Teaching Algorithms and Learning Algorithms

Abstract

*A11 teaching processes can be precisely specified by means of Helmar Frank's six didactic variables (each of which can in turn be interpreted as a vector of vectors). These are: learning system, teaching system, subject matter, target standard, environment and teaching algorithm. In order to improve understanding and retention of the subject matter, teaching programmes use longer and more complex teaching algorithms than do conventional instruction and lectures. Retention requires a certain amount of well‐spaced repetition. The control of the repetition function can be exercized by the teaching system or by the learning system, provided the latter is willing and able to do so. Conventional instruction leaves the control of the repetition function (and other learning functions) to the learning system and often fails to reach the target standard because it has overestimated the ability or willingness of the learning system to control its own learning activities. Programmed instruction makes a considerably lower estimate of the learning system's learning abilities and compensates by providing a longer and more complex teaching algorithm which greatly reduces the learner's freedom, thus allowing less self‐instruction to take place than does conventional instruction. While the willingness of the learner cannot easily be increased except by confining instruction to learners who ask for it, the ability of learners to learn can be improved by teaching them learning procedures (learning algorithms). The use of such learning algorithms by willing learners would raise the target standards which can be reached by means of conventional instruction and enable the teaching algorithms of programmed instruction to be shortened or simplified or to be presented by less complex teaching systems without lowering the target standard. The criteria for determining which are the most desirable combinations of teaching algorithm and learning algorithm in respect of their length and complexity depends on the agency which decides that a teaching process is to be carried out; this agency may or may not be the learner. Efficiency is not necessarily a valid criterion for all such agencies. At the present time of unemployment among US teachers and great general unemployment in Great Britain, any agency which regarded school primarily as an instrument to keep teachers in employment and to keep pupils off the labour market for as long as possible would have an obvious motive to extend the upper age limit for compulsory schooling and to favour inefficient methods of instruction. The paper concludes with an example of a learning algorithm for paired associate learning in foreign languages, shorthand, etc.

*This paper was presented to the Annual Conference of the Association for Programmed Learning and Educational Technology, held at the University of Bath, Somerset, England from 27 to 30 March 1972. For a variety of reasons publication has been delayed for a decade. Unfortunately (or fortunately?), the points made in the paper appear to be as relevant today as they were then. Many important issues have been bypassed by fashion rather than solved. The paper is therefore published virtually unchanged, except for the odd footnote that has been added for clarification. Readers who wish to see how the author's perspective has been sharpened in the meantime and see the contents of this paper in the wider framework of educational cybernetics are referred to the encyclopaedic article ‘Educational Cybernetics’ by Bung and Lansky 1978.

I am indebted to my teacher, Mr John L. M. Trim, then of Cambridge University and now director of the Centre for Information on Language Teaching, whose criticism of the original sections three to seven lead to the writing of section two and all the insights this gave me.

Motto

O glucklich, wer noch hoffen kann,

Aus diesem Meer des Irrtums aufzutauchen!

Was man nicht weiss, das eben brauchte man,

Und was man weiss, kann man nicht brauchen

(Oh fortunate man who can still hope,

to emerge from this sea of error!

What we do not know is exactly what we need,

And what we know is of no use)

Goethe: Faust

I seem to have been only like a boy

playing on the seashore, and

diverting myself in now and then

finding a smoother pebble

or a prettier shell than ordinary,

whilst the great ocean of truth

lay all undiscovered before me

Newton

Notes

*This paper was presented to the Annual Conference of the Association for Programmed Learning and Educational Technology, held at the University of Bath, Somerset, England from 27 to 30 March 1972. For a variety of reasons publication has been delayed for a decade. Unfortunately (or fortunately?), the points made in the paper appear to be as relevant today as they were then. Many important issues have been bypassed by fashion rather than solved. The paper is therefore published virtually unchanged, except for the odd footnote that has been added for clarification. Readers who wish to see how the author's perspective has been sharpened in the meantime and see the contents of this paper in the wider framework of educational cybernetics are referred to the encyclopaedic article ‘Educational Cybernetics’ by Bung and Lansky 1978.

I am indebted to my teacher, Mr John L. M. Trim, then of Cambridge University and now director of the Centre for Information on Language Teaching, whose criticism of the original sections three to seven lead to the writing of section two and all the insights this gave me.