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336 The Journal of Risk and Insn^rance
TEACHERS, COMPUTERS, AND TEACHING
James A. Wickman
An increasingly familiar sight along the the paths of academia are a number of hunched figures with output paper and punch cards askew, invoking "do-loops," "diagnostics" and "Hollerith counts."
Computer technology is an unsettling innovation to many who have only re- cently acquired creditable speed and ac- curacy in using a desk calculator. Fur- thermore, the reactions of colleagues and students can often be predicted by refer- ence to the "Cee Whiz Syndrome." The nature of the "Cee Whiz Syndrome" can be approximated by imagining the follow- ing conversation:
COMPUTER USER: "I wrote this pro- gram in FORTAN, rather than FAP becau. . ."
LISTENER: "Cee whiz!" COMPUTER USER: ". . . so it took me
twelve runs to de-bug this.. ." LISTENER: "Cee Whiz!" COMPUTER USER: ". . . and now I
can do two plus two three thousand times in 37 microseconds."
LISTENER: "CEE WHIZ!"
On the other hand, worship of peri- pheral input-output devices and central processing units is not the inevitable result of using the high speed data-manipulation powers of data processing systems. The relative newness of computers and the obvious complexity of their inner mechan- isms do seem to reduce some causal users of computer facilities to a state of hysteria bordering upon absolute reverence.
One can raise psychological defenses against these forms of idol-worship by in- sisting and believing that the modem computer is essentially a large, ultra-high speed, printing calculator with logical ca- pacity to make "yes-no" decisions. A com-
puter can be instructed to do various com- putational series, has the power to remem- ber what it has calculated and to use these values in later calculations. These com- prise a fair intuitive understanding of the basic elements of raodern computer technology. Increasing familiarity with computers can even breed a feeling akin to "contempt" when the computer slav- ishly follows illogical instructions to pro- duce meaningless answers. To student and professor alike, there is utility (and per- haps sanity) in becoming acquainted with the powers and shortcomings of data proc- essing equipment.
Becoming a Computer User
Happily, it is not necessary to become a computer programmer to be a success- ful and prolific computer user, any more than it is necessary to become a proficient automobile mechanic to be a capable auto- mobile driver. One who wants to try his hand at using the computer will often find that an existing set of computer instruc- tions can be utilized to solve his problem. There are a great many such "canned pro- grams" available which will solve general or specialized types of problems.
Information About Programs
One of the more useful "families" of "canned" programs is the BMD series of computer programs.^ These cover a broad range of typical statistical computations, as well as several advanced statistical com- putation programs.
An eflBcient index to many existing com- puter proigrams is the Key-Word-In-Con- text (KWIC) Index published by IBM. This source lists programs in a format which emphasizes each key word in the
^ These programs are described in BMD— Biomedical Computer Programs, W. J. Dixon, editor. The latest edition was published January 1, 1964, by the Health Sciences Computing Facility, Department of Preventive Medicine and Public Health, School of Medicine, University of California, Los Angeles.
Communications 337
title, resulting in an ability to scan the index rapidly in search of a program or programs which have sought-for capabil- ities. Each program is also described in a brief abstract in another section of this publication, along with instructions for ordering a copy of the program.
Many campus computer installations have acquired some of these programs as a service for their users. Additional pro- grams can be acquired and made availa- ble on request. Typically, the computer installation will also maintain a library of lists and indexes regarding available pro- grams.
A special-purpose index of "canned" programs dealing with insurance and risk problems, for research or classroom dem- onstration purposes, would be useful. While none is known to exist at the pre- sent time, the American Risk and Insur- ance Association, in the author's opinion, should consider creating a clearinghouse for information about existing programs. Perhaps space in this Journal could be devoted to brief listings so that interested teachers could be informed of the eflForts of others.
"Canned^' Programs and Teaching
"Canned" programs offer many oppor- tunities to a teacher to develop a variety of classroom demonstrations which would otherwise represent a prohibitive invest- ment of time and energy to perform the calculations. Supplied with these demon- strations, a teacher can concentrate his major eflEorts on explaining the rationale of methodology and the interpretation of results to students. Students can also use such programs to work problems that would have been inappropriate if the com- putational work had to be done by hand or by desk calculator.
Even if a "canned program" is not read- ily available, a teacher still does not have to develop programming ability himself. He can describe the desired computations
and the desired format of results to a qualified programmer.^ The programmer then takes over the "ritualistic" task of preparing a formal set of computer in- structions to solve the problem and com- municate the results. In this fashion, a teacher can avoid getting involved in the mechanical aspects of computer program- ming and reserve his time for concentrat- ing on analytic method.
Additional Computer Features
Beyond the saving in computational time offered by computer programs, "canned" or otherwise, additional features must be considered in assessing the teach- ing usefulness of the computer. Today's technology will be widely available on the campus tomorrow (three to five years) to allow the instructor to communicate with the computer from the classroom. He can ask the proper questions of the central computing facility and get an immediate response in the form of printed output, displays of frequency distributions on a cathode-ray tube, etc., using pre-stored programs and data. Or the students can do so.
The computer can be told what pro- gram to use; it will ask the students for appropriate information, do the computa- tions, and report the results. AH of this can occur simultaneously in many class- rooms on the same campus. Actually, the computer will work on the problem for one class for a few thousandths of a sec- ond, go to the next, and so on through the list of problems and back to the be- ginning of the circuit.^ The effect of this time-switching arrangement on computer
^ "Qualified programmer," in a pragmatic sense, means someone who is able to "perform the ritual" of expressing instructions in appro- priate language for the computer. Students make excellent "qualified" programmers.
^ Several imiversides are adopting remote con- soles and time-switching arrangements within the next year; among these are MIT, Carnegie, and Michigan.
338 The Journal of Risk and Insurance
speed is virtually undiscernible in the classroom. Thus neither the students nor the instructor need to know programming (but the instructor may need to know a programmer).
Even without these "Gee Whiz" addi- tions to computer technology, special pro- grams can be incorporated along with computational instructions to portray the results of calculations in graphic form. The calculational results and graphic out- put can be reproduced for classroom dis- tribution using additional features of the normal computer installation.
Risk and Insurance Courses In teaching risk and insurance courses,
the instructor must refer frequently to sta- tistical concepts and measures. The teacher who wants to include course ma- terials dealing with the application of basic and advanced statistics to risk man- agement and insurance concepts faces two major difficulties, here referred to as the "capital investment" and "statistical block" problems.
"Capital Investment" First of all, "capital investment" by the
instructor in developing illustrations which show the application of statistics will be great. Developing any one illustration will involve a lot of calculational time. Even slight variations in the assumptions under- lying the illustration will usually require complete recalculation. At this rate, it will take a long time for an instructor to de- velop a reasonably complete kit of illustra- tions to cover even one course. "Canned" programs, such as the one described be- low, can be used to reduce the "capital investment" required of any single in- structor.
"Statistical Block" Secondly, many students are not able
or willing to utilize their prior training in statistics to investigate risk and insurance principles because their prior training in
statistics is clouded with a "statistical block." Their first training in statistics did not "take" as well as might be hoped, giv- ing these students great difficulty in ap- plying a statistical frame of reference to the principles and problems of a different subject matter area.*
A risk and insurance teacher can avoid confronting this awkwardness by eliminat- ing all but the mildest of statistical refer- ences in his course materials. In doing so, the instructor may weaken significantly the vigor of the course. A more satisfac- tory way of dealing with both of these problems lies in using the computational power of computer programs, "canned" or otherwise, to alleviate tedious calcula- tions and allow greater emphasis on inter- preting the results.
Illustrative Teaching Problem For example, basic statistics can be in-
tegrated with risk and insurance problems by exploring the common observation that "the mortality table portrays a risk con- verging on a certainty over time." This ob- servation is intuitively correct, as will be explained, but how does a teacher effec- tively communicate this understanding to a non-intuitive student? The phrase can be repeated again and again, using differ- ent words, but this pedagogical device may not be too helpful.
The formal reasoning lying behind this observation could be explored and ex- plained verbally:
A mortality table displaying number of deaths by age is a specialized portrayal of a frequency distribution. As with many other frequency distributions, it is possible and logical to compute the mean. The mean in this instance represents the average age at death for those at the initial age of the mortality table. For each greater age the frequency distribution is obtained by trun- cating to eliminate earlier ages from con- sideration. The mean of e;ach such distribu- ^ Editor's note: At some universities, of course,
statistics is not a prerequisite to courses in risk management and insurance.
Communications 339
tion is the average age at death for each new initial age. The average age at death is a useful meas- ure for many purposes, but it does not adequently demonstrate that some people die well before attaining the average age and others live considerably longer than the average age at death for persons in their group. There is, therefore, risk in such a situation since actual ages at death are dispersed around the most likely result, the average age at death. To understand the statement that 'the mortality table por- trays a risk converging on certainty over time,' the dispersion of actual ages at death should be examined to see if this dispersion does in fact narrow or converge, over time, upon the average age at death. The standard deviation is a common meas- ure of dispersion. The standard deviation can be used to measure and express the concentration or scatter of data around its mean value. By calculating, for each age, the standard deviation as well as the average age at death, absolute dispersion can be expressed. Confidence intervals can be estimated. Another way of looking at variability in a set of data uses the coeiBcient of variation as an indicator of relative dispersion or scatter. The standard deviation is divided by the mean to calculate the coefficient of variation. A decreasing coefficient of varia- tion signifies that the relative dispersion is lessening. Computing the standard deviation and the coefficient of variation should show that as age increases actual deaths occur more and more closely to the average age at death. The coefficient of variation approaches zero as a limit. Thus, 'mortality is a risk converging upon a certainty over time.'
To express sucb a line of reasoning verbally in a classroom without specific measures of tbe mean, standard deviation, and coefficient of variation would be fool- hardy. On the other band, the calcula- tional work will be extensive and tedious. Table 1 and Chart 1 are exact reproduc- tions of the output of a computer pro- gram, LFXP, written to perform this multitude of calculations.' An instructor
^ This program, written by the author, derives its code name from LiFe EXPectation. Purists
can use reproductions of this tabular and graphic output to demonstrate the results of the calculation process as well as the logic of the argument. By using the same computer program but different mortality tables, certain of the differences between mortality tables can be demonstrated and examined.
Appendix A presents an abbreviated description of the computer program used to calculate and produce the information contained in Table 1 and Chart 1. Addi- tional computer programs are being pre- pared to investigate and demonstrate other applications of mortality tables.*
Summary
Rapid evolution of computer technol- ogy, although often bewildering, need not be terrifying. Teachers and students both will benefit from a thorough exploita- tion of the high speed data manipulating capacity of modern computers. Teaching many of the statistical aspects of risk and insurance can be highlighted and assisted through the use of prepared computer programs with tabular and graphic pre- sentation of output. The use of such pro- grams does not require programming abil- ity. By avoiding the monumental task of hand calculation, the instructor can con- centrate on demonstrating the relevance of statistical measures to risk and insur- ance problems with less effort and greater probable success.
Appendix A
LFXP is relatively simple to use. Four mortality tables are "built in" the pro- may object to the use of upper-case letters in place of the customary lower-case form of actu- arial notation. This is defended pragmatically on grounds of second-best. Computer-related print- ers only print in upper-case; the choice is to have no symbols, or to have symbols in uncon- ventional form.
* Perhaps to be published, ultimately, as "Ex- ploring Mortality Tables with Punch Card and Computer."
340 The Journal of Risk and Insurance
gram;'' others may provide the data for calculations at the instructor's option. A single card is prepared to instruct the program what to do; this problem card selects the mortality table, specifies the confidence limits desired for graphic out- put, and specifies the age-interval for tab- ular output. This problem card is included with the program deck and submitted to the campus computer installation for proc- essing.
The first calculation performed by the program computes the complete expecta- tion of life, beginning with initial age equal to birth and then increasing initial age by one until the limiting age of the mortality table is reached. The complete expectation of life for each initial age is added to the initial age to estimate the average age at death.
Next, the standard deviation around the average age at death is calculated for each initial age. This is used to compute the coefficient of variation and to estimate the confidence limits.
If graphic output is requested by the user, the program next calls upon the plot- ting subroutine to prepare and print out the requested graph. Following this, the program instructs the computer to print a
'These are: 1941 CSO; 1958 CSO; 1937 Standard Annuity, set back five years; and 1959- 61 U.S. Life Table for the Total Population.
tabular summary. At this point the main work of the program is completed. The computer is instructed to check for an- other problem to be run, performing the same sequence of operations on a differ- ent set of data. When no further problems are requested, the computer turns its at- tention to other jobs waiting for process- ing.
LFXP is written in the FORTRAN IV language. Version 13, for the IBM 7094- 7040 DCS system at the Research Com- puter Laboratory of the University of Washington. The program uses several standard systems routines in performing the calculations. The graphic output is obtained by calling on the UM PLOT sub- routine.^ as modified for the University of Washington system. The graph of output is optional with the user.
This brief discussion deals with the ma- jor aspects of the program. More extensive documentation may be obtained by writ- ing to the author. Progiram listings and punched-card decks (approximately 500 cards) of the source program can be ob- tained for the cost of materials and mail- ing charges. Within limits, the author will attempt to assist interested instructors in adapting the program to be compatible with their campus computer requirements.
8 SHARE, Distribution No. 1085.
Communications 341
Chart 1 AVERAGE AGE AT DEATH FOR PERSONS NOW AGE X dASED UPON THE 1958 CSO MORTALITY TABLE
( 95.000 0/0 CONFIDENCE LIMITS)
1 00 .0 + U U- + ---.i^.^-..-..-.-.- ... .( ... U--^-
A V E R A G E
83.a
66.3
49.5
I I I I I I
32.7 L-
I I 1 I I I I I I
I I I I I I I I * *
I I I I I I I I I
I I 1
u uI U U I I I I 1 1 I
I I I I I I * • *
* # • I I
I I I I I I I I I
I I L L L
. J, IJ 1
U U I U U U U I I I I I I
I I * I * I » I *
» * t * 1
I I L
I I L I I L I I L I L
L I
L I I I
U [ U * [ U L J »
[ * I L 1 *
L
KEY TO PLOTTING CHARACTERS
# = AVERAGE AGE AT DEATH U = UPPER CONFIDENCE LIMIT
LOWER CONFIDENCE LIMIT I
25 50 - PRESENT AGE -
75 100
SOURCE — LFXP
342 The Journal of Risk and Insurarwe
Table 1
AVERAGE AGE AT DEATH FOR PERSONS NOW AGE X BASED UPON THE 1958 CSO MORTALITY TABLE
f. .-- I AGE
[ <X)
I 0-
: 5
: 10
: 15
[ 20
25
30
35
40
45
50
55
60
65
70
75
80 ]
85 I
90 :
95 :
100 ] I
I NUMBER ALIVE I AT AGE X t L(X)
I 10000000
: 9868375
: 9805870
: 9743175
9664994
9575636
9480358
9373807-
9241359
9048999
8762306
8331317
7698698
6800531
5592012
4129906
2626372
1311348
,468174
97165
0
I .1 I
I I I I I I I I I I I I I I I I I I I I I I I I I
I II I I I I I I I I I I I I I I
NUMBER DYING WHILE AGE X
D(X)
70800
13322
1 1865
14225
17300
18481
20193
23528
32622
48412
72902
108,307
156592
215917
278426
303011
288648
211311
106809
34128
0
I I I
I I I I I I I I I I I I I I I I I I I I I I I I I
I I I I I I I I I I I I I I I I 1
H AVERAGE AGE AT DEATH
68.3
69.2
69.6
70.0
70.4
70.8
71.3
71.7
72.2
72.8
73.6
74.7 I
76.1 I
77.9 :
80.1 I
82.8 I
.85.9
89.3 I
93.1 I
96.8 ]
0.0 I
), -„.
COEF. OF VARIATION
V(X)
0.266
0.239
0.228
0.218
0.207
0.196
0.186
0.176
0.167
0.1 5fe
0.144
0.130
0.114
0.098
0.081
0.065
0.050
0.037
0.026
0.014
0.000
+
•-••
1 I
I I I I I I I I I I I I I I I 1
I I I I I I I I
I I I I I I I I I I I I I I I I
—. + YEARS OF LIFE' I REMAINING
E<X>
68.3
64.2
59.6
55.0
50.4
45.8
41.3
36.7
32.2
27.8
23.6
19.7
16.1
12.9
10.1
7.8
5.9
4.3
3.1
1 •B
0.0
]
i —t
I I I I I I I i I I I .1 I I I I I I I I 1 I I I I I •I I I I I I I I I I I I I I I I
SOURCE — LFXP
