HOW TO "AVOID" WORK. UNDERSTANDING THE WAYS IN WHICH PHYSICS USES MATHEMATICS WITH A NEW METHOD TO RECOGNIZE THE CONSTANT OF MOTION OF MECHANICAL ENERGY (11 pages)
HOW TO "AVOID" WORK. UNDERSTANDING THE WAYS IN WHICH PHYSICS USES
MATHEMATICS WITH A NEW METHOD TO RECOGNIZE THE CONSTANT OF
MOTION OF MECHANICAL ENERGY
Marisa Michelini, Gian Luigi Michelutti, Department of Physics, University of Udine, Italy
Researchers and teachers often find themselves faced by the difficulties which students have with
the mathematical instruments which physics uses both on the descriptive level and also on the
interpretative level; almost as a logical, unquestionable consequence, they look for ways to avoid or
reduce involvement on the formal level [1,2,3]. For example, they try to give greater weight to
experimental activities (the educational role of which is beyond discussion for an experimental
subject) [4,5,6], or they try to entrust to operativity and/or informal education the connection
between the perception and observation of phenomenology and the physical description [7,8,9].
Didactic projects done in the 60s and 70s throughout the Western world  are examples of a
translation of the various pedagogical theories into operational strategies for effective teaching.
These projects mainly relied on experimental activity to construct a gradual awareness of the formal
relationships between the significant variables in selected experiments (PSSC, IPS, PS2), even
when the formulation was of a historic type (PPC). Such experiments were conducted over a wide
scale, and established that it is not sufficient to optimize teaching in order to achieve good learning,
and that other types of difficulties occur , such as those linked to the lack of connection between
common-sense interpretation and physical interpretation [12,13], or those linked to the ability to use
ways of representing things which physics uses, for example graphs .
The difficulties in mechanics are particularly well-known [15-21]. If we examine them we notice
that the difficulties are of a conceptual type, both with regard to the significance of the elements of
formulas which physics introduces to describe and interpret, and also with regard to the styles of
formalization which physics assumes.
Studies on learning processes [22,23], and theories on conceptual change  have given useful
indications for involving students, for the processes of building knowledge, for ways to encourage
the contextualization of concepts, and for the ways in which to help students look at the world from
a physical point of view. Research into the use of the computer in physics teaching has given an
important contribution to the ability of looking at processes from a physical point of view, to
reading and using graphs [25-29]. Such research has contributed decisively to putting into students'
hands the process of constructing formalized physical models starting from qualitative hypotheses
With regard on how to make students aware of the ways physics uses mathematics to deal with
descriptive and interpretative problems in various circumstances: this problem is still open. It seems
to us that this cannot be considered a secondary problem for a subject like ours, which has assumed,
as a work style, a predictive capacity based on the description of phenomena by means of
mathematical tools. It is a style which is a part of the epistemic roots of physics and we do not think
it is possible to give this up, if we want to give young people the opportunity to develop a passion
for this discipline . Therefore, we need contributions which show the ways physics uses
mathematics, which familiarize students with these ways, and which give young people the
opportunity to operate on this level without inhibitions, overcoming the prejudice that the symbolic
language is impossible for them to manage.
This work wants to give a contribution to this end, and offer a new way of recognizing mechanical
energy as a constant of motion.
2. Definition of the proposal
The point of view which directs this proposal favors the principles of energy conservation in the
knowledge of physics and associates them with the existence of one or more constants of motion. In