Advances in E-learning-Experiences and Methodologies

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Integrating Technology and Research in Mathematics Education communication and semiosis The activities described in the previous section are a good example of communication that involves the adoption of different registers (i.e., use-related linguistic varieties). The students have to understand each other, but also to convey some mathematical ideas. These two tasks may require different linguistic resources, and students have to switch between informal registers, in order to communicate each other as persons, and more formal ones, in order to describe mathematical ideas. Looking at the files produced by the students during the activities, we can find a range of examples of conversion between different registers and semiotic systems. The following two questions posed by a student require conversion between an informal register and a mathematical one: “Write the Cauchy problem (in mathematical language)” and conversely “Explain by words the Cauchy problem.” We also note that, even if the students did not explicitly use graphical tools in their activities, some questions they posed involved some sort of figural representation, as shown by a question like “In the Cauchy problem, which means graphically the expression y’(x 0 )=y 0 ?” which requires to switch from an analytic expression to a graphical one and then to explain by words. Furthermore, many of the students’ questions regard the interpretation of symbols in a given setting, such as “Which indicates c B (v)?”, “Which represents the column j of the homomorphism representative matrix?” If we try to trace the evolution of the use of language by the students through the activities described, we can say that at beginning the use of language is seemingly more formal, and in some sense more precise from the mathematical viewpoint. Actually, it is only a more rigid usage, due to the fact that students are not used to “talk of mathematics” and then their questions are standard (e.g., “How a group is defined in Algebra?”) so that the answers exactly conform to some piece of a book or lecture. Going on, students try to pose questions requiring some consideration for different topics or registers or semiotic systems, with the obvious consequence that answers cannot exactly conform to the style of a textbook (e.g., “Why the main coefficients of a conic after the rotation are the eigenvalues of the original quadratic matrix?”, “Which is the relation between the rank and the determinant of a matrix?”, “What are the admissible representations of a vector space?”, “Is the intersection of two distinct planes in R 3 a vector space? Justify your answer.”). The presence of non standard questions has been increasing as much as the activities have gone on, with an average of 45% on the total amount of the questions. So, for one thing, this is a good advance in mathematical thinking, for another thing, although they use a number of informal or even inaccurate expressions, students gradually improve their understanding of the meanings involved in mathematical expressions. A platform, anyway, provides plenty of opportunities for designing communication situations involving the use of a wide range of linguistic resources. More generally, ICT provides matchless opportunities for designing tasks involving conversion of semiotic systems, as defined. The following problem can be quite easily inserted as an item in different e-learning modules. 1. Consider the function f defined for any x∈ 5 x by f(x) = − x . 7 a. Find f’(x) ...... b. Compute f’(0) ...... Among the following graphs mark at least two which do not match f. Explain.
Integrating Technology and Research in Mathematics Education A) B) C)
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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 s
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A Heideggerian View on E-Learning o
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A Heideggerian View on E-Learning M
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A Heideggerian View on E-Learning W
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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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Chapter V Training Teachers for E-L
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Training Teachers for E-Learning FL
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Training Teachers for E-Learning ne
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Training Teachers for E-Learning A
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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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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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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 Haina
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Evaluation and Effective Learning p
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Evaluation and Effective Learning r
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Evaluation and Effective Learning t
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Evaluation and Effective Learning m
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Evaluation and Effective Learning c
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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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0 Chapter XVII Designing an Online
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Designing an Online Assessment in E
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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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