Project Summary
Modern IT-driven societies demand highly skilled professionals who can successfully
design complex systems at ever-increasing levels of reliability and security.
But is also requires from the general user a higher degree of "mathematical
fluency", i.e., the ability to resort to mathematical language and method
to build models of problems and situations and reasoning effectively within
them. Such an ability is at the heart of what it means "to understand" and
it may be considered a fundamental ingredient of democratic citizenship.
That effective use of Mathematics has enormous economic potential in
the IT society has already been acknowledged by the eminent computer scientist
E.W. Dijkstra, who once put it that "high technology so celebrated today
is essentially a mathematical technology".
There is little hope, however, that such expectations and demands be met
by current standards in school maths education. Not only there is a disturbing
gap between style and contents of middle school and high school maths, but
also never have indicators and statistics been so appalling in what concerns
the country's overall ranking in maths education. Worst of all, mathphobia
- which seems to be spreading everywhere - has become a hot spot for the
media.
This situation calls for emergency policies capable of reinvigorating maths
education and its effective application at all problem-solving levels. This
should include not only the uniform adoption of well-established calculation
techniques which have proven to scale up from the school desk to the engineer's
desk tackling complex, real-life problems, but also the design of innovative
tools able to support such a technological challenge in a uniform and effective
way.
In this context,
MathIS aims to exploit the dynamics of algorithmic problem
solving and calculational reasoning in both maths education and the practice
of software engineering, in an integrated way, thus meeting the challenges
of nowadays and future information society.
The project's overall approach stems from two decades of research on
correct-by-construction program design which brought to scene a whole discipline
of problem-solving and shed light on the underlying mathematical structures,
modelling and reasoning principles. A most relevant consequence has been
the systematization of a calculational style of reasoning which can greatly
improve on the traditional verbose proofs in natural language, proceeding
in a formal, essentially syntatic way.
At the educational level,
MathIS will reframe a collection of themes in
pre-university mathematics along these lines and assess its merits not only
on the development of general calculational and algorithmic skills, but also
as a tool for discovery. (Recall, for example, that it was the formal manipulation
of Maxwell's equations that led to conjecturing the existence of electromagnetic
waves, confirmed experimentally shortly afterwards.)
At the software engineering level,
MathIS will push forward in the
development of new algorithmic design
calculi in the emerging area of global computating.
On the technology side,
MathIS will capitalize on recent developments and
increased flexibility in Human-computer interaction technology, which we
believe is mature enough to provide an infra-structure for the envisaged
methodological shift. In this context, a second axis in
MathIS concerns the development
of innovative computer-based tools exploiting Tablet PC technologies, as well as e-learning
principles and platforms (in particular, associated to the semantic-driven automatic
correction of algorithms). Such tools will provide learning environments oriented
to calculational reasoning and algorithmic problem solving, which, although
consistent with traditional blackboard-style teaching, will exploit enhanced facilities provided by computers.