Abstract:

The M.In.E.R.Va. (Interactive Mathematics Exercises) project wants to give teachers a flexible informatic tool to create courses for students, helping them to recover their deficiencies in Mathematics or to enhance their abilities. This project is the product of a research on teaching technologies carried on by a group of professors at Catholic University of Milan.

Various tools are already available to create theoretical and practical courses and they are used both in secondary schools and in Universities (to recover basic knowledge in Mathematics).

Our software is different from the others for the following reasons:
1. the possibility of taking the course individually and offline;
2. a wide range of exercises, besides multiple choice questions (MCQ): short answer questions (SAQ) with numerical, vector or text answer, fill in the blanks, multiple answer questions (MAQ);
3. the possibility of using the software without installing other applications (only a few files on a server are needed for the online mode);
4. the independence from the operating system (at least on the client side).

Four kinds of contents have been produced:
1. theoretical schemes to enforce or create knowledge;
2. guided exercises to show the basic modalities to solve a problem;
3. enforcement and self-evaluation exercises;
4. exercises to verify students' results.

Contents can show different levels of interactivity and can be used both offline and online.

The student can automatically receive the following feedbacks:
1. total score,
2. wrong and correct answer,
3. suggestion to find the solution,
4. reference to theory,
5. solution.
The software is highly flexible, in fact it allows to produce, from the same file of exercises, different outputs:
1. individual exercises (with or without evaluation),
2. exercises monitored by the teacher,
3. classwork.

Random parameters can also be inserted in exercises: this allows students to repeat similar exercise, with different numbers, to enforce the comprehension of the subject proposed.
The software is based on LaTeX, a typesetting system very similar to a programming language.

We have developed a group of LaTeX packages which allow to create interactive online or offline PDF files or written classworks.
We have also developed a web platform (in Italian), which can be reached at the link http://progettominerva.unicatt.it. On this platform, the student can see the theoretical lessons, download the offline exercises, access the online exercises and self evaluation tasks. The teacher can organize the theoretical and practical files, prepare the courses, follow his students through a web interface in which he can see all the scores and the answers given.

We are developing a database of exercises which can be used for different purposes. This database is created by the teachers of the schools which participate in the project, supervised by the mantainers of the project.

All the project is almost entirely developed using free or open source software.

We have also created virtual classrooms using Facebook groups, to give support to the students during their activities. This tool has allowed the development of a more informal and interactive way of communication between students and teachers, thus enhancing the learning process.

Keywords:

e-learning, Online assessment, Online exams, LaTeX, PDF, Social Networks in the learning process.