SELF-ORGANIZING TEACHING SYSTEMS

Transcription

1 SELF-ORGANIZING TEACHING SYSTEMS EP-RR 20 S. KANEFF A. N. VLADCOFF December, 1968 Department of Engineering Physics Research School of Physical Sciences THE AUSTRALIAN NATIONAL UNIVERSITY HANCOCK Canberra, A.C.T., Australia. ftj163. A87 EP-RR20 A.N.U. LIBRARY

2 This book was published by ANU Press between This republication is part of the digitisation project being carried out by Scholarly Information Services/Library and ANU Press. This project aims to make past scholarly works published by The Australian National University available to a global audience under its open-access policy.

3 SELF-ORGANIZING TEACHING SYSTEMS by S. KANEFF and A. N. VLADCOFF December 1968 Publication EP-RR 20 Department of Engineering Physics R esearch School of Physical Sciences THE AUSTRALIAN NATIONAL UNIVERSITY Canberra, A.C.T. Australia

4 2 8 SEP 1870

5 CONTENTS Page SUMMARY iii 1. INTRODUCTION 1 2. MECHANIZED TEACHING SYSTEMS Inadequacies of Existing System s The Machine as an Adaptive C ontrol System A Philosophy of A pproach for M echanized Teaching Functional R equirem ents Com plexity and S elf-o rganization SELF-ORGANIZING SYSTEMS R elevance to Teaching System s An E lem entary E volutionary Teaching System E ssential F eatures of a Simple Evolutionary Model D escription of the Teaching System O peration of the System Application to a Specific Problem D iscussion C onclusions FURTHER WORK CONCLUSIONS REFERENCES 37 ii

6 SUMMARY P ossible high level teaching system s using self-organizing principles are discussed. The E volutionary ch aracter of a self-organizing system is used as a b asis for a sim ple teaching system im plem ented on a digital com puter. D eficiencies in the system suggest features of a m ore complex system which is being developed with the aim of providing a powerful re searc h tool through which eventually high level system s m ay be developed. The g en eral approach of finding constraints and action capabilities to produce a self-organizing system which can enhance its own cap a b ilities through learn in g, is suggested. iii

7 1. INTRODUCTION We are concerned here with the role of a machine in a high level teaching system. H itherto, the machine itself has played an intellectually triv ial p a rt in attem pts to produce teaching m achines. It is our view that this situation need not p e rsist, and that the role of the machine can be considerably updated. Given an adequate initial organization of inform ation, a suitable physical (hardware) stru ctu re, and provided with sets of strateg ies, operating ru les and d ecision c rite ria, together with the opportunity to com m unicate, gather and re-organize inform ation, p articu larly the ability to produce and continually to update a model of the student(s), a m echanized sy stem can be reasonably expected to: (a) adapt its operation to take account of individual student capabilities and biases, selecting inform ation for optimum presentation, determ ining the nature of d ifficu lties, and instituting help sequences when student p erfo rm an ce re q u ire s these; (b) optim ize its existing strateg ies, ru les and decision c rite ria through experience w ith single students and with groups of students; (c) act as an inform ation sto re, allowing a student to ask for, and be supplied with, inform ation which he d e sires or needs; (d) provide adequate challenge and stim ulation; (e) generally provide a powerful m easurem ent and control system for te sting theories, approaches and strateg ies in a re a listic environm ent, thereby providing inform ation enabling the machine designers and educational re searc h w orkers to enhance the system s capabilities and perform ance, ultim ately enabling specification of a p ractical teaching system to be made. The potential capability of a suitable m achine s tru c tu re to update its p e rform ance through the integrated re su lts of interacting with hundreds of individual students should not be underestim ated, as the p ro cess of im provem ent can be achieved extrem ely rapidly, unlike the corresponding p ro cess in a human teacher, whose experience m ust be developed over a long period, due to his lim ited inform ation p ro cessing rate. What is very clearly necessary at this stage of m achine development, however, is that the provision of new inform ation on topics to be taught, the enrichm ent of stru ctu re and the provision of new strateg ies, ru les and decision c rite ria, m ust come from the educational re se a rc h w orker and machine designer - the machine, by its own actions, can be expected to im prove its perform ance, both short and long term, only by selecting stra teg ies, ru le s and decision c rite ria (which are present), thereby improving and optim izing its perform ance and adapting to each student, In this sense, it might be said to le a rn to be a better teacher, but (at the p resen t stage of knowledge) it cannot be expected to invent new strateg ies, ru le s and decision c rite ria, although, by acting within its stru ctu re and general organization, it might well produce sequences of interaction with a student which have not been anticipated by the machine designer. (Invention of new strateg ies need not be ruled out com pletely, however, because if given appropriate capabilities for re -stru c tu rin g inform ation, an

8 2 INTRODUCTION opportunity to review inform ation, and to seek further inform ation by being able to Task questions, even this aspect might eventually be handled). E ssentially, it might be anticipated that a high level m echanized teaching system which can be devised in the light of p resen t knowledge, would be an extrem ely powerful re searc h tool in the hands of an educational re searc h w orker, for studying and defining the problem s involved in developing a specification for a general purpose teaching system able to learn to im prove its own perform ance. The place of the human teacher in such an environm ent would undoubtedly be as a m anager of a pow erful facility, guiding its application and updating its c ap a b ilities. 2. MECHANIZED TEACHING SYSTEMS 2.1 Inadequacies of Existing System s P redictions made (around 1960) that by the 1970 s students would be spending th eir days in front of com puterized teaching m achines have not been re a lis tic. However, the acquisition by an ever increasing num ber of educational establishm ents, including p rim ary and secondary schools, of digital com puters for general data processing requirem ents has provided a strong drive for employing such equipm ent in Computer A ssisted Instruction System s. At the p resen t stage of development many further studies m ust be undertaken before confident recom m endations can be made in reg ard to d esirable system s. The need of a large amount of researc h seem s urgent, p articu larly as large on-line tim e-sh ared educational data processing system a re being installed in some U niversities in the U. S. A. While a relatively sm all numb e r of experim ental m ulti-console system s may be w arranted in o rd er to develop this new concept in teaching, a g re a t proliferation of expensive equipm ents likely to become rapidly obsolete does not seem desirable: (Rath (1967), m entions the proposec 700 console system at the U niversity of W isconsin and predictions from the U niversity of Michigan that their system will have over 1, 000 consoles by 1970), A m ajor w eakness in p resen t com puter assisted system s lies in the inadequate m eans for com m unication between student and m achine. This involves both the language used for com m unication, which constrains the student to communicate in the m achine's te rm s, as well as the effectiveness of the term in al equipment. In a m ulti-console system, the term in als them selves will certainly contribute a large proportion of the total cost, if facilities which are non triv ial are to be provided - in th is re sp ect it is of in terest to note an estim ate by B itzer et al (1967) that one central p ro c e sser might be expected to p ro cess term in als, and the rep o rt by Goldberg et al (1966) on plans for providing term in als (via television re c e iv e rs and sm all keyboard consoles) in the homes of community groups of , 000 people, connected by co-axial cable to a cen tral com puter. In addition to technical and educational considerations, strong economic factors demand g re a t care in solving s a tisfactorily every aspect of these term in al requirem ents.

9 MECHANIZED TEACHING SYSTEMS 3 A further lim itation re la te s to the kind of m aterial which can be effectively handled by existing m echanized system s. D rill and P ra c tic e routines are pro cessed com paratively w ell because the task and subject m atter can be stated explicitly and can be program m ed exhaustively and com pletely without detracting significantly from the value of the routines. Even here, however, a g reat amount of w ork is n ecessary to ensure that system s are satisfactory, but it appears the future of this kind of interaction is assured, for even at U niversity level, there is much scope for the inculcation of factual knowledge in a lim ited context. On the other hand, the im plem entation of T utorial and Dialogue Interactive Systems is severely ham pered by the inability to p ro cess the unexpected response or the unforeseen difficulty. More fundam entally, however, existing com puter assisted approaches a re stru ctu rally and functionally unable to take into account the student attributes and the character of the topic m aterial in a sufficiently rich interactive m anner - even if this aspect is overcom e however, th ere rem ains a vast gap in knowledge concerning the in ter-relatio n sh ip s between student and topic m aterial p aram eters (including the problem of identifying those p aram eters which in fact are relevant) and the tra n s form ations necessary to achieve successful learning and understanding. Because of the inadequacy of existing theories of teaching and learning, it seem s necessary to face the problem in an em pirical, experim ental m anner in o rd er to gather adequate inform ation on which to base subsequent theories which would hopefully be useful in p ractice. Computer A ssisted Schemes usually select each following move on the b asis of the im m ediate past response only, (although the general strategy of the interaction may have been, in the first instance, selected to m atch the student on the b asis of general ability). This essentially m inim ally adaptive approach* is of extrem ely re stric te d use in higher level operation, as it takes little account of the overall perform ance over a period of tim e, and each of the prespecified branching routines, once selected, cannot take account of individual student differences which m ay apply over that routine. There now seem s little doubt that program m ed instruction with or without mechanized im plem entation is a successful form of teaching within certain re stric tio n s. Claims often made that it is successful because of its features of sm all step p ro g ressions and im m ediate knowledge of re su lts, however, are difficult to substantiate with confidence, as other factors are invariably raised - the necessity for the program m er to first clarify his concepts and objectives, the g reat redundancy incorporated in the presentation of inform ation, and so on - which contribute to the nature of the program m e. The advisability of the sm all-step approach itself has been questioned often and has led to other approaches in which la rg e r chunks of inform ation are presented - this seem s p articu larly apt with bright students and the attem pt to develop creativity (Crutchfield, 1965). These aspects need careful re-thinking continually, particularly as g re a ter num bers of research w orkers and practising teach ers * See Section 2. 2

10 4 MECHANIZED TEACHING SYSTEMS take up w riting program m es. In the developm ent of m echanized teaching system s, th ere has been a natural but reg rettab le tendency to accept existing digital computing system s and to employ state of the a r t techniques in producing experim ental teaching system s. D igital com puters have not been evolved with the objective of solving teaching system problem s and it is not su rp risin g that a m ajor m is-m atch exists in this approach. A consequence of this is, apart from the likelihood of inadequate system s resulting, that costs of system s, p articu larly when im plem ented in a half-baked m anner, are likely to be needlessly great. Undoubtedly there exists a p ressin g need to conduct intensive re se a rc h into all of the various aspects entering into m echanized teaching system s - philosophical, sociological and technological. 2,2 The M achine as an Adaptive C ontrol System It has been observed (Stolurow, 1961) that the term adaptive may be applied in a teaching sy stem to indicate the capacity of the m achine and its a s s o c iated program to adjust, in some way, to the specific needs of the individual learn er. We re serv e the term 'm inim ally adaptive for system s which have a finite (non-zero) m inim um adaptive property present: that is, the machine should be able to adapt on the basis of the previous value, only, of a single m easured p aram eter of a student, in producing the next item for presentation, in o rd e r to be called m inim ally adaptive'. (This p aram eter could, for exam ple, be the tim e taken to respond, or the co rrectn ess o r otherw ise of a response). If m ore than one student param eter influences the succeeding item (s), o r if the selection of item s is made on the basis of 2 or m ore previous values of one or m ore stu d en t-p aram eters, the system is m ore than 'm inim ally adaptive, and it seem s reasonable to designate it sim ply as adaptive. A m em oryless system which is sensitive to 2 or m ore student p a ra m e te rs, or a system with m em ory operating on one or m ore student p a ra m ete rs, seem s m ore than 'm inim ally adaptive' and will be term ed adaptive. This use of the term adaptive' seem s not inconsistent with that employed by P ask to describe his own developm ents of teaching system s. F u rth er complexity is introduced when the facto rs, p aram eters or individual previous responses are them selves in te r-rela te d in a m anner taken into consideration by the teaching system ; then pattern s of p aram eter variations and of responses may influence selection of item s. Eventually the complexity of an adaptive system m ight be increased to the point w here it would w arran t the designation self-organizing system, as introduced in C hapter 3. P ask seem s to have been the first to have produced (and understood the significance of) a device able to modify or adapt its presentation to m atch the student being taught, in m ore than just a triv ial m anner. His original work began with a system to teach keyboard skills (training punch-card operators) and has since extended to the teaching of such skills as making m anagerial decisions, the use of

11 MECHANIZED TEACHING SYSTEMS 5 scientific inference in re searc h, diagnosis and fault-detection in electronic equipment, and others. (Pask, 1957, 1958a, 1958b, 1960a, 1960b, 1961, 1962, 1965, 1967; P ask and Lewis, 1962). The principle used in all of these activities is that of including in the system an adaptive m echanism which in teracts with the student, and allows the machine to learn appropriate student ch aracte ristic s, which are used to modify the training routine according to these individual featu res. His devices have employed various form s of m em ory of past responses as well as m em ory of processed resp o n ses. Design of such a system involves a control-engineering problem, with the machine acting as the control m echanism to modify the student s behaviour (Pask, 1965). Such a m an/m achine system can be com pared to a hom eostatic p ro cess, as it seeks an equilibrium defined in term s of accurate responses to the m ost difficult questions which the m achine can offer (B eer, 1959). A dynamic equilibrium is set up at the completion of the task, with the machine presenting the m ost difficult questions, and the student co rrectly making responses to these questions. To achieve stability, the teaching machine m akes tria l moves which are initially unbiased; however, as interaction proceeds, the teaching machine learn s about the student s behaviour p attern and, as a resu lt of this, m odifies its own strategy. One requirem ent for stability of this interaction is that there should be a balance between the co-operative and the com petitive strateg ies on the p a rt of the m achine. The m achine takes the initiative. If the student is scoring well, it will com pete, by giving le ss cue inform ation and presenting m ore difficult item s. This it w ill do until m istakes begin to appear, when the machine will sta rt to co-operate by sim plifying the problem (or perhaps giving a help sequence) with resp ect to the kind of m istake which w as m ade. There is therefore a tight feedback between the two system s (student and m achine). Because of the inform ation tra n sfe r between the two system s, the adaptive teaching machine is sim ilar to a participant in a dialogue. P a sk s work has been perform ed m ainly by the construction of special purpose equipment, and appears to have been re stric te d principally to the training of various skills. Although highly successful, and certainly opening a vast new frontier of w ork, it has not attem pted the problem of devising a universal (i. e. g e n eral purpose) sy stem for teaching. System s which aim to be adaptive, in order to adjust to the specific needs of an individual student, m ust be able to discover the values of essential p a ra m eters - this can be achieved from his resp o n ses, and some form of m em ory in which to store these p aram eters (which need continual updating) appears necessary. The student and machine m ust be in constant interaction to achieve effective adaptation: the system of student plus machine may be regarded as a self-organizing system A Philosophy of A pproach for M echanized Teaching The activity w hereby a te ac h e r (tutor) im p a rts knowledge and

12 6 MECHANIZED TEACHING SYSTEMS understanding of a topic to a student, is viewed as a communication, m easurem ent and control p ro cess, in which the overall re su lt is a transfer of p articu lar inform ation from an individually organized sto re of inform ation within the te acher's brain, (including also inform ation stored in books, and so on, to which the teacher has access and which he p ro cesses in his brain before im parting this inform ation to the student), to a somewhat sim ilar individually organized store of inform ation within the student s brain. Because of hereditary and environm ental factors, the organization and in ter-relatio n sh ip s in the inform ation within the two brains will differ to a degree which depends on these factors. Even the strateg ies for processing this inform ation by the two individuals will probably differ, as will their attitudes, general levels of p ro c e ssin g capability and so on. The teacher, not knowing what actually tra n sp ire s within the student s brain (and vice versa), can rely only on the com m unication m edia between them to provide inform ation on the student s attitu d es, c ap a b ilities, level of knowledge and understanding, and other attrib u tes. In the case of a human teacher and student, the modes of communication are many - including speech, with a rich n ess of intonation, inflexion and so on: visual, through the w ritten, tj^ped or printed word, or p icto rial (diagram or picture); and the g re a t variety of inform ation which can be conveyed by general facial and body expressions, W hatever the mode, the teacher m ust rely on behavioural inform ation in order to a sse ss (m easure) the student s internal state. He does this, probably largely subconsciously, and essentially builds up a model in his own mind of just what the student s attitudes and attributes are - he uses this model, which is revised (consciously o r subconsciously) continually, and on it he bases his teaching strateg ies and item d etails, seeking to guide (control) the in te r action in a direction producing the d esired behaviour (goals) in relation to the topic being presented. Insofar as he builds up a model of the student and can devise and select his strateg ies, decision ru les and perform ance c rite ria, the teacher adapts his presentation to the needs and capabilities of the student. F urther, over a com paratively long term, he learn s, as a re su lt of many encounters with various students, which approach is m ost effective for students with p articular attributes. His success as a teach er depends in fact on how well he can m atch his approach to the student, and on how well he can select, m easure and classify appropriate relevant student attitudes and attrib u tes, and im plem ent an appropriate set of strateg ies, decision ru les and perform ance c rite ria suited to the teaching and subject m atter goals. Viewing the teacher /student interaction in the light of the above th ree p aragraphs, suggests the model on which the herein described system s are based. As illustrated in Figure 2.1, the C ontroller (experim enter or system designer), has d ire c t access to the student and to the teaching system, his aim being to m atch operation of the overall system to produce effective teaching-learning in te r actions, employing appropriate com m unication m edia between teaching system and student. The sto re of inform ation w ithin the teaching sy stem is organized by the Contro lle r on the basis of his own conceptual understanding of the topic m aterial - the

13 MECHANIZED TEACHING SYSTEMS 7 T eaching S ystem S tore of Inform ation C om m unication M edia Info rm ation to Student E xternal C o n tro ller O perating Functions Student M odel of Student Inform ation j r o m.student, j I I L D irect C o n tro ller/s tu d en t Link * I I I J Figure 2.1 Elementary Schematic of Controller/Student/Teaching System. model of the student reflects this information store in structure so that, hopefully, when the teaching-learning interactions have concluded, it will also reflect the information store content in detail. N ecessarily, the store of information in the teaching system can be only a very crude version of the organization within the Contro ller s brain, but nevertheless, this may be an advance on no organization at all; sim ilar remarks apply to the relation between the student and his model incorporated in the teaching system. The model of the student contains other details dealing with his general capabilities and attitudes - these attributes or parameters are taken into account, together with the properties of the information and general teaching goals, strategies, decision rules, and performance criteria (all inserted by the Controller) in order to produce teaching-learning interactions well matched to the student s attributes. A feature of this approach is the necessary complementary relationship between the teaching system structure and the functions which must be inserted into the structure to make it operate successfully. The task of the controller, apart from initially devising the necessary structure, organizing the information, and inserting the functions required, is to monitor behaviour with the object of improving the stru c ture and including new functions. The teaching system itself is expected to be able to optimize on the existing functions and to learn from experience which functions apply in particular ca ses - it must be provided with operating strategies to do th is.

14 8 MECHANIZED TEACHING SYSTEMS F u rth er clarification of the relationship between the inform ation sto re and the student model is necessary. It is noted that (almost) intuitively a human teacher can sum up a student s capabilities - with a little thought, he can give an opinion on the student s cognitive style, his attitudes, and other le ss readily definable qualities. The teach er is able to do this because of his own attrib u tes, som e of which have been developed through a g reat deal of training and experience. If the teach er d e sire s to discover directly the attributes of a total stran g er, he can do this e sse n t ially in two ways - he may w ait to discover them gradually through a (relatively) long perso n al acquaintance, or he can set out deliberately and quickly to discover them by te st. Thus, inferential or deductive abilities may be discovered by testing with respectively inferential or deductive item s of inform ation. By organizing a topic to be taught not only in te rm s of concepts and th eir in te r-rela tio n s, but also with each individual item for presentation to the student devised for a purpose (e.g. to discover inferential, deductive, and so on, abilities) and tagged accordingly, including d etails of the concept itself, the responses of the student can be assessed in relation to the 'tagged' c h a ra c te ristic s which they c a rry and thus, over a reasonable length sequence of interaction, a rich store of student attributes can be assem bled. The only effective lim it im posed by this approach is the ingenuity of the controller in identifying appropriate student p aram eters and devising (and suitably labelling) item s to develop and discover the student s attributes in relation to these p a ra m ete rs. Thus the inform ation sto re is organized in te rm s of concepts and th eir in ter-relatio n sh ip s with all item s for presentation, duly tagged' with the kind of p aram eters they contain, o r a re used to discover as attributes in the student. The student model, then, contains essentially a rep lica of the inform ation sto re in te rm s of its conceptual organization, so that the details of the student perform ance to the p articu lar topic can be filled in as interaction proceeds - that is, his degree of com pletion for each aspect of the topic m aterial is recorded and continually updated. Another aspect of the model contains a stru ctu re enabling a continual updating with regard to other student attributes as deduced from the scoring to the tagged item s, as well as quantities such as e rro r ra te s, response tim e, and m ore general attributes such as m otivation, p ersisten ce and so on. F u rth er student attributes may be derived from his attitude and behaviour (for exam ple, from his speed of response) and from his general p erfo rm ance to the strateg ies, ru les and c rite ria incorporated within the teaching strategy. All of these are factors for inclusion, with suitable tags, within the student model. It is of fundam ental im portance to our approach that the continually updated values of student attributes within the student m odel, (together with inform ation which can be derived from these attributes) provide the only possible quantities or c h aracte ristic s of the student which can be m easured an d /o r controlled by the teaching system (whether a human teacher or machine): consequently the ric h ness and relevance of the p aram eters incorporated in the student model essentially determ ine the level of adaptation possible - this is true w hatever the nature of the system and can serv e as a profitable basis on which to com pare different teaching sy stem s. The need for discovery or identification and quantisation of useful student

15 MECHANIZED TEACHING SYSTEMS 9 attrib u tes is therefore of param ount im portance to the future p ro g ress of high level Adaptive T eaching S ystem s. In o rd er to achieve the n ecessary teaching goals and to adapt to the p a rtic u la r student, a human teacher is guided by certain principles and strateg ies (which he may or may not have clearly enunciated), which he has acquired through training and experience, to p resen t and explain his m aterial, and to adjust in acco rd ance with the resp o n ses of the student. The teacher is characterized by extrem e flexibility in relating his approach to the subject m atter and student attrib u tes, so that he can usually achieve his purpose. It is necessary to provide a corresponding capability in the m echanized high level teaching system, so that appropriate adaptation can be achieved on the basis of the p aram eters stored in the student model - in th is case, however, the p rin cip les, strateg ies and other features cannot rem ain vague and not enunciated, (unless a com pletely random and im practicable approach is employed to gather, then organize, inform ation). The stage of developm ent of m echanization of cognitive p ro c e sses does not at presen t allow invention or creativity in a p ractical sense (e.g. A m arel, 1966; Minsky, 1961; Solomonoff, 1966) and the contro lle r seem s obliged to provide to the m achine an adequate set of strateg ies, decision ru le s, perform ance c rite ria, as well as teaching goals and subject m atter goals. In view of the partly intuitive nature of the human teaching approach, specification of p articular strateg ies, ru le s, and so on, is a difficult assignm ent. It seem s in the very nature of people that they learn, even when there are no apparent specific goals of learning indicated, or no p re-sp ecified approach to reach these goals available. Effective teaching m erely accelerates and d irects this p ro cess by providing a suitable environm ent in which the learning goals are m ore readily reached (the environm ent is essentially attained or modified by the features of m easurem ent and control of student attrib u tes in relation to the subject m aterial, and the goals, stra teg ies, decision ru le s and perform ance c rite ria applied). How this may be done is a further field for fundam ental re searc h, no less im portant than the determ ining of the appropriate quantities on which m easurem ent and control can be based, as d iscussed e a rlie r. Even the b est human teach ers are not perfect in always selecting the m ost appropriate goals, strateg ies, ru les o r c riteria: m oreover, because of lim ited processing ability w here large m asses of data are concerned, teachers do not rem em b e r detailed facts about individual students, only general principles and attrib u tes. W here a teach er in teracts with large num bers of students over a period, it takes him a long tim e to pro cess the large amount of data resulting from these interactions, into operating ru les based on this experience. Even in the human case, invention is a ra re occurrence, and a good te a c h e r's approach is based on training and experience. Again, because of human difficulty in handling the complex decision making and large amounts of data necessary in situations involving m ultivariable p ro c e sses, it is unlikely that a teacher w ill produce an optimum learning environm ent for every given student (even while tutoring to individual students), because both fa c to rs taken into

16 10 MECHANIZED TEACHING SYSTEMS account in making decisions and the data itself are first sim plified, and there is little tim e to even try to optim ize. Consequently, a human teacher is likely to learn to teach reasonably well relatively rapidly, as he can adapt quickly to individual needs as a re su lt of his general human capabilities, but will find that it takes a relatively long experience to make further im provem ents when these depend on experim entation and optim ization over a large num ber of tria ls. (Indeed, many human teachers seem not to bother to take this last step ). A m echanized adaptive system on the other hand, can have powerful inform ation processing features in that it can handle and store large m asses of data, and can engage tire le ssly in num erous experim entation tria ls and can perform optim ization studies taking account of all data. The re su lts can be organized and employed to im prove in an optimum way, the teaching and subject m atter goals, strateg ies, decision ru les, and perform ance c rite ria, all within a com paratively short tim e. M oreover, complete reco rd s of internal operation and details of m achine-student interaction may be stored and/or printed out. It is readily apparent that human capabilities, if combined with the inform ation handling pow ers of the adaptive m achine, can make a very useful and effective co-operative system for Educational R esearch, with a cen tral feature of the continual im provem ent in perform ance which can be achieved as a re su lt of experiences and modification. Because of the extrem e p resen t lack of knowledge on every aspect of the problem, an approach is favoured on the basis of an overall general stru c tu re which allows details relating to its various features to be incorporated to the extent of p resen t knowledge, but with the capability of adding fu rth er details and even refinem ent to the stru ctu re without the necessity of m ajor m odifications. The approach adopted, in the absence of adequate th eo ries of learning, m ust be to a degree, em pirical, with experim entation directed deliberately to the gathering of inform ation n ecessary to refine the stru ctu re and enrich the details of the functions within the stru ctu re Functional R equirem ents Figure 2.2 illu strates diagram m atically the general requirem ents in m ore detail than Figure 2.1. From inform ation provided by an appropriate set of stored student p a ra m ete rs (obtained initially from previous interactions, by standard te sts, or in serted by the experim enter) the teaching system should be able to select or generate item s from an appropriately organized inform ation sto re relating to the topic, based on appropriate teaching goals, subject m atter goals and on a student p aram eter dependent set of strateg ies, decision ru les and perform ance c rite ria, and p resen t these item s, suitably displayed, to the student. The student s responses are to be assessed in relation to the perform ance c rite ria, and the re s u lts used to update the student p a ra m ete rs, provide inform ation to adjust stra teg ies, ru le s and c rite ria. Study of the pattern of responses in relatio n to the item s presented, the goals, s tra t egies, ru les and c rite ria should allow the isolation of difficulties by the generation of

17 MECHANIZED TEACHING SYSTEMS 11 Figure 2.2 General Functional Requirements. Presenfati

18 12 MECHANIZED TEACHING SYSTEMS hypotheses which are then used to assem ble sequences of item s designed to test if the p articular hypothesis indeed applies. The confirm ed hypotheses m ust then cause appropriate help sequences to be organized to resolve the difficulty. The system should be able to im prove its own perform ance by modifying its goals, strateg ies, ru les and c rite ria as a resu lt of interactions with individual students and with groups of students, (Kaneff, 1967). C onsideration on how the stru c tu re s discussed above m ight be im p lem ented ra ise s fundamental problem s in every aspect. Among these, educational objectives need to be defined, inform ation m ust be appropriately organized and re p re sented, adequate meaning m ust be given to perform ance and how this is to be m easured, the nature of the student model m ust be determ ined, adequate strateg ies and decision c rite ria m ust be evolved, and effective com m unication established. In teraction should involve not only the m achine, in a sense, directing the learning p ro cess, but the student should be able to seek inform ation which he considers n ecessary, and the m achine should be able to supply it. The system should be capable of continual updating of its perform ance capabilities C om plexity and S elf-o rganization On consideration of the kind of general purpose teaching system stru ctu re which would m eet the philosophy of approach and requirem ents outlined, it is clear that a quite complex system em erges. The system m ust be m ultivariable with complex feedbacks, and, because it m ust adapt to individual student needs and p ecu liarities - that is, it m ust consider some goals, strateg ies, ru le s, and c rite ria as m ore probable than others for a given student, not allowing any of these to be dropped com pletely in case they are useful for a student of different attributes, or the sam e student during periods of different m otivation, etc. - the system m ust be b asically probabilistic. An approach in which th ere are c lear cut decisions on the above facto rs, is inferior to the probabilistic approach because of the consequent lack of variety in item s for presentation and in coping with the sam e student over spells of d isin terest and variable attributes. Self-organizing system s appear relevant in this environm ent: they a re system s which can learn and in crease th e ir behavioural re p e rto ire through the capability of building up a model of th eir environm ent by learning. 3. SELF-ORGANIZING SYSTEMS The term self-organizing system has been used in the lite ra tu re in a variety of ways, usually with referen ce to adaptive and learning system s, p articu larly to describe very complex p ro cesses such as those to be found in various living organism s. We employ the term here in the sense of B eer (1967) and Ashby (1962), to describe very complex, probabilistic system s which (a) can change their organization

19 SELF-ORGANIZING SYSTEMS 13 from a state of independent p arts to a state of dependent p a rts, o r (b) can im prove th eir organization to fulfill a certain purpose or goal, or both (a) and (b). As im plied by the above, no system of itse lf can be self-organizing - it can do so only as p art of a la rg e r system. Thus, a teacher cannot im prove his p erfo rm ance if he is in com plete isolation; but a la rg e r system of teacher and students in a re a l world environm ent, can be a self-organizing system. The theory of self-o rg an izing system s has received a g reat deal of attention in the lite ra tu re over the past decade, with reference to ord er, entropy and other concepts: we will re fra in from invoking these form alizations here - see, for exam ple, B eer (1967), Von F o e rste r (1960). Instead, it w ill be convenient to discuss inform ally the essen tial ingredients of a self-organizing system and to relate these to possible teaching system s. At the outset, it is necessary to draw attention to certain possible m isleading aspects of natural self-organizing system s. When we observe the end re su lt of a set of natural p ro cesses, we are apt to in terp ret this subjectively as a goal. This viewpoint, although som etim es a useful one, can m islead by diverting attention from the underlying p ro cesses involved. Thus, if we have a clu ster of gas m olecules in an otherw ise empty closed box, we notice that in due course, the m olecules are spread sensibly uniform ly throughout the volume of the box. From this and sim ilar observations we deduce Law s of Nature or goals relating to entropy and changes in o rd er. We can view the p ro cesses differently: given an environm ent which im poses a set of constrain ts, and given p articles of gas with certain action capabilities (e.g. the ability to move when acted on by forces), the whole system m oves probabilistically and inevitably to a situation in which the gas p a rtic le s are uniform ly dispersed. The end resu lt appears as a goal to an observ er. 3.1 R elevance to Teaching System s B eer (1967), suggests that in the p ro cess of a self-organizing system moving to its goal', entropic movem ent c a rrie s the system inevitably tow ard a pattern which guarantees an equilibrium between the system and its environm ent. When the observer has defined a set of goals as appropriate to his purpose, and has spotlighted an entropic drift which conform s to those needs, he labels the system as self-organizing, and re fe rs to the changes taking place as evidence of C ontrol. F u rth er, the degree of control exerted is dependent on the amount of effective inform ation available to the system. This picture is sim ilar to the view taken of the general purpose teaching system, which can achieve m easurem ent and control of the student attributes only on the basis of the inform ation available about them. M oreover, the teaching system is probabilistic, predictive and incorporates learning, all of which are identifiable features of Self-Organizing System s. Consequently it seem s appropriate to approach the design of the general purpose teaching system from the viewpoint of certain aspects of the principles of Self-O rganization, which can be helpful in the consideration

20 14 SELF-ORGANIZING SYSTEMS of system s with com plex m ultivariable control functions. The problem of designing a Self-O rganizing System to take advantage of 'entropic d rifts reduces to one of choosing and m aintaining a suitable environm ent within which the entropic drift can naturally and inevitably take place. F or this p ro cess to occur, the utm ost inform ation m ust be allowed to flow in o rd er to achieve effective control. F orem ost requirem ent, however, is that a goal or set of goals, understood as much as possible, m ust be viewed as the inevitable outcome of a set of environm ental co n straints and action capabilities on the p a rt of the system. It is the co n strain ts and action capabilities which the designer m ust be ingenious enough to determ ine in o rd er to produce a successful Self-O rganizing System. The entropic p ro cess which drives self-organization is hom eostatic as B eer (1967) points out, but the variety generator which gives proliferated states from which successful patterns are selected is conditioned from outside by r e s tr ic t ing total possible states; variety is dim inished by feedback precluding other states, and by a learning m echanism which biases the alleged random ness of the m utations. S im ilarities in the teaching system to the above facto rs are readily apparent An E lem en tary E volutionary Teaching System To attem pt im plem entation of the principles so far put forw ard, an elem en ta ry teaching sy stem has been sim ulated on a digital com puter (Vladcoff,1968), The developm ent of the teaching machine stru ctu re outlined below has been based on the principle of achieving features of self-organization by g en erating stru c tu re s (by the application of certain ru les), and selecting those which survive in a specified environm ent. (By stru c tu re is m eant any ordered entity). Selforganization in this sense, is that outlined in (a) in the first paragraph of this Chapter 3. This, in a very elem entary sense, is a basis of the p ro cess of evolution. The m otive in approaching the problem in this way, has been that self-organizing features can be obtained by modelling this evolutionary p ro cess which has been successful in producing complex and intelligent c re atu res. In applying this philosophy of approach to a teaching machine system, the stru c tu re s' generated are item s for presentation to the student. The student fills the role of an environm ent, in that he is the c rite rio n against which item s are tested. Those item s which are useful (in that they enhance learning) are retained, while those serving no useful purpose, in this way die off. This has been achieved by adjusting the probabilities of selection of corresponding item s. It is pointed out that in the sim ulation actually c arrie d out, the generation of item s has been re stric te d to the c lass of meaningful item s. The organization which occurs in the system during its evolution' in an environm ent (a student) is then one of continued im provem ent in presenting item s matched to the needs of the

21 SELF-ORGANIZING SYSTEMS 15 student (a form of adaptation). F urtherm ore, because the environm ent is a changing one (due to an increase in student proficiency generally), the system m ust survive under these conditions, by issuing item s which will continue to teach. This calls for certain m em ory requirem ents. The organization which re su lts in the teaching system can be plotted in n-dim ensional space. This gives a certain path of developm ent of the machine stru ctu re as interaction proceeds. However, (as in the case of evolution, w here different tre e s of organization are form ed depending on the p articular environm ent), a different path of organization w ill re su lt for each individual student. The system developed illu stra te s certain principles of generation of stru ctu res from m ore basic components. This has application of g reat im portance in teaching system s; for exam ple, in generating item s and strateg ies not foreseen by the p rogram m er. Although illu stratin g certain principles, the system has obvious lim itations as discussed later E ssential F eatures of a Simple Evolutionary Model The p ro cess to be modelled is that of a homogeneous set of p a rts becoming organized in different ways, depending on the p articular en v ironment. The basic essentials for such a p ro cess can be listed as follows (see F igure 3.1). (a) Basic raw m aterial. This constitutes building blocks which are to be structured in certain ways. An example is a raw m aterial used in nature, nam ely the amino acids. These basic elem ents are organized into various proteins during the growth of any cell: the actual protein form ed depends on the type and arrangem ent of the various amino acids (of which there are som e twenty known differen t ones acting as building blocks, used in the protein stru ctu re. (b) A rule of operation. This is a rule for the generation of organizations. The rule is actually a function for ordering the raw m aterial into complex stru c tu re s. It may be said that the genes of the chrom osom es within the nucleus of the living c e ll function as such ru le s of operation. (c) A criterio n. The purpose of this is to act as a m easure against which the stru c tu re s or organizations form ed can be tested. B asically, it is a c rite rio n for distinguishing between good* and bad* organizations. In nature, the environm ent itself provides such a c rite rio n of acceptable organization. It behaves as a selective m echanism in that the good organizations live on and reproduce, while those which do not m eet the requirem ents specified by the environm ent w ill die. It is im portant to note that what is a good or a bad organization is relative, depending on

22 16 SELF-ORGANIZING SYSTEMS raw m aterial law fo r modifying ru le operation feedback random elem ent product c rite rio n of acceptable organization Figure 3.1 Simple evolutionary model. the actual environment (Ashby, 1962). What has survived in our particular environment must therefore be n ecessarily good. But this is not to say that this organization w ill be acceptable in any other environment. A criterion is necessary in this model because the sense in which self-organization is used here, is that of parts unconnected changing to parts connected. In such a case, there is no guarantee that the organizations formed w ill be acceptable, and hence the necessity to have some measuring stick against which they can be tested. (d) A random generator. This produces the constituent which Von Foerster (1960) refers to as noise, and which Ashby (1952b) calls random information. It is best illustrated by the way it operates in nature. Here the noise arises from random gene mutations, which are a key to new creations in the evolutionary process. If such mutations were not present, the evolutionary system would m erely settle down to a dynamic equilibrium, and new creations would cease. Ashby s homeostat (Ashby, 1952a) uses random information in the sense that the various feedback factors are adjusted at random, if the system ever becom es unstable.

23 SELF-ORGANIZING SYSTEMS 17 Thus for any p ro cess of self-organization, both o rd er (present in the form of ru les of operation) and noise (from a random generator) are essential constituents. The four factors listed above have been sum m arized by the sim plified model of evolution shown in Figure 3.1. This model shows products being generated on the basis of certain ru les, together with the intervention of a random elem ent. After being tested against the environm ent, som e w ill be retained, and others rejected. Because the products which are retained c a rry within them the ru les for generating new products (in the form of the genes), there is p resen t in effect, a factor which m odifies the existing ru les. This factor is rep resen ted in the model by the block labelled "law for modifying ru le D escription of the Teaching System in Figure 3.2. The system based on the model outlined, is illu strated B riefly, the following are the essen tial features. (a) Store of concepts The set (C, C,..., C.) of concepts to be taught is the 1 ^ 1 first portion of the lesson, and corresponds to the first sub-goal. Sub-goal 2 is then achieved a fte r sub-goal 1, and so on until sub-goal n has been reach ed, which sig n ifies the com pletion of the whole lesson. The c riterio n for the com pletion of each sub-goal is that there should be answ ered, in sequence, a prespecified num ber of the m ost complex type of question in that sub-goal. It is em phasized that the sense in which the word concept is used throughout this chapter is as a single aspect of a skill or lesson to be m astered (the example of section m akes this c le a re r). Corresponding to each concept is an item designed to instru ct o r te st on this p a rtic ular aspect of the m aterial in the lesson. The ordering of the sub-goals in this way is re p re se n t ative of initial stru ctu re which has been stored in the m achine. This can be done on the basis of experience as to which o rd er of arrangem ent is m ost suitable. However, th ere is not as yet any definite ordering of concepts within each sub-goal. This o rd e r ing or stru ctu rin g is developed during an initial stage of interaction with a group of students, which p rep ares the m achine for teaching. This arrangem ent, it is seen, leads to a com prom ise between initial stru ctu re in serted, and stru ctu re developed as interaction proceeds. Such a c o rre c t balance is n ecessary in o rd er that the 'teach er' is not too rigid in behaviour, yet at the sam e tim e has som e constraint on the o rd er in which m aterial should be taught. The grouping of concepts in each sub-goal is so

24

25 SELF-ORGANIZING SYSTEMS 19 arranged that irresp ectiv e of which com bination is selected from the i concepts, a sensible item w ill resu lt from th eir combination. There w ill th erefo re be, ; + p o ssib le com binations,w here n. (b) Random Component is the num ber of ways of choosing x ite m s from Each of the blocks labelled RG in Figure 3.2, is a random generator which (without any further influence), would produce and p resen t item s taken com pletely at random from the inform ation relevant to the sub-goal. This random ness is carried to the extent that the item itself may be a question or an instruction (refer to block, Q or I ). Although a feature of the system is to allow this freedom of presentation of item s in a sub-goal, it is however, advisable to place some constraint on the order of their presentation at the beginning of the interaction. This is achieved by an initial bias ( IB ) on each random generator ( RG ). The relativ e values of the biases placed on these random generators are a ssessed from human experience in teaching that particular subject m atter, and w ill th erefo re be som ew here near their optimum values. For exam ple, it may be known from experience that it is generally better to p resen t C before. In such a case, IB^ and IBri w ill be set so th at the probability of C^ appearing before is enhanced. However, the actual optim ization of all initial biases is carried out during an initial stage of operation, w here the sy stem is allowed to in te ra c t with a group of students. (c) The Student Model A ra th e r sim ple student model was incorporated in this p relim inary developm ent, as shown in Figure As can be seen, the perform ance of each student is assessed and stored in a separate model, which reco rd s his p e rform ance to all concepts in the curriculum, the storage being based on the percentage of co rre ct responses. The perform ance of groups to each concept, is analyzed (after the com pletion of each group) a s indicated by T^, T,, T ^+., i being the num ber of concepts in the sub-goal in question. On a basis of percentage of co rre ct responses, typical statistical analyses m ay be, (see Figure 3.3 ), Tg : Peak occurring at 85% (i. e. m ost students score 85% c o rre c t responses to ). T? : Peak at 62%.

26 20 SELF-ORGANIZING SYSTEMS Figure 3. 3 Typical student e rro r curves.

27 SELF-ORGANIZING SYSTEMS 21 T. : P eak occurring at 73% Such statistical data is used in adjusting the initial b iases IB^, IB^,, IB,, through the long term feedback indicated in Figure O peration of the System The two aspects of m ost in te re st in the operation are: the method of selection of item s during norm al interaction with a student, and the long term adjustm ent of initial b iases, (which is perform ed after a group of students has p a sse d through the lesson). (a) Method of Selection of Item s governed by two factors. The selectio n of an item from the concept sto re is (i) The long te rm perform ance of the group, as incorporated in the setting of the initial biases on the random g en erato rs. (ii) The individual student perform ance as interaction proceeds. This is incorporated by the sh o rt term feedback (see F igure 3.2), which directly b iases the random gen erato rs for making a choice of concept or group of concepts. (Without the bias on the random g en erators from this sh o rt te rm feedback, together with the initial b ias, item s would be issued purely at random ). Thus, item selection is made p rim arily on individual student perform ance, but has also ingredients of group c h a ra c te ristic s, as well as a random component. For exam ple, suppose that on previous group perform ance, it had been found that m ost students experience difficulty if item s incorporating both concepts C and C are presented before item s incorporating C 1 ^ X alone. Then the initial strateg y of the machine would be tow ards presentation of p rio r to and C together ( IB, IB,, IB. achieve this biasing). However, as th ere is a Z X Z 1 random component p resen t, variations from this procedure a re possible, which if successful for any p articu lar student, a re reinforced through the short term feedback. In this way, although item presentation is p artially constrained, sufficient freedom is allowed to cope w ith student behaviours rem oved from the norm. Once the concept or group of concepts has been selected, th is is transform ed to an actual item. (In the actual sim ulation m ade, a sim ple syntax which constructed sentences, w as used). A com parison of student response with c o rre c t response is made, which leads to a weight adjustm ent (through the short te rm feedback) of the random g enerato rs, thereby directly influencing the next item

28 22 SELF-ORGANIZING SYSTEMS presentation. The student's perform ance is also updated after each response by evaluating a new percentage of c o rre c t resp o n ses. A typical rule for weight adjustm ent is to in crease the probability of selecting a concept which has been poorly understood. Other ru les consider the weight adjustm ent to be made to the random generator governing the proportion between questions and instructions. For exam ple, a good perform ance will generally give a bias tow ards a higher frequency of questions, and so proceed through the task m ore quickly, while a p o orer perform ance will lead to the p re sen t ation of m ore item s of instructional value. These ru le s, used to tran sfo rm student response into an appropriate weight adjustm ent, may not be optimum when the m achine is first used (e. g. student e rro rs may be too severely treated by presenting too many item s of instructions when an e rro r o ccurs. Or the rule used may not allow for sufficient rem edial item s to be presented for a certain e rro r). However, such rules can be read ily modified from the experience gained in using the system. The questions presented by the machine may require a constructed response, or a response from various response alternatives on the p art of the student. If the question chosen requires a response of the la tte r t5^pe, the transform ation Tj_ (see Figure 3.2) enables the relevant response alternatives to be evaluated. If an item is chosen which involves n concepts, then in the m ost general case, 2 response alternatives are required in order that a choice from one of these by the student, will give sufficient inform ation as to where the lack of understanding lie s. However, in the course of interaction, the system, having assessed which of these n concepts has been understood, will lim it the num ber of response altern ativ es so that only those which lead to new inform ation about the student are presented. As an exam ple, consider a lesson designed to distinguish green-round, g reen -sq u are, red-round and red-sq u are objects. If the system is satisfied that the student has learned colour, then it need not always p resen t four response alternatives, and in such a case, two a re sufficient. The exact form of T-^ depends on the p a rtic ular lesson being taught. (b) Adjustm ent of Initial B iases When each student of the group has com pleted the lesson, a statistic a l analysis of the group perform ance is made, on the b asis of perform ance to each of the concepts (see Figure 3.2, blocks Tg, T7,, Tg+. ) t O perator T3 then analyzes this statistic a l data, and by m eans of o p erato rs T4 and T^ (which are actually ru le s for weight adjustm ent), the initial biases on the random generators are adjusted. As an exam ple, for the fig u res Tg, Ty, Tg+. quoted p rev io u sly, a typical ru le is to adjust the initial biases so that, (i) The o rd er of presentation of C^, C^, C is m ore likely to be:

29 SELF-ORGANIZING SYSTEMS 23 and (ii) A higher percentage of instructions to questions occurs when C is selected, than when C o r C. is sele c ted. ^ X 1 Again, such ru les need to be modified from experience in using the system. F or exam ple, the setting of T 5 may be such that if le ss than 90% c o rre c t responses are received, a higher frequency of instructions is presented. What this setting should actually be, is a problem in Educational R esearch. As this feedback is made only after a group of students has interacted, it is term ed a long te rm feedback, (as distinct from any adjustm ents which may be made to the system during the course of interaction with any one p a rtic ular student). The long te rm adjustm ent can also be made after each group of 20 or 30 students has taken the lesson Application to a Specific Problem The problem chosen to illu strate operation of the system by a continuous generation of item s, is the apparently sim ple task of teaching to tell the tim e. Only a b rie f outline of the relevant concepts involved in the task is given. (a) On the Im plication of the T erm C oncept The term concept has been used in a variety of ways in the lite ra tu re, and working definitions have appeared. For exam ple, P iaget (1957) considers a concept as an explanatory ru le, or law, by which a relatio n between two or m ore events may be described. (The explanatory ru les need not be classificato ry ). A concept can be rep resen ted by mapping the set of argum ents onto the set of values of the function, and if only the two sets are known, the function might be found by induction. B runer et al (1956) state, T here a re those who argue that a concept, psychologically, is defined by the common elem ents shared by an arra y of objects and that arriving at a concept inductively is much like arriv in g a t a composite photograph by superim posing instances on a common photographic plate until all that is idiosyncratic is washed out and all that is common em erges. A second school of thought holds that a concept is not the common elem ents in an a rra y, but ra th e r is a relational thing, a relationship between constituent p a rt p ro c e sses. We subm it that such a controversy is relatively fru itle ss. We have found it m ore m eaningful to reg ard a concept as a network of sign-significate inferences by which one goes beyond a set of observed c rite ria l p ro p erties exhibited by an object or event to the class identity of the object or event in question, and thence to additional inferences about other unobserved p ro p erties of the object or event. We see an object that is red, shiny, and roundish and infer that it is an apple; we are then enabled to infer further that if it is an apple, it is also edible, juicy, w ill ro t if left unrefrig erated, etc. The working definition of a concept is the network of inferences that are or may be set into play by an act of

30 24 SELF-ORGANIZING SYSTEMS categ o rizatio n. While these and other working definitions are in te re sting and to a degree, inform ative, the task of actually handling inform ation req u ires a som ewhat le ss com plex approach, at least initially, which can sim plify a program m e r s problem in organizing the inform ation. Consequently, it is not intended here to argue on the m e rits of various points of view, but to employ the te rm concept as describing aspects of a skill or lesson to be m astered in a p ractically useful m anner, p articularly to act as building blocks, appropriately in te r-re la te d, in forming higher level concepts. This usage is, in many re sp ects, sim ilar to that employed by other w rite rs. The te st of w hether certain concepts have been grasped by a student is made in te rm s of activities he can perform or problem s he can solve. (b) B asic Concepts in Tim e Teaching The following are some aspects of behaviour to be m astered in the task of learning to tell the tim e. (i) The distinction between the two hands. (ii) The recognition of num bers (iii) The recognition of num bers (iv) (v) (vi) The recognition of a hand pointing to a num ber. The recognition of which clock has a certain hour reading. The recognition of which clock has a certain hour-m inute reading. (There are of course other aspects of understanding involved, which a re considered in m ore d etail at a la te r stage). (c) Syntax for the Form ation of Sentences To c a rry out initial experim ents, the following sim ple stru c tu re illu stra te s the form ation of a variety of sentences, depending on the concepts or com bination of concepts selected by the random g en erato rs, with appropriate biases applied. 1. I This ) clock (W hich) 2. has 3. short),, ( hand long ) Stage X Stage Y 5. r 5 \ ) ( \ 6 and j^a long handj ( at 10 Stage Z 55 12

31 SELF-ORGANIZING SYSTEMS 25 th is exam ple are: The ru les for the form ation of sentences (constraints) in (i) If sh o rt is selected in column 3, then a selection from column 4 is m ade only from the num bers However, if long is selected, then a selection from any of the num bers 12 or 5-55 can be made in column 4. (ii) If sh o rt is selected, the system can form an item up to stage X, Y or Z. But if long is selected in column 3, then the program is such that stage Y is the highest o rder item formed. (The actual choice and construction of ite m s is co n sid ered in (e)(i)), With a sim ple stru ctu re as the above, item s of the following type can be generated: - This clock has a short hand. Which clock has a short hand? (2 items) This clock has a short hand at (24 item s) Which clock has a short hand at * 12? This clock has a long hand at 12. Which clock has a long hand at 12? 5 This clock has a long hand at (2 items) (22 item s) Which clock has a long hand at )10 Which clock has a short hand at ) ) 2 j 1 / 5 ] and a long hand at \ : / j 55 [ I ( 12 1 [ 1 ) 2 and a long hand at / (288 item s)? I12 / 55 12

32 26 SELF-ORGANIZING SYSTEMS Note: In this la tte r case, if the selection of 12 is made by the long hand, so obtaining, fw hich clock has a short hand at 6, and a long hand at 12?", then the program tra n slates this to, "Which clock shows 6 o clock?" The sim ple stru ctu re in this case produces a variety of 338 different item s. (d) C orrelation of the Problem with the G eneral System The relationship of the form ation of item s, to the block diagram of Figure 3.2 is as follows: - (i) Block Q or I' = j t Ms H setting IBq = 0.4 to 0.6 (questions to in stru ctio n s). This is controlled by RG^ with an initial a rb itra ry This a rb itra ry value was evaluated on the a p rio ri b asis of beginning a lesson by presenting, in general, one or two instructions followed by a question, that is, a ratio of 1.5 to 1 (which initial approach to the lesson is varied from group experience). (ii) Block = Concept of length = long short in itial setting favouring presentation of than a single concept. The selection here is controlled by before any presentations involving m ore (iii) Block C = R ecognition of nos, Z Selection h ere is controlled by RG^. In th is c ase, the sy ste m is biased such that C9 alone does not appear (although it can be m odified to to do so), C appears only in conjunction with C, giving item s of C C concept- Z -L JL Z ual content (which re la te to identifying to which of the num bers 1-12, a hand points). (iv) Block C = Recognition of nos O RG^, with an Selection is co ntrolled by RG, with the b ias again set ü so that C alone does not appear. As indicated e a rlie r, item s which are m eaningless u

33 SELF-ORGANIZING SYSTEMS 27 a re not generated, and so no item s with content (which re la te to identify w hich do appear a re, for exam ple, those with content ing to which of the num bers 5-55, the long hand points). are form ed. However, item s (v) Block = Concept of tellin g tim e in hours. Selection is controlled by RG4, with a setting of IB4 such that item s containing C4 are not likely to be issued early in the lesson (although the possibility still exists and if the move is successful, reinforcem ent o ccu rs, so allowing the possibility of the good student passing very quickly through the ta sk ). (vi) Block C_ = Concept of telling the tim e in hours and m inutes. H ere the probability of such item s occurring is co n tro lled by RG5, with a bias on IB5 such that these are least likely to occur early in the lesson. However, it is pointed out that all the initial b iases indicated (although initially set by the program m er), a re subject to m odification from experience with groups, and so can be set at a m ore suitable value. (e) Sim ulation of the System (i) Program m ing F eatures The basic flow diagram of the system is shown in F igure 3. 5, while the method of generation of item s is indicated in Figure 3.4. Figure 3.4 shows the key words which need to be sele c t ed in the form ation of item s. This selection is made by the p a ram eters indicated u s ing the following coding. K = P a ra m e ter for form ation of item s involving C^ (initial bias is KSC ). (The SC term following p a ram eters re fe rs to an initial bias). L = P a ra m e ter for setting a question or an instruction (initial bias is LSC ). MS = P a ra m e ter for form ation of item s containing C2 (initial b ias is MSSC ).

34 28 SELF-ORGANIZING SYSTEMS ML = P a ra m e ter for form ation of item s containing C3 (initial bias is MLSC ). MH = P a ra m e ter for form ation of item s containing C4 (initial bias is M HSC). MF = P a ra m e ter for form ation of item s containing C5 (initial bias is MFSC ). F igure 3.4 shows certain initial biases (set before in t e ra c tio n - for exam ple, the probability of an item of instruction appearing is 0.6, while that of a question is These initial b iases, together with the weight adjustm ent through feedback, assign values of probability to the p a ra m ete rs. (In Figure 3.5, T = True, F = False). As an exam ple, consider that MF has been selected, with the value of L causing a question to be asked, MS indicating to concentrate on num ber 5, and ML indicating to concentrate on num ber 35. Then the item p re sen t ation selected is, "Which clock has a sh o rt hand at 5, and a long hand at 35"? (refer Figure 3.4). The actual weight adjustm ent is achieved by an increm entation of variables for corresponding c o rre c t resp o n ses. For exam ple, to adjust the random generator used as p a rt of the selection m echanism for instructions and questions, an increm entation is made in L. The details for this are as follows: - A random num ber, R = L * RANDF (1.) is g en erated, (FORTRAN CODE). which re su lts in a random num ber between 0 and L (the initial value of L is 20). Then if R-LSC is > 0, a question is chosen. O th erw ise the item presented is an instruction. ( LSC = 12 was the initial bias used, thereby giving a 0.6 probability of instructions). An increm entation in L each tim e a c o rre c t response is received, then in creases the probability of questions (there now being a g re a te r chance of R-LSC > 0 ). The degree of increm entation in L can be varied, which

35 SELF-ORGANIZING SYSTEMS 29 This Figure 3.4 Method of item generatio

36 Begin SELF-ORGANIZING SYSTEMS In itialise Set in itial bias G enerate random num ber Form sentence (see fig. 4.4). P resen t item to student Modify initial biases Com pare Item = 'Q uestion'? Accept response Check response S + 1 Adjust weights on random gen Update statistic a l record Group com plete? All groups com plete? Update store of C i, C o * C C riterio n for completion of ta sk attained? Figure 3.5 Outline of overall operation.

37 SELF-ORGANIZING SYSTEMS 31 in effect is a m odification of the rule for weight adjustm ent in the short term feedback loop. other variables. A sim ilar form of weight adjustm ent is used for the The interaction ceases when a specified num ber (in this exercise chosen between 5 and 20) of the m ost complex questions has been answ ered co rrectly. (ii) Control of the Visual Display by T ransform ation T ^ The following indicates the type of analysis c a rrie d out by T^ in form ing various response alternatives for visual display. A com plete analysis has been made for each question which can be presented, but a sam ple only is presented here to indicate the nature of the transform ations involved, Suppose the item presented is, Which clock has a short hand at (6)? (Such an item presentation involves C-^ and C9, that is, concepts of length, and recognition of num bers the actual num ber of the hour appearing is controlled by C9, which considers the student s perform ance to each of the individual num bers), p erfo rm s the following: - When an instruction such as the above appears, T^ (1) One of the clocks (chosen at random) has placed at 6 (or a fraction p ast the 6, because fractional hours a re also considered). The long hand is set at the corresponding c o rre c t position in relation to this short hand. (2) The second clock is then in co rrectly set, at a position close to the 6 (between 5 and 6), and the long hand set accordingly. The setting of the second clock in this way m akes the selection of the c o rre c t response m ore difficult. (3) Other alternative settings of the second clock face are: sh o rt hand) ; or Long hand between 6 and 7, (which then fixes the position of the The short hand placed at random, with the long hand then placed c o rre ctly in relation to it.

38 32 SELF-ORGANIZING SYSTEMS It can be seen that the choice of the in c o rre c t response alternative is a form of cue inform ation. A choice of one of the above response a lte r natives is made on the sim ple perform ance figure indicated e a rlie r, (iii) P ractic al A spects of Simulation Owing to the inaccessibility of a graphic display unit, response alternatives, such as the above, w ere generated on a standard line p rin ter (IBM # 1403 ). The long hand setting was made to the n earest 5 m inutes, with the sh o rt hand taking up positions either half-way, q u arter way, or th re e -q u a rte r way betw een any two hour-settings. F or initial te sts, and in the absence of suitable com m unication facilities, the experim enter acted as the response m echanism, by playing alternately, ro les of a 'good, m edium, and poor student to test the w orkability of the sy stem. A desirable feature apparent in the interaction was a yery rapid pro g ressio n through the m aterial (with few instructions) in the case of the good student; with a correspondingly slow er p ro gression (with m ore item s of in s truction), in the case of a poorer student, However, certain lim itations w ere apparent, as d iscu ssed in the next section. 3.2,5 D iscussion (1) The system outlined has only a sim ple m em ory, and lim ited capabilities of processing inform ation from student re c o rd s, However, the feature of lim ited learning from experience, does take the system out of the class of purely adaptive system s, It can, perhaps, be com pared with the lower form s of organism, which show a sm all degree of learning from experience (due principally to a lim ited m em ory), as well as adapting to th eir environm ental conditions, The system outlined closely resem b les this type of behaviour, F o r exam ple, (2) C ertain features of self-organization can be noted. (a) D ifferentiation occurs along different pathways, depending on the p articular interaction with the environm ent (that is, adaptation occurs), (b) There is a certain im provem ent in perform ance with experience due to the long term feedback from group analysis, (c) The system is probabilistic, in that it is not possible to define explicitly the next state of the system at any point in tim e. It is pointed out, how ever, th at w ith tim e (as the op eratio n proceeds) the sy stem behaviour becom es

39 SELF-ORGANIZING SYSTEMS 33 m o re and m ore predictable. Although p ro p erties of self-organization can be observed, they are of course at an elem entary level, due m ainly to insufficient com plexity of stru ctu re and a lim ited m em ory to c a rry forw ard useful strateg ies learnt. (3) S im ila ritie s betw een the sy stem developed P ask s adaptive system s (for training of skills), can be noted (Pask, 1958, 1960, 1961). F o r exam ple, (i) P resen tatio n is governed by student perform ance figures, with an em phasis on presentation of item s least well handled; and the participant. (ii) A corresponding m atching o r adaptation of the sy stem to T h ere a re, how ever, basic d ifferen ces, including: (a) A m ore flexible presentation (about a norm) is achieved by inclusion of a random elem ent acting on previously-acquired student behaviour figures. This has the advantage of allowing a very rapid p ro g ress through the lesson by a good student (due to useful m utations which arise). As far as we can ascertain, P ask has not considered adjustm ents on the b asis of group behaviour. (b) No allowance is made in this model for variation of rate of presentation. Pask does include such a feature, which is essen tial for attaining com petence in certain skills. In the system outlined, the em phasis is m ore on ra te of p ro g ress through the lesson concepts, ra th e r than the physical ra te of presentation of item s. (The change of em phasis here is due to the different nature of the task considered). (4) A lim itation of this p articu lar model is that selection of item s is based principally on the individual student s m ost recen t perform ance, and to som e extent, on the in teg rated effect of the group. The deficiency h ere is th at in su fficient consideration is taken of the integrated effect of a student s overall perform ance, (5) It was found in stability studies with the system, that the feedback facto rs used (i. e. the rules for weight adjustm ent ) w ere ra th e r c ritic a l, (e.g, it was possible for the system to over-com pensate by presenting too many item s of a given concept, if there had been a w eakness in this concept e a rlie r). A further cause of such instability is the absence of a m ore general student perform ance figure based on his overall perform ance. (6) A further lim itation of the m em ory is that in storing only a percentage c o rre c t figure, certain vital aspects of student behaviour are never recorded.

40 34 SELF-ORGANIZING SYSTEMS (7) While the system is modelled in a m an an evolutionary p ro cess, there is a difference in that unfavourable presentations (for a p a rtic u la r student) a re not com pletely rem oved, but only have their probability of occurrence reduced, The reaso n for this is that an unfavourable presentation in one environm ent (i.e. fo r one student), may not be so for another, ( cf. Ashby, 1962), It is therefore n ecessary to retain the possibility of such an unfavourable p re sen ta t ion being issued. (8) The behaviour of the system can be likened to a passive netw ork, in that its behaviour is controlled and shaped com pletely by the p articu lar environm ent. In other w ords, the presentation it gives depends on the environm ent in which it o perates, (The system is in fact a function transform ing student behaviour into item presentations), The lim itation here is that the system cannot assum e an active ro le, and do something positive if a student difficulty a rise s, (9) Teaching to tell the tim e, as handled by the teaching system discussed in this chapter, seem s somewhat like the training of a skill, The system outlined appears to be m ore suited to task s which involve the training of sk ills, (e.g, keyboard skills), because of the lim ited extent to which item s can be logically presen ted to teach ta sk s requiring deep understanding. (10) The principle of generating item s in a somewhat random m anner and testing against an environm ent, offers the possibility of generating item s which may not have been p re-selected by the pro g ram m er. To achieve this, a syntax is required which can operate on a set of item p aram eters, so producing sentences, (11) Experim entation with the setting of operators Tq and T 5 offers the possibility for Educational R esearch in the two problem s (among others): (a) The e rro r ra te problem, that is, "Is th ere an optimum e rro r ra te, and if so, what is this r a te? This problem can be investigated by studying perform ances of groups with different threshold values applied to T5. (b) The program m ing problem, that is, "What is the c o rre c t o rd er of presentation of m aterial in a le sso n? " Again, th is problem may be investigated from group studies, with each group assigned to different o p erato rs Tq for influencing the o rd er of presentation on a basis of past student perform ance.

41 SELF-ORGANIZING SYSTEMS , 6 Conclusions The sim ple model presented has been based on constituents of the m echanism of evolution, The m echanism consists of a rule which o rd ers raw m aterial into different stru c tu re s, together with a criterio n of acceptable organization against which the stru ctu re can be tested, This model has been applied in the design of a teaching m achine stru ctu re which organizes its behaviour to suit the p articu lar environm ent in which it operates (that is, a student), The stru ctu re itself is a com prom ise between p re-p ro g ram m ed behaviour, and behaviour learnt in a specialized environm ent, Before the machine is ready to teach, it undergoes a training period by interacting with groups, In the operating cycle, when the machine behaves as a teach er, its behaviour at firs t has a degree of uncertainty, but this is reduced as the m achine - student interaction proceeds. The selection of m aterial by the device is based on a p articular student s m ost recent perform ance, and on the long term integrated p e rform ance of a group of students. This lim ited m em ory reduces the effectiveness of the system in sev eral ways, notably in lim iting the amount of learning from experience. In this resp ect, it resem bles a lower organism. The principle under which the system operates gives ris e to the possibility of generating item s (or strategies) not pre-program m ed before interaction, This kind of system may be useful for re searc h in solving problem s which a rise in mechanized instruction, The above developm ent has highlighted certain essential requirem ents in designing a m ore general purpose system which can be used for a wide variety of task s requiring understanding in their attainm ent, as well as p ractice, 4. FURTHER WORK The sim ple model discussed in the previous chapter has shown various lim itations and suggested lines of approach for further work, The em phasis is on a general stru ctu re which can be shaped by special purpose program s to handle p a rticu lar topics, A great deal of flexibility is introduced in allowing various functions (strateg ies, decision ru les, perform ance crite ria ) as well as new inform ation, to be added at any stage, so perm itting diverse experim ental studies. The approach is generally styled on the activ itie s of a purposive o r e x p e rim entally minded tutor, who experim ents with various strateg ies and decision ru les, presenting his item s with specific goals in mind - this attitude enables appropriate constraints to be added. Several levels of strateg ies, student p a ra m ete rs and decision ru les a re envisaged, together with a well-docum ented inform ation sto re, perm itting the realization of a rich stru c tu re within which the system can be responsive' to student needs and p ecu liarities in a complex m anner, The system may

42 36 FURTHER WORK im prove its teaching perform ance from experience (for exam ple, from groups of students). The general line of approach envisages the handling of the m ultivariable probabilistic system by re fe rrin g to a higher level goal, rule or m easure, and allowing adjustm ent through the feedback of the p aram eters. The problem is approached in the sp irit that w hatever can be devised in the fir s t instance is bound to be modified in the light of further experience, consequently an attem pt must be made to provide an overall stru ctu re, conceived with the expectation th a t this its e lf m ight need little m odification, and the allowing of d e tails, including organization of inform ation, provision of stra teg ies, decision ru les and perfo rm ance c rite ria, to be filled in by the experim enter, who may wish to te st p articu lar learning theories, or discover learning th eo ries by experim entation. Consequently, two im portant com plem entary aspects in this system m ust be separately identified: (a) (b) The System Structure Itself - which allows processing of inform ation to achieve adaptation (of the system to the learn er), optim ization, and allows the m achine to learn to be a b etter 'te a c h e r'. The T ransform ations between inform ation to be im parted (in the student-m achine interactions) and the student p a ra m ete rs. W hereas (a) is reasonably explicit, (b) re la tes to an a re a in which much has yet to be discovered, and indeed it is to provide insight into these are as that has motivated the devising of (a). This c irc u lar relationship between (a) and (b) m akes very apparent the need for both aspects to p ro g ress in an iterative m anner - p ro g ress in one aspect leading to p ro g ress in the other, the net effect resulting in a general advance. The need for an experim ental approach based on all relevant knowledge seem s clear. System C h aracteristics The following are som e of the c h aracte ristic s (already discussed previously) which a re desirable: (i) The system m ust be responsive (i. e. adapt), to a whole range of student c h a ra c te ristic s. Amongst other requirem ents, this n ecessitates an extensive student model stru ctu re, able to represent accurately many aspects of student behaviour. (ii) A general stru ctu re which can handle a variety of topi lesso n s, sim ply by allocating values to various 'item p a ra m e te rs', which then specify actual item s. (iii) A system which models the behaviour of the expert tu experim enting with various strateg ies (choosing favourable approaches), and continually searching for student difficu lties which may a r is e. In th is sen se, the

43 FURTHER WORK 37 system is desired to play an active role in the teaching interaction. (iv) The system should be am enable to ex tern al control, so allow ing experim entation with a variety of strateg ies, decision ru les, perform ance c rite ria, student p a ra m ete rs, and so on, thereby perm itting continual optim ization. (v) T here should be a stru ctu re which allows self-optim ization, once certain d esired teaching objectives are specified, (vi) The system should allow the learn er to ask questions and seek inform ation which he requires. (vii) A ppropriate principles of self-organization, whereby constraints and action capabilities tire devised to ensure appropriate functioning, should be applied, Such a general system should be an aid in areas of Educational R esearch, and consequently should allow extensive m onitoring of its operation and inform ation flow. 5. CONCLUSIONS It is our view that to try to form alize the output of a human teacher (for example by form alizing theories of learning ) and then to employ such form alization in a mechanized teaching system - as essentially is being attem pted in some work - is a practically fru itless approach, We consider that the m achinery of teaching' should be studied, not the output of th is m ach in ery '. That is, we should try to discover those constraints and action capabilities which, when incorporated in a selforganizing teaching- system, lend the system to a stable situation, in terpreted as a goal, whereby a student learn s because of the interactions with the system, The system should be capable of continually increasing its behaviour re p e rto ire by le arn ing. The discussions and elem entary work reported in this paper have been addressed to the problem of eventually realizing such a system. 6. REFERENCES AMAREL, S,,(1966), "On the M echanization of C reative P ro cesse s", IEEE Spectrum, Vol. 3, No. 4, pp ASHBY, W.R., (1952a), "Design for a B rain", London; Edition R evised, 1960, Chapman & Hall, Second ASHBY, W,R., (1952b), "Can a M echanical Chess P la y e r Outplay its D esig n er?" B ritish Jo u rn al for the Philosophy of Science, Vol, 3, pp

44 38 REFEREN CES ASHBY, W.R.,( ), "P rin c ip le s of the Self-O rganizing System ", in Von F o e rs te r, H. & Zopf, J r., G.W., E d ito rs, "P rin c ip le s of S elf-o rganization", Oxford: P erg am o n P r e s s, pp BEER, S., (1967), "D ecision and C ontrol", John Wiley: London and New Y ork. BITZER, D.L., HICKS, B.L., JOHNSON, R. L., and LYMAN, E lisabeth R., (1967), "The P lato System: C u rre n t R esearc h and D evelopm ents", IEEE T ra n sactio n s on Human F a c to rs in E lectro n ics, Vol, H F E -8, No. 2, June, pp BRUNER, J. S., GOODNOW, J.J., and AUSTIN, G. A., (1956), "A Study of Thinking", New York- Jo h n W iley. CRUTCHFIELD, R. S., (1965), "Instructing the Individual in C reativ e Thinking" in "New A pproaches to Individualizing In stru ctio n ", E ducational T esting Service, P rin ceto n. GOLDBERG, A. L., TONDOW, M., and BUSH NELL, D.D.,( ), "The C om puter in E ducation - Some E xam ples", P ro c. IEEE, Vol. 54, No. 12, D ecem ber, pp KANEFF, S.,(1967), "M echanization in T eaching-l earning In te ra c tio n s", Jo u rn al of the A ssociation for P ro g ram m ed In stru ctio n, Vol. 2, No. 2, O ctober, pp MINSKY, M.,(1961), "Steps Tow ard A rtificial Intelligence", P ro c. IRE, V o l.49, No.l, Jan u ary, pp 8-30, PASK, G.,( ), "A utom atic Teaching T echniques", B ritish C om m unications and E le c tro n ic s, Vol. 4, A pril, pp PASK, G., (1958a), "T eaching M achines, P ro ceed in g s of Second C onference of In ternational A ssociation of C ybern etics, N am ur, pp PASK, G., (1958b), "E lectro n ic K eyboard T eaching M achines", E ducation and C om m erce, Vol, 24, pp 16-26, PASK, G., (1960a), "The T eaching M achine as a C ontrol M echanism ", T ra n sa c tio n s of the Society of In stru m en t Technology, Vol. 12, No. 2, June, pp PASK, G., (1960b), "A daptive T eaching w ith A daptive M achines", in L um sdaine, A. A., and G la ser, R., "T eaching M achines and P ro g ram m ed L earning: A Source Book", W ashington D. C.: N ational Education A ssociation, U. S., pp

45 REFERENCES 39 PASK, G.,(1961), "An Approach to C ybernetics, London: Hutchinson. PASK, G., (1962), "In teractio n Between a Group of Subjects and an Adaptive Automaton to Produce a Self-Organizing System for D ecision Making", in Yovits, M. C., Jacobi, G.T., and Goldstein, E.D., E ditors, "Self- Organizing System s ", W ashington D. C.: Spartan P r e s s. PASK, G.,(1965), "Teaching as a C ontrol-engineering P ro c e ss", Control, January, pp 6-11, F ebruary, pp 69-72, M arch, pp , A pril, pp PASK, G., (1967), "The Control of Learning in Small Subsystem s of a Program m ed Educational System ", IEEE T ransactions on Human F acto rs in E lectronics, Vol. H FE-8, No. 2, June, pp PASK, G., and LEWIS, B. N., (1962), "An Adaptive Automaton for Teaching Small G roups", P erceptual Motor Skills, Vol. 14, pp PIAGET, J.,( ), "Logic and Psychology", New York- B asic Books. RATH, G.J.,( ), "Com puter Teaching ", IEEE T ransactions on Human F acto rs in E lectronics, Vol. H FE-8, No. 2, June, p 59. SOLOMONOFF, R.J.,( ), "Some Recent Work in A rtificial Intelligence", P ro c. IE EE, Vol. 54, No. 12, D ecem ber, pp STOLUROW, L. M.,(1961), "Teaching by M achine", C o-o p erativ e R ese arch Monograph, No. 6, W ashington D. C.: U. S. D epartm ent of Health, Education and W elfare. VLADCOFF, A. N., (1968), "Application of C ertain P rin cip les of Self-O rganization to Teaching System S tructures", The A ustralian National U niversity, D epartm ent of Engineering P hysics Publication E P -T 4, May. VON FOERSTER, H.,(1960), "On Self-Organizing System s and T heir Environm ents", in Yovits, M. C. and Cam eron, S., E ditors, "Self-O rganizing System s", New Y ork Pergam on P re s s, pp

46 R I P ublicatio n s by D epartm ent of E ngineering P h y sics No. A uthor T itle F ir s t P ublished R e -issu e d E P -R R 1 H ibbard, L. U. E P -R R 2 C arden, P.O. E P -R R.3 M arsh all, R. A. E P -R R 4 M arsh all, R. A. C em enting R otors fo r the C a n b e rra H om opolar G e n e ra to r L im itatio n s of R ate of R ise of P u lse C u rre n t Im posed by Skin E ffect in R otors The D esign of B ru sh es for the C a n b e rra H om opolar G e n e ra to r The E lectro ly tic V ariable R e sista n c e T e st Load/Sw itch fo r the C a n b e rra H om opolar G e n e ra to r May, 1959 A p ril, 1967 Sept., 1962 A pril, 1967 Jan., 1964 A pril, 1967 May, 1964 A p ril, 1967 E P -R R 5 Inall, E.K. The M ark II Coupling and R otor C en terin g R e g iste rs fo r the C a n b e rra Hom opol a r G e n e ra to r Oct., 1964 A pril, 1967 E P -R R 6 Inall, E.K. A Review of the S pecificatio n s and D esign of the M ark II Oil L ubricated T h ru st and C entering B earin g s of the C an b erra H om opolar G en erato r Nov., 1964 A pril, 1967 E P -R R 7 Inall, E.K. P ro v in g T e sts on the C a n b e rra H om opolar G ene r a to r w ith the Two R otors C onnected in S eries F e b., 1966 A pril, 1967 E P -R R 8 B rady, T. W. N otes on Speed B alance C o n tro ls on the C an b erra H om opolar G en erato r M ar.,1966 A pril, 1967 E P -R R 9 Inall, E.K. T e sts on the C a n b e rra H om opoiai G en erato r A rran g ed to Supply the 5 M egaw att M agnet May, 1966 A p ril, 1967

47 P u b lic atio n s by D epartm ent of E ngineering P h y sics (C o n t.) R2 No. A uthor T itle E P -R R 10 B rady, T.W. A Study of the P erfo rm an c e of the 1000 kw M otor Gene r a to r Set Supplying the C a n b e rra H om opolar G ene r a to r Field F ir s t Published June, 1966 R e -issu e d A pril, 1967 E P -R R 11 M acleod, I.D.G. In stru m en tatio n and C ontrol O c t., 1966 of the C an b erra H om opolar G e n e ra to r by O n-l ine Com p u te r A pril, 1967 E P -R R 12 C arden, P.O. M echanical S tre s s e s in an J a n., 1967 Infinitely Long Homogeneous B itte r Solenoid with Finite E x tern al Field E P -R R 13 M acleod, I.D.G. A Survey of Isolation A m pli- Feb., 1967 fie r C irc u its E P -R R 14 Inall, E.K. The M ark III Coupling fo r Feb., 1967 the R o to rs of the C an b erra H om opolar G en erato r E P -R R 15 B ydder, E. L. On the Integ ratio n of M ar.,1967 Liley, B.S. "B o ltzm an n -L ik e" C ollision In te g ra ls E P -R R 16 Vance, C. F. Sim ple T h y risto r C irc u its M ar.,1967 to P u ls e - F ir e Ignitrons fo r C ap acito r D ischarge E P -R R 17 B ydder, E. L. On the E valuation of E lastic Sept.,1967 and In ela stic C ollision F r e quencies fo r H ydrogenic-l ike P la sm a s E P -R R 18 Stebbens, A. W ard, H. The D esign of B ru sh es for the H om opolar G en erato r at The A u stra lia n N ational U niversity M ar.,1964 S e p t., 1967

48 Publications by D epartm ent of Engineering P hysics (C ent.) R3 No. F irst Author T itle Published EP-R R 19 Carden, P. O. F eatures of the High Field Magnet L aboratory at the A ustralian National U niversity, C anberra J a n., 1967 R e-issued EP-RR 20 Kaneff, S. Vladcoff, A. N. Self-O rganizing teaching System s D e c., 1968 EP-RR 21 Vance, C. F. M icrowave Pow er tra n s m issio n Ratio: Its Use in Estim ating Electron Density EP-RR 22 Smith, B. D. An Investigation of A rcing in the E lectrolytic Sw itch/ T est Load Used with the Homopolar G enerator EP-RR 23 Inall, E.K. Use of the Homopolar G enerator to Pow er Xenon D ischarge Tubes and som e A ssociated Switching P roblem s EP-RR 24 Carden, P. O. Pivoted H ydrostatic B earing Pads for the C anberra Homopolar G enerator Feb.,1969 Oct.,1969 M ar.,1969 D e c.,1969 EP-RR 25 Carden, P. O. W helan, R. E. Instrum entation for the A ustralian National U niversity 300 kilogauss Experim ental Magnet Dec.,1969

49 I Copies of this and other Publications (see list inside) of the Department of Engineering Physics may be obtained from: Price: $ A 1.00 Copyright N ote: The Australian National University Press, P.O. Box 4, Canberra, A.C.T., Australia. Reproduction of this publication in whole or in part is not allowed without prior permission. It may however be quoted as a reference. National Library of Australia Card Number and ISBN