

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    Compilation of References tional Co

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    Compilation of References Vermetten

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    Compilation of References Yu, F. Y.

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    About the Contributors Juan Pablo d

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    About the Contributors part: “An

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    About the Contributors María D. R-

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    About the Contributors Applications

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    Index e-learning tools, automated p

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    Socrates 55 Sophists 55 student-foc

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