Patrick Suppes. Computer-Assisted Instruction. Derick Unwin & Ray McAleese (Eds.), The Encyclopaedia of Educational Media Communications and Technology (2nd Edition), New York: Greenwood Press, 1988, pp. 107-116. 107

COMPUTER-ASSISTED INSTRUCTION

COMPUTER-AIDED LEARNING. Synonym for computer-assistedinstruction.Fromtime to timeatgxnpts have been made to add precision to the various combinations of words possible in this context, but current usageis very mucha matter of individual preference. 1 See Computer Nomenclature. COMPUTER-ASSISTED(AIDED)INSTRUCTION (LEARNING) (CAI, CAL).This term usually refers to , systems providing on-line direct interactive instruction, ’ testing, and prescription. The dialogue may be based on many different strategies rangingfrom drill and practice in arithmetic and spelling, through Socratic inquisitory investigations, to ‘learner-controlled discovery’ ’ of scientific or literarytruths. See Computer-AssistedInstruction; Computer Nomenclature. COMPUTER-ASSISTED INSTRUCTION. INTRODUCTION The objective of this entry is to survey currentactivities in computer-assisted instruction (CAI). In a rapidly developing technology the literature is not as well defined as in the case of more theoretical matters, nor is it in easily accessiblejournals. Many of the items that I have referenced have appeared only as reports, with limited circulation; in some casesit has been difficultto establish the date the report was issued. , Before discussingthe substantive developments in CAI, there is one general issuethat is worth elaboration. It is the questionof whether or not computers and related forms of high technology constitute a new restraint on individualityand human freedom. There are several points I would like to make about the possible restraints that widespread use of computer technology might impose on education. The first is that the history of education is a history of the introduction new of technologies, which at each stage have been the subject pf criticism. Already in Plato’s dialogue Phaedrus, the Use of written records rather than oral methods of inStkction wascriticized by Socrates andtheSophists. p e introduction of books marked a departure from the personalized methodsof recitation that were widespread important for hundreds of years until this century. ,- SS schooling is perhaps the most important technochangeineducation in the last onehundredyears. -If is too easy to forget that aslate as 1870 only 2 percent af,the high school-age population in the United States :completed high school.A large proportionof the society ,w= illiterate; in most other parts of the world the pop.FaGOn was even less educated. Moreover, the absence -Pf mass schooling in many parts of the world as late as -~ is a well-documented fact. The efforts to provide .

mass schooling and the uniformity of that schooling in its basic structure throughout the world are among the most striking social facts of the twentieth century. It is easy to claim that with ihis uniform socialization of the primary school, especially, a universal form of indoctrination has been put in place. There is something to this criticism, for the similarity of curriculum and methods of instruction throughoutthe world is surprising,and no doubt in the process unique featuresof different cultures have been reduced in importance, if not obliterated. My second pointis that the increasing useof computer technology can provide a new level of uniformity and standardization. Many features sf such standardization are of course to be regarded as positive insofar as the level of instruction is raised. There are also opportunities for individualizationof instruction that willbe discussed more thoroughly in later sections, butmy real point is that thenew technology does not constitutein any serious sense a new or formidable threat to human individuality and freedom. Over a hundred years ago in his famous essay On Liberty, John Stuart Mill described how the source of difficulty is to be found elsewhere, in the lack of concern for freedom by most persons and in the tendencies of the great variety of political institutions to seriously restrain freedom, if not repress it. We do not yet realize the full potential of each individual in our society, but one of the best uses we can make of high technology in the coming decades is to reduce the personal tyranny of one individual over another, especially wherever that tyranny depends upon ignorance. The past record of such tyranny in almost all societies is too easily ignored bymanywhoseemoverlyanxiousaboutthe future. CAI IN ELEMENTARY AND SECONDARY EDUCATION In this section, some examples of CAI atthe stage of research and development for elementary and secondary schools, and also some examplesof commercial products that are fairly widely distributed, are considered. As in the case of the sections that follow, there is no attempt to survey in a detailed way the wide range of activities taking place at many different institutions. It is common knowledge that there is a variety of computer activity in secondary schools throughout the United States andin other parts of the world. A good deal of this activity is not strictly tobe classed as computer-assisted instruction, however, but rather as use of the computer in teaching programming, in problem solving, or in elementary courses in data processing oriented towardjobsinindustry. At the public school level the largest number of students participating in CAI are those taking courses of-

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fered by Computer Curriculum Corporation(CCC), with which I am associated. At the time this entry waswritten, more than 400,000 students were using theCCC courses onan essentially daily basis. This usage is spread throughout the United States; most of the ’students are disadvantaged or handicapped. The main effort at CCC has been in the development of drill-and-practice courses that supplement regular instruction in the basic skills, especially in reading and mathematics. The courses offered in 1986 by CCC are listed in Table 3, with grade levels shown after each course. The two most widely used curricula are Mathematics Skills, Grades 1-8, and Reading for Comprehension, Grades 3-6.

Strands Strategy. The strands instructional strategy plays a key role in many of these courses, and its explanation is essential to a description of the CCC curricula. A strand represents one content area within a curriculum. For example, a division strand, a decimal strand, and an equation strand areincluded in theMathematics Skills curriculum. Each strandis a string of related items whose difficulty progresses from easy to difficult. A computer program keeps records of the student’s position and performance separately for every strand. By comparing a student’s record of performance on the material in one strand with a preset performance criterion, the program determines whether the student needs more practice at the same level of difficultywithin the strand, should move back to an easier level for remedial work, or has mastered the current concept and can move ahead to more difficult work. Then the program automatically adjusts the student’s position within the strand. The process of evaluation and adjustment applies to all strands and is continuous throughout each student’s interaction with a curriculum. Evenly spaced gradations in the difficulty of the material allow positions within a strand to be matched to school grade placements by tenths of a year. Grade placement in a specific subject area can then be determined by examining a student’s position in the strand representing that area. Since performance in each strand is recorded and evaluated separately, the student may have a different grade placement in every strand of a curriculum. Teacher’s reports, available as part of each curriculum, record progress by showing the student’s grade placement in each strand at the time of the report. In a curriculum based on thestrands instructional strategy, a normal lesson consists of a mixture of exercises from different strands. Each time an item from a particular curriculum is to be presented, a computer program randomly selects the strand from which it will draw the exercise. Random selection of strands ensures that the

Table 3 CAI Courses Offered by Computer Curriculum Corporation

MATHEMATICS Math Concepts, K-3 Math Skills, 1-8 Problem Solving, 3-6 Math Enrichment Modules, 7-Adult Introduction to Logic, 7-Adult Introduction to Algebra, 9-Adult READING Audio Reading, K-Z Basic Reading, 2 Reading, 3-6 Reading for Comprehension, Revised, 3-6 Practical Reading Skills, 5-8 Critical Reading Skills, 7-Adult Adult Reading Skills, Adult LANGUAGE SKILLS Spelling Skills, 2-8 Language Arts Strands, 3-6 Writing: Process and Skills, 6-9 Fundamentals of English, 7-Adult English as a Second Language, 4-Adult Adult Language Skills I, Adult Adult Language Skills II, Adult OTHER Survival Skills, 9-Adult GED Preparation, 9-Adult Keyboard Skills, 4-Adult COMPUTER EDUCATION Computer Literacy, Elementary, 4-6 Computer Literacy, 7-Adult Programming with MICROHOST BASIC, 9-Adult Introduction to Computer Science with Pascal, 10-Adult Introduction to Data Processing with COBOL , l0 -Adul t Introduction to UNIX Operating Systems, 10-Adult COURSES BY TELEPHONE DIAL-A-DRILL DIAL-A-DRILL DIAL-A-DRILL DIAL-A-DRILL 5-Adult

Mental Arithmetic, 1-8 Spelling, 2-8 Reading, 1-4 Practical Reading,

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COMPUTER-ASSISTED INSTRUCTION

Table 4 The Strands in Mathepatics Skills, Grades 1-8

Name

Strand

1 2 3

4 5 6 7 8

9 10 l1 l2

Number Concepts Addition Subtraction Equations Measurement Metric Measurement Applications Multiplication Division Fractions Decimals Problem Solving

student will receivea mixture of different types of items instead of a series of similar items. Each curriculum also provides for rapid gross adjustment of position in all the strands as the student first begins work in the course. Students who perform very well at their entering grade levels are moved up in halfyear steps until they reach more challenging levels. Students who perform poorly are moved down in half-year steps. This adjustment of overall grade levelensures that students are appropriately placed in the curriculum and is in effect only during a student’s first ten sessions. I describe briefly three of the courses. Mathematics Skills, Grades 1-8. This course contains twelve strands, or content areas. Table4 lists the strands in the mathematics curriculum. The curriculum begins at the first-grade level and extends through grade level ?.O. ’.Each strand is organizedinto equivalence classes, or sets of exercises of similar number propertiesand struc$re. During each CAI session in mathematics, students *ive exercises from all thestrands that contain equivSence classes appropriate to their grade levels. Students notgiven anequalnumber of exercisesfromall Stands. The program adjusts the proportionof exercises %komeach strand tomatch the proportion of exercises &wering that concept in an average textbook. The curriculum materialin Mathematics Skills, Grades is not prestored but takes the form of algorithms that ‘Use radom-number techniquestogenerateexercises. a particular equivalence class is selected, a progratm generates the numerical value used in the exercise, _

L

produces the required format information for the presentation ofthe exercise, and calculates the correct response for comparison with student input. As a result, the arrangement of the lesson and the actual exercises presented differ betweenstudentsatthesameleveland between lessons for a student who remainsat a constant grade placement for several lessons. Students are ordinarily at terminals about ten minutes a day, during which time they usually work in excess of 30 exercises. Thus, a student following such a regime for the entire school year of 180 days works more than 5,000 exercises. Reading for Comprehension, Grades 3-6. This curriculum consists of reading-practice items designed to improvethestudent’sskillsinsixareas:word attack, vocabulary, literal comprehension of sentence structure, interpretation of written material, passage comprehension, and study skills. It contains material for four years ofwork at grade levels 3, 4, 5, and 6 as wellas supplementary remedia1 material that extends downward to grade level 2.5. Special features of the course include the following: optional mouse to select answers, automatic analysis of student spelling or capitalization errors, selected tutorial messages in response to contenterrors, advanced vocabularyandcomprehensionexercisesat a seventh-grade level, and capability to print out individualized worksheets to provide additional exercises. Language Arts. This curriculum stresses usage instead of grammar and presents very few grammatical terms. It is divided into two courses, LanguageArtsStrands and Language ArtsTopics. Both courses cover the same general subject areas, but their structures are different. Language ArtsStrands uses a strands structureto provide highly individualized mixed drills (Table 5 ) . In Language Arts Topics the entire class receives lessons on a topic assigned by the teacher. Evaluation. The three curriculums just described have had extensive evaluation bymany different evaluation groups, including individual school systems. More than 40 such studies are reported in Macken and Suppes(1976 EVALUATION) and Poulsen and Macken (1978 EVALUATION). A detailed mathematical study of individual studenttrajectoriesisfound in Suppes, Macken,and Zanotti ( 1978 EVALUATION).

CAI IN POSTSECONDARY EDUCATION In this section some salient examples of CAI at universities, community colleges, or other postsecondary institutions are examined to provide a sense of the conceptual variety of the work that is being undertaken. There has

COMPUTER-ASSISTED INSTRULm-

110 Table 5 The Strands in LanguageArts Skills, Grades 3-6

Content Strand

F G

H

J

Principal Parts of Verbs Verb Usage Subject-Verb Agreement Pronoun Usage Contractions, Possessives, and Negatives Modif íers Sentence Structure Mechanics

been no attempt to survey the wide range of activities taking place at many different institutions. Undergraduate Physics at Irvine. Perhaps thebestknown current example of the use of computers for instruction in college-level physics is the workdone by Alfred Bork and his associates at the University of California-Irvine. Bork has describedthis activity ina number of publications. In describing the objectives of the kind of work he has done, I draw especially upon Bork (1978 DESCRIPTION OF METHODOLOGY), in which he describes the way in which Physics 3A was taught at Irvine in the fall of 1976 to approximately300 students. The students had a choice of using a standard textbook or making extensive useofvarious computer aids. In addition, the course was self-paced; students were urged to make a deliberate choice of a pacing strategy. The course was designed asa mastery-based coursealong the lines ofwhat is called the KellerPlan (q.v.) or PSI (Personalized System of Instruction [q.v.}), in which the course is organized into a number of modules. Each module is presumed to be developed around a carefully stated set of objectives, and at the end of each module, students aregiven a test; until a satisfactorylevel of performance is achieved, they are not permitted to move to the next module. Bork describes six different ways in which the computer was used in the course. All students had computer accounts, and during the ten weeks of the term the average student used about 2.5 hours of time per week. Thus the total time involved with the approximately 300 students was about 7,500 hours in the term. Before turning to the various roles of the computer described by Bork, I would like to emphasize that, having had a personal opportunity to see some of his material, I found

theuse of graphic displays especially impressive-*aa certainly a portent of the way computer graphics wi1I-e used in the future for the teaching of physics. The first role of the computer was simply as a corn+ munication device between student and instructor. instructor, Bork, could send a message to each studè@ in the class, and the students couldindividually send' messages to him. He says that typically he wouldanswer his computer mail once a day, usually in the evening' from a terminal at his home. The second use of the computer was individual programming by the student as an aid to learning physics. The computer language APL was available to the students, and students who chose the computer track spent one of the eight units in learning APL. One reason for the choice ofAPL was the fact that the computer system at Irvine had available efficient graphic capability within APL. The third roleof the computer was as a tutorial device helping students to learn the basic physics to which they were being exposed. Bork properly emphasizes that tutorial programs are to be contrasted with large lecture courses in which the student must essentially playa passive role. The tutorial programs requiredongoing dynamic interaction with the student, and the development of material was tailored to the needs and capacities of the students in a way that is never possible in a large lecture setting. The fourth roleof the computer was as an aid to building physical intuition. In this case, extensive use was made of the graphic capabilities available on the Tektronix terminals used in the course. The fifth use of the computer was in giving the tests associated with each of the modules. Because of the way PSI courses are organized, alternate forms of each test were required in case the student hadtotakethetest several times before demonstrating mastery of the particular module. During the ten weeks of the course in the fall of 1976, over 10,OOO on-line tests were administered.Studentsperceivedthistest-givingroleas the most significant computer aspect of the course. The sixth use of the computer was in providing a course management system. As would be expected, allof the results of the on-line tests were recorded; programs were also developed toprovide students access to their records and to provide information to the instructor.

m&

Logic atStanford. Since 1972, theintroductory logic course at Stanford has beentaughtduringtheregular academic year entirely as a CAI course. Various aspects of the course have been described in a number of publb lications.Here I draw on SuppesandSheehan(198 DESCRIPTION OF METHODOLOGY).

,

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l

Basic data on the course are given in Table 6. There are 29 lessons that formthe core of the course. The number of exercises in each lesson, the mean time to complete the lesson, and the cumulative time are shown, as well as a brief description of the content of ;ach lesson. The cumulative times are shown in parentheses after the times for the individuallessons. The data are for the

academic year 1979-1980, but the data for 1985-1986 are similar. It should be emphasized that many of the exercises involve derivations of some complexity, and a strong feature of the program is its ability to accept any derivation falling within the general framework of the rules of inference available at that point in the course. For example, prior to lesson 409, students are required

Table 6 Mean Time and Cumulative Mean Time for 1979-1980

Lesson

Number of exercises

40 1 402

19 18

403 404 405

14

406 407 408

16 12

x4 19

23

Student’s time in hours .62 .95

($2) (1.57)

.M (2.21) 1.08 (3.29) 3.45 (6.74) 1.71 (8.45) 2.22 (10.67) 12.94 (23.61)

2.36 -56 .56 .50

409 410 41 1 412 413 414

24 13

7 7

(25.97) (26.53) (27.09) (27.59) -39 (27.98) 9 5 (28.93)

415

11

1-90 (30.83)

416 417

4

-96 (3 1.79) 2.24 (34.03)

418 4 19 420 42 1 422 423

8 8 8 14 28

424 425

31 22

3.64 (47.50)

426

21

1.57 (51.97)

427 428

17 23

4.28 (56.25) 6.06 (62.31)

429

40

4.01 (66.32)

7 7

7

12

1.50 (35.53) 1-53 (37.08) 1.18 (38.26) .68 (38.94) 1.94 (40.88) 2.98(43.86)

2.90 (50.40)

Content Introduction to logic Semantics for sententiallogic (truth tables) Syntax of sentential logic, parentheses Derivations, rules of inference, validity Working premises, dependencies, and conditional proof Further rules of inference New and deribcd rules of inference Further rules and indirectproof procedure Validity, counterexample, tautology Integer arithmetic Two rules about equality More rules aboutequality T h e replace q u a k rules Practice using equality in integer arithmetic The commutative axiom for integer arithmetic The associative axiom T w o axioms and a definition for commutative groups Theorems 1-3 for commutative groups Theorems 4-7 for commutative groups Noncommutauve groups Finding axioms exercises Symbolizing sentential arguments Symbolizing English sentences in predicate logic Inferences involving quantifiers Quantifiers: restrictions and derived rules Using interpretations toshow arguments invalid Quantifiers and interpretation Consistency of premises and independence of axioms The logic of identity (and sorted theories)

saurce: P. Suppes and J. Sheehan, “CAI Course In Loglc.” In Unlverslty-Level Computer-Asslsted Instructron at Stanford, 1968-1980, ed p SUpPes. Stanford, Calif.: Stanford University, Institute for Mathematical Studies ln the Social Sclences, 1981, p. 194

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to use particular rules of sentential inference, and only in lesson 409 are they introduced to a general tautological rule of inference. Lesson 410, it may be noted, is devoted to integer arithmetic, which would often not be included in a course in logic. The reason for it i n the present context is that this is the theory within which interpretations are given in the course to show that arguments are invalid, premises consistent, or axiomsindependent. In a non-computer-based course, such interpretations to show invalidity and so forth are ordinarily given informally and without explicit proof of their correctness. In the present framework, the students are asked to prove that their interpretations are correct, and to do this we have fixed upon the domainof integer arithmetic as providing a simple model. It should be noted that students taking a Pass level require on the average about 75 hours of connect time at a computer terminal, which, at present,may be about the highestof any standard computer-basedcourse in the country. Moreover,forstudentswho go on totake a letter grade of A or B, additional work is required, depending upon the particular sequence of applications they take. For example, those choosing the lesson sequence on social decision theory will require an average of somewhat more than 20 additional hours. Those whotake the lesson sequence on Boolean algebra and qualitative foundations of probability will require somewhat less connect time, but they do more proofs that benefit from reflection about strategic lines of attack, which need not necessarily occur while signed on at a terminal. Also, the number of hours of connect time just discussed does not include the finding-axioms exercises but only the introduction to them in lesson 421. These exercises present the student with a number of statements about a particular theory, for example, statements about elementary properties of betweenness on the line. The student is asked to select not more than a certain number of the statements, for example, five or six, as axioms, and prove the remainder as theorems. This kind of exercise has been advocated by a number of mathematical educators.

Set Theory at Stanford. The curriculum of the course in set theory is classical; it follows closely the content of my earlier book (Suppes, 1960 BACKGROUND READING). The course is based on the Zermelo-Fraenkel axioms for settheory.Thefirstchapterdealswiththe historical context of the axioms; the next chapter deals with relations and functions. The course then concentrates on finite and infinite sets, the theory of cardinal numbers, the theory of ordinal numbers, and the axiom of choice. Students who take the course for a Pass stop proving theorems at the endof the chapter on the theory

COMPUTER-ASSISTED INSTRUCTION

of cardinal numbers. Those who go on for a letter grade of A or B must prove theorems in the theory of ordinal numbersandstandard results involvingtheaxiom of choice. Although the conceptualcontent of the courseis classical, the problemswe have facedin making ita complete CAI course are not. The logic course just described is in many ways deceptive as a model of how to approach mathematically oriented courses, for the proofs can be formal and the theory of what is required is, although intricate, relativelystraightforwardcomparedwith the problems of having reasonable rules of proof to match thestandardinformal style of proofsto befoundin courses at the levelof difficulty of the one in set theory. The problems of developing powerful informal mathematical proceduresfor matching the qualityof informal proofs found in textbooks are examined in some detail later andconsequentlywillnot be consideredfurther here. There are about 500 theorems that make up the core of thecurriculum. The studentsareasked toprove a subset of these theorems. The number of students is ordinarily between eight and twelve term, per and therefore individual student lists are easily constructed. Students ordinarily prove between40 and 50 theorems, depending uponthegradelevelthey are seeking inthecourse. Details of the courseare reported in Suppes and Sheehan (1981a DESCRIPTION OF METHODOLOGY).

Computer Programming.Various international efforts at computer-aided teachingof programming havebeen documented in theliterature. For example, Santos and Millan (1975BACKGROUNDREADING)describesuch efforts in Brazil;BallabenandErcoli(1975 BACKGROUND READING) describe the work ofan Italian team; and Su and Emam(1975 BACKGROUND READING) describe a CAI approach to teaching software systems on a minicomputer.Extensiveefforts inCAI to teach BASIC have been undertaken by my colleagues at Stanford (Barr, Beard, and Atkinson, 1974, 1975; Lorton and Cole, 1981 BACKGROUND READING). A joint effort at Stanford, undocumented in the literature, was also made to teach the initial portion ofthecoursein LISP byCAI methods. On the other hand, there is a surprisingly small number of courses in computer programming that are taught entirelyby CAI and that have anything like the total number of individual student hours atterminalscomparabletothelogiccoursedescribed above. The use of CAI for total instruction in computer programming is not nearly as developed as would have been anticipated ten years ago. Forezgn Languages. Work at Stanford in the 1960s began in the teaching of Slavic languages and was conducted

COMPUTER-ASSISTED INSTRUCTION

primarily by JosephVanCampen (198la, 19818b BACKGROUND READING) and his colleague Richard Schupbach (1981 BACKGROUND READING). CAI efforts at Stanford have been devoted to a number of other languages, in particular an extensive effort in French, German, Mandarin Chinese, and Armenian.

CURRENT RESEARCH

][nthis section I analyze someof the main areasof current researchmostsignificant for CAI. The first concerns natural-language processing; the second, the use of digital speech; andthe third, informal mathematical procedures. Natural-Language Processing. Without doubt, the problems of either accepting natural-language input or producing acceptable informal natural-language output constitute some of the mostsevere constraints on current operational efforts and research in CAI. It is fair to say that there have beenno dramatic breakthroughs inthe problems of processing English, as either input or output, during the period covered by this entry. Moreover, these problems are not simply a focus of research in CAI but have wider implications for many diverse uses of computers. No doubt the current intensive efforts at developing and marketing sophisticated word processors for office use will have, in the next decade, an impact on the level of natural-language processing that canbe implemented efficiently and atreasonable cost in hardware that is just becoming available. All thesame, during the period coveredby this entry, the difficultiesof adequately inputting or outputting natural language by a program run by a computer, no matter howpowerful, have become apparenttoall whoare seriouslyengaged inthinking about or trying todo something about the problem.From a theoretical standpoint, linguists have come to realize that syntax alone cannot be a satisfactory conceptual basis for languageprocessing,andmodel-theoreticsemanticists represented by logiciansandphilosophers have eome to recognize how far any simple model-theoretic view of the semantics of natural language is from the iIWicate and subtle details of actual informal usage. In gddition, the romantic hopeof some computer scientists that the theoretical problems can be bypassed by complicatedprogramsthatdonot have a well-articulated theoretical basis in syntax andsemantics, as well as pragÍ h i s , has also been dashed. Perhaps the most instructive thing thatcan be said is that we are much more aware Of the difficulties now than we were at the beginningof

-$e 1970s. Uses #Digital Speech. The importance of spoken speech

b instruction has been recognized from time immemo*d-The earliest articulate and sophisticated advocacy

j-.

113 of the importanceof spoken dialogueas the highest form of instructionis in Plato’s dialogue Phaedrus, where Socrates criticizes the impersonal and limited character of written records as a means of instruction. The experiments on the use of audio for CAI at the Institute for Mathematical Studies in the Social Sciences at Stanford are among the most extensive in the world and because of my own close association with them can most easily be reported here. However, I emphasize that the use of audio in CAI is the focus of continued workat other centers as well. Research on digital speech has been a central and dominant theme of research on CAI in the institute for many years. After several years of attempting to use audiotapes of various design, beginning in the later 1960s the institute concentratedondigital speech, forthree good reasons. First, it was too difficult to get adequate reliability from tape devices that were to be usedon a roundthe-clock basis. Second, it was too difficult to get tape devices that provided sufficiently fast seek times to retrieve any one of a large number of required messages. Third, itwasultimatelyunsatisfactorytousewithout exceptionprestoredmessages.Ordinaryinstruction by tutors and teachers does not take place in this fashion. Sentences are constructed on the spot, contingent upon the requirements of the moment. In similar fashion, a really satisfactory computer-driven speech device must be able to synthesize messages as required. No tape devices on the market then or now are able to meet this requirement. Even the promising videodiscsthat will be available in the near future will most certainly not have seek times and transfer rates sufficiently fast to permit the synthesis of messages from stored words, syllables, or phonemes. Thetechnicalaspects of the institute’s researchon digital speech will not be reported here. Twelve articles reporting the work in depth are published in Suppes ( 198l AUDIO RESEARCH). Informal Mathematical Proofs. Sincetheearly1960s there has been an interest in the development of proof checkers and interactive theorem provers. The initial interest was no doubt simply concern with the question of demonstrating that an application in this area was possible, even if not practical. My own interest in the subject began early in 1963, almost as soon as our work in CAI in the Institute for Mathematical Studies in the Social Sciences began. In order to take account of limited machine capacity, the early workconcentratedondeveloping a logiccourse for elementary-schoolstudents (Suppes, 1972 DESCRIPTIONOF METHODOLOGY). In the late 1960stheinterestbegantofocus on more powerful proof checkers that could be used for teaching

,

COMPUTER-ASSISTED INSTRUCTION

114 logic at the college level. Since 1972 the introductory logic course, at Stanford has been taught entirely at computer terminals. Beginning in the early 1970s we had the idea of developing a more powerful interactive tfieorem prover that could be used for proofsthat were not from thestandpoint of the use put into explicit logical form. In the development of this theorem prover we concentrated on axiomatic set theory, as a subject close to logic but still one with proofs ordinarily given informally. In fact, itis generally recognized that it would not be practical or feasible to ask students or instructors to produce proofs that satisfied explicit formal criteria. I want to be clear on the point that no one, or practically no one, has ever suggested that the formal proofs characterized explicitly and completely in mathematical logic were ever meant to be a practical approach to the giving of proofs in any nontrivial mathematical domain. The characterization of proofs in this formal way is meant to serve an entirely different purpose, namely, that of providing a setting for studying proofs as mathematical objects. Since 1974 the undergraduate course in axiomatic set theory at Stanford has been taught entirely at computerbased terminals. The effort at producing the programs, especially the programs embodying the interactive theorem prover in its various versions, has been the result of the extended work of many people. The main improvements on the system since 1975 are the use of more natural and more powerful facilities replacing simply the use of a resolution theorem prover earlier, more student aids such as an extended HELP system, and the use of more informal English in the summarization of proofs. These new facilities are illustrated by the output of the informal summary of review of a proof for the Hausdorff maximal principle. It 1s a classical exercise required of students in the course to prove that the Hausdorff maximal pnnciple 1s equivalent to the axiom of choice. What is given here is the proof of the maximal pnnciple using Zorn’s lemma, which has already been derived earlier from the axiom of choice. Hausdorff Maximal Principle: If A is a family of sets then every cham contained in A 1s contained ln some maximal chain ln A. Proof. Assume (1) A 1s a family of sets Assume (2) C 1s a chain and C 2 A Abbreviate:

{B: B 1s a cham and C 2 B and B 2 A) by- C!chns

By Zorn’s lemma, (3) C!chns has a maximal element Let B be such that (4) B is a maximal element of C!chns

Hence

(5) B is a chain and C 2 B and, B 2 A It follows that,

(6) B is a maximal chain in A Therefore,

(7) C is contained in some maximal chain in A

This summarized proof would not be much shorter written in ordinary textbook fashion. It does not show the use of the more powerful inference procedures, which are deleted in the proof summarization, but the original interactive version generated by the student did make use of these stronger rules. THE FUTURE It would be foolhardy to make detailed quantitative predictions about CAI usage in the years ahead. The current developments in computers are moving at too fast a pace to permit a forecast to be made of instructional activities that involve computers ten years from now. However, without attempting a detailed quantitative forecast it is still possible to say some things about the future that are probably correct and that, when not correct, may be interesting because of the kinds of problems they implicitly involve. l . It is evident that the continued development of more powerful hardware for less money will have a decided impact on usage. It is reasonable to anticipate that by 1990 there will be widespread use of CAI in schools and colleges in the United States, and a rapidly accelerating pattern of development in other parts of the world. 2. By the year 2000 it is reasonable to predict a substantial use of home CAI. Advanced delivery systems will still be in the process of being put in place, but it may well be that stand-alone personal computers will be widely enough distributed and powerful enough by then to support a variety of educational activities in the home. At this point,the technical problems of getting such instructional instrumentation into the home do not seem as complicated and asdifficult as organizing the logistical and bureaucratic effort of course production and accreditation procedures. Extensive research on home instruction in the last 50 years shows clearly enough that one of the central problems is providing clear methods of accreditation for the work done. There IS, I think, no reason to believe that this situation will change radically because computers are being used for instruction rather

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than the simpler means of the past. It will still remain of central importance to the student who is working at home to have well-defined methods of accreditation and a well-defined institutionalstructure within which to conduct his instructionalactivities, even though theyare centered in the home. There has been a recent increasing movement to offer television courses in community colleges and to reduce drastically the number of times the student is required to come to the campus. There are many reasons to believe that a similar kind of model will be effective in institutionalizing and accrediting homebased instructionof the interactivesort that CAI methods can provide. 3. It is likely that videodiscs or similar devices will offer a variety of programming possibilities that are not yet available for CAI. Butif videodisc courses are to have anything like the finished-production qualities of educational films or television, thecostswill be substantial, and it is not yet clear how those costs can be recovered. To give some idea of the magnitude ofthe matter, we may take as a very conservative estimate in 1986 dollars that the production of educational films costs a thousand dollars per minute. This means that the costs of ten courses, each with 50 hours of instruction, would be approximately $30 million. There is as yet no market toencourageinvestorstoconsiderseriouslyinvesting capital funds in these amounts. No doubt, as good, reliable videodisc systems or their technological equivalents become available, courses will be produced, but there will Ge a continuing problem about the production of high-qualitymaterialsbecause of thehighcapital costs. 4. Each of the areas reviewedin the Current Research section should have major developments in the next decade. It would indeed be disappointing ifby 1995 fairly freenatural-languageprocessing inlimitedareas of knowledge were not possible. By then, the critical question may turn out to be how to do it efficiently rather than the question now of how to do it at all. Also, computers which are mainly silent should begin to be noisily talking “creatures’ ’ by 1995 and certainly very much so by 2000. It is true that not all uses of computers have a natural place for spokenspeech, but many do, and moreover, as such speech becomes easily available, it is reasonable to anticipate that auxiliary functions at least will depend upon spoken messages. In any case, the central use of spoken language in instruction is scarcely a debatable issue, and it is conservative to predict that computer-generated speech will be one of the significant CAI efforts in the decade ahead. - The matter of informalmathematicalprocedures, or rich procedures of a more general sort for mathematics md science instruction, is a narrower and more sharply

focused topic than that of either natural-language processing or spoken speech, but the implicationsfor teaching of the availability of such procedures are important. By theyear 2000, thekind of role that is played by calculators in elementary arithmetical calculations should beplayedby computers on a very general basis in all kinds of symbolic calculations or in giving the kinds of mathematical proofs now expected of undergraduates in a wide variety of courses. I also predict that the number of people who make use of such symbolic calculations ormathematicalproofswill continue to increasedramatically. Oneway of making sucha prediction dramatic would be to hold that the number of people a hundred years from now who use such procedures will stand in relation to the number now as the number who have taken a course in some kind of symbolic mathematics (algebra or geometry, for example) in the 1970s stand in relation to the number who took sucha course in the 1870s. The increase will probably notbe this dramatic, but it should be quite impressive all the same, as the penetration of science and technology into all phases of our lives, including our intellectual conception of the world we live in, continues. 5. Finally, I come to my last remark about thefuture. As speech-recognition research, which I have not previously mentioned in this entry, begins to make serious progress of the sort that some of the recentwork reported indicates maybe possible, we should have bythe year 2000, orshortlythereafter,CAIcoursesthathavethe features that Socrates thought so desirable so long ago. What is said in Plato’s dialogue Phaedrus about teaching should be true in the twenty-first century, but now the intimate dialogue between student and tutor will be conducted witha sophisticatedcomputer tutor. The computer tutor will be able to talk to the student at great length and will at leastbe able to accept and to recognize limited responses by the student. As Phaedrussaysinthe dialogue named after him, what we should aspire to is “the living word of knowledge which has a soul, and of which the written word is properly no more than an image. ”

Patrick Suppes

REFERENCE

Audio Research Suppes, P., ed. (198 1) University-Level Computer-Asszsted Instruction at Stanford: 1968-1980. Stanford, Calif.: Stanford University, Institute for Mathematical Studles in the Social Sciences.

Background Reading Ballaben, G . and Ercoli, P. (1975) “Computer-Aided Teaching of Assembler Programming.” In Computers zn educatzon,

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ed. O. Lecarme and R. Lewis. Amsterdam: IFIP, NorthHolland, pp. 217-22 l . Barr, A., Beard, M., and Atkinson, R. C. (1974) A Rationale and Description of the BASIC Instructional Program, Technical Report 228, Psychology and Education Series. Stanford, Calif.: Stanford University, Institute for Mathematical Studies in the Social Sciences. .(l 975) ‘‘Information Networksfor CAI Curriculums.’’ In Computers in Education, ed. O. Lecarme and R. Lewis. Amsterdam: IFIP, North-Holland, pp 477-482. Lorton, P. and Cole, P. (1981) “Computer-Assisted Instruction Computer in Programming: SIMPER, LOGO, and BASIC, 1968-1970.” In University-Level Computer-Assisted Instruction at Stanford: 1968-1980, ed. P. Suppes. Stanford, Calif.; Stanford University, Institute for Mathematical Studies in the Social Sciences, pp. 841-876. Santos, S. M.dosand Millan, M. R. (1975) “A System for TeachingProgrammingbyMeansof a BrazilianMinicomputer.” In Computers in Education, ed. O. Lecarme and R. Lewis. Amsterdam: IFIP, North-Holland, pp.2 1 1216 Schupbach, R. (1981)“Computer-AssistedInstructionfor a Course in the History of theRussian Literary Language.” In Unrversity-LevelComputer-Assisted Instruction at Stanford: 1968-1980, ed. P. Suppes. Stanford, Calif.: Stanford university, Institute for Mathematical Studies in the Social Sciences, pp. 657-664. Su, S.Y.W. andEmam,A. E. (1975) “TeachingSoftware Systems on a Minicomputer: A CAI Approach.” In Computers in Educatton, ed. O. Lecarme and R. Lewis. Amsterdam: IFIP, North-Holland, pp. 223-229. Suppes, P. (1960)Axiomatic Set Theory. New York: Van Nostrand. Slightly rev. ed. New York: Dover, 1972. Van Campen, J . (1981a) “A Computer-Assisted Course in Russian.’’ In University-Level Computer-Assisted InstructionatStanfurd: 1968-1 980, ed. P. Suppes. Stanford, Calif.: StanfordUniversity,InstituteforMathematical Studies in the Social Sciences, pp. 603-646. . (1981b) “Computer-Generated Dnlls in Second-LanguageInstruction. ’ ’ In Universrty-Level Computer-Asslsted Instruction at Stanford: 1968-1980, ed. P. Suppes Stanford, Calif.: Stanford University, Institute for Mathematical Studies in the Social Sciences, pp. 647-655.

Description of Methodology Bork, A ( 1978)“Computers,Education,andtheFuture of Educational Institutions. ’ In Computing in College and Untversrty: 1978 and Beyond. Gerard P. Weeg Memorial Conference. Iowa Clty: University of Iowa, p. l 19. Suppes, P. (1972)“Computer-AssistedInstruction at Stanford. In Man andComputer. Proceedings of International conference, Bordeaux, 1970. Basel: Karger, pp. 298-330. Suppes, P. and Sheehan, J. (198 1 a) “CAI Course in Axiomatic In University-Level Computer-Assisted SetTheory. Instructzun at Stanford: 1968-1980, ed. P. Suppes. Stanford, Calif.; Stanford University, Institute for Mathematical Studies in the Social Sciences, pp. 3-80. .(1981b) “CAI Course In Loglc.” In Universrty-Level ”

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Computer-Assisted Instruction at Stanford: 1968-1980, ed. P. Suppes. Stanford, Calif.: Stanford University, Institute for Mathematical Studies in the Social Sciences, pp. 193-226.

Evaluation Macken, E. and Suppes, P. (l 976) ‘‘Evaluation Studies of CCC Elementary-School Curriculums, 1971- 1975. CCC Educational Studies 1: 1-37. Poulsen, G. and Macken, E. (1978) Evaluation Studies ofCCC Elementary Curriculums, 1975-1977. Palo Alto, Calif.: Computer Curriculum Corporation. Suppes, P., Macken, E., and Zanotti, M. (1978) “The Role ofGlobalPsychologicalModelsinInstructionalTechnology. In Advances in Instructional Psychology, vol. l , ed. R. Glaser. Hillsdale, N.J.: Erlbaum, pp. 229-259. ”

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