Abstract:

The project started in September 2018 as GeoUniud a user-friendly platform, where lessons and exercises are stored and organized with a careful use of randomized controlled contents as exercises, geometrical pictures and abstract reasoning. The lessons are augmented by a virtually infinite collection of examples, and by interactive representations of concepts. The training pages offer randomly generated exercises, along with a system in place to verify the student's answers, flagging errors and giving contextual feedback. The platform stores information about the user's performances. Starting to support first year Linear Algebra students of Math degree in Udine, it is currently moving to expanded into MatUniud, covering all the basic mathematics courses in Scientific Area. Innovative digital materials will be created, chosen in relation to the needs of single course teachers and taking into account the difficulties of the students documented both by currently research studies and teacher experience. In many foreign universities there are special Learning and Teaching Project managers, often distinguished by macro area, who support the teacher in the design of the course and the choice of technologies to be used. Unfortunately, this is lacking in most Italian Universities.

The proposed tools fit into the context of asynchronous and blended learning, moving from a teacher-centered approach to a student-centered approach. The teacher therefore has the most complex task of guiding and facilitating. The aim is to promote the widening of the "horizontal" dimension of student preparation, putting at his disposal innovative didactic material supported by self-evaluation tools, in familiar format for students. The contents will be structured by degrees of difficulty that will progressively prepare the user not only to solve exercises but also to produce well-constructed formal proofs. The material is suitable for use for flipped learning classroom or mastery learning.

The material and the exercises, are designed following MATH taxonomy (Mathematical Assessment Task Hierarchy), using eight different descriptors: Factual knowledge; Comprehension (recognition of formulas and situations); Routine use of procedure or algorithms; Information transfer (classification of math objects); Application in new situations (planning work, selection of methods); Justifying, proof, reasoning and interpreting; Implications, making conjectures, comparisons and finding patterns; Evaluation. It is well documented that regular exercises encourage students to keep up with the course content as it is presented, provide immediate feedback to students about their level of learning, and help the teacher identify parts of the course content that students are struggling with and that require further explanation.

Research in mathematics education has long highlighted the complex and systemic nature of mathematics teaching/learning situations, which requires, even in the case of e-learning, a specificity in the production and organization of the learning environment Albano and Ferrari has overcome the current separation between technology and educational research, as their joint use can provide matchless opportunities for dealing with most of the learning problems related to mathematical concepts as well as to linguistic, metacognitive, and noncognitive factors.

Keywords:

e-learning, Linear Algebra, e-assesment.