The research activity in mathematics education is mainly devoted to integrating technological tools in the teaching and learning processes at university level. This research topic is motivated by the difficulties which we find in our students, both in cognitive and psychological terms and with regard to labor organization, especially at the university entry level. From the cognitive point of view they have to face concepts of greater complexity and the need for developing an advanced mathematical thinking. The psychological and organizational aspects are implicit in the transition from the high-school to the university environment, which require a change in the ways of studying and of learning.
With this respect, our research activity extends on two different but interrelated lines: on the one hand, we develop research topics on the suitability of using technological activities in the teaching-learning process in a university environment; on the other hand, we develop multimedia material for the students, in support of the traditional lectures in the mathematics courses. The upshot of this research activity is far reaching since it involves: the professional profile of the university teacher, who is able to monitor the work and the learning level of the students, besides being able to evaluate them automatically; the learning strategies of the students, who can become aware of their learning level in a constructive way through the interaction with the digital files; the academic institution, which can invest in this teaching-learning activity with the goal to reduce the share of early school leavers.
From a theoretical point of view, the topics on which we focus our interest are:
The design and implementation of multimedia files and paths in a digital environment are built on the basis of the existing literature in mathematics education and of the typical misconceptions of the students. It has the goal of fostering an aware and fully developed understanding of the mathematical concepts, and of supporting the students in progressively developing independent thinking. The interaction with the multimedia activities leads the students, through exploratory patterns useful also in increasing their motivation and involvement, to the personal deepening of the mathematical concepts introduced during the course. These activities favor a reflexive understanding and lend themselves to develop cooperative working, thus offering a possible remedy to the psychological and organizational difficulties mentioned above. At the cognitive level, the applets pursue targeted and heterogeneous goals: some allow the visualization and intuition of abstract theoretical concepts, others favor the handling of multiple representations, allowing the student to modify parameters and start animations; other activities are devoted to self evaluation, by means of a comparison of the solution given by the student and the correct solution (accompanied by suitable comments), which is made available to the student at the end of the activity; some activities aim at developing an “anticipatory thinking”, which may allow the students to foresee and control the outcomes of the calculations through the meaning and the implications of the very same calculations. Often, the files foresee the automatic sending of specific feedback, which depends upon the mistakes and the behavior of the students in the digital environment. This working method enhances the individualization of the teaching-learning process by the use of technology.
The educational tools which we have produced activate multiple comprehension channels in the student, which is, on one side, supported by the digital files by means of hints, feedback and organized paths and, on another side, stimulated in developing his/her own independence, since he/she has to build personally his/her own path by choosing among the available resources, by exploring the mathematical concepts. Also, the self-evaluation tools make him/her aware of his cognitive needs.
The technological tools offer also the opportunity of consulting repeatedly the material, when and where the student wishes, thus favoring the learning process in ways that are compatible with the learning speed and habits of each person.
For this research activity the group has obtained a financial support with the University Project “Progetto Strategico di Ateneo – 2016: Didattica Multimediale della Matematica” (“Multimedia teaching of Mathematics”). The multimedia material has been made accessible on the Moodle university platform at the address