COMPUTER-ASSISTED INSTRUCTION 107

COMPUTER-AIDED LEARNING. Synonym for computer-assisted instruction. From time to time at- gxnpts have been made to add precision to the various combinations of words possible in this context, but cur- rent usage is very much a 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 ranging from drill and practice in arithmetic and spelling, through Socratic inquisitory investigations, to ‘learner-controlled discovery’ ’ of sci- entific or literary truths. See Computer-Assisted In- struction; Computer Nomenclature.

COMPUTER-ASSISTED INSTRUCTION.

INTRODUCTION

The objective of this entry is to survey current activities in computer-assisted instruction (CAI). In a rapidly de- veloping technology the literature is not as well defined as in the case of more theoretical matters, nor is it in easily accessible journals. Many of the items that I have referenced have appeared only as reports, with limited circulation; in some cases it has been difficult to establish the date the report was issued. , Before discussing the substantive developments in CAI, there is one general issue that is worth elaboration. It is the question of whether or not computers and related forms of high technology constitute a new restraint on individuality and human freedom. There are several points I would like to make about the possible restraints that widespread use of computer technology might im- pose on education. The first is that the history of edu- cation is a history of the introduction of new 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 in- Stkction was criticized by Socrates and the Sophists. p e introduction of books marked a departure from the personalized methods of recitation that were widespread

important for hundreds of years until this century. SS schooling is perhaps the most important techno- . change in education in the last one hundred years. -If is too easy to forget that as late as 1870 only 2 percent af,the high school-age population in the United States :completed high school. A large proportion of 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 indoc- trination has been put in place. There is something to this criticism, for the similarity of curriculum and meth- ods of instruction throughout the world is surprising, and no doubt in the process unique features of different cul- tures have been reduced in importance, if not obliterated.

My second point is that the increasing use of 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 individualization of instruction that will be discussed more thoroughly in later sections, but my real point is that the new technology does not constitute in 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 ten- dencies 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 per- sonal 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 by many who seem overly anxious about the future.

CAI IN ELEMENTARY AND SECONDARY EDUCATION

In this section, some examples of CAI at the stage of research and development for elementary and secondary schools, and also some examples of 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 and in other parts of the world. A good deal of this activity is not strictly to be 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 toward jobs in in- dustry.

At the public school level the largest number of stu- dents participating in CAI are those taking courses of-

108

fered by Computer Curriculum Corporation (CCC), with which I am associated. At the time this entry was written, more than 400,000 students were using the CCC courses on an 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 in-

’ struction 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 Math- ematics Skills, Grades 1-8, and Reading for Compre- hension, 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 ex- ample, a division strand, a decimal strand, and an equa- tion strand are included in the Mathematics Skills curriculum. Each strand is a string of related items whose difficulty progresses from easy to difficult. A computer program keeps records of the student’s position and per- formance 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 difficulty within 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 ma- terial allow positions within a strand to be matched to school grade placements by tenths of a year. Grade place- ment in a specific subject area can then be determined by examining a student’s position in the strand repre- senting 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 curric- ulum. Teacher’s reports, available as part of each cur- riculum, record progress by showing the student’s grade placement in each strand at the time of the report.

In a curriculum based on the strands instructional strat- egy, a normal lesson consists of a mixture of exercises from different strands. Each time an item from a partic- ular 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,

Practical Reading Skills, 5-8 Critical Reading Skills, 7-Adult Adult Reading Skills, Adult

3-6

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,

Adult Language Skills I, Adult Adult Language Skills II, Adult

4-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

Introduction to Data Processing with

Introduction to UNIX Operating Systems,

Pascal, 10-Adult

COBOL , l0 -Adul t

10-Adult

COURSES BY TELEPHONE

DIAL-A-DRILL Mental Arithmetic, 1-8 DIAL-A-DRILL Spelling, 2-8 DIAL-A-DRILL Reading, 1-4 DIAL-A-DRILL Practical Reading,

5-Adult

COMPUTER-ASSISTED INSTRUCTION 109

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

Strand Name

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 receive a mixture of different types of items instead of a series of similar items.

Each curriculum also provides for rapid gross adjust- ment 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 half- year steps until they reach more challenging levels. Stu- dents who perform poorly are moved down in half-year steps. This adjustment of overall grade level ensures 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. Table 4 lists the strands in the mathematics curriculum. The curriculum begins at the first-grade level and extends through grade level ?.O.

_ L ’.Each strand is organized into equivalence classes, or sets of exercises of similar number properties and struc- $re. During each CAI session in mathematics, students *ive exercises from all the strands that contain equiv- Sence classes appropriate to their grade levels. Students

not given an equal number of exercises from all Stands. The program adjusts the proportion of exercises %kom each strand to match the proportion of exercises &wering that concept in an average textbook.

The curriculum material in Mathematics Skills, Grades is not prestored but takes the form of algorithms that

‘Use radom-number techniques to generate exercises. a particular equivalence class is selected, a pro-

gratm generates the numerical value used in the exercise,

produces the required format information for the presen- tation of the exercise, and calculates the correct response for comparison with student input. As a result, the ar- rangement of the lesson and the actual exercises pre- sented differ between students at the same level and between lessons for a student who remains at 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 curric- ulum consists of reading-practice items designed to im- prove the student’s skills in six areas: word attack, vocabulary, literal comprehension of sentence structure, interpretation of written material, passage comprehen- sion, and study skills. It contains material for four years of work at grade levels 3, 4, 5, and 6 as well as sup- plementary 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 content errors, advanced vocab- ulary and comprehension exercises at a seventh-grade level, and capability to print out individualized work- sheets 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, Language Arts Strands and Language Arts Topics. Both courses cover the same general subject areas, but their structures are different. Language Arts Strands uses a strands structure to 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 by many 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 EVAL- UATION). A detailed mathematical study of individual student trajectories is found in Suppes, Macken, and Zanotti ( 1978 EVALUATION).

CAI IN POSTSECONDARY EDUCATION

In this section some salient examples of CAI at univers- ities, community colleges, or other postsecondary insti- tutions are examined to provide a sense of the conceptual variety of the work that is being undertaken. There has

110 COMPUTER-ASSISTED INSTRULm-

Table 5 The Strands in Language Arts Skills, Grades 3-6

Strand Content J

F G H

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 the best- known current example of the use of computers for in- struction in college-level physics is the work done by Alfred Bork and his associates at the University of Cal- ifornia-Irvine. Bork has described this activity in a num- ber 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 approximately 300 students. The students had a choice of using a standard textbook or making extensive use of various 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 as a mastery-based course along the lines of what is called the Keller Plan (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 are given a test; until a satisfactory level of performance is achieved, they are not permitted to move to the next module.

Bork describes six different ways in which the com- puter was used in the course. All students had computer accounts, and during the ten weeks of the term the av- erage 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 turn- ing to the various roles of the computer described by Bork, I would like to emphasize that, having had a per- sonal opportunity to see some of his material, I found

the use 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. m& instructor, Bork, could send a message to each studè@ in the class, and the students could individually send' messages to him. He says that typically he would answer his computer mail once a day, usually in the evening' from a terminal at his home.

The second use of the computer was individual pro- gramming by the student as an aid to learning physics. The computer language APL was available to the stu- dents, and students who chose the computer track spent one of the eight units in learning APL. One reason for the choice of APL was the fact that the computer system at Irvine had available efficient graphic capability within APL.

The third role of the computer was as a tutorial device helping students to learn the basic physics to which they were being exposed. Bork properly emphasizes that tu- torial programs are to be contrasted with large lecture courses in which the student must essentially play a pas- sive role. The tutorial programs required ongoing dy- namic 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 role of the computer was as an aid to build- ing physical intuition. In this case, extensive use was made of the graphic capabilities available on the Tektro- nix 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 had to take the test several times before demonstrating mastery of the par- ticular module. During the ten weeks of the course in the fall of 1976, over 10,OOO on-line tests were admin- istered. Students perceived this test-giving role as 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, all of the results of the on-line tests were recorded; programs were also developed to provide students access to their records and to provide information to the instructor.

Logic at Stanford. Since 1972, the introductory logic course at Stanford has been taught during the regular academic year entirely as a CAI course. Various aspects of the course have been described in a number of pub- lications. Here I draw on Suppes and Sheehan (198 lb , DESCRIPTION OF METHODOLOGY).

COMPUTER-ASSISTED INSTRUCTION 111

Basic data on the course are given in Table 6. There are 29 lessons that form the core of the course. The number of exercises in each lesson, the mean time to

l 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 individual lessons. The data are for the

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

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

Student’s

Lesson exercises in hours Number of time

Content

40 1 402

403 404 405

406 407 408

409 410 41 1 412 413 414

415

416 417

418 4 19 420 42 1 422 423

424 425

426

427 428

429

19 18

14 x4 19

16 12 23

24 13 7 7 7 7

11

4 7

8 8

12 8

14 28

31 22

21

17 23

40

.62 ($2)

.95 (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 (25.97) -56 (26.53) .56 (27.09) .50 (27.59) -39 (27.98) 9 5 (28.93)

1-90 (30.83)

-96 (3 1.79) 2.24 (34.03)

1.50 (35.53) 1-53 (37.08) 1.18 (38.26) .68 (38.94)

1.94 (40.88) 2.98 (43.86)

3.64 (47.50) 2.90 (50.40)

1.57 (51.97)

4.28 (56.25) 6.06 (62.31)

4.01 (66.32)

Introduction to logic Semantics for sentential logic (truth

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 indirect proof

Validity, counterexample, tautology Integer arithmetic Two rules about equality More rules about equality The replace q u a k rules Practice using equality in integer

The commutative axiom for integer

The associative axiom T w o axioms and a definition for

Theorems 1-3 for commutative groups Theorems 4-7 for commutative groups Noncommutauve groups Finding axioms exercises Symbolizing sentential arguments Symbolizing English sentences in

Inferences involving quantifiers Quantifiers: restrictions and derived

Using interpretations to show arguments

Quantifiers and interpretation Consistency of premises and

independence of axioms The logic of identity (and sorted

theories)

tables)

procedure

arithmetic

arithmetic

commutative groups

predicate logic

rules

invalid

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

112 COMPUTER-ASSISTED INSTRUCTION

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 interpre- tations are given in the course to show that arguments are invalid, premises consistent, or axioms independent. In a non-computer-based course, such interpretations to show invalidity and so forth are ordinarily given infor- mally 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 domain of integer arithmetic as pro- viding 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 highest of any standard computer-based course in the country. Moreover, for students who go on to take a letter grade of A or B, additional work is required, de- pending upon the particular sequence of applications they take. For example, those choosing the lesson sequence on social decision theory will require an average of some- what more than 20 additional hours. Those who take the lesson sequence on Boolean algebra and qualitative foun- dations 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 dis- cussed does not include the finding-axioms exercises but only the introduction to them in lesson 421. These ex- ercises 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 ex- ercise 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 READ- ING). The course is based on the Zermelo-Fraenkel ax- ioms for set theory. The first chapter deals with the historical context of the axioms; the next chapter deals with relations and functions. The course then concen- trates 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 end of the chapter on the theory

of cardinal numbers. Those who go on for a letter grade of A or B must prove theorems in the theory of ordinal numbers and standard results involving the axiom of choice.

Although the conceptual content of the course is clas- sical, the problems we have faced in making it a 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, relatively straightforward compared with the problems of having reasonable rules of proof to match the standard informal style of proofs to be found in courses at the level of difficulty of the one in set theory.

The problems of developing powerful informal math- ematical procedures for matching the quality of informal proofs found in textbooks are examined in some detail later and consequently will not be considered further here.

There are about 500 theorems that make up the core of the curriculum. The students are asked to prove a subset of these theorems. The number of students is or- dinarily between eight and twelve per term, and therefore individual student lists are easily constructed. Students ordinarily prove between 40 and 50 theorems, depending upon the grade level they are seeking in the course. Details of the course are reported in Suppes and Sheehan (1 98 1 a DESCRIPTION OF METHODOLOGY).

Computer Programming. Various international efforts at computer-aided teaching of programming have been doc- umented in the literature. For example, Santos and Millan (1975 BACKGROUND READING) describe such ef- forts in Brazil; Ballaben and Ercoli (1975 BACK- GROUND READING) describe the work of an Italian team; and Su and Emam (1 975 BACKGROUND READ- ING) describe a CAI approach to teaching software sys- tems on a minicomputer. Extensive efforts in CAI to teach BASIC have been undertaken by my colleagues at Stanford (Barr, Beard, and Atkinson, 1974, 1975; Lorton and Cole, 198 1 BACKGROUND READING). A joint effort at Stanford, undocumented in the literature, was also made to teach the initial portion of the course in LISP by CAI methods. On the other hand, there is a surprisingly small number of courses in computer pro- gramming that are taught entirely by CAI and that have anything like the total number of individual student hours at terminals comparable to the logic course described 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 113

primarily by Joseph Van Campen (198 la, 1981 8b BACKGROUND READING) and his colleague Richard Schupbach (1981 BACKGROUND READING). CAI ef- forts 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

][n this section I analyze some of the main areas of current research most significant for CAI. The first concerns natural-language processing; the second, the use of dig- ital speech; and the third, informal mathematical pro- cedures.

Natural-Language Processing. Without doubt, the prob- lems of either accepting natural-language input or pro- ducing acceptable informal natural-language output constitute some of the most severe constraints on current operational efforts and research in CAI. It is fair to say that there have been no dramatic breakthroughs in the 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 com- puters. No doubt the current intensive efforts at devel- oping and marketing sophisticated word processors for office use will have, in the next decade, an impact on the level of natural-language processing that can be im- plemented efficiently and at reasonable cost in hardware that is just becoming available. All the same, during the period covered by this entry, the difficulties of adequately inputting or outputting natural language by a program run by a computer, no matter how powerful, have become apparent to all who are seriously engaged in thinking about or trying to do something about the problem. From a theoretical standpoint, linguists have come to realize that syntax alone cannot be a satisfactory conceptual basis for language processing, and model-theoretic semanti- cists represented by logicians and philosophers 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 hope of some computer scientists that the theoretical problems can be bypassed by com- plicated programs that do not have a well-articulated theoretical basis in syntax and semantics, as well as prag- Í h i s , has also been dashed. Perhaps the most instruc- tive thing that can be said is that we are much more aware Of the difficulties now than we were at the beginning of -$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-.

of the importance of spoken dialogue as the highest form of instruction is in Plato’s dialogue Phaedrus, where Socrates criticizes the impersonal and limited character of written records as a means of instruction. The exper- iments 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 work at other centers as well.

Research on digital speech has been a central and dom- inant 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 in- stitute concentrated on digital speech, for three good reasons. First, it was too difficult to get adequate relia- bility from tape devices that were to be used on a round- the-clock basis. Second, it was too difficult to get tape devices that provided sufficiently fast seek times to re- trieve any one of a large number of required messages. Third, it was ultimately unsatisfactory to use without exception prestored messages. Ordinary instruction 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 de- vices on the market then or now are able to meet this requirement. Even the promising videodiscs that 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.

The technical aspects of the institute’s research on digital speech will not be reported here. Twelve articles reporting the work in depth are published in Suppes ( 198 l AUDIO RESEARCH).

Informal Mathematical Proofs. Since the early 1960s there has been an interest in the development of proof checkers and interactive theorem provers. The initial in- terest was no doubt simply concern with the question of demonstrating that an application in this area was pos- sible, 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 ma- chine capacity, the early work concentrated on devel- oping a logic course for elementary-school students (Suppes, 1972 DESCRIPTION OF METHODOLOGY). In the late 1960s the interest began to focus on more ,

powerful proof checkers that could be used for teaching

114 COMPUTER-ASSISTED INSTRUCTION

logic at the college level. Since 1972 the introductory logic course, at Stanford has been taught entirely at com- puter terminals.

Beginning in the early 1970s we had the idea of de- veloping a more powerful interactive tfieorem prover that could be used for proofs that were not from the standpoint of the use put into explicit logical form. In the devel- opment of this theorem prover we concentrated on axi- omatic set theory, as a subject close to logic but still one with proofs ordinarily given informally. In fact, it is 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 computer- based terminals. The effort at producing the programs, especially the programs embodying the interactive theo- rem prover in its various versions, has been the result of the extended work of many people. The main improve- ments 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 max- imal 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 writ- ten 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 pre- dictions 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 im- plicitly 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 sub- stantial 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 as difficult as organizing the logistical and bureaucratic effort of course production and accre- ditation procedures. Extensive research on home instruc- tion 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

COMPUTER-ASSISTED INSTRUCTION 115

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 institutional structure within which to con- duct his instructional activities, even though they are centered in the home. There has been a recent increasing movement to offer television courses in community col- leges 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 home- based instruction of the interactive sort 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. But if videodisc courses are to have anything like the finished-production qualities of educational films or television, the costs will be sub- stantial, and it is not yet clear how those costs can be recovered. To give some idea of the magnitude of the 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 to encourage investors to consider seriously investing capital funds in these amounts. No doubt, as good, re- liable videodisc systems or their technological equiva- lents become available, courses will be produced, but there will Ge a continuing problem about the production of high-quality materials because of the high capital costs.

4. Each of the areas reviewed in the Current Research section should have major developments in the next dec- ade. It would indeed be disappointing if by 1995 fairly free natural-language processing in limited areas of knowledge were not possible. By then, the critical ques- tion may turn out to be how to do it efficiently rather than the question now of how to do it at all. Also, com- puters 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 spoken speech, but many do, and more- over, as such speech becomes easily available, it is rea- sonable 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 de- batable issue, and it is conservative to predict that com- puter-generated speech will be one of the significant CAI efforts in the decade ahead. - The matter of informal mathematical procedures, 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 pro- cessing or spoken speech, but the implications for teach- ing of the availability of such procedures are important. By the year 2000, the kind of role that is played by calculators in elementary arithmetical calculations should be played by 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 or mathematical proofs will continue to increase dra- matically. One way of making such a 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 such a course in the 1870s. The increase will probably not be this dramatic, but it should be quite impressive all the same, as the penetration of science and technology into all phases of our lives, in- cluding our intellectual conception of the world we live in, continues.

5. Finally, I come to my last remark about the future. As speech-recognition research, which I have not pre- viously mentioned in this entry, begins to make serious progress of the sort that some of the recent work reported indicates may be possible, we should have by the year 2000, or shortly thereafter, CAI courses that have the 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 con- ducted with a sophisticated computer tutor. The computer tutor will be able to talk to the student at great length and will at least be able to accept and to recognize limited responses by the student.

As Phaedrus says in the dialogue named after him, what we should aspire to is “the living word of knowl- edge 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 In-

struction at Stanford: 1968-1980. Stanford, Calif.: Stan- ford 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,

1 l6 COMPUTER-ASSISTED LEARNING

ed. O. Lecarme and R. Lewis. Amsterdam: IFIP, North- Holland, pp. 2 17-22 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 Math- ematical Studies in the Social Sciences.

. (l 975) ‘ ‘Information Networks for 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 in Computer Programming: SIMPER, LOGO, and BASIC, 1968-1970.” In University-Level Computer-As- sisted Instruction at Stanford: 1968-1980, ed. P. Suppes. Stanford, Calif.; Stanford University, Institute for Math- ematical Studies in the Social Sciences, pp. 841-876.

Santos, S. M. dos and Millan, M. R. (1975) “A System for Teaching Programming by Means of a Brazilian Mini- computer.” In Computers in Education, ed. O. Lecarme and R. Lewis. Amsterdam: IFIP, North-Holland, pp. 2 1 1 - 216

Schupbach, R. (1981) “Computer-Assisted Instruction for a Course in the History of the Russian Literary Language.” In Unrversity-Level Computer-Assisted Instruction at Stan- ford: 1968-1980, ed. P. Suppes. Stanford, Calif.: Stan- ford university, Institute for Mathematical Studies in the Social Sciences, pp. 657-664.

Su, S.Y.W. and Emam, A. E. (1975) “Teaching Software Systems on a Minicomputer: A CAI Approach.” In Com- puters in Educatton, ed. O. Lecarme and R. Lewis. Am- sterdam: IFIP, North-Holland, pp. 223-229.

Suppes, P. (1960) Axiomatic Set Theory. New York: Van Nos- trand. Slightly rev. ed. New York: Dover, 1972.

Van Campen, J . (198 1 a) “A Computer-Assisted Course in Russian. ’ ’ In University-Level Computer-Assisted Instruc- tion at Stanfurd: 1968-1 980, ed. P. Suppes. Stanford, Calif.: Stanford University, Institute for Mathematical Studies in the Social Sciences, pp. 603-646.

. (1981 b) “Computer-Generated Dnlls in Second-Lan- guage Instruction. ’ ’ In Universrty-Level Computer-As- slsted Instruction at Stanford: 1968-1980, ed. P. Suppes Stanford, Calif.: Stanford University, Institute for Math- ematical Studies in the Social Sciences, pp. 647-655.

Description of Methodology Bork, A ( 1978) “Computers, Education, and the Future 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-Assisted Instruction at Stan- ford. ” In Man and Computer. Proceedings of International conference, Bordeaux, 1970. Basel: Karger, pp. 298-330.

Suppes, P. and Sheehan, J. (1 98 1 a) “CAI Course in Axiomatic Set Theory. ” In University-Level Computer-Assisted Instructzun at Stanford: 1968-1980, ed. P. Suppes. Stanford, Calif.; Stanford University, Institute for Math- ematical Studies in the Social Sciences, pp. 3-80.

.( 1981b) “CAI Course In Loglc.” In Universrty-Level

Computer-Assisted Instruction at Stanford: 1968-1980, ed. P. Suppes. Stanford, Calif.: Stanford University, In- stitute 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, 197 1- 1975. ” CCC Ed- ucational 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 of Global Psychological Models in Instructional Tech- nology. ” In Advances in Instructional Psychology, vol. l , ed. R. Glaser. Hillsdale, N.J.: Erlbaum, pp. 229-259.