Giuseppe SCOLLO

Current research activities

Interest toward investigating the integration of traditional and modern technologies in the design of inclusive tools for mathematical education arises from a specific educational experience carried out across several years within the Computer architecture course, viz. the construction and analysis of manipulative algorithms for arithmetical operations using a number system representation with Maya symbols. On the Maya abacus, numbers are represented by sequences of groups of objects. The additive and ostensive nature of groups which form the digits facilitates the understanding of the rationale behind the manipulative actions which form the execution of the operations and makes them very simple to understand as well as to execute. For example, multiplication can be computed without prior, mnemonic learning of its table, and much in the same way in a positional system with nondecimal base. Moreover, the tactile perception of represented numbers fits the execution of the operations by visually impaired people, in principle. However, in order to make this effectively possible, tactile recognizability of the abacus structure is needed, too. A current research objective to this purpose is the design of an abacus for arithmetic with Maya symbols that would prove suitable to visually impaired users. The use of a 3D-printer is investigated to that purpose, together with the development of constructive solid geometry models, described in the OpenSCAD functional language. This is a preliminary activity for an intended contribution to the PRIN project "Mathematics as a glue for interdisciplinary teaching and learning", if funding will be granted to the project proposal. Furthermore, this activity fits nicely in the framework of project "Vietato non toccare" (Forbidden not to touch), funded by MIUR following the granting of the "Italian Teacher Prize" to Prof. Daniela Ferrarello, project which he takes part to as an Expert. As a matter of fact, the use of 3D-printing with OpenSCAD model development is planned in this project as well, for the construction of a math machines lab.

Research activities for future development

His more recent interests from previous research relate to:

• problems in combinatorics: Four color theorem, Collatz problem, Pentagonal number theorem;
• parallel algorithms for computational arithmetic: implementation of parallel algorithms for functions from the Collatz problem, in software on a grid (COMETA project) and in hardware on FPGA (Dedicated systems lab);
• symbolic dynamical systems: dynamics of state transition systems expressed in relational terms.

Research interest on the aforementioned topics is not vanished, it's just deferred.