THE CONCEPT OF PARTIAL ORDER IN LANGUAGE PROGRAMMING AND THE FREEDOM OF THE CONSUMER

Abstarct

This is the first part of an article. Language teaching consists of developing in the student the ability to manipulate efficiently the mechanics of the target language and of teaching him to use the language mechanics in life‐like situations. The former aspect of language teaching can be dealt with by means of programmed instruction. All language skills (in the above sense of “ manipulation “) can be described by rules. The term rule is extended to cover also so‐called exceptions and directions to perform purely imitative tasks. All rules can then be interpreted as mappings of the following types:

(1) ϕ : A —> B (mapping of one set into another: paired associate learning, copying)

(2) ψ?: A ‐>p(A) (mapping of one set into its partition: classificatory skills).

Rules can be formulated as quasi‐algorithms (QAs). A QA must be explicit, i.e. it must contain only elementary operations. The concept of “ elementary operation” in QAs is relative and depends on the prior knowledge/ skill of the addressee. Between pairs of QAs bilateral relations are established, expressed as a —> b (i.e. a must precede b), in accordance with the principle: all operations contained in a QA must either be explicitly described by a preceding QA or be contained in the addressee's initial repertory of skills. This condition is satisfied by imposing a partial order on the set of all QAs. The pedagogical grammar is defined as a partially ordered set (POS) of QAs satisfying the above condition. A hierarchy of POSs is developed, where a teaching step T is an ordered set of elements, an exercise E is either a strictly ordered set of Ts or a “ totally unordered” set of Ts. An assembly of exercises, Q, is the partially ordered set of exercises E realising a given QA. A section S is the POS of Qs dealing with Similar subject‐matter. A component C is the POS of sections S all of which demand responses in the same medium (graphic or acoustic). A diagram D is the “ totally unordered set” of components representing “ communication skills.” A task analysis at the level of sections is given. It is then demonstrated that a teaching program which is conceived as a POS of elements maximises the freedom of choice for the learner and the teacher, whereas this freedom is minimised both in conventional teaching programs (linear and branching alike) and in traditional classroom teaching.