The mathematics education research community has been involved in lively debate concerning the use of ICT, particularly computers, in the teaching and learning of mathematics for over two decades. However, despite research evidence that computers have the potential to contribute to the learning of mathematics in significant ways, this potential is frequently under utilised and the use of computers in mathematics classrooms has not become embedded to the extent that early research suggested might have occurred. Reviews of the research literature suggest a need for attention to the processes in which students engage as they work on computer-mediated tasks in authentic mathematics classrooms. This study contributes to this research agenda, by exploring in detail students’ mathematical activity in these situations. It aims to investigate the mathematical learning of the students as they engage in classroom mathematics tasks which involve the use of computers. Two further aims are to investigate the ways in which computer feedback and teacher interventions influence the students’ learning. The thesis develops a theoretical framework for the analysis of student learning, suggesting that students need to engage in a range of ‘dialectics’ within both the pragmatic/empirical and the mathematical/systematic fields. The analysis of the data shows that, from the perspective of this framework, the students’ mathematical learning was limited. The analysis provides evidence of the important mediational roles of teacher interventions and computer feedback; but shows that neither supported the students in making transitions between the pragmatic/empirical and mathematical/systematic fields or in engaging in all types of dialectics. Analysis of the design of the task, however, demonstrates the key importance of the task in promoting or inhibiting the students’ mathematical learning. The findings point to the need for teachers to consider the dialogic relationship between mathematics and computer feedback in engineering classroom tasks, so as to exploit the power of computer feedback and plan their own interventions accordingly.

Teaching effectively requires a clear presentation of the material being taught and interaction with the students. Studies have shown that Tablet PCs provide a good technological support for teaching. The aim of the work presented in this thesis is to design a structure editor of handwritten mathematics that explores the facilities provided by Tablet PCs. The editor is made available in the form of a class library that can be used to extend existing tools. The central feature of the library is the definition of structure for handwritten mathematical expressions which allows syntactic manipulation of expressions. This makes it possible to accurately select, copy and apply algebraic rules, while avoiding the introduction of errors. To facilitate structured manipulation, gestures are used to apply manipulation rules and animations that demonstrate the use of these rules are introduced. Also, some experimental features that can improve the user’s experience and the usability of the library are presented. Furthermore, it is described how to integrate the library into existing tools. In particular, Classroom Presenter, a system developed to create interactive presentations using a Tablet PC, is extended and used to demonstrate how the library’s features can be used in some teaching scenarios. Although there are limitations in the current system, tests performed with teachers and students indicate that it can help to improve the experience of teaching and learning mathematics, particularly calculational mathematics.

Τα τελευταία χρόνια γίνονται επιταχυνόμενες προσπάθειες για να ενσωματωθούν αποτελεσματικά οι ψηφιακές τεχνολογίες στην εκπαίδευση. Στόχος είναι να προσθέσει η ενσωμάτωση αυτή πραγματική και μετρίσιμη αξία στην εκπαιδευτική διαδικασία. Σκοπός αυτής της εργασίας είναι να παρουσιάσουμε τους τρόπους που η καθιερωμένη markup γλώσσα για τα μαθηματικά, η MathML, μπορεί να βοηθήσει την εκπαίδευση στον τομέα των μαθηματικών. Εξετάζουμε την MathML σαν ένα από τα εργαλεία που προσφέρει η ταχεία ανάπτυξη του Σημασιολογικού Ιστού (Semantic Web). Ειδικότερα παρουσιάζονται οι markup γλώσσες XML, HTML5, MathML και κάποια εργαλεία που βοηθούν στην ενσωμάτωση τέτοιων τεχνολογιών. Για την MathML, δημιουργήθηκε ένας οδηγός χρήσης, προσιτός σε κάθε χρήστη. Στον τομέα της εκπαίδευσης, θα δούμε με ποιους τρόπους ο Σ.Ι. και η MathML προσθέτουν άξια στην εκπαιδευτική διαδικασία. Δημιουργήθηκε σε MathML ένα σενάριο διδασκαλίας στην Τριγωνομετρίας. Μέσω του Θεμελιώδους θεωρήματος Λογισμού, θα δούμε πως μπορεί η MathML να χρησιμοποιηθεί σε συνδυασμό με μια μελλοντική οντολογία αυτόνομων ενοτήτων στα Μαθηματικά όπου η κάθε ενότητα μπορεί να αποτελεί βάση αυτομάθησης/αυτοαξιολόγησης. Τέλος, θα αναφερθούμε στις προοπτικές που υπάρχουν στο άμεσο μέλλον. / In latest years, people making efforts to integrate digital technology effectively in education. The aim of this Postgraduate Work is to give real and measurable value in educational process. The goal is to present some ways that the usual markup language, MathML may help in mathematical education. We investigate MathML, as one of the tools, which are offered by the development of Semantic Web. More specifically, we present XML, HTML5 and MathML markup languages, and some tools which are helpful in integration of these technologies. We create a more approachable guide for helping anyone to understand MathML. In education, we will investigate how Semantic Web and MathML can give extra value in education process. Also we created a teaching scenario using MathML, in Trigonometry. Through the Fundamental Calculus Theorem, we will see a usage of MathML combing it in a future ontology of autonomous units in Mathematics, where each unit can be a base in autoeducate/autoevaluate. In the end, we will refer in future perspectives.