The RTM(E) Model

Last modified: 12/14/2007 11:14 PM

Articulations of scientific knowledge: The RTM(E) Model

It is extremely important for the teacher to both clearly express the learning goals, i.e., what he wants the students to have learned by the end of their training, and to have an appropriate typology to describe the knowledge to be transmitted as it is to state the learning objectives.

In didactics, the well-established distinction between knowledge and know-how is emphasized. Develay says that "declarative knowledge falls under the section of discourse and knowledge, whereas procedural knowledge falls under the section of action and know-how. This distinction is obviously vital, but it is too broad for our purposes.

Unable as we were to find in the literature a model that fully met our needs, we are proposing one here, called RTM(E), in which the knowledge to be transmitted is grouped into four broad interrelated categories, namely Reality, Theory, Methods (and Examples).

The study of Reality (, i.e., nature and technology, observed facts, matter…) by observation, analysis and experimentation, makes it possible to develop or refine Theory , i.e., an explanatory diagram highlighting the similarities between the different observations of Reality and explaining them in a way that is both coherent and as simple and generic as possible. Theory on the one hand constitutes an interpretive graph for Reality, and on the other hand serves as a guide for the development of Methods (and/or operational tools) for solving problems, making use of specific concepts if necessary.

We believe that this typology is a good way to categorize knowledge relative to a scientific discipline, especially if it is rounded out by the principal applied Examples, which concretely illustrate how to resolve a class of problems (using Methods in the context of a Theory) relative to a particular aspect (of Reality).

Learning a scientific discipline requires the acquisition of both declarative knowledge for Reality and Theory, and procedural knowledge for Methods, which in essence correspond to know-how.

During learning, the examplesare a key element. Therefore, the examples must be realistic. If not, the perception the students will have of the question field will be wrong. They will have the idea or the feeling that it doesn't solve the real problems. This last remarks is a counter-argument against the classical method of teaching thermodynamics : if we too much stress the perfect gas model (supposedly in order to simplify), then the students conclude on this thought that the discipline solving capacity is very limited.

Reality, Theory, Methods and Examples are an essential part of what Kuhn, in the afterward to the 2nd French edition of La Structure des Révolutions Scientifiques, calls the disciplinary matrix, which represents what a group of scientists have in common (instead of the term Reality, he speaks of nature, instead of Theory, he uses symbolic generalizations, but the meaning is really the same, and he strongly stresses the objective of "normal science" which is to solve enigmas , which requires the development of Methods, and also the key role played by Examples). The disciplinary matrix is important in that it is typical of the identity of the group and in that its content is an integral part of the training of students, due to the fundamental role it plays in structuring schemas. This is in line with a comment by Develay, who says that "the knowledge to be taught constitutes the legacy that one generation wants to leave to the next".

Remembering these four classes, we can split up the contents of a course on energy powered systems in the following manner.

Reality

The study of Reality (, i.e., nature and technology, observed facts, matter…) by observation, analysis and experimentation.

Concerning reality, the contents of the teaching is not particularly good for a controversy. We have to present on one hand the various technologies and their usings, on the other hand the matter properties, at least on a qualitative level, and finally the typology of the proposed problems. That for, the most used pedagogic modalities are visits, lectures, presentations of slide-shows, projections of films, readings, some assemblings/ disassemblings, and practical works ...Please note that reality represents a very large part of the teaching, because the students' initial knowledge on this question is very reduced, at least in the initial training.

It is our opinion that the following points must be approached :

On-going problems about context and especially about environment.
The kinds of proposed problems (conception – design, audit – improvement, regulation).
The architecture of the various technologies.
The description of technologies, with presentation of the main construction requirements, especially regarding the used materials.
The history of technologies, of industriial creations and realisations, of the manufacturers.
The technical documentation, the estimations of sizes for construction.
The qualitative presentation of fluids properties.

Theory

The thermodynamic theory covers a very wide domain (hypothesis, equations, fluids models ...). Therefore choices have to be made during the selection of what will be explained or described. About theory, the students generally have some initial knowledge, which unfortunately is very often weak and fragmented, and which has to be repeated from the beginning, most often by magisterial presentations (lectures) and tutorial classes or seminars. In the today pedagogic debate, this is probably the most questioned teaching, and especially regarding the question of equations to be presented.

The other themes to be taught on a theoretical point of view are generally :

Carnot's cycle, which constitutes a reference for numerous cyles.
The thermodynamics concerning mere components (compression, expansion, combustion ...) at least on a qualitative way.
The theory of heat-exchangers.

Methods

The methods are necessary to proceed from theory to applications, therefore, as part of the Instances, they are especially necessary to solve the proposed problemes. This proceeding corresponds to the modelling operation and to the know-how acquisition. Reversing the idea, we may say that theory represents some abstractions of the various solving methods.

To precise our thought : let us consider the expression of the first thermodynamical principle for an opened system onto a flow with a negligible kinetic energy. The practiced calculation (method) of one heat-exchanger can be written as follows : Delta h = Q. As for a compressor or a turbine we write : Delta h = tau. And as for a gas expansion without thermodynamic work we write : Delta h = 0. We have here three particular modes of the same abstraction : the First Principle, which can be written as follows : Delta h = tau + Q.

The knowledge of Methods the students have, is quite generally in some embryonic stages, because it is uncoupled from applications. As we have seen it before, the teaching may make some profit in studying the solved basic instances and in practising some exercises which intend to turn the students operational. Regarding this question essentially, the simulators present some interest as aids for innovative pedagogies.

In our sense, the concerned knowledge is the following : (we do not think that this question is controversial.)

The use of state functions and of usual physical quantities (h, Q, tau ...).
The use of charts
Building up the conservative and entropic balances.
The calculation methodology of simple components (compression, expansion, combustion ...).
The characteristic curves of the components.
The practised calculation of heat-exchangers (LMTD, NTU).
The modelling principles of complex systems.

Examples

It is mainly about Instances that these links, which exist between the three poles of references (Reality, Theory, Methods), are the most clearly explicited.

Thus, they are basically important in learning this discipline. Considering the reasons hereabove, it is in particular absolutely necessary that these instances should be realistic and that they should show through which methods, the theories are applied. The presentations are generally centered about :

The four basic examples : refrigeration machines, steam power station, gas turbines, reciprocating internal combustion engines.
Their variants.

References

Develay, M. , De l'apprentissage à l'enseignement, ESF, 1992

Kuhn, T.S. , postface to "The Structure of the scientific revolutions", Flammarion, 1972