Giovannina Albano

IWT: an innovative solution for AGS e-learning model

This paper is a technological development and realisation of the e-learning model presented by Albano G., Gaeta M. and Salerno S. (AGS) which appeared in the previous issue of IJKL, focused on the advanced features provided by Intelligent Web Teacher (IWT) an innovative learning platform available in the market. In this paper, the approaches used in IWT for knowledge representation and management through ontologies are examined in detail. Similarly, the way the special component Learner Intelligent Advisor (LIA) uses these and other information available on the system for creating personalised learning paths taking into account the single user preferences including present knowledge state and preferred didactic approach, etc. is carefully studied. IWT is in continuing evolution. In particular, we are improving LIA structure and algorithm and integrating IMS learning design for the description of our unit of learning. We paid particular attention to the issue of giving an insight into the main ideas and challenges underlying the solutions we chose.

Knowledge, Skills, Competencies: A Model for Mathematics E-Learning

This work concerns modelling competence in mathematics in e-learning environment. Competence is something complex, which goes further the cognitive level, but involves meta-cognitive and non-cognitive factors. Anyway it requires the students to master knowledge and skills, at first, and some measurable abilities, defined as competencies. We present a model that, exploiting the innovative technological features of the platform IWT, aims at defining a personalised learning experience allowing the students to build up their competence in mathematics.

Adaptive Peer Grading and Formative Assessment

Peer grading is a process whereby students are required to grade some of their peers’ assignments as part of their own assignment. Peer grading is capable of improving students’ learning outcomes, metacognition and critical thinking and, at the same time, it can support formative assessment, saving teacher’s time and providing fast feedback, especially for large classes. In this paper we report the results of an experiment where a technology supported peer grading exercise has been assigned to students within a University course on calculus and linear algebra. To improve the reliability of students’ grades, several approaches have been experimented and the obtained results have been compared to grades coming from the teacher. Moreover, we attempted to understand how the peer grading task has contributed to reinforce the development of student’s explanation and argumentation processes

Linguistic competence and mathematics learning: the tools of e-learning

This paper addresses the issue of mathematics education in e-learning platforms. In the frame of discursive approach to mathematics learning, the discussion is focused on multisemioticity and multivariety, as they characterize mathematical practice and students’ linguistic competence seems to be strictly linked to their success in mathematics learning. E-learning platforms offer plenty of opportunities to plan and implement activities apt to improve such competence. To this aim, the tools available are investigated and some examples of their use are shown.

E-Learning and Affective Student’s Profile in Mathematics

This paper is concerned with the personalisation of teaching/learning paths in mathematics education. Such personalisation would exploit the research results on the connection between the affective experience of the student learning mathematics and his/her success or failure in mathematics, which produces the learnerâ??s attitude towards mathematics. We present a model for the learnerâ??s affective profile in mathematics, which would extend the current user profile in an e-learning platform taking into account the learnerâ??s attitude, to be used in order to offer and manage a Unit of Learning in mathematics better tailored on the global studentâ?? needs. Tools for the implementation of the model in an e-learning platform have been devised. Activities templates suitable to various attitudes towards mathematics have been designed and their experimentation is in progress.

An online Vygotskian learning activity model in mathematics

This paper describes part of a broader research aimed to investigate the possibility of using, an e-learning platform to implement the Vygoskijan educational model, based on mediation and peer interactions, for mathematics education. We define a Learning Activity model within a Digital Interactive Storytelling in Mathematics and report how it has been implemented using Moodle. The activity uses both experiential and discursive approaches to mathematics learning and foresees individual and social tasks. The implementation exploited some features of Moodle Lesson and GeoGebra to define two new types of questions with automatic assessment: one allowing the student to interact with graphical objects and then to conjecture and test; one other allows to construct sentences starting from a given set of word-blocks (approaching the automatic assessment of open-ended questions).

e-Mathematics Engineering for Effective Learning

Education in digital age requires a strong focus on “engineering of learning”, as an emergent field of study and design of effective innovative learning experiences and environments. In this respect, the chapter addresses mathematics education in e-learning settings according to a tetrahedron model, as extension of the classical didactical triangle, to which adds a fourth vertex: the ‘author’ (A). The introduction of the vertex Author is due to our view that full exploitation of e-environment and its integration with results from research in mathematics education requires properly designed didactical interventions, based on a scientific approach, such as Didactic Engineering. Moreover, such exploitation should consider the centrality of the student, which means that the vertex-positions of the tetrahedron can be assumed also by the student along the learning process. We discuss the didactic engineering work from the perspectives of the tetrahedron faces and taking into account the dynamicity of the vertex-positions.

Personalized Learning in Mathematics

This work shows an innovative solution in order to enable the predisposition to the mathematics, by using auto-regulation of learning objectives, personalization for obtaining, in such a way, a learning path more compliant to the learners needs. For addressing these objectives, the learning platform IWT has been integrated with the Wolfram Mathematica environment and new and interactive Learning Objects that show the potentiality of the symbolic calculus.

A Knowledge-Skill-Competencies e-Learning Model in Mathematics

This paper concerns modelling competence in mathematics in an e-learning environment. Competence is something complex, which goes beyond the cognitive level, and involves meta-cognitive and non-cognitive factors. It requires students to master knowledge and skills and at least some measurable abilities, which Niss calls ‘competencies’. We present a model that exploits the innovative technological features of the IWT platform to define a personalised learning experience allowing students to increase their competence in mathematics. It is based on knowledge and skills representations by means of a graph metaphor, and on a theoretical framework for modelling competence.ResumenEste trabajo se centra en la competencia matemática en un entorno de aprendizaje virtual. La competencia es algo complejo, que trasciende el nivel cognitivo, e implica factores metacognitivos y no cognitivos. Exige de los estudiantes su dominio sobre conocimientos y destrezas y, por lo menos, sobre algunas capacidades medibles, a las que Niss llama «competencias específicas» [competencies]. El modelo que presentamos utiliza las innovadoras características tecnológicas de la plataforma IWT para definir una experiencia de aprendizaje personalizado que permite a los estudiantes aumentar su competencia en matemáticas. Se basa en la representación de conocimientos y destrezas mediante metáforas gráficas y en un marco teórico para modelar la competencia.

A webmathematica application for mathematics learning

In this talk we would like to present MoMAMath, an on-line interactive software for mathematics learning, based on Mathematica and WebMathematica. The software has been realized by the authors and it has been experimented to support classical courses of basic mathematics for first year engineering students at the University of Salerno. MoMAMath aims to improve to the didactic potentialities of the traditional textbook. In fact it is completely interactive and based on the learning by doing approach. MoMAMaths distinctive feature is the possibility of on-line interactive exercise sessions, besides other classical services like theory sessions, asynchronous communication with teachers, and so on.