G. 1. Breneman Eastern Washington State College Cheney, 99004
MCAI: Minicomputer-Aided Instruction
CAI or computer-aided instruction is currently much discussed and seems to be very appropriate for chemistry education. The ideal CAI system is based on a large timesharing computer. However, large computers are not universally available and even where they are available the interactive facilities needed for CAI are not always supported. Minicomputers, which in the past have been used mainly for instrument automation, may partially solve this problem because of great reductions in price over the last few years. For example, in 1967 a Digital Equipment Corporation PDP-8 with 4K ( K = 1024) core memory and an ASR-33 teletype cost approximately $20,000. Today, a PDP-8/E with the same core and teletype costs $6,450.' This system is expandable a t additional cost allowing the power to be increased in steps as the money becomes available. This price is attractive if the minicomputer will do the job. During the winter quarter of 1972, a series of programs were developed on a minimum system consisting of a PDP-8/L computer with 4K core memory and an ASR-33 teletype to see if the minicomputer could do the job. This system was borrowed from Digital Equipment Corporation. Many of the programs were used in a first quarter General Chemistry course to obtain student reaction and to determine the facilities needed to handle an entire undergraduate chemistry curriculum. The programming language used was FOCAL2 a DEC developed language similar to BASIC hut optimized for the minicomputer. FOCAL allows the usual arithmetical and logical operations and includes many built-in functions such as square-root, sine, and the especially useful random number generator. The system allows removal of part of the functions to allow more core to be available to the programmer.
tion function for hydrogen-like ions. A choice of orbital and nuclear charge is given so the student can compare different situations. The plot must he scaled so it will fit. on the paper and the distance the plot extends from the nucleus is variable. Hydrogen atomic orbitals can be plotted with ease as seen in the figure. A choice of the is, 2s, 5, 2p, 3p, 3dZZ, or 3d,, orhital can he made. The square of the wave functcon is calculated for each grid point in the 1-2 plane and scaled to give a reasonable plot. The scaled probability is then multiplied by a random number between zero and
Program Examples
GDIAL DISTRIBUTION FUNC VERSES DISTANCE FROM NUCLEUS FOR IS,
Introduction
ORBITAL?: 2S NUCLEAR CHARGE?: 1 MAX VALUE?: 2 MAX DISTANCE?: 6
To introduce the student to using the computer, a variety of games furnished with most systems can he used. Or one can write his own introductory program such as in Table 1. (Student's input is in italics in all examples. All other characters are output by the computer.) This introduction gives the student practice in getting a program started and "talking" with the computer and also allows him to overcome any uneasiness he may have about using computers.
Table 1. Partial Output of Program to Introduce Student to the Computer
.,;
HELLO. M Y N A M E IS HAL. J R WHATIS VOI'R hAhlE" HI1 I. YOUHAVE ANICE NAME. I WOULD LIKE TO ASK YOU SOME MORE QUESTIONS IF YOU DON'T MlNU IT WOULD HELP MEIFYOU WOULD ANSWERTHEMYES ORNO. AREYOUTAKING CHEM 151 THIS QUARTER?: YES THATISVERY NICE. DO YOU KNOWTHATIAM HERETO HELPYOUPASSTHISCOURSE?: YES HOW NICE. YOU ALREADY KNOW SOMETHING ABOUTME. LETMEBRIEFLY TELLYOUHOW IWlLLTRYTO HELPYOU.
Table 2. Output of Program that Plots Radial Distribution Function for Hydrogen-LikeOrbitals. ZS, 38. 2P, 3P, OR3D HMROGEN-LIKE ORBITALS
0
MAX = 0 . m
Plotting Because the teletype outputs single characters rather than lines of characters, plotting is very easy and does not require storage of the whole line before output. Table 2 shows the output of a program to plot the radial distribuPresented at the Symposium on Student Self-Instruction at the 27th Annual Northwest Regional Meeting of the American Chemical Society, June, 1972 1 Digital Equipment Corporation price list, July 1,1971. Z"Programming Languages," Digital Equipment Corporation, 146 Main Street, Maynard, MA 01754, 1972, Volume 2, pages 11-1 to 11-65.
NEW PLOT?YES ORNO: NU
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Table 4. Output of Program that Plots Curve for Titration of a Weak Acid with a Strong Base
-
-.
-
-
-
MOLARCONCENTRATION OF ACID: .01 MOLARCONCENTRATION OFBASE: .02 AMOUNT OF ACIDTO BETITRATEDIN ML: 50 TOTALVOLUME OF BASETOBE ADDED IN ML:50 ALIQUOT SIZE OF BASEIN ML: 2.5
Plots 01 some of the hydrogen atomic orbitals Table 3. Output of Program to Fit First-Order Kinetic Data to a Straight Line Using Least-Squares .(i
LFAST-SQUARES RT OF FIRST ORDER KINETIC DATA TO THE EQUATION LN(AIX)= K.T + B
:72W
CONCENTRATIONS
:XJ
:I* :I"
DEVIATIONS OFPOINTS FROM LINE
--
= 0.106012E-01
-0710440E-02 0.23L147E-02
= -01785&2E~01 = = 0.786495E-02
0.4179968.02
RATE CONSTANT. K = 048675lE-03 INTERCEPT. R = 0.371437E~OL ( B SHOULD BE ABOUT0 IF REACTION IS REALLY FIRST STANDARD DEVIATION OF K = 0.237025E-05 STANDARD DEWATION OFB = 0.110770E-01
one. If this result is above a certain fixed value, an asterisk is printed a t that grid point. If the result is helow this fixed value, a space is output. The random number gives a shaded effect so areas of lower probability have a lower density of asterisks. It is also responsible for the ragged edges of the plots. This particular program is compute bound written in FOCAL and requires about 13 min to plot the over 3000 grid points for each orbital on the scale shown in the figure. Routine.Calculations Calculations that would be too time-consuming to be carried out routinely by hand or electronic calculator can 3
0.123E-05 means 0.123 X low.
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quickly be done on minicomputers. Table 3 shows the output for a least-squares fit of first-order kinetic data to a straight line.3 If the initial concentration, A, is not known, it can be set equal to 1 and the intercept, B, will equal -ln(A) instead of zero. The maximum number of points that can be entered for one calculation is 18. Laboratory Simulation Simulation of laboratory experiments gives the student a better feel for how varying the experimental parameters affects the results without the need for time-consuming repetition of experiments in lab. Table 4 shows how the titration curve for reacting a weak acid with a strong base looks for a particular acid and one possible set of experimental parameters. The calculation is based on the usual approximations for a weak acid so the useful range of acid dissociation constantsis limited. Problem Generation Fullest advantage of interactive computing is taken in the area of ~ r o b l e mneneration. The computer can generate u n i q ~ e - ~ r o b l e mand 8 check the student's answers when the student's interest is greatest: immediately after working the problem. This approach can be used for programmed review and/or quiz generation. Outlined below is a general approach for setting up such programs. Most problems can be expressed in several different forms, e.g., by rearranging the equation involved. The form of the problem is selected a t random using the random number generator. The actual data is also selected at random. This can be limited so the sizes of the numbers are reasonable. The computer states the problem and checks the answer after it is input by the student. A leeway of +1% is allowed in the answer so a slide rule can be used for the calculation. If the answer is correct, the computer offers to give the student another problem and the above steps can be repeated. If the answer is incorrect, the computer notifies the student. The computer can then offer the student help by giving a brief discussion of the fundamentals involved and allow him to try the same problem again. If the student does not eventually get the correct answer, he can get the correct answer from the computer by refusing to work the problem again. The computer then offers to give him a new problem. Several
Table 5. Output of Program that Generates HCI Analysis Problems
Table 7. Output of Program that Plays a Mole-Gram Conversion Game
G ' ANALYSIS OFAN HCLSOLUTION MOLECULAR WEIGHTOFTHEPRIMARY STANDARDKHP = m.22 A WEIGHT OF KHP = 0.75 GRAMS WAS TITRATED WITH A VOLUME OF NAOH =
4L.55ML
MOLARlTY OFNAOH?: ,167 WRONG NEED S O M E H W ? YES OR NO: YES HBACTION IS: KHP + NAOH = HPO + K S A P I'll1 i h l O L E S l I F U A O H = \lOI.E\OFKHP \IOl.hKIIY z \lOLESOFNAOH \Ol.llhlF.IISL~EHStOPNAOll TRY AGAIN? YES ORNO: YES MOLARITY OFNAOH?: ,0880 CORRECT, NOW THE NAOHIS STANDARDIZED 5 M L OF HCL WAS TITRATEDWITH A VOLUME OFTHIS NOAH = 17.53ML MOLARITY OFHCL?: . I 2 3
-
WT1ONC .....
NEEI)SOMEHELP?SESOH YO YES MULES NAOH = MOLARITYOP NAOH.YOI.IIME IN II'I V K i f OF NAOH RF-aCI'1ON 15 HCL + KAOH = H2O r NACL
HVl. = hlOl.I'S S.\Oll LIL)I.AKII'SOFHCL = \IDLVSHTI. VOLl \lE$INIJTEKS
'I'HIlS M O I I S
O I IICLTITR4TEO
TRY AGAIN? YES ORNO: YES MOLARITY OF HCL?: ,309
C~NVERSIONBETWEEN MOLES AND GRAMS A GAME OFCHANCE YOU ARE B m N G THATYOU CAN SOLVEMY PROBLEMS MINIMUM BET = $10, MAXIMUM BET = $YM ODDS ARE 1:l WINP15W TO BREAK THE BANK YOURBET: 5W H O B ' \ l A ~ \ G b I A M S U F A l'U\Il'UUNI> DO YOU HA\'I'IFTHEtiU\IHFHOF \IOI.ElOFTIIATCOhlPOllhn = l i X A Y D T I I E hlOl.ECI'IARU'FII7lIT=rri 16' \ O I H \ S i U FR , N 1P YOU WIN YOUR WINNINGS = 5W.W NEW PROBLEM? YES OR NO: YES
HOWMANY MOLES O F A COMPOUNDDO YOU HAVEIFTHE NUMBEROF GRAMS OFTHAT COMPOUND = 1129ANDTHE MOLECULAR WEIGHT = 41.10? YOURANSWER: I W 4 YOU WIN YOUR WINNINGS = 1SWW . YOUHAVEBROKENTHEBANK. IQUIT!
Table 8. List of Additional Programs A NEW PROBLEM? YES ORNO: NO
Table 6. Output of Program that Generates Electronic Configuration Problems
Calmlate8mean value, standard deviation, and pmbable error. I.eaat-a9uarea fit of datatoaatralght line.
..
Generates ideal gas law problems. Calculstes empirical formula fmm % eompoaition (and malecular formula if molerular
.I7 ELI'CTKONF COSRl;IR4TION OFAT011S FNERGS LEVEL OKIIEH OF'THE ATOMII'ORBITALS liii1P3S3~eS~I~rviSlnsPciS4FiD61'~SjF611
\ I A X I > l U M NI.\IRFR OF F.I.ECTRUKS IN VACH'IYI'FOFORBITAL
IF THE TOTAL NUMBER OF ELECTRONSIN AN ATOM = S1 HOW MANY ELECTRONSAREIN THE4PORBITAL?: 2 TOO MANY TRY AGAIN?YES ORNO: NO ANSWER = 1 NEW PROBLEM?YES ORNO: YES IFTHETOTAL NUMBEROFELECTRONS IN AN ATOM = 96 HOW MANY ELECTRONS ARE INTHESF ORBITAL?: 8 CORRECT NEW PROBLEM? YES ORNO: NO
examples follow which illustrate these points and show how complex a problem can be set up on the minimum system. Table 5 shows the output of a programthat generates problems for determining the concentration of an HC1 solution by titration with NaOH solution. The problems include the standardization of the NaOH solution. Table 6 shows the output of a program that generates electronic configuration problems. No exceptions to the general order of filling of the orbitals are recognized. The highest energy orbital containing electrons is always picked for the question. Atomic numbers of 1through 106 are selected at random. Table 7 shows the output of a program that generates mole-gram conversion problems. This prohlem is made more interesting by putting it in a gambling context. If the student's losses reach $1000, he can start all over. Missed problems can be tried over again but a new bet must he made. Discussion
Even with less than 1K of the memory available to the user, much can be done on this system. Programs involving large amounts of memory, such as calculations using large matrices, cannot be considered, however. Table 8 lists other programs developed on this system. This choice
of programs was dictated by time limitations, material covered in the general chemistry course that quarter, and consideration of what might be done in other chemistry courses. Only listings of these programs are available from the author due to lack of paper tape copying facilities a t present. About 50 students in general chemistry ran one problem each week for the quarter. Their response in general was very enthusiastic and many claimed the computer to he a great aid in helping them master the problems presented in this manner. They thought one problem per week to he about the rieht amount. Based on this o ~ i n i o nand the amount of time used by this number of students, a system canable of handlina an entire undermaduate curriculum with 450 students was determined. One such svstem consists of a P D P d I E comouter with 8K memory, 32K word disk, and four terminals (ASR-33 Teletv~es).All four terminals can be runnine simultanew& to execute FOCAL programs and/or to develop new FOCAL programs. The programs can he stored on and called from the disk eliminating any fixed schedule as to when who runs what. Another advantage over the minimum system is being able to chain program segments together automatically, allowing for more complex programs than those shown in this paper. About half of a 9-hr day will allow each student to run one program per week. The other half of the time will allow programs to be written by students and faculty. The system can be expanded to seven terminals by simply adding three terminals. The purchase cost of the four-terminal system is under $21,000. A maintenance contract costs an additional $250 per month. This is very economical when one considers this equipment will be in almost continuous use. The same cannot be said for very many, if any, other pieces of equipment in the chemistry department. An on-site minicomputer has two possible advantages
a
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over remote time-sharing systems. Graphics terminals (e.g., those based on a CRT display) can be used without possible limitations from telephone line transmission speeds. These terminals are especially useful for plotting and for developing new programs because of their high output speed. Also a minicomputer can he used for instruction in instrument control, although additional hardware is required and only one terminal can be used in this mode.
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MCAl or minicomputer-aided instruction is a viable alternative to CAI, especially where large interactive computer facilities are not available. I t is well worth considering in light of the cost. The present cost and services of already available computing facilities will he a large factor in any decision, however. Great thanks is extended to Richard J. Epler of Digital Equipment Corporation for use of the PDP-8/L system that made this work possible.
